Two-loop quarkonium Hamiltonian in annihilation channel

TL;DR

This paper computes the two-loop quarkonium Hamiltonian in the annihilation channel using potential-NRQCD, confirming previous results and extending to more general gauge groups, completing the full two-loop Hamiltonian.

Contribution

It provides a comprehensive two-loop quarkonium Hamiltonian in the annihilation channel, including a more general color structure, advancing theoretical understanding.

Findings

Results agree with previous four-quark operator calculations in NRQCD.

Derived a more general color structure applicable to other gauge groups.

Completed the full two-loop quarkonium Hamiltonian.

Abstract

We calculate the two-loop quarkonium Hamiltonian in the annihilation channel within the framework of potential-NRQCD effective field theory. The result agrees with the previous calculation of the corresponding four-quark operator in NRQCD for SU(N) color gauge group. We further obtain an expression with a more general color structure applicable to other gauge groups. Combined with the recently calculated two-loop Hamiltonian in the non-annihilation channel, this completes the full two-loop quarkonium Hamiltonian.