Light Meson Physics from Maximally Twisted Mass Lattice QCD (0911.5061v1)

Abstract: We present a comprehensive investigation of light meson physics using maximally twisted mass fermions for two mass-degenerate quark flavours. By employing four values of the lattice spacing, spatial lattice extents ranging from 2.0 fm to 2.5 fm and pseudo scalar masses in the range 280 MeV to 650 MeV we control the major systematic effects of our calculation. This enables us to confront our data with chiral perturbation theory and extract low energy constants of the effective chiral Lagrangian and derived quantities, such as the light quark mass, with high precision.

Light Meson Physics from Maximally Twisted Mass Lattice QCD

The paper "Light Meson Physics from Maximally Twisted Mass Lattice QCD" addressed by the ETM Collaboration presents an in-depth investigation into light meson physics utilizing a lattice QCD approach with maximally twisted mass fermions. The paper focuses on $N_f=2$ mass-degenerate quark flavors, providing refined computations and analyses using varied lattice spacings and extents. This methodology significantly aids in controlling systematic effects and enhances the precision of the calculations performed.

Key Findings

The researchers have meticulously employed four values of lattice spacings concurrent with spatial lattice extents ranging from 2.0 fm to 2.5 fm, alongside pseudo scalar masses observed within the 280 to 650 MeV range. Through this, they've successfully mitigated major systematic effects, ensuring the accuracy of their results. The paper's confrontation with chiral perturbation theory has led to the extraction of numerous low-energy constants related to the effective chiral Lagrangian. As a notable result, the dynamical fermions parametrization for two mass-degenerate quarks shows that $\mathcal{O}(a^2)$ effects are minimal, which aligns well with the expected theoretical behavior.

Among prominent physical outputs from this investigation are the precision determinations of the light quark mass ($$m_{u,d}^{\overline{\mathrm{MS}}(\mu=2\, \mathrm{GeV})}=3.54(26)\, \mathrm{MeV}$$), pseudo scalar decay constant in the chiral limit ($f_0=122(1)\, \mathrm{MeV}$), and the scalar condensate ($[\Sigma^{\overline{\mathrm{MS}}(\mu=2\, \mathrm{GeV})]^{1/3}=270(7)\, \mathrm{MeV}$).

Implications and Future Directions

The implications of the work stretch both theoretical and practical borders within Quantum Chromodynamics (QCD). The precise extraction of low-energy constants aids in bolstering our comprehension of meson dynamics in the lattice QCD framework, particularly emphasizing the subleading lattice artifacts and potential isospin breaking phenomena exclusively observed in the twisted mass formulation. Although the Twisted Mass Lattice QCD showed large cutoff effects in the neutral pseudo scalar mass, such discrepancies primarily relate to discretization effects and are manageable within the utilized theoretical framework.

Future explorations might explore integrating strange and charm degrees within such QCD simulations to broaden the applicability and refine the theoretical estimates further. The confirmed smallness of the lattice artefacts encourages extending this approach into broader QCD aspects and accommodating comprehensive quark dynamics.

The integration of twisted mass fermions serves as an instrumental technique for refining lattice QCD simulations. It showcases the potential to achieve $\mathcal{O}(a)$ improvement automatically. As demonstrated, despite the inherent complexity and additional systematic endeavors needed to tackle unexplored areas, such computational advancements promise further granularity in the theoretical investigation of QCD.