  We present the first quenched lattice QCD study of the form factors relevant
for the hyperon semileptonic decay Sigma -> n l nu. 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 K0 -> pi- l nu, the SU(3)-breaking
corrections to the vector form factor at zero-momentum transfer, f1(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 f1(0) also the
axial to vector ratio g1(0) / f1(0), which is relevant for the extraction of
the CKM matrix element Vus, 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 f1(0) = -0.948 +/- 0.029 and g1(0) / f1(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 f1(0) = -0.988 +/- 0.029(lattice) +/-
0.040(HBChPT). Our findings indicate that SU(3)-breaking corrections are
moderate on both f1(0) and g1(0). They also favor the experimental scenario in
which the weak electricity form factor, g2(0), is large and positive, and
correspondingly the value of |g1(0) / f1(0)| is reduced with respect to the one
obtained with the conventional assumption g2(q**2) = 0 based on exact SU(3)
symmetry.
