QCD spin effects in the heavy hybrid potentials and spectra

Abstract

The spin-dependent operators for heavy quarkonium hybrids have been recently obtained in a nonrelativistic effective field theory approach up to next-to-leading order in the heavy-quark mass expansion. In the effective field theory for hybrids several operators not found in standard quarkonia appear, including an operator suppressed by only one power of the heavy-quark mass. We compute the matching coefficients for these operators in the short heavy-quark-antiquark distance regime, r ≪ 1=Λ QCD , by matching weakly coupled potential nonrelativistic QCD to the effective field theory for hybrids. In this regime the perturbative and nonperturbative contributions to the matching coefficients factorize, and the latter can be expressed in terms of purely gluonic correlators whose form we explicitly calculate with the aid of the transformation properties of the gluon fields under discrete symmetries. We detail our previous comparison with direct lattice computations of the charmonium hybrid spectrum, from which the unknown nonperturbative contributions can be obtained, and extend it to datasets with different light-quark masses.

Nonrelativistic effective field theory for heavy exotic hadrons

“…Hence, the basic assumptions are that (i) the heavy quark masses are larger than any other energy scale in the system, and (ii) the heavy quark binding energies are smaller than the typical hadronic scale Λ QCD . We pose no extra assumption on the relative size of the typical momentum exchanges between the heavy quarks ∼1=r and Λ QCD such as in previous works [28,29,43,44,50]. The effective theory consists of wave function fields interacting with potentials, which are a function of r and Λ QCD .…”

“…This was already noted in the specific case of quarkonium hybrids in Refs. [42][43][44]. Furthermore, the 1=m Q terms may also mix different representations of the Oð3Þ group.…”

“…These projection vectors for κ ¼ 1 were used in Refs. [35,36,43,44,47] in the construction of EFT for hybrid quarkonium. The spin operator projected into the heavy quark pair axis can be expanded in these projector vectors…”

“…[32,[38][39][40][41]. The EFT for heavy hybrids has been extended beyond leading order to include spin-dependent operators up to 1=m Q [42] and up to 1=m 2 Q [43,44]. In Refs.…”

“…In Refs. [35,43,44] the dependence of the potentials in the interquark distance, r, was obtained in the short-distance regime, that is, assuming that the typical size of the system r is much smaller than the typical hadronic size 1=Λ QCD . In the case of the static potential, which can be obtained from the lattice QCD calculations, the results from Ref.…”