  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.

High Energy Physics - Phenomenology;Nuclear Theory