Baryon masses with dynamical twisted mass fermions

TL;DR

The paper investigates the nucleon and Δ masses using two dynamical degenerate twisted mass quarks, assessing discretization, finite-volume, and isospin-breaking effects. By performing simulations at two lattice spacings and volumes with pion masses ranging from about $m_bc ightarrow 0.3$–$0.69$ GeV, the authors extract ground-state baryon masses using Gaussian-smearing improved correlators and analyze the data with heavy baryon chiral perturbation theory. They report minimal cutoff and finite-volume effects, extract the lattice spacing from the nucleon mass as $a(eta=3.9)=0.0879(12)$ fm (consistent with the $f_pi$-based determination), and obtain physical-limit nucleon and Δ masses that agree with experimental values within uncertainties; isospin breaking in the Δ system is found to be negligible. Overall, the work validates twisted mass QCD for baryon spectroscopy and demonstrates robust chiral extrapolations and scale setting in this framework.

Abstract

We present results on the mass of the nucleon and the $Δ$ using two dynamical degenerate twisted mass quarks. The evaluation is performed at four quark masses corresponding to a pion mass in the range of 690-300 MeV on lattices of size 2.1 fm and 2.7 fm. We check for cutoff effects by evaluating these baryon masses on lattices of spatial size 2.1 fm with lattice spacings $a(β=3.9)=0.0855(6)$ fm and $a(β=4.05)=0.0666(6)$ fm, determined from the pion sector and find them to be within our statistical errors. Lattice results are extrapolated to the physical limit using continuum chiral perturbation theory. The nucleon mass at the physical point provides a determination of the lattice spacing. Using heavy baryon chiral perturbation theory at ${\cal O}(p^3)$ we find $a(β=3.9)=0.0879(12)$ fm, with a systematic error due to the chiral extrapolation estimated to be about the same as the statistical error. This value of the lattice spacing is in good agreement with the value determined from the pion sector. We check for isospin breaking in the $Δ$-system. We find that $Δ^{++,-}$ and $Δ^{+,0}$ are almost degenerate pointing to small flavor violating effects.

Figures (9)

• Figure 1: Lines of constant r.m.s radius as 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 when APE smearing is used.
• Figure 3: Nucleon effective mass (LS: asterisks, SS: open triangles) for $\beta=3.9$ versus time separation in lattice units.
• Figure 4: $\Delta^{++,-}$ (asterisks) and $\Delta^{+,0}$ (open triangles) effective masses for $\beta=3.9$ versus time separation in lattice units.
• Figure 5: The nucleon mass as a function of $m_\pi^2$ for $\beta=3.9$ on a lattice of size $24^3\times 48$ (filled triangles) and on a lattice of size $32^3\times 64$ (open triangles). Results at $\beta=4.05$ are shown with the stars. The physical nucleon mass is shown with the asterisk. Results with dynamical staggered fermions for $N_F=2+1$ (filled circles) and $N_F=2$ (open circle) on a lattice of size $20^3\times 64$ with $a=0.125$ fm are from Ref. staggered.