Search results for "gluon"
showing 10 items of 697 documents
Gluon mass scale through nonlinearities and vertex interplay
2019
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 …
Multigluonic scattering amplitudes of heavy quarks
2005
We consider heavy quark and antiquark off-shell spinorial currents with emission of an arbitrary number of gluons of positive helicity. From this results we calculate the corresponding on-shell scattering amplitude and the quark-antiquark vector current. Then, we show that in the heavy top quark effective theory the holomorfic component of the Higgs $\to q \bar{q} + n$-gluon amplitude vanish for helicity conserving configurations.
Unquenching the gluon propagator with Schwinger-Dyson equations
2012
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…
Nonperturbative structure of the ghost-gluon kernel
2019
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…
Ghost propagator and ghost-gluon vertex from Schwinger-Dyson equations
2013
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 …
Gauge invariant Ansatz for a special three-gluon vertex
2011
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…
Effects of divergent ghost loops on the Green’s functions of QCD
2013
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…
Born amplitudes in QCD from scalar diagrams
2005
We review recent developments for the calculation of Born amplitudes in QCD. This includes the computation of gluon helicity amplitudes from MHV vertices and an approach based on scalar propagators and a set of three- and four-valent vertices. The latter easily generalizes to amplitudes with any number of quark pairs. The quarks may be massless or massive.
Fermions and the scattering equations
2014
This paper investigates how tree-level amplitudes with massless quarks, gluons and/or massless scalars transforming under a single copy of the gauge group can be expressed in the context of the scattering equations as a sum over the inequivalent solutions of the scattering equations. In the case where the amplitudes satisfy cyclic invariance, KK- and BCJ-relations the only modification is the generalisation of the permutation invariant function $E(z,p,\varepsilon)$. We present a method to compute the modified $\hat{E}(z,p,\varepsilon)$. The most important examples are tree amplitudes in ${\mathcal N}=4$ SYM and QCD amplitudes with one quark-antiquark pair and an arbitrary number of gluons. …
Applications of integrand reduction to two-loop five-point scattering amplitudes in QCD
2018
We review the current state-of-the-art in integrand level reduction for five-point scattering amplitudes at two loops in QCD. We present some benchmark results for the evaluation of the leading colour two-loop five-gluon amplitudes in the physical region as well as the partonic channels for two quarks and three gluons and four quarks and one gluon.