A lattice QCD study of the strong decay width and coupling constant of decuplet baryons to an octet baryon - pion state is presented. The transfer matrix method is used to obtain the overlap of lattice states with decuplet baryon quantum numbers on t
he one hand and octet baryon-pion quantum numbers on the other as an approximation to the matrix element of the corresponding transition. By making use of leading order effective field theory, the coupling constants, as well as the widths for the various decay channels are determined. The transitions studied are $ Delta to pi ,N$, $Sigma^* to Lambda,pi$, $Sigma^* to Sigma,pi$ and $Xi^* to Xi,pi$. We obtain results for two ensembles of $N_f=2+1$ dynamical fermion configurations, one using domain wall valence quarks on a staggered sea at a pion mass of $350,mathrm{MeV}$ and a box size of $3.4,mathrm{fm}$ and a second one using domain wall sea and valence quarks at pion mass $180,mathrm{MeV}$ and box size $4.5,mathrm{fm}$.
We study the transfer matrix for domain wall fermions to understand the origin and significance of oscillatory contributions to hadron correlation functions that arise for M >1. For a free particle in one space, one time, and one flavor dimension, th
e eigenmodes of the one-body operator appearing in the transfer matrix are calculated, and the role of the negative eigenmodes arising when M > 1 is studied. In the case of three space dimensions, oscillatory behavior for hadron correlation functions in QCD is shown to emerge for free fermions when M exceeds 1, and to increase with increasing M. Analogous behavior is observed for domain wall fermions on HYP smeared MILC lattices, and a procedure is demonstrated for subtracting oscillating terms from physical observables.
