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

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 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 chiral perturbation theory, finding small values of order 1% even at the physical point.

Figure 1

Fit results with the linear formula [Eq. (1)] for the octet baryon masses. Experimental values are given in lattice units with $a^{-1}=2.176\mathrm{GeV}$ in Ref. [1].

Figure 2

Fit results with the linear formula [Eq. (1)] for the decuplet baryon masses. Experimental values are given in lattice units with $a^{-1}=2.176\mathrm{GeV}$ in Ref. [1].

Figure 3

Convergence behavior for the octet baryon masses with the linear formula [Eq. (1)]. $m_{\mathrm{s}}$ is fixed at the measured value at $({\kappa }_{\mathrm{ud}},{\kappa }_{\mathrm{s}})=(0.13754,0.13640)$.

Figure 4

Convergence behavior for the decuplet baryon masses with the linear formula [Eq. (1)]. $m_{\mathrm{s}}$ is fixed at the measured value at $({\kappa }_{\mathrm{ud}},{\kappa }_{\mathrm{s}})=(0.13754,0.13640)$.

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 $a^{-1}=2.176\mathrm{GeV}$ in Ref. [1].

Figure 6

Convergence behavior for the octet masses with the SU(3) HBChPT up to LO. $m_{\mathrm{s}}$ is fixed with the measured value at $({\kappa }_{\mathrm{ud}},{\kappa }_{\mathrm{s}})=(0.13754,0.13640)$.

Figure 7

Fit results with the SU(3) HBChPT up to NLO for the octet baryon masses. Experimental values are given in lattice units with $a^{-1}=2.176\mathrm{GeV}$ in Ref. [1].

Figure 8

Fit results with the SU(3) HBChPT up to NLO for the octet baryon masses. $D$, $F$, and $\mathcal{C}$ are fixed at the phenomenological estimates. Experimental values are given in lattice units with $a^{-1}=2.176\mathrm{GeV}$ in Ref. [1].

Figure 9

Convergence behavior for the octet masses with the SU(3) HBChPT up to NLO. $D$, $F$, and $\mathcal{C}$ are fixed at the phenomenological estimates. $m_{\mathrm{s}}$ is fixed with the measured value at $({\kappa }_{\mathrm{ud}},{\kappa }_{\mathrm{s}})=(0.13754,0.13640)$.

Figure 10

Fit results with the SU(3) HBChPT up to LO for the decuplet baryon masses. Experimental values are given in lattice units with $a^{-1}=2.176\mathrm{GeV}$ in Ref. [1].

Figure 11

Convergence behavior for the decuplet masses with the SU(3) HBChPT up to LO. $m_{\mathrm{s}}$ is fixed with the measured value at $({\kappa }_{\mathrm{ud}},{\kappa }_{\mathrm{s}})=(0.13754,0.13640)$.

Figure 12

Fit results with the SU(3) HBChPT up to NLO for the decuplet baryon masses. Experimental values are given in lattice units with $a^{-1}=2.176\mathrm{GeV}$ in Ref. [1].

Figure 13

Fit results with the SU(3) HBChPT up to NLO for the decuplet baryon masses. $\mathcal{C}$ is fixed at the phenomenological estimates. Experimental values are given in lattice units with $a^{-1}=2.176\mathrm{GeV}$ in Ref. [1].

Figure 14

Convergence behavior for the decuplet masses with the SU(3) HBChPT up to NLO. $\mathcal{C}$ is fixed at the phenomenological estimates. $m_{\mathrm{s}}$ is fixed with the measured value at $({\kappa }_{\mathrm{ud}},{\kappa }_{\mathrm{s}})=(0.13754,0.13640)$.

Figure 15

Fit results with the SU(2) HBChPT up to NLO for the nucleon mass (left) and comparison of LO and NLO contributions (right). Experimental values are given in lattice units with $a^{-1}=2.176\mathrm{GeV}$ in Ref. [1].