The static hybrid potential in D dimensions at short distances

TL;DR

This paper calculates the short-distance static hybrid energy in various dimensions using effective field theory, providing new two-loop results for the potential and decay width, and discusses implications in two dimensions.

Contribution

It presents novel two-loop calculations of the static hybrid energy and decay width in three and four dimensions using pNRQCD, extending previous knowledge.

Findings

Computed the static hybrid energy at short distances in D=4,3 dimensions.

Provided two-loop ultrasoft contributions to hybrid and singlet energies.

Discussed the non-existence of hybrids in two dimensions.

Abstract

We compute the energy of a static hybrid, i.e. of a hybrid quarkonium with static quark and antiquark, at short distances in D=4,3 dimensions. The soft contribution to this energy is the static potential of a color octet quark-antiquark pair at short distances, which is known at two loops for arbitrary D. We have checked this expression employing thermal field theory methods. Using the effective field theory pNRQCD we calculate the ultrasoft contributions to the hybrid (and singlet) static energy at the two-loop level. We then present new results for the static hybrid energy/potential and the hybrid decay width in three and four dimensions. Finally we comment on the meaning of the perturbative results in two space-time dimensions, where the hybrid does not exist.