Long-range properties of $1S$ bottomonium states

TL;DR

This paper derives analytical expressions for the chromo-polarizability of 1S bottomonium states and uses chiral effective field theory to compute long-range properties, including mass corrections and van der Waals interactions.

Contribution

It provides new analytical formulas for bottomonium chromo-polarizability and long-range interactions, improving upon previous theoretical results.

Findings

Analytical expression for chromo-polarizability matches previous results.

Computed leading chiral logarithm correction to bottomonium mass.

Derived van der Waals potential between two 1S bottomonium states.

Abstract

In the framework of weakly-coupled pNRQCD, we derive, first, an analytical expression for the chromo-polarizability of $1S$-bottomonium states in agreement with previous determinations. Then we use the QCD trace anomaly to obtain the two-pion production amplitude for the chromo-polarizability operator and match the result to a chiral effective field theory with $1S$-bottomonium states and pions as degrees-of-freedom. In this chiral effective field theory we compute some long-range properties of the $1S$ bottomonium generated by the pion coupling such as the leading chiral logarithm to the $1S$-bottomonium mass and the van der Waals potential between two $1S$-bottomonium states. Both results improve on previously known expressions.