The low-lying baryon spectrum with two dynamical twisted mass fermions

TL;DR

This paper computes the low-lying baryon spectrum (octet and decuplet) using two dynamical twisted mass quarks at maximal twist on two lattice spacings and volumes, enabling controlled finite-volume, discretization, and chiral extrapolations. It tunes the strange valence mass to reproduce m_K/m_π, applies SU(2) HBχPT for chiral extrapolations, and uses lattice-spacing scales from fπ and r0 to reach the physical point. The results show small lattice artifacts and isospin-breaking effects vanish in the continuum, with continuum masses in good agreement with experiment; GMO relations hold for the octet but show larger deviations in the decuplet, and the nucleon σ-term is around 64 MeV under standard fits. The study validates twisted-mass QCD for baryon spectroscopy and lays groundwork for future Nf=2+1+1 simulations to fully capture strange-quark dynamics.

Abstract

The masses of the low lying baryons are evaluated using two degenerate flavors of twisted mass sea quarks corresponding to pseudo scalar masses in the range of about 270-500 MeV. The strange valence quark mass is tuned to reproduce the mass of the kaon in the physical limit. The tree-level Symanzik improved gauge action is employed. We use lattices of spatial size 2.1 fm and 2.7 fm at two values of the lattice spacing with $r_0/a=5.22(2)$ and $r_0/a=6.61(3)$. We check for both finite volume and cut-off effects on the baryon masses. We performed a detailed study of the chiral extrapolation of the octet and decuplet masses using SU(2) $χ$PT. The lattice spacings determined using the nucleon mass at the physical point are consistent with the values extracted using the pion decay constant. We examine the issue of isospin symmetry breaking for the octet and decuplet baryons and its dependence on the lattice spacing. We show that in the continuum limit isospin breaking is consistent with zero, as expected. The baryon masses that we find after taking the continuum limit and extrapolating to the physical limit are in good agreement with experiment.

Figures (25)

• Figure 1: The low lying baryons belonging to the octet representation labeled by the value of $I_3$ and hypercharge.
• Figure 2: The low lying baryons belonging to the decuplet representation labeled by the value of $I_3$ and hypercharge.
• Figure 3: Effective masses of the octet states for $\beta = 3.9$, $a\mu = 0.004$ on a $32^3\times 64$ lattice using $232$ configurations.
• Figure 4: Effective masses of the decuplet states for $\beta = 3.9$, $a\mu = 0.004$ on a $32^3\times 64$ lattice using $232$ configurations.
• Figure 5: Octet states measured in our different gauge ensembles. Physical points are indicated by their name symbols (magenta). The data at $\beta=3.9$, $L/a=24$ are connected by dotted lines to guide the eye.