Perturbative corrections to heavy quark-diquark symmetry predictions for doubly heavy baryon hyperfine splittings
Doubly heavy baryons (QQq) and singly heavy antimesons (Qq) are related by the heavy quark-diquark (HQDQ) symmetry because in the mQ→∞ limit, the light degrees of freedom (d.o.f.) 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/mQ) 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 nonrelativistic 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/mQ2×αS/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(αs2/mQ) and comes with a small coefficient. For values of αs 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 ΛQCD2/mQ2 rather than ΛQCD/mQ. Corrections should be ≈10% in the charm sector and smaller in heavier systems.
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