FLAG Review 2019
Sinya Aoki, Yasumichi Aoki, Damir Bečirević, Tom Blum, Gilberto Colangelo, Sara Collins, Michele Della Morte, P. Dimopoulos, Stephan Dürr, Hidenori Fukaya, Maarten Golterman, Steven Gottlieb, Rajan Gupta, S. Hashimoto, Urs M. Heller, Gregorio Herdoíza, R. Horsley, Andreas Jüttner, T. Kaneko, C.-J. David Lin, Enrico Lunghi, Robert D. Mawhinney, Amy Nicholson, T. Onogi, C. Peña, Antonin Portelli, Alberto Ramos, Stephen R. Sharpe, James N. Simone, Silvano Simula, Rainer Sommer, R. G. Van de Water, A. Vladikas, Urs Wenger, Hartmut Wittig
Abstract
Abstract We review lattice results related to pion, kaon, D -meson, B -meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $$f_+(0)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mo>+</mml:mo></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> arising in the semileptonic $$K \rightarrow \pi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>K</mml:mi><mml:mo>→</mml:mo><mml:mi>π</mml:mi></mml:mrow></mml:math> transition at zero momentum transfer, as well as the decay constant ratio $$f_K/f_\pi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi>K</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mi>π</mml:mi></mml:msub></mml:mrow></mml:math> and its consequences for the CKM matrix elements $$V_{us}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>us</mml:mi></mml:mrow></mml:msub></mml:math> and $$V_{ud}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>ud</mml:mi></mml:mrow></mml:msub></mml:math> . Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of $$SU(2)_L\times SU(2)_R$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mi>L</mml:mi></mml:msub><mml:mo>×</mml:mo><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mi>R</mml:mi></mml:msub></mml:mrow></mml:math> and $$SU(3)_L\times SU(3)_R$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mn>3</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mi>L</mml:mi></mml:msub><mml:mo>×</mml:mo><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mn>3</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mi>R</mml:mi></mml:msub></mml:mrow></mml:math> Chiral Perturbation Theory. We review the determination of the $$B_K$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>B</mml:mi><mml:mi>K</mml:mi></mml:msub></mml:math> parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $$m_c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>m</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math> and $$m_b$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>m</mml:mi><mml:mi>b</mml:mi></mml:msub></mml:math> 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. We review the status of lattice determinations of the strong coupling constant $$\alpha _s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>α</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math> . Finally, in this review we have added a new section reviewing results for nucleon matrix elements of the axial, scalar and tensor bilinears, both isovector and flavor diagonal.