Review of lattice results concerning low-energy particle physics (1607.00299v1)

Abstract: We review lattice results related to pion, kaon, D- and B-meson physics with the aim of making them easily accessible to the particle physics community. More specifically, we report on the determination of the light-quark masses, the form factor f+(0), arising in the semileptonic K -> pi transition at zero momentum transfer, as well as the decay constant ratio fK/fpi and its consequences for the CKM matrix elements Vus and Vud. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of SU(2)LxSU(2)R and SU(3)LxSU(3)R Chiral Perturbation Theory. We review the determination of the BK parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. The latter quantities are an addition compared to the previous review. For the heavy-quark sector, we provide results for mc and mb (also new compared to the previous review), as well as those for D- and B-meson decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. Finally, we review the status of lattice determinations of the strong coupling constant alpha_s.

• The paper provides precise lattice QCD evaluations of light and heavy quark masses and CKM matrix elements, underpinning accurate Standard Model tests.
• The review consolidates decay constants, form factors, and low-energy constants, enhancing our understanding of meson dynamics.
• It applies rigorous averaging, continuum and chiral extrapolations, and renormalization techniques to ensure reliability in lattice simulation results.

Overview of Lattice Results in Low-Energy Particle Physics

The paper "Review of lattice results concerning low-energy particle physics," authored by the FLAG Working Group, provides a comprehensive overview of lattice QCD simulations focused on the low-energy properties of the Standard Model, particularly concerning pion, kaon, and heavy-light meson physics. Lattice QCD serves as a non-perturbative approach crucial for precision measurements that impact crucial areas such as the determination of quark masses and CKM matrix elements, thus containing implications for testing the Standard Model and potential new physics.

Key Results and Topics

1. Quark Masses: The determination of light- (up, down, strange) and heavy-quark (charm, bottom) masses remains a central topic. The precision in determining these masses hinges upon lattice simulations' ability to account for finite spacing and volume effects, as well as systematic uncertainties inherent to renormalization and continuum extrapolation. The FLAG results reflect consolidated values based on recent lattice computations, reported at various quark mass (N_f) setups, particularly focusing on N_f=2, N_f=2+1, and N_f=2+1+1 flavor configurations.
2. CKM Matrix Elements: Utilizing lattice results for decay constants and form factors, the paper assesses CKM matrix elements |V_ud| and |V_us|. The lattice calculations of the kaon semileptonic decay form factor $f_+(0)$ and the ratio of kaon to pion decay constants $f_{K^\pm}/f_{\pi^\pm}$ refine the determination of V_us, which, alongside experimental results, supports stringent tests of CKM unitarity.
3. Chiral Perturbation Theory (ChPT): Lattice results are crucial for determining low-energy constants (LECs) of ChPT, providing insight into the non-perturbative structure of QCD. These are essential for describing the quark mass dependence of observables and are vital in the ChPT extrapolation of lattice data to phenomenologically relevant regimes.
4. Heavy Meson Decays and Mixing: The working group reviews lattice determinations of B-meson decay constants and form factors, emphasizing their impact on the CKM unitarity triangle. These calculations are complicated by the need for effective field theory treatments to handle heavy quark dynamics accurately.
5. Lattice Determination of Alpha_s: The paper also examines the status of lattice determinations of the strong coupling constant $\alpha_s$, including systematic issues surrounding effective field theories and the matching scale required for high precision.

Methodology and Standards

The paper adopts a rigorous protocol for averaging across multiple lattice calculations. Essential criteria include continuum and chiral extrapolations, finite volume corrections, and renormalization techniques. The use of color-coded quality measures facilitates an objective assessment of different lattice results' reliability. Additionally, the paper emphasizes the importance of renormalization and scale setting in lattice QCD to ensure consistency across various lattice abstractions.

Implications and Future Work

While current lattice QCD results show extraordinary potential in precision physics, challenges remain in controlling all systematic errors and fully including isospin-breaking effects such as electromagnetism. Progress in these areas is essential for even more precise tests of the Standard Model. Future developments hinge on improved lattice techniques, computing resources, and innovative methods for handling heavy quarks.

The FLAG review highlights the pivotal role of lattice QCD in modern particle physics, not only for current theoretical explorations and phenomenological consistency checks but also for ensuring that potential signals of new physics beyond the Standard Model are robustly interpreted with well-grounded theoretical predictions.