Higher partial wave contamination in finite-volume formulae for 1-to-2 transitions

Abstract

It is common practice to truncate the finite-volume formula for $K\to\pi\pi$, and other one-to-two transitions, to only include the lowest partial wave, as in the original derivation by Lellouch and L\"uscher. However, as the precision of lattice calculations increases, it may become important to asses the systematic effect of this approximation. With this motivation, we compare the $S$-wave-only ($\ell=0$) results with those truncated at the next lowest value of angular momentum.