Nonrelativistic effective field theory for heavy exotic hadrons

Abstract

We propose an effective field theory to describe hadrons with two heavy quarks without any assumption on the typical distance between the heavy quarks with respect to the typical hadronic scale. The construction is based on nonrelativistic QCD and inspired in the strong coupling regime of potential nonrelativistic QCD. We construct the effective theory at leading and next-to-leading order in the inverse heavy quark mass expansion for arbitrary quantum numbers of the light degrees of freedom. Hence our results hold for hybrids, tetraquarks, double heavy baryons and pentaquarks, for which we also present the corresponding operators at a nonrelativistic level. At leading order, the effective theory enjoys heavy quark spin symmetry and corresponds to the Born-Oppenheimer approximation. At next-to-leading order, spin and velocity-dependent terms arise, which produce splittings in the heavy quark spin symmetry multiplets. A concrete application to double heavy baryons is presented in an accompanying paper.

Effective field theory for double heavy baryons at strong coupling

“…That is, incorporating an adiabatic expansion in the energy The EFT describing heavy exotic hadrons and double heavy baryons up to 1=m Q for any spin of the light quark and gluonic degrees of freedom has been presented in Ref. [14]. In the case of double heavy baryons corresponding to the static states of Fig.…”

“…The matching of the potentials in Eqs. 12, (13), and (14) in terms of static Wilson loops has been presented in Ref. [14].…”

“…12, (13), and (14) in terms of static Wilson loops has been presented in Ref. [14]. These Wilson loops are nonperturbative quantities and should be computed on the lattice.…”

“…[13]. In fact, this paper may be considered a concrete example of a more general formalism developed in an accompanying one [14]. This EFT is built upon the heavy quark mass expansion, m Q ≫ Λ QCD , and an adiabatic expansion between the dynamics of the heavy quarks, and the light degrees of freedom, the gluons and light quarks, Λ QCD ≫ E bin .…”

“…Lattice NRQCD, expanded about the static limit, is also necessary to compute the matching coefficients of the EFT presented here, namely the BO potentials. This can be done by using the expressions of the matching coefficients as operator insertions in the Wilson loop that we present in an accompanying paper [14]. An example of this are the static energies computed in Refs.…”