Light Hadron Spectroscopy with Two Flavors of Dynamical Quarks on the Lattice

TL;DR

The paper presents a first-principles lattice QCD study of light hadron spectroscopy with two degenerate dynamical up/down quarks and a quenched strange quark, conducted at three lattice spacings to enable a continuum extrapolation. Using a renormalization group–improved gauge action and a mean-field improved clover quark action, the authors perform chiral extrapolations across multiple sea and valence masses and compare the full two-flavor theory to quenched QCD with the same actions. They find that meson masses in full QCD are closer to experimental values than in quenched QCD, while light baryons show possible finite-size effects, and they observe substantial scaling violations in decay constants that motivate nonperturbative renormalization efforts. The results demonstrate clear sea quark effects on the spectrum and quark masses, emphasize the importance of continuum and finite-size control, and guide future work toward incorporating dynamical strange and nonperturbative renormalization. Overall, the work marks a significant step toward realistic QCD spectroscopy with controlled systematic errors.

Abstract

We present results of a numerical calculation of lattice QCD with two degenerate flavors of dynamical quarks, identified with up and down quarks, and with a strange quark treated in the quenched approximation. The lattice action and simulation parameters are chosen with a view to carrying out an extrapolation to the continuum limit as well as chiral extrapolations. Gauge configurations are generated with a renormalization-group improved gauge action and a mean field improved clover quark action at three values of $β$ and four sea quark masses. The sizes of lattice are chosen so that the physical spatial size is kept constant. Hadron masses, light quark masses and meson decay constants are measured at five valence quark masses. We also carry out complementary quenched simulations with the same improved actions. The quenched spectrum from this analysis agrees well in the continuum limit with the one of our earlier work using the standard action. We find the two-flavor full QCD meson masses in the continuum limit to be much closer to experimental meson masses than those from quenched QCD. We take these results as manifestations of sea quark effects in two-flavor full QCD. For baryon masses full QCD values for strange baryons are in agreement with experiment, while they differ increasingly with decreasing strange quark content, resulting in a nucleon mass higher than experiment. The pattern suggests finite size effects as a possible origin for this deviation. For light quark masses in the continuum limit we obtain values which are reduced by about 25% compared to the values in quenched QCD. We also present results for decay constants where large scaling violations obstruct a continuum extrapolation. Need for a non-perturbative estimate of renormalization factors is discussed.

Figures (42)

• Figure 1: Schematic plot for the choice of sea and valence hopping parameters. For circles at the points $\kappa_{\rm val}=\kappa_{\rm sea}$ the corresponding pseudoscalar to vector meson mass ratio is indicated.
• Figure 2: Effective mass plots for pseudoscalar, vector, nucleon and $\Delta$ channels with degenerate valence hopping parameters $\kappa_{\rm val}=\kappa_{\rm sea}=0.1445$ at $\beta=1.8$. Circles represent effective masses obtained when all quark propagators are calculated with point sources. For squares all quark propagators have smeared sources and triangles are for mixed combinations of sources. Solid lines denote the results from correlated mass fits to smeared source hadron propagators. Dashed lines show the one standard deviation error band determined by jack-knife analysis with a bin size of 10 configurations.
• Figure 3: Effective mass plots for pseudoscalar, vector, nucleon and $\Delta$ channels with degenerate valence hopping parameters $\kappa_{\rm val}=\kappa_{\rm sea}=0.1400$ at $\beta=1.95$. Symbols have the same meaning as in Fig. \ref{['fig:effmassB18']}.
• Figure 4: Effective mass plots for pseudoscalar, vector, nucleon and $\Delta$ channels with degenerate valence hopping parameters $\kappa_{\rm val}=\kappa_{\rm sea}=0.1374$ at $\beta=2.1$. Symbols have the same meaning as in Fig. \ref{['fig:effmassB18']}.
• Figure 5: Effective mass plots of potential data at $r = L/4$ for sea quark mass corresponding to $m_{\rm PS}/m_{\rm V} \approx 0.7$. The scale is fixed from $\rho$ meson mass at the physical point.