Study of the $Λ\to p \ell \barν_\ell$ semileptonic decay in lattice QCD

TL;DR

The study provides the first lattice QCD determination of the Λ→N vector and axial-vector form factors at the physical point, enabling a nonperturbative extraction of $|V_{us}|$ from hyperon semileptonic decays. By combining a physical-point ensemble with a robust excited-state control and a model-independent $z$-expansion for the $q^2$-dependence, it delivers the full set of form factors, including second-class contributions, and uses them to compute decay rates and the ratio $R^{\mu e}$. The results yield a precise determination of $|V_{us}|$ and a CKM unitarity check consistent with the SM, while highlighting the importance of including the full $q^2$-dependence and radii terms to avoid percent-level biases. The work also constrains non-standard scalar/tensor interactions through the muon/electron decay-rate ratio, illustrating the power of lattice inputs to hyperon decays for flavor physics and CKM phenomenology.

Abstract

We present the first lattice QCD determination of the $Λ\to N$ vector and axial-vector form factors, which are essential inputs for studying the semileptonic decay $Λ\to p \ell \barν_\ell$. This channel provides a clean, theoretically controlled avenue for extracting the CKM matrix element $|V_{us}|$ from the baryon sector. Our analysis uses a gauge ensemble with physical light, strange, and charm quark masses and yields the most precise determination to date of the full set of transition form factors -- including second-class contributions -- as well as the associated couplings, radii, and the ratio of muon-to-electron decay rates, an observable sensitive to possible non-standard scalar and tensor interactions. We compare our non-perturbative results with next-to-next-to-leading order expansions in the small parameter $δ= (m_Λ- m_N)/m_Λ\approx 0.16$. We find that the common phenomenological approximation of neglecting the $q^2$-dependence of the form factors leads to a $\sim 4\%$ deviation in the decay rate. This underscores the critical importance of precise, fully non-perturbative form factor inputs for achieving the sub-percent precision targets of upcoming experimental programs.

Figures (8)

• Figure 1: Momentum transfer dependence of the Weinberg form factors. Red points denote selected lattice data. The red band represents the $z$-expansion fit, while the brown band shows results from QCD sum rules Zhang:2024ick. Vertical dashed lines indicate the kinematic region relevant for the semileptonic decay rate, $q^2 \in [0, q^2_{\max}]$.
• Figure 2: Comparison of ratios of coupling constants with experimental and phenomenological ones. Points marked with a cross do not have uncertainties. The experimental values for $g_1/f_1$ and $f_2/f_1$ are taken from the Particle Data Group (PDG) ParticleDataGroup:2024cfk and are shown in black. Results from phenomenology include QCD sum rules Zhang:2024ick, 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 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.
• Figure 4: Results on the decay rates in the electron and muon channels and their ratio. The notation of the red points is the same as in Fig. \ref{['fig:vues']}. The PDG value is shown by the black points ParticleDataGroup:2024cfk and the QCD sum rules value by the brown points Zhang:2024ick.
• Figure 5: Differential decay rates for the electron and muon channels. Brown lines show central values from the QCD sum rules study Zhang:2024ick, without error bands. In contrast, our results in red include uncertainty bands. The curves are computed using $|V_{us}^{\rm PDG}| = 0.2243(8)$ for visualization purposes.