Expansion Aspect of Color Transparency on the Lattice

Abstract

The opportunity to observe color transparency (CT) is determined by how rapidly a small-sized hadronic wave packet expands. Here we use SU(2) lattice gauge theory with Wilson fermions in the quenched approximation to investigate the expansion. The wave packet is modeled by a point hadronic source, often used as an interpolating field in lattice calculations. The procedure is to determine the Euclidean time (t), pion channel, Bethe-Salpeter amplitude $Ψ(r,t)$, and then evaluate $b^2(t)=\int d^3 r Ψ(r,t) r^2 sin^2 θΨ_π(r)$. This quantity represents the soft interaction of a small-sized wave packet with a pion. The time dependence of $b^2(t)$ is fit as a superposition of three states, which is found sufficient to reproduce a reduced size wave packet. Using this superposition allows us to make the analytic continuation required to study the wave packet expansion in real time. We find that the matrix elements of the soft interaction $\hat b^2$ between the excited and ground state decrease rapidly with the energy of the excited state.