FLAG review 2024

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.