Validity of non-perturbative Casimir scaling for the Collins–Soper kernel

Determine whether Casimir scaling between the gluon and quark Collins–Soper kernels remains valid in the non-perturbative regime.

Background

The paper extracts the non-perturbative contribution to the gluon Collins–Soper kernel from double-J/ψJ/\psi production and compares it with quark-kernel extractions by applying Casimir scaling, relating the quark and gluon kernels through their color factors. The comparison is compatible with some recent phenomenological fits but disagrees with an earlier extraction based on a different non-perturbative parametrization.

Because the available phenomenological comparisons do not establish that the scaling relation holds beyond the perturbative region, the authors identify its non-perturbative validity as requiring further investigation.

References

The validity of such scaling thus is not confirmed and calls for further investigation.

— NNLL fit of the transverse-momentum-dependent distribution of unpolarised gluons to LHCb data on $J/ψ$-pair production  (2609.01000 - Boer et al., 1 Sep 2026) in Section 7, Conclusions