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.
Highlights
In this communication we present selected results from a recent study [1] of long-range properties of bottomonium
The assumption can be questioned for some heavy quarkonium states, but once assumed, one can construct in a rigorous way an effective field theory (EFT) appropriate to describe the color van der Waals (vdW) force
One can integrate out the ultra-soft scale mα2s and match potential nonrelativistic QCD (pNRQCD) to an EFT [18], that we name gluonic van der Waals EFT, whose degrees of freedom are color-singlet quarkonium and gluon fields at the scale ΛQCD, with a coupling given by the polarizability
Summary
In this communication we present selected results from a recent study [1] of long-range properties of bottomonium. The assumption can be questioned for some heavy quarkonium states, but once assumed, one can construct in a rigorous way an EFT appropriate to describe the color vdW force This is achieved through a chain of EFTs by sequentially integrating out degrees of freedom at different scales that appear in the interaction. One can integrate out the ultra-soft scale mα2s and match pNRQCD to an EFT [18], that we name gluonic van der Waals EFT (gWEFT), whose degrees of freedom are color-singlet quarkonium and gluon fields at the scale ΛQCD, with a coupling given by the polarizability.
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