Search results for "Mathematical physics"
showing 10 items of 2687 documents
One-loop renormalization of Resonance Chiral Theory: scalar and pseudoscalar resonances
2005
We consider the Resonance Chiral Theory with one multiplet of scalar and pseudoscalar resonances, up to bilinear couplings in the resonance fields, and evaluate its beta-function at one-loop with the use of the background field method. Thus we also provide the full set of operators that renormalize the theory at one loop and render it finite.
Linear Wave Equations and Effective Lagrangians for Wigner Supermultiplets
1995
The relevance of the contracted SU(4) group as a symmetry group of the pion nucleon scattering amplitudes in the large $N_c$ limit of QCD raises the problem on the construction of effective Lagrangians for SU(4) supermultiplets. In the present study we suggest effective Lagrangians for selfconjugate representations of SU(4) in exploiting isomorphism between so(6) and ist universal covering su(4). The model can be viewed as an extension of the linear $\sigma$ model with SO(6) symmetry in place of SO(4) and generalizes the concept of the linear wave equations for particles with arbitrary spin. We show that the vector representation of SU(4) reduces on the SO(4) level to a complexified quatern…
A simple formula for the infrared singular part of the integrand of one-loop QCD amplitudes
2010
We show that a well-known simple formula for the explicit infrared poles of one-loop QCD amplitudes has a corresponding simple counterpart in unintegrated form. The unintegrated formula approximates the integrand of one-loop QCD amplitudes in all soft and collinear singular regions. It thus defines a local counter-term for the infrared singularities and can be used as an ingredient for the numerical calculation of one-loop amplitudes.
Next-to-next-to-leading order prediction for the photon-to-pion transition form factor
2003
We evaluate the next-to-next-to-leading order corrections to the hard-scattering amplitude of the photon-to-pion transition form factor. Our approach is based on the predictive power of the conformal operator product expansion, which is valid for a vanishing $\beta$-function in the so-called conformal scheme. The Wilson--coefficients appearing in the non-forward kinematics are then entirely determined from those of the polarized deep-inelastic scattering known to next-to-next-to-leading accuracy. We propose different schemes to include explicitly also the conformal symmetry breaking term proportional to the $\beta$-function, and discuss numerical predictions calculated in different kinemati…
Sliding Vacua in Dense Skyrmion Matter
2003
In continuation of our systematic effort to understand hadronic matter at high density, we study dense skyrmion matter and its chiral phase structure in an effective field theory implemented with the trace anomaly of QCD applicable in the large $N_c$ limit. By incorporating a dilaton field $\chi$ associated with broken conformal symmetry of QCD into the simplest form of skyrmion Lagrangian, we simulate the effect of "sliding vacua" influenced by the presence of matter and obtain what could correspond to the ``intrinsic dependence" on the background of the system, i.e., matter density or temperature, that results when a generic chiral effective field theory of strong interactions is matched …
Gauge-invariant truncation scheme for the Schwinger-Dyson equations of QCD
2008
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.
Including long-distance effects in theKL−KSmass splitting
1990
In the framework of the standard model we propose an approach to the computation of the {ital K}{sub {ital L}}-{ital K}{sub {ital S}} mass difference which does not rely on an effective local Hamiltonian. Using partial conservation of axial-vector current, low-momentum Ward identities, and working at leading order in 1/{ital N}{sub {ital c}}, we relate box diagrams to others where strong interactions can be resummed. After subtracting the {ital K}-to-vacuum transitions, an expression involving only hadronic quantities is obtained. A numerical evaluation is performed by using a method of analytic continuation from the high-energy behavior given by QCD. The resulting contribution is found sma…
Comparison between two strictly local QCD sum rules
1989
Two strictly local QCD sum rules, analytic extrapolation by conformal mapping and analytic continuation by duality, are developed and presented in full detail. They allow the extrapolation of the QCD amplitude to a single point near zero in the complex {ital q}{sup 2} plane. Being orthogonal to the usual QCD sum rules, they present a drastic enlargement of phenomenological applications. In addition, the stability of both methods is shown explicitly, a fact which makes them particularly reliable. The difference between the two methods is illustrated in connection with the determination of the hadronic ({ital g}{minus}2) factor of the muon. Their effectiveness is demonstrated in the calculati…
Complete amplitude and cross section structure of one-loop contributions toe + e ??q $$\bar q$$ g
1985
We calculate theO(α 2 ) one-loop contributions to the seven (inn≠4) independent invariant amplitudes describinge + e −→q $$\bar q$$ g in massless QCD. After folding with theO(α 1/2 ) Born term contribution we obtain the nine independentO(α 2 ) structure functions that describe the parity-conserving and parity-violating contributions toe + e −→q $$\bar q$$ g. We use dimensional regularization to control infrared and ultraviolet divergencies.
THE OPERATOR PRODUCT EXPANSION OF THE QCD PROPAGATORS
1992
We bring together for the first time the coefficients in covariant gauges of all the condensates of dimension four or less in the operator product expansion (OPE) of the quark, gluon and ghost propagators. It is stressed that contrary to general belief the condensates do not enter the OPE of the propagators in gauge-invariant combinations like [Formula: see text] and 〈G2〉. The results are presented in arbitrary dimension to lowest order in the light quark masses for the SU (Nc) internal symmetry group. All terms which, through the equations of motion, may be viewed as being effectively of order αs are included. The importance of the equations of motion if one is to fulfill the Slavnov-Tayl…