Perturbative Corrections to Heavy Quark-Diquark Symmetry Predictions for Doubly Heavy Baryon Hyperfine Splittings

Abstract

Doubly heavy baryons $\left(QQq\right)$ and singly heavy antimesons $\left(\bar{Q}q\right)$ are related by the heavy quark-diquark (HQDQ) symmetry because in the $m_Q\to \infty$ limit, the light degrees of freedom in both the hadrons are expected to be in identical configurations. Hyperfine splittings of the ground states in both systems are nonvanishing at $O(1/m_Q)$ in the heavy quark mass expansion and HQDQ symmetry relates the hyperfine splittings in the two sectors. In this paper, working within the framework of Non-Relativistic QCD (NRQCD), we point out the existence of an operator that couples four heavy quark fields to the chromomagnetic field with a coefficient that is enhanced by a factor from Coulomb exchange. This operator gives a correction to doubly heavy baryon hyperfine splittings that scales as $1/m_Q^2\times {\alpha }_S/r$, where $r$ is the separation between the heavy quarks in the diquark. This correction can be calculated analytically in the extreme heavy quark limit in which the potential between the quarks in the diquark is Coulombic. In this limit, the correction is $O({\alpha }_s^2/m_Q)$ and comes with a small coefficient. For values of ${\alpha }_s$ relevant to doubly charm and doubly bottom systems, the correction to the hyperfine splittings in doubly heavy baryons is only a few percent or smaller. We also argue that nonperturbative corrections to the prediction for the hyperfine splittings are suppressed by ${\Lambda }_{\mathrm{QCD}}^2/m_Q^2$ rather than ${\Lambda }_{\mathrm{QCD}}/m_Q$. Corrections should be $\approx 10\%$ in the charm sector and smaller in heavier systems.

arXiv comment15 pages, 6 figures, Added Section III and updated references and author name. Journal version

References in corpus (34)

• Rigorous QCD Analysis of Inclusive Annihilation and Production of Heavy Quarkonium
• Potential NRQCD: an effective theory for heavy quarkonium
• Observation of the doubly charmed baryon ${\Xi }_{cc}^{++}$
• First Observation of the Doubly Charmed Baryon Xi_cc^+
• Confirmation of the Double Charm Baryon Xi_cc+ via its Decay to p D+ K-
• Charmed bottom baryon spectroscopy from lattice QCD
• Baryons with two heavy quarks: Masses, production, decays, and detection
• Observation of New States Decaying into ${\Lambda }_c^{+}{K}^{-}{\pi }^{+}$ and ${\Lambda }_c^{+}{K}_S^0{\pi }^{-}$
• Renormalization group scaling in nonrelativistic QCD
• Baryons with two heavy quarks
• Effective Field Theory Lagrangians for Baryons with Two and Three Heavy Quarks
• Search for Doubly Charmed Baryons Xi_cc^+ and Xi_cc^++ in BABAR
• Charmed and Bottom Baryons from Lattice NRQCD
• First observation of the doubly charmed baryon decay ${\Xi }_{cc}^{++}\to {\Xi }_c^{+}{\pi }^{+}$
• Baryon spectrum with $N_f=2+1+1$ twisted mass fermions
• Chiral Lagrangian with Heavy Quark-Diquark Symmetry
• Charmed baryons at the physical point in 2+1 flavor lattice QCD
• Charmed-Baryon Spectroscopy from Lattice QCD with N_f=2+1+1 Flavors
• Charmed baryons in lattice QCD
• Charmed baryon spectroscopy and light flavour symmetry from lattice QCD
• Doubly Heavy Baryons, Heavy Quark-DiQuark Symmetry and NRQCD
• Spectroscopy of doubly-charmed baryons from lattice QCD
• Search for doubly charmed baryons and study of charmed strange baryons at Belle
• Implications of Heavy Quark-Diquark Symmetry for Excited Doubly Heavy Baryons and Tetraquarks
• Low-lying baryon masses using $N_f=2$ twisted mass clover-improved fermions directly at the physical point
• Spectroscopy of Doubly-Charmed Baryons in Lattice QCD
• Doubly heavy baryons at LHC
• Baryon Masses in Lattice QCD with Exact Chiral Symmetry
• Lattice QCD study of doubly-charmed strange baryons
• Lifetimes of Doubly Charmed Baryons
• Lattice QCD with $N_f=2+1+1$ domain-wall quarks
• Lifetimes of Doubly Heavy Baryons ${\mathcal{B}}_{bb}$ and ${\mathcal{B}}_{bc}$
• The Direct Coupling of Light Quarks to Heavy Di-quarks
• An Estimate of the Inclusive Branching Ratio to ${\bar{B}}_c$ in ${\Xi }_{bbq}$ Decay

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• One Born$-$Oppenheimer Effective Theory to rule them all: hybrids, tetraquarks, pentaquarks, doubly heavy baryons and quarkonium
• Effective field theory for double heavy baryons at strong coupling
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• Strong decays of the low-lying doubly bottom baryons
• Double Heavy baryons and Corrections to Heavy Quark-Diquark Symmetry Prediction for Hyperfine Splitting
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