First lattice QCD study of the axial and vector form factors with 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 us , 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 nextto-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.

Semileptonic decays of the lightJP=1/2+ground state baryon octet

“…Finally, we would like to stress that our results for the various semileptonic couplings of the decay mode Σ − → ne −ν e are in good agreement with the predictions of the lattice approach [35]. In Table 9 we give a detailed comparison with the results of Ref.…”

“…In Table 9 we give a detailed comparison with the results of Ref. [35] using our conventions for the semileptonic matrix elements. It is useful to parametrize our predictions for the weak magnetic couplings F 2 in terms of SU(3) symmetric couplings together with first order SU(3) symmetry-breaking parameters.…”

Baryon vector current in the chiral and1/Ncexpansions

“…Important inroads are being made by Lattice QCD calculations of form factors [19][20][21][22]. These and future results are very significant, as one will be able to test explicitly the behavior of the vector form factor with the quark masses, and in particular understand more accurately the SU(3) SB effects on f 1 , helping clarify the issues mentioned above.…”

Nucleon form factors with2+1flavor dynamical domain-wall fermions

“…There has also been an increasing amount of interest in the form factors of other baryons [27,30,31,32,33].…”