Approximate NNNLO Higgs cross section from analiticity and resummations

by Giovanni Ridolfi

Tuesday 13 May 2014, 15:00 → 16:00 Europe/Rome

131 (Building C, Ground Floor)

We construct an approximate expression for the cross section for Higgs production in gluon fusion at next-to-next-to-next-to-leading order in $\alpha_s$ ($\alpha_s^3$ relative to leading order) with finite top mass. We argue that an accurate approximation can be constructed by exploiting the analiticity of the cross section in the space of the complex variable $N$, Mellin conjugate to $m_H^2/s$, and the information on its singularity structure coming from large $N$ (soft gluon, Sudakov) and small $N$ (high energy, BFKL) all order resummation. We find that the approximate N$^3$LO result amounts to a correction of $17\%$ to the NNLO QCD cross section for production of a 125~GeV Higgs at the LHC (8~TeV), larger than previously estimated, and it significantly reduces the scale dependence of the NNLO result.