# Sum rules for leading vector form factors in hyperon semileptonic decays

## TL;DR

This paper derives sum rules for vector form factors in hyperon semileptonic decays using SU(3) symmetry and QCD 1/N_c expansion, testing their validity with chiral perturbation theory results.

## Contribution

It introduces new sum rules based on SU(3) symmetry and evaluates symmetry-breaking effects using 1/N_c expansion and chiral perturbation theory.

## Key findings

- One sum rule vanishes even with symmetry breaking.
- The other sum rule is mainly influenced by 10+rac{10}{ar{10}} representations.
- Results at order O(p^2) in chiral expansion are consistent with the sum rules.

## Abstract

By considering that the weak currents and the electromagnetic current are members of the same SU(3) octet, two sum rules involving leading vector form factors in hyperon semileptonic decays are derived in the limit of exact flavor SU(3) symmetry. Deviations from this limit arise from second-order SU(3) symmetry-breaking effects, according to the Ademollo-Gatto theorem. The 1/N_c expansion of QCD is used to evaluate such effects. One sum rule vanishes identically even in the presence of symmetry breaking and the other one obtains contributions mainly from the 10+\overline{10} representation. Results obtained in (heavy) baryon chiral perturbation theory are used to test the validity of these sum rules. To order O(p^2) in the chiral expansion, results are encouraging.