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Review of lattice results concerning low-energy particle physics

S. Aoki, Y. Aoki, D. Becirevic, C. Bernard, T. Blum, G. Colangelo, M. Della Morte, P. Dimopoulos, S. Dürr, H. Fukaya, M. Golterman, Steven Gottlieb, S. Hashimoto, U. M. Heller, R. Horsley, A. Jüttner, T. Kaneko, L. Lellouch, H. Leutwyler, C. -J. D. Lin, V. Lubicz, E. Lunghi, R. Mawhinney, T. Onogi, C. Pena, C. T. Sachrajda, S. R. Sharpe, S. Simula, R. Sommer, A. Vladikas, U. Wenger, H. Wittig

TL;DR

The determination of the light-quark masses, the form factor, and the decay constant ratio arising in the semileptonic $$K \rightarrow \pi $$K→π transition at zero momentum transfer are reported on.

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.

Review of lattice results concerning low-energy particle physics

TL;DR

The determination of the light-quark masses, the form factor, and the decay constant ratio arising in the semileptonic K→π transition at zero momentum transfer are reported on.

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.

Paper Structure

This paper contains 133 sections, 280 equations, 32 figures, 169 tables.

Table of Contents

  1. Introduction
  2. FLAG composition, guidelines and rules
  3. Citation policy
  4. General issues
  5. Quality criteria, averaging and error estimation
  6. Systematic errors and colour code
  7. Systematic effects and rating criteria
  8. Heavy-quark actions
  9. Conventions for the figures
  10. Averages and estimates
  11. Averaging procedure and error analysis
  12. Quark masses
  13. Masses of the light quarks
  14. Contributions from the electromagnetic interaction
  15. Pion and kaon masses in the isospin limit
  16. ...and 118 more sections

Figures (32)

  • Figure 1: ${\overline{\mathrm{MS}}}$ mass of the strange quark (at 2 GeV scale) in MeV. The upper three panels show the lattice results listed in Tabs. \ref{['tab:masses2']}, \ref{['tab:masses3']} and \ref{['tab:masses4']}, while the bottom panel collects a few sum rule results and also indicates the current PDG estimate. Diamonds and squares represent results based on perturbative and nonperturbative renormalization, respectively. The black squares and the grey bands represent our estimates (\ref{['eq:quark masses Nf=2']}) , (\ref{['eq:nf3msmud']}) and (\ref{['eq:nf4msmud']}). The significance of the colours is explained in Sec. \ref{['sec:qualcrit']}.
  • Figure 2: Mean mass of the two lightest quarks, $m_{ud}=\frac{1}{2}(m_u+m_d)$ (for details see Fig. \ref{['fig:ms']}).
  • Figure 3: Results for the ratio $m_s/m_{ud}$. The upper part indicates the lattice results listed in Tab. \ref{['tab:ratio_msmud']} together with the FLAG averages for each value of $N_f$. The lower part shows results obtained from $\chi$PT and sum rules, together with the current PDG estimate.
  • Figure 4: Lattice results and FLAG averages at $N_f = 2$, $2+1$, and $2+1+1$ for the charm-quark mass $\overline{m}_c(3~\mathrm{Ge V})$.
  • Figure 5: Lattice results for the ratio $m_c / m_s$ listed in Tab. \ref{['tab:mcoverms']} and the FLAG averages corresponding to $N_f =2$, $2+1$ and $2+1+1$.
  • ...and 27 more figures