Relation between spin and momentum diffusion coefficients

Determine the precise quantitative relation between the heavy-quark spin-diffusion coefficient and momentum-diffusion coefficient arising from the underlying in-medium color-field correlations, in order to connect heavy-quark transport phenomenology with spin-sensitive observables.

Background

The paper models heavy-quark spin dynamics through rotational Brownian motion and introduces a spin-diffusion coefficient, while conventional heavy-quark transport is characterized by momentum drag and momentum-diffusion coefficients. Both types of transport coefficients are expected to originate from related in-medium color-field correlations, but the paper does not derive their quantitative connection. Establishing this relation would link energy-loss and momentum-diffusion phenomenology to observables such as quarkonium spin alignment and hyperon polarization.

References

The spin-diffusion coefficient is expected to be related to the same underlying in-medium color-field correlations that govern heavy-quark momentum transport, although their quantitative relation is not established here.

— Rotational Brownian Motion and $\mathrm{J/ψ}$ Spin Alignment in Heavy-Ion Collisions  (2609.17486 - Sahoo et al., 15 Sep 2026) in Section 1, Introduction

Our results motivate a systematic study of spin relaxation induced by the chromomagnetic and chromoelectric fields of the medium, which we leave for future work.

— Spin relaxation of heavy quarks from momentum diffusion in the quark-gluon plasma  (2610.01791 - Kumar et al., 1 Oct 2026) in Section 5, Direct chromomagnetic contribution

On the other hand, relativistic extensions of heavy-quark diffusion in the QGP have been investigated previously; incorporating the corresponding relativistic corrections into the present framework is left for future work.

— Spin relaxation of heavy quarks from momentum diffusion in the quark-gluon plasma  (2610.01791 - Kumar et al., 1 Oct 2026) in Section 5, Direct chromomagnetic contribution; Section 6, Conclusion

Nevertheless, the estimates obtained here should be regarded as effective estimates of the Thomas-precession contribution, and a quantitatively complete treatment incorporating the full relativistic diffusion kernel and the space-time evolution of the QGP is left for future work.

— Spin relaxation of heavy quarks from momentum diffusion in the quark-gluon plasma  (2610.01791 - Kumar et al., 1 Oct 2026) in Section 6, Conclusion