{"work":{"id":"6cf9f064-3878-4e86-8a6b-82725bc923db","openalex_id":null,"doi":null,"arxiv_id":"2111.09849","raw_key":null,"title":"FLAG Review 2021","authors":null,"authors_text":"Y","year":2021,"venue":"hep-lat","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 $f_+(0)$ arising in the semileptonic $K \\to \\pi$ transition at zero momentum transfer, as well as the decay constant ratio $f_K/f_\\pi$ and its consequences for the CKM matrix elements $V_{us}$ and $V_{ud}$. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of $SU(2)_L\\times SU(2)_R$ and $SU(3)_L\\times SU(3)_R$ Chiral Perturbation Theory. We review the determination of the $B_K$ 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 $m_c$ and $m_b$ 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 $\\alpha_s$. We consider nucleon matrix elements, and review the determinations of the axial, scalar and tensor bilinears, both isovector and flavor diagonal. Finally, in this review we have added a new section reviewing determinations of scale-setting quantities.","external_url":"https://arxiv.org/abs/2111.09849","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-07-09T19:26:28.325277+00:00","pith_arxiv_id":"2111.09849","created_at":"2026-05-09T06:07:29.616229+00:00","updated_at":"2026-07-09T19:26:28.325277+00:00","title_quality_ok":false,"display_title":"Aoki et al.,FLAG Review 2021, Eur","render_title":"Aoki et al.,FLAG Review 2021, Eur"},"hub":{"state":{"work_id":"6cf9f064-3878-4e86-8a6b-82725bc923db","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":21,"external_cited_by_count":null,"distinct_field_count":4,"first_pith_cited_at":"2023-05-03T16:23:57+00:00","last_pith_cited_at":"2026-07-08T09:11:10+00:00","author_build_status":"not_needed","summary_status":"needed","contexts_status":"needed","graph_status":"needed","ask_index_status":"not_needed","reader_status":"not_needed","recognition_status":"not_needed","updated_at":"2026-08-23T09:39:36.861067+00:00","tier_text":"hub"},"tier":"hub","role_counts":[{"context_role":"dataset","n":3},{"context_role":"background","n":2},{"context_role":"baseline","n":1}],"polarity_counts":[{"context_polarity":"use_dataset","n":3},{"context_polarity":"background","n":2},{"context_polarity":"baseline","n":1}],"runs":{},"summary":{},"graph":{},"authors":[]}}