$Z$ boson production in bottom-quark fusion: a study of $b$-mass effects beyond leading order

International audienceWe compute the total cross-section for Z boson production in bottom-quark fusion, applying to this case the method we previously used for Higgs production in bottom fusion. Namely, we match, through the FONLL procedure, the next-to-next-to-leading-log five-flavor scheme result, in which the b quark is treated as a massless parton, with the next-to-leading-order $\mathcal{O}(\alpha _s^3)$ four-flavor scheme computation in which bottom is treated as a massive final-state particle. Also, we add to our formalism the possibility of varying the heavy quark matching scale. The results obtained with the FONLL formalism can thus be compared directly to recent results obtained in various approximations, and used as a proxy to assess and discuss the issues of scale dependence and treatment of heavy quarks. Finally, We use our results in order to improve the prediction for the total Z production cross-section