Abstract
We present an effective field theory for doubly heavy baryons that goes beyond the compact heavy diquark approximation. The heavy-quark distance $r$ is only restricted to $m_Q\gg 1/r \gg E_{bin}$, where $m_Q$ is the mass of the heavy quark and $E_{bin}$ the typical binding energy. This means that the size of the heavy diquark can be as large as the typical size of a light hadron. We start from Non-Relativistic QCD, and build the effective field theory at next-to-leading in the $1/m_Q$ expansion. At leading order the effective field theory reduces to the Born-Oppenheimer approximation. The BO potentials are obtained from available lattice QCD data. The spectrum for double charm baryons below threshold is compatible with most of the lattice QCD results. We present for the first time the full spin averaged double bottom baryon spectrum below threshold based on QCD. We also present model-independent formulas for the spin splittings.
Highlights
The recent discovery of the Ξþccþ baryon by the LHCb Collaboration [1,2], together with the expectation that other states can be confirmed or discovered in the near future, has revitalized the interest of the theoretical community on double heavy baryons
The heavy quark distance r is only restricted to mQ ≫ 1=r ≫ Ebin, where mQ is the mass of the heavy quark and Ebin the typical binding energy
For doubly heavy charm or bottom baryons, for which the attraction of the Coulomb-like potential is twice weaker than that for quarkonium, the assumption Ebin ∼ ΛQCD seems unlikely to hold. It is the aim of this paper to build an effective theory (EFT) for QQq systems in which the hypothesis r ≪ 1=ΛQCD is released, along the lines suggested in Ref. [13]
Summary
The recent discovery of the Ξþccþ baryon by the LHCb Collaboration [1,2], together with the expectation that other states can be confirmed or discovered in the near future, has revitalized the interest of the theoretical community on double heavy baryons. For doubly heavy charm or bottom baryons, for which the attraction of the Coulomb-like potential is twice weaker than that for quarkonium, the assumption Ebin ∼ ΛQCD seems unlikely to hold. It is the aim of this paper to build an EFT for QQq systems in which the hypothesis r ≪ 1=ΛQCD is released, along the lines suggested in Ref. Lattice NRQCD, expanded about the static limit, is 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]. In Appendix A we derive the coupled Schrödinger equations for the κp 1⁄4 ð3=2Þ− states, which are a mixture of the ð1=2Þu and ð3=2Þu static energies, and in Appendix B we collect the plots of the double heavy baryon radial wave functions
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