Nucleon Observables and Loop Diagrams in Cavity QCD

Abstract

Using a technique which is based on dimensional regularization, loop corrections to vertex diagrams of a massless quark moving in a spherical cavity are calculated in an arbitrary covariant gauge. Including the finite one-gluon-exchange diagrams, the corrections to the magnetic moments, vector and axial vector coupling constants, and the various r.m.s. radii of the nucleon are evaluated to order : S .

Hadron masses in cavity quantum chromodynamics to order $\alpha_{\rm s}^2$

“…where u n ( x) and a µ mΣ ( x) are the quark and gluon cavity modes, respectively [11]. The result is…”

“…Here, we have used the quark and gluon propagators in the Feynman gauge [11]. The subscripts of the quark creation and annihilation operators stand for the color, flavor, and orbital quantum numbers, respectively.…”

Calculation of the regularized vacuum energy in cavity field theories

“…Here the a D,N n,l,µ (x) denote the scalar cavity modes for either Dirichlet or Neumann boundary conditions, and the N D,N n,l stand for their normalization constants [15,24], respectively, as explained in Appendix A.1. Using the plane-wave representation of the free-space propagator implies a z −3 divergence in the free-space part of Eq.…”

“…Using Eq. ( 8), the mode summation representing the cavity Dirac propagator [15,24], the spherical representation of the free-space propagator, and introducing the Schwinger z-integral, we obtain, after an angular integration, θ00 (r)…”

“…bag model on a static, spherical surface. Using the cavity mode representation of the propagators [15,23,24], the numerical evaluation is done by summing over the cavity mode quantum numbers first and integrating the resulting spectral z-form subsequently. An integration over a regularization volume yields the canonical regularized energy.…”