Framework for the chiral extrapolation of the charmed baryon ground-state masses

Yonggoo Heo,Xiao-Yu Guo,Matthias F M Lutz

doi:10.1103/physrevd.98.054012

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.

Highlights

Corresponding sets of low-energy parameters to be used in flavor SU(3) chiral Lagrangians were established from the available lattice data on such hadron masses [1,2]
We identify a single parameter combination c3 that probes the product of a quark mass with the second power of some meson mass
While at leading order in the 1=number of colors (N c) expansion there are 5 unknown parameters, at subleading order we derived the relevance of

Summary

Introduction

QCD lattice simulations offer the opportunity to determine low-energy parameters of the chiral Lagrangian.Since the simulations are performed at quark masses distinct to those needed to reproduce the physical hadron masses new information is generated that may help to determine so far unknown low-energy constants.Such programs have already been successfully set up for the masses of baryons and mesons in their ground states with JP 1⁄4 12þ ; 32þ and JP 1⁄4 0− ; 1− quantum numbers [1,2,3].Corresponding sets of low-energy parameters to be used in flavor SU(3) chiral Lagrangians were established from the available lattice data on such hadron masses [1,2].The purpose of the present work is to establish a corresponding framework for the masses of charmed baryons, which can eventually be applied to the current QCD lattice data. Since the simulations are performed at quark masses distinct to those needed to reproduce the physical hadron masses new information is generated that may help to determine so far unknown low-energy constants. Such programs have already been successfully set up for the masses of baryons and mesons in their ground states with JP 1⁄4 12þ ; 32þ and JP 1⁄4 0− ; 1− quantum numbers [1,2,3]. Corresponding sets of low-energy parameters to be used in flavor SU(3) chiral Lagrangians were established from the available lattice data on such hadron masses [1,2]. Given the rather scarce data set that is provided so far on the charmed baryon masses [4,5,6,7,8,9] it is important to derive additional constraints from

Objectives

Results

Conclusion