Recent results on the $Λ\rightarrow p\ell \barν_\ell$ semileptonic decay

Abstract

We present a lattice-QCD determination of the $Λ\to p$ vector and axial-vector form factors, providing theoretical input for studies of the semileptonic decay $Λ\to p\ell\barν_\ell$. The calculation is carried out on a single gauge ensemble with physical light, strange, and charm quark masses and delivers a precise determination of the complete set of transition form factors, including second-class contributions. Using these form factors, we compute decay rates for both the electronic and muonic channels, as well as their ratio, which offers a sensitive test of lepton-flavor universality and possible non-standard scalar or tensor interactions. This decay mode provides a theoretically well-controlled avenue for extracting the CKM matrix element $|V_{us}|$ from the baryon sector. Our estimate of $|V_{us}|$ is obtained by combining our recent lattice-QCD results with recent measurements of the relevant branching fraction reported by BESIII and LHCb.

Figures (3)

• Figure 1: Comparison of ratios of coupling constants with experimental and phenomenological ones. Points marked with a cross do not have uncertainties. The experimental values for $g_1/f_1$, $f_2/f_1$ and $g_2/f_1$ are taken from Table \ref{['tab:ExpCh']} and are shown in black. Results from phenomenology include QCD sum rules Zhang:2024ickZhang:2025qmg, Cabibbo's model Cabibbo:2003cu, chiral perturbation theory ($\chi$PT) Geng:2009ik, the soliton model—where points with errors are from Ref. Yang:2015era and those without from Ref. Ledwig:2008ku—the quark model—where $f_1$ is taken from Ref. Schlumpf:1994fb, and $g_1/f_1$ and $f_2/f_1$ from Ref. Faessler:2008ix—and the $1/N_c$ expansion Flores-Mendieta:1998tfv.
• Figure 2: Results on the branching fractions in the electron and muon channels and their ratio. For this work we also provide the branching fraction using as input the PDG average value $|V_{us}^{\rm PDG}| = 0.2243(8)$. The Experimental values $R^{\mu e}_{PDG}$ = 0.181(23), $R^{\mu e}_{PDG/BESIII}$ = 0.185(24) and $R^{\mu e}_{LHCb/PDG}$ = 0.175(12) are shown by the black points, and the QCD sum rules value by the brown points Zhang:2024ickZhang:2025qmg. The grey dashed line represents the 0.162 value which comes from Eq. \ref{['eq.Rat']} when the experimental values are adopted.
• Figure 3: Determination of $V_{us}$ (left) and the resulting CKM unitarity relation (right). Our results are shown in red: the top one uses lattice-determined nucleon and $\Lambda$ masses, approach (a), while the second one with open symbols uses PDG values, approach (b). The black points correspond to the values by Cabbibo et al.Cabibbo:2003cu, where the empty point is the value derived from the $\Lambda$ semileptonic decay, while the full point combines results from various hyperon decays. The green point is obtained from the unitarity relation. The remaining blue points show results on decay rates using lattice QCD combined with experimental data. Going from top to bottom, the first blue square is from inclusive $\tau$ decays ExtendedTwistedMass:2024myu, the second from kaon semileptonic decays Moulson:2017iveCarrasco:2016kpyBazavov:2018kjgFlavourLatticeAveragingGroupFLAG:2024oxs, the third from the ratio of kaon to pion leptonic decays in the muonic channel Dowdall:2013ryaCarrasco:2014poaBazavov:2017lyhMiller:2020xhyAlexandrou:2021bfrMoulson:2017iveFlavourLatticeAveragingGroupFLAG:2024oxs, and the last is the PDG average of the latter two ParticleDataGroup:2024cfk.