Updated Higgs cross section at approximate N$^3$LO
  We update our estimate of the cross section for Higgs production in gluon fusion at next-to-next-to-next-to-leading order (N$^3$LO) in $\alpha_s$ in view of the recent full computation of the result in the soft limit for infinite top mass, which determines a previously unknown constant. We briefly discuss the phenomenological implications. Results are available through the updated version of the ggHiggs code. 
Marco Bonvini, Richard D. Ball, Stefano Forte, Simone Marzani,   Giovanni Ridolfi
hep-ph hep-ex