FLAG Review 2021

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 $$f_+(0)$$ f + ( 0 ) arising in the semileptonic $$K \rightarrow \pi $$ K → π transition at zero momentum transfer, as well as the decay constant ratio $$f_K/f_\pi $$ f K / f π and its consequences for the CKM matrix elements $$V_{us}$$ V us and $$V_{ud}$$ V ud . Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of $$SU(2)_L\times SU(2)_R$$ S U ( 2 ) L × S U ( 2 ) R and $$SU(3)_L\times SU(3)_R$$ S U ( 3 ) L × S U ( 3 ) R Chiral Perturbation Theory. We review the determination of the $$B_K$$ 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 $$m_c$$ m c and $$m_b$$ 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 $$\alpha _s$$ α 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.

Scale setting and the light baryon spectrum in $N_f=2+1$ QCD with Wilson fermions

“…The scale parameter 𝑡 0,ph has been determined previously in 𝑁 𝑓 = 2 + 1 QCD [2,5,6,13,20] and 𝑁 𝑓 = 2 + 1 + 1 QCD [8,15,16,18], using different input quantities and different extrapolation strategies. In figure 26 we compare our result (red square and shaded grey region) with previous determinations as well as with the 2021 FLAG averages [110]. HPQCD [15] and ETM [16] used the pion decay constant to set the scale while MILC [18], Bruno et al [2] as well as CLS [20] (both on CLS ensembles) used combinations of the pion and kaon decay constants.…”

“…To be safely within the so-called 𝑝-regime of ChPT we not only restrict the linear box size to 𝐿 ≫ 𝑀 −1 𝜋 but we also require this to be much larger than the inverse pseudo-critical temperature. To this end, in the latest Flavour Lattice Averaging Group (FLAG) report [110] an extent 𝐿 > 2 fm is advocated. Here we set the somewhat stricter limit 𝐿 > 2.3 fm.…”

“…The experimental quantities used as an input to set the scale are indicated in brackets. Also shown as green triangles are the averages of the FLAG Review 2021 [110].…”

A novel approach to semileptonic heavy-to-light $B$ decays through the Dispersive Matrix method

“…Since many years, the heavy-to-light semileptonic 𝐵-meson transitions are intriguing processes mainly because of a long-standing tension between the inclusive and the exclusive determinations of the CKM matrix element |𝑉 𝑢𝑏 |. The most recent version of the FLAG report [1] quotes for the exclusive estimate of |𝑉 𝑢𝑏 | the value |𝑉 𝑢𝑏 | 𝑒𝑥𝑐𝑙 • 10 3 = 3.74 (17) from 𝐵 → 𝜋ℓ𝜈 ℓ decays. This value is well compatible with other recent analyses present in literature, see for instance [2].…”

“…HFLAV Collaboration [3] quotes the value |𝑉 𝑢𝑏 | 𝑖𝑛𝑐𝑙 • 10 3 = 4.19 (12) (+11) (− 12) , where the errors correspond to experimental and theoretical uncertainties, respectively. In the last FLAG review [1] one finds |𝑉 𝑢𝑏 | 𝑖𝑛𝑐𝑙 • 10 3 = 4.32 (29). Finally, the last PDG review [4] quotes |𝑉 𝑢𝑏 | 𝑖𝑛𝑐𝑙 • 10 3 = 4.13 (26).…”