Soft gluon resummation for gluon fusion <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>Z</mml:mi> <mml:mi>H</mml:mi> </mml:math> production

We examine the effects of soft gluons on Higgs boson production in association with a Z boson at the Large Hadron Collider (LHC). Utilizing the universal cusp anomalous dimensions and splitting kernels, we analyze effects of soft gluons on the gluon fusion Z H process, focusing on the total production cross section as well as the invariant mass distribution at the next-to-leading logarithmic level. Additionally, we estimate the next-to-soft effects on this subprocess to the same level of accuracy. A detailed phenomenological analysis is performed for the 13.6 TeV LHC. Finally, combining these results with those from other subprocesses, we provide comprehensive predictions for the Z H production cross section and the invariant mass distribution that will be valuable for comparison with experimental data from the upcoming LHC run as well as the future hadron colliders.