Abstract
Expressions for the potentials appearing in the nonrelativistic effective field theory description of doubly heavy baryons are known in terms of operator insertions in the Wilson loop. However, their evaluation requires nonperturbative techniques, such as lattice QCD, and the relevant calculations are often not available. We propose a parametrization of these potentials with a minimal model dependence based on an interpolation of the short- and long-distance descriptions. The short-distance description is obtained from weakly-coupled potential NRQCD and the long-distance one is computed using an effective string theory. The effective string theory coincides with the one for pure gluodynamics with the addition of a fermion field constrained to move on the string. We compute the hyperfine contributions to the doubly heavy baryon spectrum. The unknown parameters are obtained from heavy quark-diquark symmetry or fitted to the available lattice-QCD determinations of the hyperfine splittings. Using these parameters we compute the double charm and bottom baryon spectrum including the hyperfine contributions. We compare our results with those of other approaches and find that our results are closer to lattice-QCD determinations, in particular for the excited states. Furthermore, we compute the vacuum energy in the effective string theory and show that the fermion field contribution produces the running of the string tension and a change of sign in the L\"uscher term.
Highlights
The discovery of more than two dozen exotic quarkonium states, as well as the more recent measurements of pentaquarks and double charm baryons, has increased interest in the wider class of hadrons containing two heavy quarks
In this paper we present an Effective String Theory (EST) for two static heavy quarks and one valence light quark, which is suitable to compute the long-distance part of the potentials of BOEFT for doubly heavy baryons
The short-distance regime is characterized by r ≪ Λ−Q1CD. In this regime the heavy-quark-pair distance and Λ−Q1CD are well-separated scales the matching of NRQCD to the BOEFT for doubly heavy baryons can be done in two steps
Summary
The discovery of more than two dozen exotic quarkonium states, as well as the more recent measurements of pentaquarks and double charm baryons, has increased interest in the wider class of hadrons containing two heavy quarks. The relative momentum is integrated out perturbatively in order to build weakly-coupled pNRQCD [10,11,12], and second, one integrates out the ΛQCD modes This procedure results in multipole expanded expressions of the potentials in BOEFT where the dependence on the heavy-quark-pair distance is explicit and the nonperturbative dynamics is encoded in some unknown constants. We obtain the mapping between different operator insertions in the Wilson loop and correlators in the ESTand use it to compute the static potential and the heavy-quark spin and angular-momentum dependent potentials in the long-distance regime. In Appendix B we give expressions for the shortdistance regime constants as correlators in weakly-coupled pNRQCD
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