First lattice QCD study of the [formula omitted] axial and vector form factors with [formula omitted] breaking corrections

Abstract

We present the first quenched lattice QCD study of the form factors relevant for the hyperon semileptonic decay Σ − → n ℓ ν . The momentum dependence of both axial and vector form factors is investigated and the values of all the form factors at zero-momentum transfer are presented. Following the same strategy already applied to the decay K 0 → π − ℓ ν , the SU ( 3 ) -breaking corrections to the vector form factor at zero-momentum transfer, f 1 ( 0 ) , are determined with great statistical accuracy in the regime of the simulated quark masses, which correspond to pion masses above ≈ 0.7 GeV . Besides f 1 ( 0 ) also the axial to vector ratio g 1 ( 0 ) / f 1 ( 0 ) , which is relevant for the extraction of the CKM matrix element V u s , is determined with significant accuracy. Due to the heavy masses involved, a polynomial extrapolation, which does not include the effects of meson loops, is performed down to the physical quark masses, obtaining f 1 ( 0 ) = − 0.948 ± 0.029 and g 1 ( 0 ) / f 1 ( 0 ) = − 0.287 ± 0.052 , where the uncertainties do not include the quenching effect. Adding a recent next-to-leading order determination of chiral loops, calculated within the Heavy Baryon Chiral Perturbation Theory in the approximation of neglecting the decuplet contribution, we obtain f 1 ( 0 ) = − 0.988 ± 0.029 lattice ± 0.040 HBChPT . Our findings indicate that SU ( 3 ) -breaking corrections are moderate on both f 1 ( 0 ) and g 1 ( 0 ) . They also favor the experimental scenario in which the weak electricity form factor, g 2 ( 0 ) , is large and positive, and correspondingly the value of | g 1 ( 0 ) / f 1 ( 0 ) | is reduced with respect to the one obtained with the conventional assumption g 2 ( q 2 ) = 0 based on exact SU ( 3 ) symmetry.