Lattice study of flavor SU(3) breaking in hyperon beta decay

TL;DR

This study uses lattice QCD with domain wall fermions to analyze flavor SU(3) breaking effects in hyperon beta decay, providing detailed form factor calculations and revealing significant SU(3) symmetry deviations.

Contribution

It presents the first quenched lattice calculation of all six hyperon beta decay form factors, highlighting SU(3) breaking patterns and nonzero second-class form factors.

Findings

SU(3) breaking corrections to f_1(0) are less than a few percent and likely negative.

f_2(0)/f_1(0) and g_1(0)/f_1(0) receive positive corrections of about 16% and 5%.

Nonzero second-class form factors f_3(0)/f_1(0) and g_2(0)/g_1(0) are observed.

Abstract

We present a quenched lattice calculation of all six form factors: vector [f_1(q^2)], weak magnetism [f_2(q^2)], induced scalar [f_3(q^2)], axial-vector [g_1(q^2)], weak electricity [g_2(q^2)] and induce pseudoscalar [g_3(q^2)] form factors in hyperon semileptonic decay Xi^0 -> Sigma^{+} l nu using domain wall fermions. The q^2 dependences of all form factors in the relatively low q^2 region are examined in order to evaluate their values at zero momentum transfer. The Xi^0 -> Sigma^+ transition is highly sensitive to flavor SU(3) breaking since this decay corresponds to the direct analogue of neutron beta decay under the exchange of the down quark with the strange quark. The pattern of flavor SU(3) breaking effects in the hyperon beta decay is easily exposed in a comparison to results for neutron beta decay. We measure SU(3)-breaking corrections to f_1(0), f_2(0)/f_1(0) and g_1(0)/f_1(0). A sign of the leading order corrections, of which the size is less than a few %, on f_1(0) is likely negative, while f_2(0)/f_1(0) and g_1(0)/f_1(0) receive positive corrections of order 16% and 5% respectively. The observed patterns of the deviation from the values in the exact SU(3) limit does not support some of model estimates. We show that there are nonzero second-class form factors in the Xi^0 -> Sigma^+ decay, measuring f_3(0)/f_1(0)=0.14(10) and g_2(0)/g_1(0)=0.68(18), which are comparable to the size of first-order SU(3) breaking. It is also found that the SU(3) breaking effect on g_3(0)/g_1(0) agree with the prediction of the generalized pion-pole dominance.