Light baryon masses with dynamical twisted mass fermions

TL;DR

The authors compute light baryon masses using two dynamical twisted mass quarks on three lattice spacings with pion masses down to ~$m_\pi\approx$300 MeV, performing continuum extrapolations via HB$\chi$PT. They demonstrate automatic $O(a)$ improvement and assess finite-volume and isospin-breaking effects, finding negligible lattice artifacts for the nucleon and vanishing ${O}(a^2)$ isospin breaking in the Δ system within errors. A combined HB$\chi$PT analysis yields $m_N^{phys}=0.963(12)(8)$ GeV and lattice spacings $a_{β=3.9}=0.0889(12)$ fm, $a_{β=4.05}=0.0691(10)$ fm, with $\sigma_N\approx66.7$ MeV; Δ masses are close to the experimental value and degenerate in the continuum. The work validates twisted mass fermions for reliable baryon spectroscopy and provides a cross-check of scale setting against the pion sector, with implications for future baryon-structure studies.

Abstract

We present results on the mass of the nucleon and the Delta using two dynamical degenerate twisted mass quarks and the tree-level Symanzik improved gauge action. The evaluation is performed at four quark masses corresponding to a pion mass in the range of about 300-600 MeV on lattices of 2.1-2.7 fm. We check for cut-off effects by evaluating these baryon masses on lattices of spatial size 2.1 fm at beta=3.9 and beta=4.05 and on a lattice of 2.4 fm at beta=3.8. The values we find are compatible within our statistical errors. Lattice results are extrapolated to the physical limit using continuum chiral perturbation theory. Performing a combined fit to our lattice data at beta=3.9 and beta=4.05 we find a nucleon mass of 964\pm 28 (stat.) \pm 8 (syst.) MeV. The nucleon mass at the physical point provides an independent determination of the lattice spacing. Using heavy baryon chiral perturbation theory at O(p^3) we find a_{β=3.9}=0.0890\pm 0.0039(stat.) \pm 0.0014(syst.) fm, and a_{β=4.05}= 0.0691\pm 0.0034(stat.) \pm 0.0010(syst.) fm, in good agreement with the values determined from the pion decay constant. Isospin violating lattice artifacts in the Delta-system are found to be compatible with zero for the values of the lattice spacings used in this work. Performing a combined fit to our lattice data at beta=3.9 and beta=4.05 we find for the masses of the Delta^{++,-} and Delta^{+,0} 1316 \pm 60 (stat.) MeV and 1330 \pm 74 (stat.) MeV respectively. We confirm that in the continuum limit they are also degenerate.

Figures (18)

• Figure 1: Lines of constant r.m.s radius as a function of the smearing parameters $\alpha$ and $n$. The asterisk shows the values $\alpha=2.9$, $n=30$ and the cross $\alpha=4.0$, $n=50$.
• Figure 2: $m_{\rm eff}^N$ versus time separation both in lattice units. Crosses show results using local sink and source (LL), circles (asterisks) using Gaussian smearing at the sink (SL) with $\alpha=2.9$ and $n=30$ ( $\alpha=4$ and $n=50$), and filled triangles with $\alpha=4$ and $n=50$ and APE smearing. The dashed line is the plateau value extracted by fitting results when APE smearing is used.
• Figure 3: Comparison of effective masses for $\Delta^{++,-}$ for $a\mu=0.0085$ at $\beta=3.9$ on the lattice volume $24^3 \times48$, obtained with (filled triangles) or without (open squares shifted to the left for clarity) spin projection, using a sample of 90 configurations. The mass difference with projection and without projection is much smaller than the statistical error.
• Figure 4: Comparison of effective masses for $\Delta^{+}$ for $a\mu=0.011$ at $\beta=3.8$ on the lattice volume $24^3 \times48$, obtained with $3/2$-spin (filled triangles) or with $1/2$-spin projection, using a sample of 50 configurations.
• Figure 5: Nucleon effective mass (LS: asterisks, SS: open triangles) for $\beta=3.9$ versus time separation in lattice units, for $a\mu=0.010$ (upper left), $0.0085$ (upper right), $0.0064$ (lower left) and $0.0040$ (lower right). The constant lines are the best fits to the data over the range spanned by the lines.