Calculation of the decay width of decuplet baryons

TL;DR

This paper uses lattice QCD to calculate decay widths of decuplet baryons, providing a new method applicable for near-degenerate energy levels and presenting results consistent with experimental data.

Contribution

It introduces a transfer matrix method in lattice QCD for calculating baryon decay widths, applicable under near-degeneracy conditions, and provides numerical results for several decuplet baryons.

Findings

Calculated decay width of Delta to pion-nucleon: 119(8)(8) MeV

Provided decay widths for Sigma* and Xi* baryons

Demonstrated method effectiveness with different lattice setups

Abstract

We calculate the coupling constant and decay width of the decuplet to octet baryon transitions in lattice QCD using the transfer matrix method. The transition amplitude is related to the coupling constant and via the Fermi's Golden Rule to the decay width. The method is applicable for near-degeneracy of the energy levels of initial and final states and, when this condition is fulfilled, yields a good estimate of the decay width. We present results using a hybrid action with domain wall valence quarks on a staggered sea with $350$ MeV pion mass as well as for a domain wall fermion action with $180$ MeV pion mass. We find $\Gamma\left( \Delta \to \pi\,N \right) = 119\,( 8)\,( 8)$ MeV for the transition of Delta to pion-nucleon within the unitary domain wall setup. We also report values for the decay widths of the $\Sigma^*$ and $\Xi*$ baryons.