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 Non-Relativistic QCD and inspired in the strong coupling regime of Potential Non-Relativistic 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 Non-Relativistic 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.
Highlights
Exotic hadrons, which may be defined as hadrons that are neither mesons nor baryons, were already foreseen in the early days of QCD [1]
Whereas mesons and baryons are well-defined objects in the nonrelativistic quark model, they are not so in the context of QCD. This is because the light quark masses are much smaller than the typical hadronic scale ΛQCD, and light quark-antiquark pairs can be created both in mesons and baryons turning them into tetraquark or pentaquark states, or even into states with a higher number of quarks and antiquarks
We have put forward a general formalism to build effective field theory (EFT) for exotic hadrons with two heavy quarks as well as double heavy baryons
Summary
Exotic hadrons, which may be defined as hadrons that are neither mesons (quark-antiquark states) nor baryons (three quark states), were already foreseen in the early days of QCD [1]. The different terms in the potential have been evaluated in lattice QCD [22,23,24] It is the aim of this paper to put forward a general effective field theory (EFT) framework, analogous to the one described above for heavy quarkonium, for any heavy hadron, containing a heavy quark-antiquark or two heavy quarks, and a gluon and light quark state with arbitrary quantum numbers. The leading-order Lagrangian for the EFT for heavy exotic hadrons consists of wave function fields interacting with a mass-independent and heavy quark spin-independent potential, and coincides with the Born-Oppenheimer approximation. Some technical details are relegated to the Appendixes A and B
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