Dimensional regularization and the self-energy of a massive quark in a cavity

Nucleon Observables and Loop Diagrams in Cavity QCD

“…Secondly, there is a part which is finite for massless quarks (the free-space analogue is zero). For massive quarks, this term also diverges, and would need to be cancelled by a mass renormalization counter-term [11]. It is found that the finite part is responsible for the large O(: s ) corrections, and it seems to have the``wrong'' sign.…”

“…The analogous result in free-space theory is zero. For massive quarks, this term diverges, and a counter-term must be introduced into the cavity Lagrangian to renormalize the mass [11]. However, here we shall restrict our attention to massless quarks.…”

“…Recently, a reliable method for regularizing cavity loop-diagrams has been developed and applied to the self-energies of confined quarks [8,11], and gluons [12] and the axial and vector coupling constant of the nucleon [9]. In this method, divergences due to the unreflected part of the propagators are extracted from loop integrals by using techniques similar to those of dimensional regularization in free space.…”

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

“…bag model on a statics sphere (CQCD) [1][2][3], is a consistent relativistic quantum field theory on its own. Indeed, CQCD may be expanded perturbatively [4], and the diverging Feynman graphs have been shown to be renormalizable [5][6][7][8], e.g. in the MS scheme.…”

“…However, this good agreement has been obtained by neglecting the selfenergies of the quarks. More recently, the self-energies have been calculated, but unfortunately they turned out to be quite large [6][7][8], thus spoiling the good agreement to order α s . One has therefore argued that the self-energies should perhaps be discarded, because the boundary conditions already account for at least part of them.…”