A framework for the chiral extrapolation of the charmed baryon ground-state masses

TL;DR

This paper develops a chiral extrapolation framework for charmed baryon ground-state masses up to N$^3$LO, enabling precise dependence calculations on quark masses for lattice QCD simulations.

Contribution

It introduces a systematic N$^3$LO chiral expansion framework for charmed baryon masses, incorporating large-Nc sum rules for counter term correlations.

Findings

Demonstrates convergence with physical masses from PDG.

Provides a scale-invariant renormalization scheme.

Systematically relates counter terms via large-Nc sum rules.

Abstract

We consider the chiral Lagrangian for charmed baryon fields with $J^P =\frac{1}{2}^+$ or $J^P =\frac{3}{2}^+$ quantum numbers. A chiral expansion framework for the baryon ground state masses is worked out to N$^3$LO as to compute their dependence on the up, down and strange quark masses for finite box QCD lattice simulations. It is formulated in terms of on-shell meson and baryon masses. The convergence of such a scheme is illustrated with physical masses as taken from the PDG. The counter terms relevant at N$^3$LO are correlated systematically by large-$N_c$ sum rules to leading and subleading order in a manner that keeps the renormalization scale invariance of the approach.