FLAG review 2024
Y. Aoki, T. Blum, S. Collins, L. Del Debbio, M. Della Morte, P. Dimopoulos, X. Feng, M. Golterman, Steven Gottlieb, R. Gupta, G. Herdoíza, P. Hernandez, A. Jüttner, T. Kaneko, E. Lunghi, S. Meinel, C. Monahan, A. Nicholson, T. Onogi, P. Petreczky, A. Portelli, A. Ramos, S. R. Sharpe, J. N. Simone, S. Sint, R. Sommer, N. Tantalo, R. Van de Water, A. Vaquero, U. Wenger, H. Wittig, Flavour Lattice Averaging Group (FLAG)
Abstract
We review lattice results related to pion, kaon, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>D</a:mi> </a:math> -meson, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>B</c:mi> </c:math> -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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>f</e:mi> <e:mo>+</e:mo> </e:msub> <e:mo stretchy="false">(</e:mo> <e:mn>0</e:mn> <e:mo stretchy="false">)</e:mo> </e:math> arising in the semileptonic <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>K</i:mi> <i:mo stretchy="false">→</i:mo> <i:mi>π</i:mi> </i:math> transition at zero momentum transfer, as well as the decay-constant ratio <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:msub> <l:mi>f</l:mi> <l:mi>K</l:mi> </l:msub> <l:mo>/</l:mo> <l:msub> <l:mi>f</l:mi> <l:mi>π</l:mi> </l:msub> </l:math> and its consequences for the Cabibbo–Kobayashi–Maskawa (CKM) matrix elements <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:msub> <n:mi>V</n:mi> <n:mrow> <n:mi>u</n:mi> <n:mi>s</n:mi> </n:mrow> </n:msub> </n:math> and <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:msub> <p:mi>V</p:mi> <p:mrow> <p:mi>u</p:mi> <p:mi>d</p:mi> </p:mrow> </p:msub> </p:math> . We review the determination of the <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:msub> <r:mi>B</r:mi> <r:mi>K</r:mi> </r:msub> </r:math> parameter of neutral kaon mixing as well as the additional four <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:mi>B</t:mi> </t:math> parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"> <v:msub> <v:mi>m</v:mi> <v:mi>c</v:mi> </v:msub> </v:math> and <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:msub> <x:mi>m</x:mi> <x:mi>b</x:mi> </x:msub> </x:math> as well as those for the decay constants, form factors, and mixing parameters of charmed and bottom mesons and baryons. 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 <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:msub> <z:mi>α</z:mi> <z:mi>s</z:mi> </z:msub> </z:math> . We review the determinations of nucleon charges from the matrix elements of both isovector and flavor-diagonal axial, scalar and tensor local quark bilinears, and momentum fraction, helicity moment and the transversity moment from one-link quark bilinears. We also review determinations of scale-setting quantities. Finally, in this review we have added a new section on the general definition of the low-energy limit of the Standard Model.