SU(2) and SU(3) chiral perturbation theory analyses on baryon masses in 2+1 flavor lattice QCD

TL;DR

This study tests chiral perturbation theory for baryon masses in 2+1 flavor lattice QCD by applying SU(3) HBChPT up to NLO to octet and decuplet baryons and SU(2) HBChPT to the nucleon. It finds that while LO SU(3) fits are reasonable, NLO fits require LECs that conflict with phenomenology, indicating convergence issues for realistic strange quark masses; conversely, SU(2) HBChPT for the nucleon describes the data near the chiral limit but loses accuracy as $m_{ud}$ grows. Finite size corrections are found to be small (below ~1%) at the physical point. The work highlights limitations of SU(3) ChPT for baryons with physical strange mass and motivates direct simulations at the physical point on larger volumes to reduce extrapolation uncertainties.

Abstract

We investigate the quark mass dependence of baryon masses in 2+1 flavor lattice QCD using SU(3) heavy baryon chiral perturbation theory up to one-loop order. The baryon mass data used for the analyses are obtained for the degenerate up-down quark mass of 3 MeV to 24 MeV and two choices of the strange quark mass around the physical value. We find that the SU(3) chiral expansion fails to describe both the octet and the decuplet baryon data if phenomenological values are employed for the meson-baryon couplings. The SU(2) case is also examined for the nucleon. We observe that higher order terms are controlled only around the physical point. We also evaluate finite size effects using SU(3) heavy baryon chiralperturbation theory, finding small values of order 1% even at the physical point.

Figures (15)

• Figure 1: Fit results with the linear formula Eq. (\ref{['eq:linear_su2']}) for the octet baryon masses. Experimental values are given in lattice units with $a^{-1}=2.176$ GeV in Ref. pacscs_nf3.
• Figure 2: Fit results with the linear formula Eq. (\ref{['eq:linear_su2']}) for the decuplet baryon masses. Experimental values are given in lattice units with $a^{-1}=2.176$ GeV in Ref. pacscs_nf3.
• Figure 3: Convergence behavior for the octet baryon masses with the linear formula Eq. (\ref{['eq:linear_su2']}). $m_{\rm s}$ is fixed at the measured value at $(\kappa_{\rm ud},\kappa_{\rm s})=(0.13754,0.13640)$.
• Figure 4: Convergence behavior for the decuplet baryon masses with the linear formula Eq. (\ref{['eq:linear_su2']}). $m_{\rm s}$ is fixed at the measured value at $(\kappa_{\rm ud},\kappa_{\rm s})=(0.13754,0.13640)$.
• Figure 5: Fit results with the SU(3) HBChPT up to LO for the octet baryon masses. Experimental values are given in lattice units with $a^{-1}=2.176$ GeV in Ref. pacscs_nf3.