$P$-wave quarkonium wavefunctions at the origin in the $\overline{\rm MS}$ scheme

Abstract

We compute $P$-wave quarkonium wavefunctions at the origin in the $\overline{\rm MS}$ scheme based on nonrelativistic effective field theories. We include nonperturbative effects from the long-distance behaviors of the potential, while the short-distance behaviors are determined from perturbative QCD. We obtain $\overline{\rm MS}$-renormalized $P$-wave quarkonium wavefunctions at the origin that have the correct scale dependences that are expected from factorization formalisms, so that the dependences on the scheme and scale cancel in physical quantities. This greatly reduces the theoretical uncertainties associated with scheme and scale dependences in predictions of decay and production rates. Based on the calculation of the $P$-wave wavefunctions at the origin in this work, we make first-principles predictions of electromagnetic decay rates and exclusive electromagnetic production rates of $P$-wave charmonia and bottomonia, and compare them with measurements.