On the definition and observability of the neutrino charge radius

We present a brief summary of recent results concerning the unambiguous definition and experimental extraction of the gauge-invariant and process-independent neutrino charge radius.

Observability of the Neutrino Charge Radius

It is shown that the probe-independent charge radius of the neutrino is a physical observable; as such, it may be extracted from experiment, at least in principle. This is accomplished by expressing a set of experimental ${\ensuremath{\nu}}_{\ensuremath{\mu}}\mathrm{\text{\ensuremath{-}}}e$ cross sections in terms of the finite charge radius and two additional gauge- and renormalization-group-invariant quantities, corresponding to the electroweak effective charge and mixing angle.

Asymptotic properties of Born-improved amplitudes with gauge bosons in the final state

For processes with gauge bosons in the final state we show how to continuously connect with a single Born-improved amplitude the resonant region, where resummation effects are important, with the asymptotic region far away from the resonance, where the amplitude must reduce to its tree-level form. While doing so all known field-theoretical constraints are respected, most notably gauge-invariance, unitarity and the equivalence theorem. The calculations presented are based on the process $f\bar{f}\to ZZ$, mediated by a possibly resonant Higgs boson; this process captures all the essential features, and can serve as a prototype for a variety of similar calculations. By virtue of massive cancel…

Massive Yang-Mills model and diffractive scattering

We argue that the massive Yang-Mills model of Kunimasa and Goto, Slavnov, and Cornwall, in which massive gauge vector bosons are introduced in a gauge-invariant way without resorting to the Higgs mechanism, may be useful for studying diffractive scattering of strongly interacting particles. We perform in this model explicit calculations of S-matrix elements between quark states, at tree level, one loop, and two loops, and discuss issues of renormalisability and unitarity. In particular, it is shown that the S-matrix element for quark scattering is renormalisable at one-loop order and is only logarithmically non-renormalisable at two loops. The discrepancies in the ultraviolet regime between…

B physics and extra dimensions

We compute the dominant new physics contributions to the processes Z -> b b and B - B in the context of two representative models with extra dimensions. The main thrust of the calculations focuses on how to control the effects of the infinite tower of Kaluza-Klein modes inside the relevant one-loop diagrams. By comparing the results with the existing experimental data, most importantly those for Rb, we show that one may derive interesting lower bounds on the size of the compactification scale Mc.

On the observability of the neutrino charge radius

It is shown that the probe-independent charge radius of the neutrino is a physical observable; as such, it may be extracted from experiment, at least in principle. This is accomplished by expressing a set of experimental neutrino-electron cross-sections in terms of the finite charge radius and two additional gauge- and renormalization-group-invariant quantities, corresponding to the electroweak effective charge and mixing angle.

Displacement Operator Formalism for Renormalization and Gauge Dependence to All Orders

We present a new method for determining the renormalization of Green functions to all orders in perturbation theory, which we call the displacement operator formalism, or the D-formalism, in short. This formalism exploits the fact that the renormalized Green functions may be calculated by displacing by an infinite amount the renormalized fields and parameters of the theory with respect to the unrenormalized ones. With the help of this formalism, we are able to obtain the precise form of the deformations induced to the Nielsen identities after renormalization, and thus derive the exact dependence of the renormalized Green functions on the renormalized gauge-fixing parameter to all orders. As…

Chiral fermions and gauge fixing in five-dimensional theories

We study in detail the issue of gauge-fixing in theories with one universal extra dimension, i.e. theories where both bosons and fermions display Kaluza-Klein (KK) excitations. The extra dimension is compactified using the standard orbifold construction for a massless chiral fermion. We carry out the gauge-fixing procedure at the level of the five-dimensional theory and determine the tree-level propagators and interaction vertices needed for performing perturbative calculations with the effective four-dimensional theory resulting after the compactification. The gauge-independence of the tree-level S-matrix involving massive KK modes is verified using specific examples. In order to obtain ma…

Gauge-invariant 3-boson vertices and their ward identities in the standard model

In the context of the Standard Model we extend the S--matrix pinch technique for non--conserved currents to the case of three boson vertices. We outline in detail how effective gauge invariant three boson vertices can be constructed, with all three incoming momenta {\it off--shell}. Explicit closed expressions for the vertices γW−W+, ZW−W+, and χW−W+ are reported. The three boson vertices so constructed satisfy naive QED--like Ward identities which relate them to the gauge invariant gauge boson self--energies previously constructed by the same method. The derivation of the aforementioned Ward identities relies on the sole requirement of complete gauge invariance of the S--matrix element con…

Tau anomalous magnetic moment form factor at Super B/Flavor factories

The proposed high-luminosity B/Flavor factories offer new opportunities for the improved determination of the fundamental physical parameters of standard heavy leptons. Compared to the electron or the muon case, the magnetic properties of the $\tau$ lepton are largely unexplored. We show that the electromagnetic properties of the $\tau$, and in particular its magnetic form factor, may be measured competitively in these facilities, using unpolarized or polarized electron beams. Various observables of the $\tau$'s produced on top of the $\Upsilon$ resonances, such as cross-section and normal polarization for unpolarized electrons or longitudinal and transverse asymmetries for polarized beams,…

The QCD analytic effective charge and its dependence on the pion mass

A new model for the QCD analytic running coupling, which incorporates the effects due to the $\pi$ meson mass, is proposed. The properties of this invariant charge in spacelike and timelike regions are examined. Its main distinctive features are a finite infrared limiting value, which depends on the pion mass, and the "plateau-like" behavior in the deep infrared domain of the timelike region.

Gravitational scattering on a global monopole

The scattering amplitude and the total scattering cross section of massless particles propagating in the gravitational field of a global monopole are derived. We find that the physical signature of such defects is a ringlike angular region where the scattering amplitude is very large. The size of this ringlike region is determined by the ratio of the global monopole mass to the Planck mass and its appearance stems from the fact that the metric of the global monopole is not asymptotically flat but rather displays the characteristic spherical angle defect. The situation is therefore very much reminiscent of scattering in the gravitational field of the cosmic string.

Charge radius of the neutrino

Using the pinch technique we construct at one-loop order a neutrino charge radius, which is finite, depends neither on the gauge-fixing parameter nor on the gauge-fixing scheme employed, and is process independent. This definition stems solely from an effective proper photon-neutrino one-loop vertex, with no reference to box or self-energy contributions. The role of the $\mathrm{WW}$ box in this construction is critically examined. In particular it is shown that the exclusion of the effective $\mathrm{WW}$ box from the definition of the neutrino charge radius is not a matter of convention but is in fact dynamically realized when the target fermions are right-handedly polarized. In this way …

Two-loop electroweak corrections to the ρ parameter beyond the leading approximation

We show that in the framework of the pinch technique the universal part of the $\rho$ parameter can be meaningfully defined, beyond one loop. The universal part so obtained satisfies the crucial requirements of gauge-independence, finiteness, and process-independence, even when subleading contributions of the top quark are included. The mechanism which enforces the aforementioned properties is explained in detail, and several subtle field theoretical issues are discussed. Explicit calculations of the sub-leading two-loop corrections of order $O(G_{\mu}^{2}m^{2}_{t}M_{Z}^{2})$ are carried out in the context of an $SU(2)$ model, with $M_{W}=M_{Z}$, and various intermediate and final results a…

New Schwinger-Dyson equations for non-Abelian gauge theories

We show that the application of the pinch technique to the conventional Schwinger-Dyson equations for the gluon propagator, gluon-quark vertex, and three-gluon vertex, gives rise to new equations endowed with special properties. The new series coincides with the one obtained in the Feynman gauge of the background field method, thus capturing the extensive gauge cancellations implemented by the pinch technique at the level of individual Green's functions. Its building blocks are the fully dressed pinch technique Green's functions obeying Abelian all-order Ward identities instead of the Slavnov-Taylor identites satisfied by their conventional counterparts. As a result, and contrary to the sta…

Two-loop pinch technique in the electroweak sector

The generalization of the two-loop Pinch Technique to the Electroweak Sector of the Standard Model is presented. We restrict ourselves to the case of conserved external currents, and provide a detailed analysis of both the charged and neutral sectors. The crucial ingredient for this construction is the identification of the parts discarded during the pinching procedure with well-defined contributions to the Slavnov-Taylor identity satisfied by the off-shell one-loop gauge-boson vertices; the latter are nested inside the conventional two-loop self-energies. It is shown by resorting to a set of powerful identities that the two-loop effective Pinch Technique self-energies coincide with the cor…

Pinch technique self-energies and vertices to all orders in perturbation theory

The all-order construction of the pinch technique gluon self-energy and quark-gluon vertex is presented in detail within the class of linear covariant gauges. The main ingredients in our analysis are the identification of a special Green's function, which serves as a common kernel to all self-energy and vertex diagrams, and the judicious use of the Slavnov-Taylor identity it satisfies. In particular, it is shown that the ghost-Green's functions appearing in this identity capture precisely the result of the pinching action at arbitrary order. By virtue of this observation the construction of the quark-gluon vertex becomes particularly compact. It turns out that the aforementioned ghost-Green…

Gluon mass scale through nonlinearities and vertex interplay

We present a novel analysis of the gluon gap equation, where its full nonlinear structure is duly taken into account. In particular, while in previous treatments the linearization of this homogeneous integral equation introduced an indeterminacy in the scale of the corresponding mass, the current approach determines it uniquely, once the value of the gauge coupling at a given renormalization point is used as input. A crucial ingredient for this construction is the "kinetic term" of the gluon propagator, whose form is not obtained from the complicated equation governing its evolution, but is rather approximated by suitable initial {\it Ans\"atze}, which are subsequently improved by means of …

CP violation and the H-A lineshape

In two-Higgs doublet models (and particularly in the MSSM) the CP-even (H) and CP-odd (A) neutral scalars are nearly degenerate in mass, and their s-channel production would lead to nearly overlapping resonances. CP-violating effects may connect these two Higgs bosons, giving origin to one-loop particle mixing, which, due to their mass proximity, can be resonantly enhanced, altering their lineshape significantly. We show that, in general, the effect of such a CP-violating mixing cannot be mimicked by (or be re-absorbed into) a simple redefinition of the H and A masses in the context of a CP-conserving model. Specifically, the effects of the CP-mixing are such that, either the mass-splitting…

Coupled dynamics in gluon mass generation and the impact of the three-gluon vertex

We present a detailed study of the subtle interplay transpiring at the level of two integral equations that are instrumental for the dynamical generation of a gluon mass in pure Yang-Mills theories. The main novelty is the joint treatment of the Schwinger-Dyson equation governing the infrared behaviour of the gluon propagator and of the integral equation that controls the formation of massless bound-state excitations, whose inclusion is instrumental for obtaining massive solutions from the former equation. The self-consistency of the entire approach imposes the requirement of using a single value for the gauge coupling entering in the two key equations; its fulfillment depends crucially on …

A gauge-technique Ansatz for the three gluon vertex of the background field method

The vertex connecting one background gluon with two quantum ones constitutes a central ingredient in the gauge-invariant Schwinger-Dyson equation that determines the non-perturbative dynamics of the gluon propagator. This vertex satisfies a Ward identity with respect to the background gluon, and a Slavnov-Taylor identity with respect to the two quantum gluons. We present a complete Ansatz for this vertex, which satisfies both aforementioned identities. This entire construction depends crucially on a set of constraints relating the various form-factors of the ghost Green's functions appearing in the Slavnov-Taylor identity satisfied by the vertex. The validity of these constraints is demonst…

Fully coupled functional equations for the quark sector of QCD

We present a comprehensive study of the quark sector of $2+1$ flavour QCD, based on a self-consistent treatment of the coupled system of Schwinger-Dyson equations for the quark propagator and the full quark-gluon vertex. The individual form factors of the quark-gluon vertex are expressed in a special tensor basis obtained from a set of gauge-invariant operators. The sole external ingredient used as input to our equations is the Landau gauge gluon propagator with $2+1$ dynamical quark flavours, obtained from studies with Schwinger-Dyson equations, the functional renormalisation group approach, and large volume lattice simulations. The appropriate renormalisation procedure required in order t…

Chiral symmetry breaking with lattice propagators

We study chiral symmetry breaking using the standard gap equation, supplemented with the infrared-finite gluon propagator and ghost dressing function obtained from large-volume lattice simulations. One of the most important ingredients of this analysis is the non-abelian quark-gluon vertex, which controls the way the ghost sector enters into the gap equation. Specifically, this vertex introduces a numerically crucial dependence on the ghost dressing function and the quark-ghost scattering amplitude. This latter quantity satisfies its own, previously unexplored, dynamical equation, which may be decomposed into individual integral equations for its various form factors. In particular, the sca…

Effective gluon mass and infrared fixed point in QCD

We report on a special type of solutions for the gluon propagator of pure QCD, obtained from the corresponding non-linear Schwinger-Dyson equation formulated in the Feynman gauge of the background field method. These solutions reach a finite value in the deep infrared and may be fitted using a massive propagator, with the crucial characteristic that the effective ``mass'' employed depends on the momentum transfer. Specifically, the gluon mass falls off as the inverse square of the momentum, as expected from the operator-product expansion. In addition, one may define a dimensionless quantity, which constitutes the generalization in a non-Abelian context of the universal QED effective charge.…

Effects of divergent ghost loops on the Green’s functions of QCD

In the present work we discuss certain characteristic features encoded in some of the fundamental QCD Green's functions, whose origin can be traced back to the nonperturbative masslessness of the ghost field, in the Landau gauge. Specifically, the ghost loops that contribute to these Green's functions display infrared divergences, akin to those encountered in the perturbative treatment, in contradistinction to the gluonic loops, whose perturbative divergences are tamed by the dynamical generation of an effective gluon mass. In d=4, the aforementioned divergences are logarithmic, thus causing a relatively mild impact, whereas in d=3 they are linear, giving rise to enhanced effects. In the ca…

Heavy quark decomposition of the S matrix and its relation to the pinch technique.

We propose a decomposition of the S-matrix into individually gauge invariant sub-amplitudes, which are kinematically akin to propagators, vertices, boxes, etc. This decompsition is obtained by considering limits of the S-matrix when some or all of the external particles have masses larger than any other physical scale. We show at the one-loop level that the effective gluon self-energy so defined is physically equivalent to the corresponding gauge independent self-energy obtained in the framework of the pinch technique. The generalization of this procedure to arbitrary gluonic $n$-point functions is briefly discussed.

Connection between the pinch technique and the background field method

The connection between the pinch technique and the background field method is further explored. We show by explicit calculations that the application of the pinch technique in the framework of the background field method gives rise to exactly the same results as in the linear renormalizable gauges. The general method for extending the pinch technique to the case of Green's functions with off-shell fermions as incoming particles is presented. As an example, the one-loop gauge independent quark self-energy is constructed. We briefly discuss the possibility that the gluonic Green's functions, obtained by either method, correspond to physical quantities.

The pinch technique at two loops

It is shown that the fundamental properties of gauge-independence, gauge-invariance, unitarity, and analyticity of the $S$-matrix lead to the unambiguous generalization of the pinch technique algorithm to two loops.

Universal extra dimensions andZ→bb¯

We study, at the one loop level, the dominant contributions from a single universal extra dimension to the process $\stackrel{\ensuremath{\rightarrow}}{Z}b\overline{b}.$ By resorting to the gaugeless limit of the theory we explain why the result is expected to display a strong dependence on the mass of the top quark, not identified in the early literature. A detailed calculation corroborates this expectation, giving rise to a lower bound for the compactification scale which is comparable to that obtained from the $\ensuremath{\rho}$ parameter. An estimate of the subleading corrections is furnished, together with a qualitative discussion on the difference between the present results and thos…

Nonperturbative structure of the ghost-gluon kernel

The ghost-gluon scattering kernel is a special correlation function that is intimately connected with two fundamental vertices of the gauge sector of QCD: the ghost-gluon vertex, which may be obtained from it through suitable contraction, and the three-gluon vertex, whose Slavnov-Taylor identity contains that kernel as one of its main ingredients. In this work we present a detailed nonperturbative study of the five form factors comprising it, using as starting point the `one-loop dressed' approximation of the dynamical equations governing their evolution. The analysis is carried out for arbitrary Euclidean momenta, and makes extensive use of the gluon propagator and the ghost dressing funct…

Yang-Mills two-point functions in linear covariant gauges

In this work we use two different but complementary approaches in order to study the ghost propagator of a pure SU(3) Yang-Mills theory quantized in the linear covariant gauges, focusing on its dependence on the gauge-fixing parameter $\xi$ in the deep infrared. In particular, we first solve the Schwinger-Dyson equation that governs the dynamics of the ghost propagator, using a set of simplifying approximations, and under the crucial assumption that the gluon propagators for $\xi>0$ are infrared finite, as is the case in the Landau gauge $(\xi=0)$. Then we appeal to the Nielsen identities, and express the derivative of the ghost propagator with respect to $\xi$ in terms of certain auxiliary…

Nonperturbative gluon and ghost propagators in d = 3

We study the nonperturbative gluon and ghost propagators in d=3 Yang-Mills, using the Schwinger-Dyson equations of the pinch technique. The use of the Schwinger mechanism leads to the dynamical generation of a gluon mass, which, in turn, gives rise to an infrared finite gluon propagator and ghost dressing function. The propagators obtained are in very good agreement with the results of SU(2) lattice simulations.

Unified description of seagull cancellations and infrared finiteness of gluon propagators

We present a generalized theoretical framework for dealing with the important issue of dynamical mass generation in Yang-Mills theories, and, in particular, with the infrared finiteness of the gluon propagators, observed in a multitude of recent lattice simulations. Our analysis is manifestly gauge-invariant, in the sense that it preserves the transversality of the gluon self-energy, and gauge-independent, given that the conclusions do not depend on the choice of the gauge-fixing parameter within the linear covariant gauges. The central construction relies crucially on the subtle interplay between the Abelian Ward identities satisfied by the nonperturbative vertices and a special integral i…

Gauge invariance and unstable particles.

A gauge-independent approach to resonant transition amplitudes with nonconserved external currents is presented, which is implemented by the pinch technique. The analytic expressions derived with this method are $U(1)_{em}$ invariant, independent of the choice of the gauge-fixing parameter, and satisfy a number of required theoretical properties, including unitarity. Although special attention is paid to resonant scatterings involving the $\gamma WW$ and $ZWW$ vertices in the minimal Standard Model, our approach can be extended to the top quark or other unstable particles appearing in renormalizable models of new physics.

Gluon mass and freezing of the QCD coupling

Infrared finite solutions for the gluon propagator of pure QCD are obtained from the gauge-invariant non-linear Schwinger-Dyson equation formulated in the Feynman gauge of the background field method. These solutions may be fitted using a massive propagator, with the special characteristic that the effective mass employed drops asymptotically as the inverse square of the momentum transfer, in agreement with general operator-product expansion arguments. Due to the presence of the dynamical gluon mass the strong effective charge extracted from these solutions freezes at a finite value, giving rise to an infrared fixed point for QCD.

Scrutinizing the Green's functions of QCD: Lattice meets Schwinger-Dyson

Proceedings of the International Workshop Light Cone 2009 (LC2009): Relativistic Hadronic and Particle Physics. Sao Jose dos Campos, Brazil, July 8-13, 2009.

Nonperturbative study of the four gluon vertex

In this paper we study the nonperturbative structure of the SU(3) four-gluon vertex in the Landau gauge, concentrating on contributions quadratic in the metric. We employ an approximation scheme where "one-loop" diagrams are computed using fully dressed gluon and ghost propagators, and tree-level vertices. When a suitable kinematical configuration depending on a single momentum scale $p$ is chosen, only two structures emerge: the tree-level four-gluon vertex, and a tensor orthogonal to it. A detailed numerical analysis reveals that the form factor associated with this latter tensor displays a change of sign (zero-crossing) in the deep infrared, and finally diverges logarithmically. The orig…

Gluon mass generation in the PT-BFM scheme

In this article we study the general structure and special properties of the Schwinger-Dyson equation for the gluon propagator constructed with the pinch technique, together with the question of how to obtain infrared finite solutions, associated with the generation of an effective gluon mass. Exploiting the known all-order correspondence between the pinch technique and the background field method, we demonstrate that, contrary to the standard formulation, the non-perturbative gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions. We next present a comprehensive review of several subtle issues relevant to the search …

Massless bound-state excitations and the Schwinger mechanism in QCD

The gauge invariant generation of an effective gluon mass proceeds through the well-known Schwinger mechanism, whose key dynamical ingredient is the nonperturbative formation of longitudinally coupled massless bound-state excitations. These excitations introduce poles in the vertices of the theory, in such a way as to maintain the Slavnov-Taylor identities intact in the presence of massive gluon propagators. In the present work we first focus on the modifications induced to the nonperturbative three-gluon vertex by the inclusion of massless two-gluon bound-states into the kernels appearing in its skeleton-expansion. Certain general relations between the basic building blocks of these bound-…

A novel integral representation for the Adler function

New integral representations for the Adler D-function and the R-ratio of the electron-positron annihilation into hadrons are derived in the general framework of the analytic approach to QCD. These representations capture the nonperturbative information encoded in the dispersion relation for the D-function, the effects due to the interrelation between spacelike and timelike domains, and the effects due to the nonvanishing pion mass. The latter plays a crucial role in this analysis, forcing the Adler function to vanish in the infrared limit. Within the developed approach the D-function is calculated by employing its perturbative approximation as the only additional input. The obtained result …

Set of sum rules for anomalous gauge boson couplings

The dependence of the differential cross-section for on-shell W-pair production on the anomalous trilinear gauge couplings invariant under C and P is examined. It is shown that the contributions of the anomalous magnetic moments of the W boson due to the photon and the Z can be individually projected out by means of two appropriately constructed polynomials. The remaining four anomalous couplings are shown to satisfy a set of model-independent sum rules. Specific models which predict special relations among the anomalous couplings are then studied; in particular, the composite model of Brodsky and Hiller, and the linear and non-linear effective Lagrangian approaches. The relations predicted…

Pinch technique at two loops

It is shown that the fundamental properties of gauge-independence, gauge-invariance, unitarity, and analyticity of the S-matrix lead to the unambiguous generalization of the pinch technique algorithm to two loops.

Gluon mass generation in the massless bound-state formalism

We present a detailed, all-order study of gluon mass generation within the massless bound-state formalism, which constitutes the general framework for the systematic implementation of the Schwinger mechanism in non-Abelian gauge theories. The main ingredient of this formalism is the dynamical formation of bound states with vanishing mass, which give rise to effective vertices containing massless poles; these latter vertices, in turn, trigger the Schwinger mechanism, and allow for the gauge-invariant generation of an effective gluon mass. This particular approach has the conceptual advantage of relating the gluon mass directly to quantities that are intrinsic to the bound-state formation its…

Method for determining anomalous gauge boson couplings from e(+)e(-) experiments

We present a model-independent method for determining anomalous gauge boson couplings from ongoing and future e^{+}e^{-} -> W^{+} W^{-} experiments. First we generalize an already existing method, which relies on the study of four observables constructed through appropriate projections of the unpolarized differential cross-section. In particular, we retain both linear and quadratic terms in the unknown couplings, and compute contributions to these observables originating from anomalous couplings which do not separately conserve the discrete C, P, and T symmetries. Second, we combine the above set of observables with three additional ones, which can be experimentally obtained from the total …

Process-independent strong running coupling

We unify two widely different approaches to understanding the infrared behaviour of quantum chromodynamics (QCD), one essentially phenomenological, based on data, and the other computational, realised via quantum field equations in the continuum theory. Using the latter, we explain and calculate a process-independent running-coupling for QCD, a new type of effective charge that is an analogue of the Gell-Mann--Low effective coupling in quantum electrodynamics. The result is almost identical to the process-dependent effective charge defined via the Bjorken sum rule, which provides one of the most basic constraints on our knowledge of nucleon spin structure. This reveals the Bjorken sum to be…

Gauge-invariant proper self-energies and vertices in gauge-theories with broken symmetry

Using the pinch technique, we show how to recover, from the {ital S} matrix of a spontaneously broken non-Abelian gauge theory, proper self-energies and vertices which are fully gauge invariant when one or more momenta are off shell. Explicit calculations are carried out at the one-loop level for gauge-boson self-energies and fermion--gauge-boson vertices in a simple SU(2) gauge theory with a Higgs boson. The same technique allows us to calculate, at one-loop order, a neutrino electromagnetic form factor which is gauge invariant at all photon momenta, thus resolving a long-standing problem. We show how massless Goldstone bosons, not present in the {ital S} matrix, must be introduced into Gr…

Gauge- and renormalization-group-invariant formulation of the Higgs-boson resonance

A gauge- and renormalization-group- invariant approach implemented by the pinch technique is formulated for resonant transitions involving the Higgs boson. The lineshape of the Higgs boson is shown to consist of two distinct and physically meaningful contributions: a process-independent resonant part and a process-dependent non-resonant background, which are separately gauge independent, invariant under the renormalization group, satisfy naive, tree-level Ward identities, and respect the optical and equivalence theorem individually. The former process-independent quantity serves as the natural extension of the concept of the effective charge to the case of the Higgs scalar, and constitutes …

Dynamical zero in (v)over-bar(e)-e(-) scattering and the neutrino magnetic moment

The Standard Model differential cross section for ν¯e−e− elastic scattering vanishes exactly, at lowest order, for forward electrons and incident ν¯e energy close to the rest energy of the electron. This dynamical zero is not induced by a fundamental symmetry of the Lagrangian but by a destructive interference between the left- and right-handed chiral couplings of the electron in the charged and neutral current amplitudes. We show that lowest order analyses based on this favorable kinematic configuration are only mildly affected by the inclusion of the O(α) radiative corrections in the ν¯e−e− differential cross section, thus providing an excellent opportunity for the search of ``new physics…

Natural constraints on the gluon-quark vertex

In principle, the strong-interaction sector of the Standard Model is characterised by a unique renormalisation-group-invariant (RGI) running interaction and a unique form for the dressed--gluon-quark vertex, $\Gamma_\mu$; but, whilst much has been learnt about the former, the latter is still obscure. In order to improve this situation, we use a RGI running-interaction that reconciles both top-down and bottom-up analyses of the gauge sector in quantum chromodynamics (QCD) to compute dressed-quark gap equation solutions with 1,660,000 distinct Ansaetze for $\Gamma_\mu$. Each one of the solutions is then tested for compatibility with three physical criteria and, remarkably, we find that merely…

Gauge-invariant 4-gluon vertex and its ward identity

We use the S-matrix pinch technique to construct at one-loop order a four-gluon vertex for QCD, which is independent of the choice of the gauge parameter, when one or more of the incoming momenta are off shell. We discuss some of the technical subtleties in the application of the pinch technique and show that this vertex satisfies a very simple Ward identity, relating it to a previously constructed gauge-independent three-gluon vertex, also found with the same technique. This analysis serves as a prelude to the construction of an effective potential for QCD, which is gauge-independent order by order in the dressed-loop expansion.

Gauge-independent approach to resonant transition amplitudes

We present a new gauge-independent approach to resonant transition amplitudes with nonconserved external currents, based on the pinch technique method. In the context of $2\to 2$ and $2\to 3$ scattering processes, we show explicitly that the analytic results derived respect $U(1)_{em}$ gauge symmetry and do not depend on the choice of the $SU(2)_L$ gauge fixing. Our analytic approach treats, on equal footing, fermionic as well as bosonic contributions to the resummed gauge boson propagators, does not contain any residual space-like threshold terms, shows the correct high-energy unitarity behaviour, admits renormalization, and satisfies a number of other required properties, including the op…

On the zero crossing of the three-gluon vertex

We report on new results on the infrared behaviour of the three-gluon vertex in quenched Quantum Chormodynamics, obtained from large-volume lattice simulations. The main focus of our study is the appearance of the characteristic infrared feature known as 'zero crossing', the origin of which is intimately connected with the nonperturbative masslessness of the Faddeev-Popov ghost. The appearance of this effect is clearly visible in one of the two kinematic configurations analyzed, and its theoretical origin is discussed in the framework of Schwinger-Dyson equations. The effective coupling in the momentum subtraction scheme that corresponds to the three-gluon vertex is constructed, revealing t…

QCD effective charge from the three-gluon vertex of the background-field method

In this article we study in detail the prospects of determining the infrared finite QCD effective charge from a special kinematic limit of the vertex function corresponding to three background gluons. This particular Green's function satisfies a QED-like Ward identity, relating it to the gluon propagator, with no reference to the ghost sector. Consequently, its longitudinal form factors may be expressed entirely in terms of the corresponding gluon wave function, whose inverse is proportional to the effective charge. After reviewing certain important theoretical properties, we consider a typical lattice quantity involving this vertex, and derive its exact dependence on the various form facto…

Gauge coupling instability and dynamical mass generation in N=1 three-dimensional supersymmetric QED

Using superfield Dyson-Schwinger equations, we compute the infrared dynamics of the semi-amputated full vertex, corresponding to the effective running gauge coupling, in N-flavor N51 three-dimensional supersymmetric QED. It is shown that the presence of a supersymmetry-preserving mass for the matter multiplet stabilizes the infrared gauge coupling against oscillations present in the massless case, and we therefore infer that the massive vacuum is thus selected at the level of the ~quantum! effective action. We further demonstrate that such a mass can indeed be generated dynamically in a self-consistent way by appealing to the superfield Dyson-Schwinger gap equation for the full matter propa…

Distribution Amplitudes of Heavy-Light Mesons

A symmetry-preserving approach to the continuum bound-state problem in quantum field theory is used to calculate the masses, leptonic decay constants and light-front distribution amplitudes of empirically accessible heavy-light mesons. The inverse moment of the $B$-meson distribution is particularly important in treatments of exclusive $B$-decays using effective field theory and the factorisation formalism; and its value is therefore computed: $\lambda_B(\zeta = 2\,{\rm GeV}) = 0.54(3)\,$GeV. As an example and in anticipation of precision measurements at new-generation $B$-factories, the branching fraction for the rare $B\to \gamma(E_\gamma) \ell \nu_\ell$ radiative decay is also calculated…

Gauge-invariant resummation formalism for two-point correlation functions

The consistent description of unstable particles, renormalons, or other Schwinger--Dyson-type of solutions within the framework of perturbative gauge field theories necessitates the definition and resummation of off-shell Green's functions, which must respect several crucial physical requirements. A formalism is presented for resummation of off-shell two-point correlation functions, which is mainly based on arguments of analyticity, unitarity, gauge invariance and renormalizability. The analytic results obtained with various methods, including the background field gauges and the pinch technique are confronted with the physical requirements imposed; to one-loop order the pinch technique appr…

Infrared finite ghost propagator in the Feynman gauge

We demonstrate how to obtain from the Schwinger-Dyson equations of QCD an infrared finite ghost propagator in the Feynman gauge. The key ingredient in this construction is the longitudinal form factor of the non-perturbative gluon-ghost vertex, which, contrary to what happens in the Landau gauge, contributes non-trivially to the gap equation of the ghost. The detailed study of the corresponding vertex equation reveals that in the presence of a dynamical infrared cutoff this form factor remains finite in the limit of vanishing ghost momentum. This, in turn, allows the ghost self-energy to reach a finite value in the infrared, without having to assume any additional properties for the gluon-g…

Gauge-invariant 3-gluon vertex in QCD

By resumming the Feynman graphs which contribute to any gauge-invariant process we explicitly construct, at one-loop order, a three-gluon vertex for QCD which is completely independent of the choice of gauge. This vertex satisfies a Ward identity of the type encountered in ghost-free gauges, relating the vertex to the proper self-energy of a previously constructed gluon propagator, also found by resumming graphs; like the vertex, this self-energy is completely gauge invariant. We also derive the gauge-invariant propagator and vertex via a second related technique which minimizes the dependence on embedding these objects in a gauge-invariant process; the same results are found as in the firs…

Infrared facets of the three-gluon vertex

We present novel lattice results for the form factors of the quenched three-gluon vertex of QCD, in two special kinematic configurations that depend on a single momentum scale. We consider three form factors, two associated with a classical tensor structure and one without tree-level counterpart, exhibiting markedly different infrared behaviors. Specifically, while the former display the typical suppression driven by a negative logarithmic singularity at the origin, the latter saturates at a small negative constant. These exceptional features are analyzed within the Schwinger-Dyson framework, with the aid of special relations obtained from the Slavnov-Taylor identities of the theory. The em…

Indirect determination of the Kugo-Ojima function from lattice data

We study the structure and non-perturbative properties of a special Green's function, u(q), whose infrared behavior has traditionally served as the standard criterion for the realization of the Kugo-Ojima confinement mechanism. It turns out that, in the Landau gauge, u(q) can be determined from a dynamical equation, whose main ingredients are the gluon propagator and the ghost dressing function, integrated over all physical momenta. Using as input for these two (infrared finite) quantities recent lattice data, we obtain an indirect determination of u(q). The results of this mixed procedure are in excellent agreement with those found previously on the lattice, through a direct simulation of …

Non-perturbative QCD effective charges

Using gluon and ghost propagators obtained from Schwinger-Dyson equations (SDEs), we construct the non-perturbative effective charge of QCD. We employ two different definitions, which, despite their distinct field-theoretic origin, give rise to qualitative comparable results, by virtue of a crucial non-perturbative identity. Most importantly, the QCD charge obtained with either definition freezes in the deep infrared, in agreement with theoretical and phenomenological expectations. The various theoretical ingredients necessary for this construction are reviewed in detail, and some conceptual subtleties are briefly discussed.

Quark gap equation within the analytic approach to QCD

The compatibility between the QCD analytic invariant charge and chiral symmetry breaking is examined in detail. The coupling in question incorporates asymptotic freedom and infrared enhancement into a single expression, and contains only one adjustable parameter with dimension of mass. When inserted into the standard form of the quark gap-equation it gives rise to solutions displaying singular confining behavior at the origin. By relating these solutions to the pion decay constant, a rough estimate of about 880 MeV is obtained for the aforementioned mass-scale.

Breit-Wigner formalism for non-Abelian theories

The consistent description of resonant transition amplitudes within the framework of perturbative field theories necessitates the definition and resummation of off-shell Green's functions, which must respect several crucial physical requirements. In particular, the generalization of the usual Breit-Wigner formalism in a non-Abelian context constitutes a highly non-trivial problem, related to the fact that the conventionally defined Green's functions are unphysical. We briefly review the main field-theoretical difficulties arising when attempting to use such Green's functions outside the confines of a fixed order perturbative calculation, and explain how this task has been successfully accom…

Probing the WW gamma vertex at hadron colliders

We present a new, model independent method for extracting bounds for the anomalous $\gamma WW$ couplings from hadron collider experiments. At the partonic level we introduce a set of three observables which are constructed from the unpolarized differential cross-section for the process $d\bar{u}\to W^{-}\gamma$ by appropriate convolution with a set of simple polynomials depending only on the center-of-mass angle. One of these observables allows for the direct determination of the anomalous coupling usually denoted by $\Delta\kappa$, without any simplifying assumptions, and without relying on the presence of a radiation zero. The other two observables impose two sum rules on the remaining th…

Infrared finite effective charge of QCD

We show that the gauge invariant treatment of the Schwinger-Dyson equations of QCD leads to an infrared finite gluon propagator, signaling the dynamical generation of an effective gluon mass, and a non-enhanced ghost propagator, in qualitative agreement with recent lattice data. The truncation scheme employed is based on the synergy between the pinch technique and the background field method. One of its most powerful features is that the transversality of the gluon self-energy is manifestly preserved, exactly as dictated by the BRST symmetry of the theory. We then explain, for the first time in the literature, how to construct non-perturbatively a renormalization group invariant quantity ou…

Mass generation in Yang-Mills theories *

In this talk we review recent progress on our understanding of the nonperturbative phenomenon of mass generation in non-Abelian gauge theories, and the way it manifests itself at the level of the gluon propagator, thus establishing a close contact with a variety of results obtained in large-volume lattice simulations. The key observation is that, due to an exact cancellation operating at the level of the Schwinger-Dyson equations, the gluon propagator remains rigorously massless, provided that the fully-dressed vertices of the theory do not contain massless poles. The inclusion of such poles activates the well-known Schwinger mechanism, which permits the evasion of the aforementioned cancel…

Intrinsic CPT violation and decoherence for entangled neutral mesons

We present a combined treatment of quantum-gravity-induced effects and intrinsic CPT violation in entangled neutral-Kaon states. Our analysis takes into consideration two types of effects: first, those associated with the loss of particle-antiparticle identity, as a result of the ill-defined nature of the CPT operator, and second, effects due to the non-unitary evolution of the Kaons in the space-time foam. By studying a variety of phi-factory observables, involving identical as well as general final states, we derive analytical expressions, to leading order in the associated CPT violating parameters, for double-decay rates and their time-integrated counterparts. Our analysis shows that the…

Quark gap equation with non-Abelian Ball-Chiu vertex

The full quark-gluon vertex is a crucial ingredient for the dynamical generation of a constituent quark mass from the standard quark gap equation, and its non-transverse part may be determined exactly from the nonlinear Slavnov-Taylor identity that it satisfies. The resulting expression involves not only the quark propagator, but also the ghost dressing function and the quark-ghost kernel, and constitutes the non-abelian extension of the so-called "Ball-Chiu vertex", known from QED. In the present work we carry out a detailed study of the impact of this vertex on the gap equation and the quark masses generated from it, putting particular emphasis on the contributions directly related with t…

Dual gauge-fixing property of the S matrix.

The {ital S} matrix is known to be independent of the gauge-fixing parameter to all orders in perturbation theory. In this paper by employing the pinch technique we prove at one loop a stronger version of this independence. In particular, we show that one can use a gauge-fixing parameter for the gauge bosons inside quantum loops which is different from that used for the bosons outside loops, and the {ital S} matrix is independent of both. Possible phenomenological applications of this result are briefly discussed. {copyright} {ital 1996 The American Physical Society.}

Effective Charge of the Higgs Boson

The Higgs-boson lineshape is studied within the pinch technique resummation formalism. It is shown that any resonant Higgs-boson amplitude contains a universal part which is gauge independent, renormalization-group invariant, satisfies the optical and equivalence theorems, and constitutes the natural extension of the QED effective charge to the case of the Higgs scalar.

The effective neutrino charge radius

It is shown that at one-loop order a neutrino charge radius (NCR) may be defined, which is ultraviolet finite, does not depend on the gauge-fixing parameter, nor on properties of the target other than its electric charge. This is accomplished through the systematic decomposition of physical amplitudes into effective self-energies, vertices, and boxes, which separately respect electroweak gauge invariance. In this way the NCR stems solely from an effective proper photon-neutrino one-loop vertex, which satisfies a naive, QED-like Ward identity. The NCR so defined may be extracted from experiment, at least in principle, by expressing a set of experimental electron-neutrino cross-sections in te…

Impact of the pion mass on nonpower expansion for QCD observables

A new set of functions, which form a basis of the massive nonpower expansion for physical observables, is presented in the framework of the analytic approach to QCD at the four-loop level. The effects due to the $\pi$ meson mass are taken into account by employing the dispersion relation for the Adler function. The nonvanishing pion mass substantially modifies the functional expansion at low energies. Specifically, the spacelike functions are affected by the mass of the $\pi$ meson in the infrared domain below few GeV, whereas the timelike functions acquire characteristic plateaulike behavior below the two-pion threshold. At the same time, all the appealing features of the massless nonpower…

Bridging a gap between continuum-QCD and ab initio predictions of hadron observables

Within contemporary hadron physics there are two common methods for determining the momentum-dependence of the interaction between quarks: the top-down approach, which works toward an ab initio computation of the interaction via direct analysis of the gauge-sector gap equations; and the bottom-up scheme, which aims to infer the interaction by fitting data within a well-defined truncation of those equations in the matter sector that are relevant to bound-state properties. We unite these two approaches by demonstrating that the renormalisation-group-invariant running-interaction predicted by contemporary analyses of QCD's gauge sector coincides with that required in order to describe ground-s…

Pinch Technique: Theory and Applications

We review the theoretical foundations and the most important physical applications of the Pinch Technique (PT). This general method allows the construction of off-shell Green’s functions in non-Abelian gauge theories that are independent of the gauge-fixing parameter and satisfy ghost-free Ward identities. We first present the diagrammatic formulation of the technique in QCD, deriving, at one loop, the gauge independent gluon self-energy, quark–gluon vertex, and three-gluon vertex, together with their Abelian Ward identities. The generalization of the PT to theories with spontaneous symmetry breaking is carried out in detail, and the profound connection with the optical theorem and the disp…

The massive analytic invariant charge in QCD

The low energy behavior of a recently proposed model for the massive analytic running coupling of QCD is studied. This running coupling has no unphysical singularities, and in the absence of masses displays infrared enhancement. The inclusion of the effects due to the mass of the lightest hadron is accomplished by employing the dispersion relation for the Adler D function. The presence of the nonvanishing pion mass tames the aforementioned enhancement, giving rise to a finite value for the running coupling at the origin. In addition, the effective charge acquires a "plateau-like" behavior in the low energy region of the timelike domain. This plateau is found to be in agreement with a number…

Non-Abelian Ball-Chiu vertex for arbitrary Euclidean momenta

We determine the non-Abelian version of the four longitudinal form factors of the quark-gluon vertex, using exact expressions derived from the Slavnov-Taylor identity that this vertex satisfies. In addition to the quark and ghost propagators, a key ingredient of the present approach is the quark-ghost scattering kernel, which is computed within the one-loop dressed approximation. The vertex form factors obtained from this procedure are evaluated for arbitrary Euclidean momenta, and display features not captured by the well-known Ball-Chiu vertex, deduced from the Abelian (ghost-free) Ward identity. The potential phenomenological impact of these results is evaluated through the study of spec…

Schwinger mechanism in linear covariant gauges

In this work we explore the applicability of a special gluon mass generating mechanism in the context of the linear covariant gauges. In particular, the implementation of the Schwinger mechanism in pure Yang-Mills theories hinges crucially on the inclusion of massless bound-state excitations in the fundamental nonperturbative vertices of the theory. The dynamical formation of such excitations is controlled by a homogeneous linear Bethe-Salpeter equation, whose nontrivial solutions have been studied only in the Landau gauge. Here, the form of this integral equation is derived for general values of the gauge-fixing parameter, under a number of simplifying assumptions that reduce the degree of…

New method for determining the quark-gluon vertex

We present a novel nonperturbative approach for calculating the form factors of the quark-gluon vertex, in a general covariant gauge. The key ingredient of this method is the exact all-order relation connecting the conventional quark-gluon vertex with the corresponding vertex of the background field method, which is Abelian-like. When this latter relation is combined with the standard gauge technique, supplemented by a crucial set of transverse Ward identities, it allows the approximate determination of the nonperturbative behavior of all twelve form factors comprising the quark-gluon vertex, for arbitrary values of the momenta. The actual implementation of this procedure is carried out in …

CPT violation in entangled B0–B¯0 states and the demise of flavour tagging

Abstract We discuss the demise of flavour tagging due to the loss of the particle–antiparticle identity of neutral B -mesons in the Einstein–Podolsky–Rosen correlated states. Such a situation occurs in cases where the CPT operator is ill-defined, as happens, for example, in quantum gravity models with induced decoherence in the matter sector. The time evolution of the perturbed B 0 – B ¯ 0 initial state, as produced in B -factories, is sufficient to generate new two-body states. For flavour specific decays at equal times, we discuss two definite tests of the two body entanglement: (i) search for the would-be forbidden B 0 B 0 and B ¯ 0 B ¯ 0 states; (ii) deviations from the indistinguishabl…

Pinch technique and the Batalin-Vilkovisky formalism

In this paper we take the first step towards a non-diagrammatic formulation of the Pinch Technique. In particular we proceed into a systematic identification of the parts of the one-loop and two-loop Feynman diagrams that are exchanged during the pinching process in terms of unphysical ghost Green's functions; the latter appear in the standard Slavnov-Taylor identity satisfied by the tree-level and one-loop three-gluon vertex. This identification allows for the consistent generalization of the intrinsic pinch technique to two loops, through the collective treatment of entire sets of diagrams, instead of the laborious algebraic manipulation of individual graphs, and sets up the stage for the…

Can power corrections be reliably computed in models with extra dimensions?

We critically revisit the issue of power-law running in models with extra dimensions. The analysis is carried out in the context of a higher-dimensional extension of QED, with the extra dimensions compactified on a torus. It is shown that a naive $\beta$ function, which simply counts the number of modes, depends crucially on the way the thresholds of the Kaluza-Klein modes are crossed. To solve these ambiguities we turn to the vacuum polarization, which, due to its special unitarity properties, guarantees the physical decoupling of the heavy modes. This latter quantity, calculated in the context of dimensional regularization, is used for connecting the low energy gauge coupling with the cou…

Ghost dynamics in the soft gluon limit

We present a detailed study of the dynamics associated with the ghost sector of quenched QCD in the Landau gauge, where the relevant dynamical equations are supplemented with key inputs originating from large-volume lattice simulations. In particular, we solve the coupled system of Schwinger-Dyson equations that governs the evolution of the ghost dressing function and the ghost-gluon vertex, using as input for the gluon propagator lattice data that have been cured from volume and discretization artifacts. In addition, we explore the soft gluon limit of the same system, employing recent lattice data for the three-gluon vertex that enters in one of the diagrams defining the Schwinger-Dyson eq…

Nonperturbative comparison of QCD effective charges

We study the non-perturbative behavior of two versions of the QCD effective charge, one obtained from the pinch technique gluon self-energy, and one from the ghost-gluon vertex. Despite their distinct theoretical origin, due to a fundamental identity relating various of the ingredients appearing in their respective definitions, the two effective charges are almost identical in the entire range of physical momenta, and coincide exactly in the deep infrared, where they freeze at a common finite value. Specifically, the dressing function of the ghost propagator is related to the two form factors in the Lorentz decomposition of a certain Green's function, appearing in a variety of field-theoret…

Ghost spectral function from the spectral Dyson-Schwinger equation

We compute the ghost spectral function in Yang-Mills theory by solving the corresponding Dyson-Schwinger equation for a given input gluon spectral function. The results encompass both scaling and decoupling solutions for the gluon propagator input. The resulting ghost spectral function displays a particle peak at vanishing momentum and a negative scattering spectrum, whose infrared and ultraviolet tails are obtained analytically. The ghost dressing function is computed in the entire complex plane, and its salient features are identified and discussed.

The dynamical equation of the effective gluon mass

In this article we derive the integral equation that controls the momentum dependence of the effective gluon mass in the Landau gauge. This is accomplished by means of a well-defined separation of the corresponding "one-loop dressed" Schwinger-Dyson equation into two distinct contributions, one associated with the mass and one with the standard kinetic part of the gluon. The entire construction relies on the existence of a longitudinally coupled vertex of nonperturbative origin, which enforces gauge invariance in the presence of a dynamical mass. The specific structure of the resulting mass equation, supplemented by the additional requirement of a positive-definite gluon mass, imposes a rat…

Universal extra dimensions and Z -> b(b)over-bar

We study, at the one loop level, the dominant contributions from a single universal extra dimension to the process (Z\to b\bar{b}). By resorting to the gaugeless limit of the theory we explain why the result is expected to display a strong dependence on the mass of the top-quark, not identified in the early literature. A detailed calculation corroborates this expectation, giving rise to a lower bound for the compactification scale which is comparable to that obtained from the ρ parameter. An estimate of the subleading corrections is furnished, together with a qualitative discussion on the difference between the present results and those derived previously for the non-universal case.

Pinch technique for Schwinger-Dyson equations

40 pages, 11 figures.-- ISI Article Identifier: 000245922000041.-- ArXiv pre-print available at: http://arxiv.org/abs/hep-ph/0611354

Gluon mass generation without seagull divergences

Dynamical gluon mass generation has been traditionally plagued with seagull divergences, and all regularization procedures proposed over the years yield finite but scheme-dependent gluon masses. In this work we show how such divergences can be eliminated completely by virtue of a characteristic identity, valid in dimensional regularization. The ability to trigger the aforementioned identity hinges crucially on the particular Ansatz employed for the three-gluon vertex entering into the Schwinger-Dyson equation governing the gluon propagator. The use of the appropriate three-gluon vertex brings about an additional advantage: one obtains two separate (but coupled) integral equations, one for t…

Renormalization group analysis of the gluon mass equation

In the present work we carry out a systematic study of the renormalization properties of the integral equation that determines the momentum evolution of the effective gluon mass. A detailed, all-order analysis of the complete kernel appearing in this particular equation reveals that the renormalization procedure may be accomplished through the sole use of ingredients known from the standard perturbative treatment of the theory, with no additional assumptions. However, the subtle interplay of terms operating at the level of the exact equation gets distorted by the approximations usually employed when evaluating the aforementioned kernel. This fact is reflected in the form of the obtained sol…

The Pinch Technique and its Applications to Non-Abelian Gauge Theories

Non-Abelian gauge theories, such as quantum chromodynamics (QCD) or electroweak theory, are best studied with the aid of Green's functions that are gauge-invariant off-shell, but unlike for the photon in quantum electrodynamics, conventional graphical constructions fail. The Pinch Technique provides a systematic framework for constructing such Green's functions, and has many useful applications. Beginning with elementary one-loop examples, this book goes on to extend the method to all orders, showing that the Pinch Technique is equivalent to calculations in the background field Feynman gauge. The Pinch Technique Schwinger-Dyson equations are derived, and used to show how a dynamical gluon m…

Power-law running of the effective gluon mass

The dynamically generated effective gluon mass is known to depend non-trivially on the momentum, decreasing sufficiently fast in the deep ultraviolet, in order for the renormalizability of QCD to be preserved. General arguments based on the analogy with the constituent quark masses, as well as explicit calculations using the operator-product expansion, suggest that the gluon mass falls off as the inverse square of the momentum, relating it to the gauge-invariant gluon condensate of dimension four. In this article we demonstrate that the power-law running of the effective gluon mass is indeed dynamically realized at the level of the non-perturbative Schwinger-Dyson equation. We study a gauge…

Alternative large-n limit for QCD and its implications for low-energy nuclear phenomena

The Corrigan-Ramond model for large-{ital N} QCD is analyzed in detail. The spectrum, leading-order results for interactions, and an effective Lagrangian describing large-{ital N} interactions are derived. This Lagrangian, when quantized, provides an effective quantum field theory for mesons and baryons. The applicability of such a theory to low-energy nuclear phenomena is studied. The model has features that distinguish it clearly from standard large-{ital N} QCD.

Novel type of CPT violation for correlated Einstein-Podolsky-Rosen states of neutral mesons.

We discuss modifications to the concept of an "antiparticle," induced by a breakdown of the CPT symmetry at a fundamental level, realized within an extended class of quantum gravity models. The resulting loss of particle-antiparticle identity in the neutral-meson system induces a breaking of the Einstein-Podolsky-Rosen correlation imposed by Bose statistics. This is parametrized by a complex parameter associated with the contamination by the "wrong symmetry" state. The physical consequences are studied, and novel observables of CPT violation in phi factories are proposed.

Super Heavy Dark Matter Anisotropies from D-particles in the Early Universe

We discuss a way of producing anisotropies in the spectrum of superheavy Dark matter, which are due to the distortion of the inflationary space time induced by the recoil of D-particles upon their scattering with ordinary string matter in the Early Universe. We calculate such distortions by world-sheet Liouville string theory (perturbative) methods. The resulting anisotropies are found to be proportional to the average recoil velocity and density of the D-particles. In our analysis we employ a regulated version of de Sitter space, allowing for graceful exit from inflation. This guarantees the asymptotic flatness of the space time, as required for a consistent interpretation, within an effec…

Ghost propagator and ghost-gluon vertex from Schwinger-Dyson equations

We study an approximate version of the Schwinger-Dyson equation that controls the nonperturbative behavior of the ghost-gluon vertex in the Landau gauge. In particular, we focus on the form factor that enters in the dynamical equation for the ghost dressing function, in the same gauge, and derive its integral equation, in the "one-loop dressed" approximation. We consider two special kinematic configurations, which simplify the momentum dependence of the unknown quantity; in particular, we study the soft gluon case and the well-known Taylor limit. When coupled with the Schwinger-Dyson equation of the ghost dressing function, the contribution of this form factor provides considerable support …

Appendix: Feynman rules

Analyzing dynamical gluon mass generation

We study the necessary conditions for obtaining infrared finite solutions from the Schwinger-Dyson equation governing the dynamics of the gluon propagator. The equation in question is set up in the Feynman gauge of the background field method, thus capturing a number of desirable features. Most notably, and in contradistinction to the standard formulation, the gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions. Various subtle field-theoretic issues, such as renormalization group invariance and regularization of quadratic divergences, are briefly addressed. The infrared and ultraviolet properties of the obtained so…

Gluon mass generation in the presence of dynamical quarks

We study in detail the impact of dynamical quarks on the gluon mass generation mechanism, in the Landau gauge, for the case of a small number of quark families. As in earlier considerations, we assume that the main bulk of the unquenching corrections to the gluon propagator originates from the fully dressed quark-loop diagram. The nonperturbative evaluation of this diagram provides the key relation that expresses the unquenched gluon propagator as a deviation from its quenched counterpart. This relation is subsequently coupled to the integral equation that controls the momentum evolution of the effective gluon mass, which contains a single adjustable parameter; this constitutes a major impr…

On dynamical gluon mass generation

The effective gluon propagator constructed with the pinch technique is governed by a Schwinger-Dyson equation with special structure and gauge properties, that can be deduced from the correspondence with the background field method. Most importantly the non-perturbative gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions, a property which allows for a meanigfull truncation. A linearized version of the truncated Schwinger-Dyson equation is derived, using a vertex that satisfies the required Ward identity and contains massless poles. The resulting integral equation, subject to a properly regularized constraint, is so…

Gauge-independent off-shell fermion self-energies at two loops: The cases of QED and QCD

We use the pinch technique formalism to construct the gauge-independent off-shell two-loop fermion self-energy, both for Abelian (QED) and non-Abelian (QCD) gauge theories. The new key observation is that all contributions originating from the longitudinal parts of gauge boson propagators, by virtue of the elementary tree-level Ward identities they trigger, give rise to effective vertices, which do not exist in the original Lagrangian; all such vertices cancel diagrammatically inside physical quantities, such as current correlation functions or S-matrix elements. We present two different, but complementary derivations: First, we explicitly track down the aforementioned cancellations inside …

Pinch technique to all orders

The generalization of the pinch technique to all orders in perturbation theory is presented. The effective Green's functions constructed with this procedure are singled out in a unique way through the full exploitation of the underlying Becchi-Rouet-Stora-Tyutin symmetry. A simple all-order correspondence between the pinch technique and the background field method in the Feynman gauge is established. Comment: 10 pages, 4 figures; one reference added, typos corrected; final version to match the pubblished one

The QCD analytic running coupling and chiral symmetry breaking

We study the dependence on the pion mass of the QCD effective charge by employing the dispersion relations for the Adler D function. This new massive analytic running coupling is compared to the effective coupling saturated by the dynamically generated gluon mass. A qualitative picture of the possible impact of the former coupling on the chiral symmetry breaking is presented.

CPT violation in entangled BO-anti-BO states and the demise of flavour tagging

We discuss the demise of flavour tagging due to the loss of the particle-antiparticle identity of neutral B-mesons in the Einstein-Podolsky-Rosen correlated states. Such a situation occurs in cases where the CPT operator is ill-defined, as happens, for example, in quantum gravity models with induced decoherence in the matter sector. The time evolution of the perturbed B0-B0bar initial state, as produced in B-factories, is sufficient to generate new two-body states. For flavour specific decays at equal times, we discuss two definite tests of the two body entanglement: (i) search for the would-be forbidden B0 B0 and B0bar B0bar states; (ii) deviations from the indistinguishable probability be…

QCD effective charges from lattice data

We use recent lattice data on the gluon and ghost propagators, as well as the Kugo-Ojima function, in order to extract the non-perturbative behavior of two particular definitions of the QCD effective charge, one based on the pinch technique construction, and one obtained from the standard ghost-gluon vertex. The construction relies crucially on the definition of two dimensionful quantities, which are invariant under the renormalization group, and are built out of very particular combinations of the aforementioned Green's functions. The main non-perturbative feature of both effective charges, encoded in the infrared finiteness of the gluon propagator and ghost dressing function used in their…

Pinch technique at two loops: The case of massless Yang-Mills theories

The generalization of the pinch technique beyond one loop is presented. It is shown that the crucial physical principles of gauge-invariance, unitarity, and gauge-fixing-parameter independence single out at two loops exactly the same algorithm which has been used to define the pinch technique at one loop, without any additional assumptions. The two-loop construction of the pinch technique gluon self-energy, and quark-gluon vertex are carried out in detail for the case of mass-less Yang-Mills theories, such as perturbative QCD. We present two different but complementary derivations. First we carry out the construction by directly rearranging two-loop diagrams. The analysis reveals that, quit…

Nonlinear dynamics in three-dimensional QED and nontrivial infrared structure

In this work we consider a coupled system of Schwinger-Dyson equations for self-energy and vertex functions in QED_3. Using the concept of a semi-amputated vertex function, we manage to decouple the vertex equation and transform it in the infrared into a non-linear differential equation of Emden-Fowler type. Its solution suggests the following picture: in the absence of infrared cut-offs there is only a trivial infrared fixed-point structure in the theory. However, the presence of masses, for either fermions or photons, changes the situation drastically, leading to a mass-dependent non-trivial infrared fixed point. In this picture a dynamical mass for the fermions is found to be generated c…

Power corrections in models with extra dimensions

We critically revisit the issue of power-law running in models with extra dimensions. The general conclusion is that, in the absence of any additional physical principle, the power-corrections tend to depend strongly on the details of the underlying theory.

Standard model higher order corrections to the WW gamma/WWZ vertex

Using the S--matrix pinch technique we obtain to one loop order gauge independent $\gamma W^-W^+$ and $Z W^-W^+$ vertices in the context of the standard model, with all incoming momenta off--shell. We show that the vertices so constructed satisfy simple QED--like Ward identities. These gauge invariant vertices give rise to expressions for the magnetic dipole and electric quadrupole form factors of the $W$ gauge boson, which, unlike previous treatments, satisfy the crucial properties of infrared finiteness and perturbative unitarity.

Gauge invariant Ansatz for a special three-gluon vertex

We construct a general Ansatz for the three-particle vertex describing the interaction of one background and two quantum gluons, by simultaneously solving the Ward and Slavnov-Taylor identities it satisfies. This vertex is known to be essential for the gauge-invariant truncation of the Schwinger-Dyson equations of QCD, based on the pinch technique and the background field method. A key step in this construction is the formal derivation of a set of crucial constraints (shown to be valid to all orders), relating the various form factors of the ghost Green's functions appearing in the aforementioned Slavnov-Taylor identity. When inserted into the Schwinger-Dyson equation for the gluon propagat…

Infrared enhanced analytic coupling and chiral symmetry breaking in QCD

We study the impact on chiral symmetry breaking of a recently developed model for the QCD analytic invariant charge. This charge contains no adjustable parameters, other than the QCD mass scale $\Lambda$, and embodies asymptotic freedom and infrared enhancement into a single expression. Its incorporation into the standard form of the quark gap equation gives rise to solutions for the dynamically generated mass that display a singular confining behaviour at the origin. Using the Pagels-Stokar method we relate the obtained solutions to the pion decay constant $f_{\pi}$, and estimate the scale parameter $\Lambda$, in the presence of four active quarks, to be about 880 MeV.

Three-gluon Green functions: low-momentum instanton dominance and zero-crossing

International audience; We will report on a some efforts recently made in order to gain a better understanding of some IR properties of the 3-point gluon Green function by following both lattice and continuum QCD approaches.

Unquenching the gluon propagator with Schwinger-Dyson equations

In this article we use the Schwinger-Dyson equations to compute the nonperturbative modifications caused to the infrared finite gluon propagator (in the Landau gauge) by the inclusion of a small number of quark families. Our basic operating assumption is that the main bulk of the effect stems from the "one-loop dressed" quark loop contributing to the full gluon self-energy. This quark loop is then calculated, using as basic ingredients the full quark propagator and quark-gluon vertex; for the quark propagator we use the solution obtained from the quark gap equation, while for the vertex we employ suitable Ans\"atze, which guarantee the transversality of the answer. The resulting effect is i…

All-order equation of the effective gluon mass

We present the general derivation of the full non-perturbative equation that governs the momentum evolution of the dynamically generated gluon mass, in the Landau gauge. The entire construction hinges crucially on the inclusion of longitudinally coupled vertices containing massless poles of non-perturbative origin, which preserve the form of the fundamental Slavnov-Taylor identities of the theory. The mass equation is obtained from a previously unexplored version of the Schwinger-Dyson equation for the gluon propagator, particular to the PT-BFM formalism, which involves a reduced number of "two-loop dressed" diagrams, thus simplifying the calculational task considerably. The two-loop contri…

The effective neutrino charge radius in the presence of fermion masses

Abstract We show how the crucial gauge cancellations leading to a physical definition of an effective neutrino charge radius persist in the presence of non-vanishing fermion masses. An explicit one-loop calculation demonstrates that, as happens in the massless case, the pinch technique rearrangement of the Feynman amplitudes, together with the judicious exploitation of the fundamental current relation J α ( 3 ) = 2 ( J Z + sin θ w 2 J γ ) α , leads to a completely gauge independent definition of the effective neutrino charge radius. Using the formalism of the Nielsen identities it is further proved that the same cancellation mechanism operates unaltered to all orders in perturbation theory.

Unraveling the organization of the QCD tapestry

I review some key aspects of the ongoing progress in our understanding of the infrared dynamics of the QCD Green's functions, derived from the close synergy between Schwinger-Dyson equations and lattice simulations. Particular attention is dedicated to the elaborate nonperturbative mechanisms that endow the fundamental degrees of freedom (quarks and gluons) with dynamical masses. In addition, the recently established connection between the effective interaction obtained from the gauge sector of the theory and that needed for the veracious description of the ground-state properties of hadrons is briefly presented.

CP violation through particle mixing and theH-Alineshape

We consider the possibility of looking for CP-mixing effects in two-Higgs doublet models (and particularly in the MSSM) by studying the lineshape of the CP-even (H) and CP-odd (A) neutral scalars. In most cases H and A come quite degenerate in mass, and their s-channel production would lead to nearly overlapping resonances. CP-violating effects may connect these two Higgs bosons, giving origin to one-loop particle mixing, which, due to their mass proximity, can be resonantly enhanced. The corresponding transition amplitude contains then CP-even and CP-odd components; besides the signal of intereference between both amplitudes, leading to a CP-odd asymmetry, we propose to look for the mixing…

The neutrino charge radius is a physical observable

We present a method which allows, at least in principle, the direct extraction of the gauge-invariant and process-independent neutrino charge radius (NCR) from experiments. Under special kinematic conditions, the judicious combination of neutrino and anti-neutrino forward differential cross-sections allows the exclusion of all target-dependent contributions, such as gauge-independent box-graphs, not related to the NCR. We show that the remaining contributions contain universal, renormalization group invariant combinations, such as the electroweak effective charge and the running mixing angle, which must be also separated out. By considering the appropriate number of independent experiments …

First search for dyons with the full MoEDAL trapping detector in 13 TeV pp collisions

The MoEDAL trapping detector, consists of approximately 800 kg of aluminium volumes. It was exposed during Run-2 of the LHC program to 6.46 fb^-1 of 13 TeV proton-proton collisions at the LHCb interaction point. Evidence for dyons (particles with electric and magnetic charge) captured in the trapping detector was sought by passing the aluminium volumes comprising the detector through a SQUID magnetometer. The presence of a trapped dyon would be signalled by a persistent current induced in the SQUID magnetometer. On the basis of a Drell-Yan production model, we exclude dyons with a magnetic charge ranging up to 5 Dirac charges, and an electric charge up to 200 times the fundamental electric …

Gluon and ghost propagators in the Landau gauge: Deriving lattice results from Schwinger-Dyson equations

We show that the application of a novel gauge invariant truncation scheme to the Schwinger-Dyson equations of QCD leads, in the Landau gauge, to an infrared finite gluon propagator and a divergent ghost propagator, in qualitative agreement with recent lattice data.

Gauge-invariant truncation scheme for the Schwinger-Dyson equations of QCD

We present a new truncation scheme for the Schwinger-Dyson equations of QCD that respects gauge invariance at any level of the dressed loop expansion. When applied to the gluon self-energy, it allows for its non-perturbative treatment without compromising the transversality of the solution, even when entire sets of diagrams (most notably the ghost loops) are omitted, or treated perturbatively.

Effective charge from lattice QCD

Using lattice configurations for quantum chromodynamics (QCD) generated with three domain-wall fermions at a physical pion mass, we obtain a parameter-free prediction of QCD's renormalisation-group-invariant process-independent effective charge, $\hat\alpha(k^2)$. Owing to the dynamical breaking of scale invariance, evident in the emergence of a gluon mass-scale, this coupling saturates at infrared momenta: $\hat\alpha(0)/\pi=0.97(4)$. Amongst other things: $\hat\alpha(k^2)$ is almost identical to the process-dependent (PD) effective charge defined via the Bjorken sum rule; and also that PD charge which, employed in the one-loop evolution equations, delivers agreement between pion parton di…

Gluon mass through ghost synergy

In this work we compute, at the "one-loop-dressed" level, the nonperturbative contribution of the ghost loops to the self-energy of the gluon propagator, in the Landau gauge. This is accomplished within the PT-BFM formalism, which guarantees the gauge-invariance of the emerging answer. In particular, the contribution of the ghost-loops is automatically transverse, by virtue of the QED-like Ward identities satisfied in this framework. Using as nonperturbative input the available lattice data for the ghost dressing function, we show that the ghost contributions have a rather sizable effect on the overall shape of the gluon propagator, both for $d=3,4$. Then, by exploiting a recently introduce…

Bounds on models with one latticized extra dimension

We study an extension of the standard model with one latticized extra dimension accessible to all fields. The model is characterized by the size of the extra dimension and the number of sites, and contains a tower of massive particles. At energies lower than the mass of the new particles there are no tree-level effects. Therefore, bounds on the scale of new physics can only be set from one-loop processes. We calculate several observables sensitive to loop-effects, such as the $\rho$ parameter, $b\to s \gamma$, $Z\to b\bar b$, and the $B^0\rightleftharpoons\bar{B}^0$ mixing, and use them to set limits on the lightest new particles for different number of sites. It turns out that the continuo…

Dynamical zero in ν¯e–e− scattering and the neutrino magnetic moment

Abstract The Standard Model differential cross section for ν ¯ e – e − elastic scattering vanishes exactly, at lowest order, for forward electrons and incident ν ¯ e energy close to the rest energy of the electron. This dynamical zero is not induced by a fundamental symmetry of the Lagrangian but by a destructive interference between the left- and right-handed chiral couplings of the electron in the charged and neutral current amplitudes. We show that lowest-order analyses based on this favorable kinematic configuration are only mildly affected by the inclusion of the O ( α ) radiative corrections in the ν ¯ e – e − differential cross section, thus providing an excellent opportunity for the…

Nonperturbative gluon and ghost propagators for d=3 Yang-Mills theory

We study a manifestly gauge-invariant set of Schwinger-Dyson equations to determine the non-perturbative dynamics of the gluon and ghost propagators in d = 3 Yang-Mills theory. The use of the well-known Schwinger mechanism, in the Landau gauge leads to the dynamical generation of a mass for the gauge boson (gluon in d = 3), which, in turn, gives rise to an infrared finite gluon propagator and ghost dressing function. The propagators obtained from the numerical solution of these nonperturbative equations are in very good agreement with the results of SU(2) lattice simulations. We would like to thank A. Cucchieri and T. Mendes for kindly making their lattice results available to us, and for t…