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Doubly heavy baryons $\left(QQq\right)$ and singly heavy antimesons$\left(\bar{Q}q\right)$ are related by the heavy quark-diquark (HQDQ) symmetrybecause in the $m_Q \to \infty$ limit, the light degrees of freedom in both thehadrons are expected to be in identical configurations. Hyperfine splittings ofthe ground states in both systems are nonvanishing at $O(1/m_Q)$ in the heavyquark mass expansion and HQDQ symmetry relates the hyperfine splittings in thetwo sectors. In this paper, working within the framework of Non-RelativisticQCD (NRQCD), we point out the existence of an operator that couples four heavyquark fields to the chromomagnetic field with a coefficient that is enhanced bya factor from Coulomb exchange. This operator gives a correction to doublyheavy 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. Thiscorrection can be calculated analytically in the extreme heavy quark limit inwhich the potential between the quarks in the diquark is Coulombic. In thislimit, the correction is $O(\alpha_s^2/m_Q)$ and comes with a smallcoefficient. For values of $\alpha_s$ relevant to doubly charm and doublybottom systems, the correction to the hyperfine splittings in doubly heavybaryons is only a few percent or smaller. We also argue that nonperturbativecorrections to the prediction for the hyperfine splittings are suppressed by$\Lambda^2_{\rm QCD}/m_Q^2$ rather than $\Lambda_{\rm QCD}/m_Q$. Correctionsshould be $\approx 10\%$ in the charm sector and smaller in heavier systems.

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