Pole masses of quarks in dimensional reduction

TL;DR

The paper computes quark pole masses at two-loop order in QCD within the regularization-by-dimensional-reduction (DRED) framework. It develops and applies a massive minimal subtraction (MMS) renormalization scheme that treats ε-scalars as auxiliary fields and enforces zero ε-scalar pole mass, enabling a consistent, mass-dependent calculation. The authors derive an explicit two-loop pole-mass formula (m_P/m)_f that includes a quark-loop function E(r) and provide its small- and large-mass expansions, along with discussions of decoupling, scheme matching to conventional dimensional regularization, and renormalization-group implications. The work demonstrates how non-Euclidean on-shell expansions and IBP techniques can be employed to handle light- and heavy-quark mass effects in DRED, yielding results that can be related to standard DR calculations and used for cross-checks in supersymmetric contexts.

Abstract

Pole masses of quarks in the quantum chromodynamics are calculated to the two-loop order in the framework of the regularization by dimensional reduction. For the diagram with a light quark loop, the non-Euclidean asymptotic expansion is constructed with the external momentum on the mass shell of a heavy quark.

Figures (4)

• Figure 1: The diagram with a quark loop (a) and its scalar prototype (b).
• Figure 2: Further two-loop diagrams, contributing to the pole mass of a quark, which involve no other nonzero masses. Solid lines correspond to quarks, wavy lines to gluons, and dashed lines to the Faddeev--Popov ghosts.
• Figure 3: The one-loop diagram where the asymptotic on-shell expansion in $m_2\ll m_4$, $p^2 = -m_4^2$, is performed.
• Figure 4: Three expansions for the renormalized diagram of fig. \ref{['loop']}(a) in the dimensional reduction MMS scheme. The dotted line corresponds to the small-mass expansion up to $r^6$, the dashed line to the large-mass expansion up to $1/r^6$, the solid line to the intermediate expansion up to $(r^2-1)^3$.