Gauge invariance of condensate-based non-perturbative pole masses

Determine whether the non-perturbative pole mass obtained from any finite truncation of the condensate expansion is gauge-invariant, including the contributions of condensates of non-gauge-invariant operators.

Background

The paper studies whether non-perturbative corrections to a heavy-quark pole mass can be derived from the operator-product expansion of the quark self-energy. It emphasizes that the self-energy receives contributions from condensates of non-gauge-invariant operators, which must be incorporated into any such analysis.

The authors state that, unlike the perturbative pole mass, gauge invariance of a non-perturbative pole mass obtained by truncating the condensate expansion has not been established. They suggest that reorganizing the condensate expansion to address on-shell effects might be necessary to resolve this issue.

References

As a consequence, and in contrast to what is found in perturbation theory, it is not clear that the non-perturbative pole mass obtained by any finite truncation of the condensate expansion will be gauge-invariant.

— A toy model for the quark pole mass  (2610.10059 - Marino et al., 7 Oct 2026) in Section Conclusions and outlook