Origin of the low-momentum-fraction discrepancy in bottomonium-in-jet spectra

Determine the origin of the systematically excessive low-$z_H$ enhancement in the FJF-based predictions for inclusive $$\Upsilon(1S)$, $$\Upsilon(2S)$, and $$\Upsilon(3S)$ production inside jets after fiducial acceptance corrections, including the possible effects of finite bottom-quark mass corrections and missing higher-order perturbative contributions.

Background

The NLO+LL FJF calculation reproduces the main large-zHz_H features and the qualitative broadening with increasing jet transverse momentum, but it predicts a stronger enhancement at low zHz_H than observed by CMS. The discrepancy persists after implementing the fiducial dimuon acceptance corrections and is observed for the Υ(1S)\Upsilon(1S),Υ(2S)\Upsilon(2S), andΥ(3S)\Upsilon(3S) spectra.

The paper does not identify a definitive cause. It notes that the FJF is derived in the massless limit and omits finite-mass effects, while missing higher-order corrections could also modify fragmentation evolution and the resulting momentum-fraction dependence. A more complete treatment of these effects is therefore needed for a quantitative resolution of the discrepancy.

References

The origin of this discrepancy is not fully understood within the current framework. One possible source is the treatment of heavy-quark mass effects, since the FJF used in this work is derived in the massless limit and finite-mass corrections are not included. In addition, missing higher-order perturbative corrections may affect the fragmentation evolution and the resulting $z_H$ dependence, although contributions from other perturbative ingredients cannot be excluded.

— $Υ(nS)$ Production within Jets at the LHC  (2608.18922 - Ha et al., 19 Aug 2026) in Section 4.3, Comparison with CMS results