Associated $ZH$ production in gluon fusion process at NLO+NLL

Abstract

We present precise results for invariant mass distributions and inclusive cross-sections, of associated $ZH$ production through gluon fusion in QCD. We include threshold logarithms at next-to-leading-logarithmic (NLL) accuracy and match the results to full next-to-leading-order (NLO) results with exact top-quark mass dependence in the virtual amplitudes. At 13.6 TeV energy at LHC, the NLO+NLL cross-section increases the NLO counterpart by about $20\%$. For differential distributions, at 3000 GeV, the uncertainties arising out of the unphysical renormalization and factorization scales is about $20\%$ for NLO; whereas for the resummed results it is around $12\%$. We also combine these results to the Drell-Yan type results at N$^3$LL and present the most precise results in hadron collisions.