Light hadrons from lattice QCD with light (u,d), strange and charm dynamical quarks (1004.5284v1)

Abstract: We present results of lattice QCD simulations with mass-degenerate up and down and mass-split strange and charm (N_f = 2+1+1) dynamical quarks using Wilson twisted mass fermions at maximal twist. The tuning of the strange and charm quark masses is performed at two values of the lattice spacing a~0.078 fm and a~0.086 fm with lattice sizes ranging from L~1.9 fm to L~2.8 fm. We measure with high statistical precision the light pseudoscalar mass m_PS and decay constant f_PS in a range 270 < m_PS < 510 MeV and determine the low energy parameters f_0, l_3 and l_4 of SU(2) chiral perturbation theory. We use the two values of the lattice spacing, several lattice sizes as well as different values of the light, strange and charm quark masses to explore the systematic effects. A first study of discretisation effects in light-quark observables and a comparison to N_f=2 results are performed.

• The paper presents a lattice QCD simulation method that integrates up, down, strange, and charm quarks using twisted mass fermions.
• It details precise mass tuning for strange and charm quarks and measures key observables like the light pseudoscalar mass and decay constant.
• The study finds minimal discrepancies between Nf=2 and Nf=2+1+1 setups, indicating potential for enhanced modeling of hadronic interactions.

Lattice QCD Simulations with Up, Down, Strange, and Charm Dynamical Quarks Using Twisted Mass Fermions

The paper presented by the ETM Collaboration addresses significant advancements in the simulation of Quantum Chromodynamics (QCD) through lattice techniques. Specifically, it explores the impact of introducing strange and charm sea quarks alongside the commonly analyzed up and down quarks, achieving a $N_{\rm f} = 2+1+1$ flavor setup using Wilson twisted mass fermions at maximal twist. Through this paper, the collaboration delineates the methodologies involved in mass tuning for strange and charm quarks and outlines the critical examination of discretisation effects, primarily through light-quark observables.

Methodology and Simulation Parameters

The simulations were carried out at two lattice spacings, $a\approx 0.078$\,fm and $a\approx 0.086$\,fm, with a variety of lattice sizes. A critical element of this paper is the implementation of the twisted mass lattice QCD (tmLQCD) framework, which offers notable benefits such as automatic $\mathcal{O}(a)$ improvement of observables due to tuning to maximal twist. This setup included a heavy mass-split doublet ($c,s$) alongside the light degenerate mass doublet ($u,d$), allowing for a robust analysis of quark interactions.

Numerical Analysis and Results

The paper measures pivotal observables such as the light pseudoscalar mass, $m_\mathrm{PS}$, and decay constant, $f_\mathrm{PS}$, within a pseudoscalar mass range from 270 MeV to 510 MeV. The low-energy constants $f_0$ and $\overline{l}_{3,4}$ of SU(2) chiral perturbation theory were determined, suggesting an agreement with results obtained from two-flavor simulations and other lattice QCD calculations. The effective tuning of quark masses and lattice spacings allowed the collaboration to perform a qualitative assessment of discretisation effects without considerable discrepancies between the results obtained at two different values of lattice spacing.

Discretisation and Finite Volume Effects

The team investigated the impact of discretisation by performing simulations with stout-smeared gauge fields and examining isospin breaking effects typical of twisted mass formulations. The mass splitting between charged and neutral pions was analyzed, though it was notably larger in the $N_{\rm f}=2+1+1$ setup compared to the two-flavor simulations, indicating significant contributions from the added strange and charm flavors.

Overall, the paper demonstrates significant consistency across observations, suggesting negligible differences between the $N_{\rm f}=2$ and $N_{\rm f}=2+1+1$ configurations for light meson observables at the current level of precision. However, caution is indicated due to possible undetected cancellations between higher-order contributions and lattice artifacts.

Implications and Future Directions

The implications of this research are multifaceted. The inclusion of both strange and charm quarks provides a possibility for more accurate modeling of strong interaction dynamics, aiding in a comprehensive understanding of hadronic processes and weak matrix elements. These outcomes are pivotal for refining physical constants within chiral perturbation theory frameworks.

Prospects for the future involve reducing lattice spacings further to enable a clear extrapolation to the continuum limit and quantifying systematic errors more precisely. Additionally, ensuring mass tuning that consistently replicates physical values remains a key objective.

This research contributes to the overall goal of understanding non-perturbative aspects of QCD more completely, supporting improved precision in key theoretical predictions critical for both theoretical advancements and practical applications in particle physics.