Effective field theory for long-range properties of bottomonium

Abstract

In this communication we present selected results from a recent study [N. Brambilla, G. Krein, J. Tarrus Castella and A. Vairo, Phys. Rev. D 93, 054002 ( 2016)] of long-range properties of bottomonium. An analytical expression for the chromopolarizability of 1S bottomonium states is derived within the framework of potential nonrelativistic QCD (pNRQCD). Next, after integrating out the ultrasoft scale associated with the binding energy of bottomonium, the QCD trace anomaly is used to obtain the two-pion production amplitude for the chromopolarizability operator and the result is matched to a chiral effective field theory having bottomonium states and pions as degrees of freedom. We present results for the leading chiral logarithm correction to the mass of the 1S bottomonium and the van der Waals potential between two bottomonium states.