  We study the effect of multiple parton radiation to Higgs boson plus jet
production at the LHC, by applying the transverse momentum dependent (TMD)
factorization formalism to resum large logarithmic contributions to all orders
in the expansion of the strong interaction coupling. We show that the
appropriate resummation scale should be the jet transverse momentum, rather
than the partonic center of mass energy which has been normally used in the TMD
resummation formalism. Furthermore, the transverse momentum distribution of the
Higgs boson, particularly near the lower cut-off applied on the jet transverse
momentum, can only be reliably predicted by the resummation calculation which
is free of the so-called Sudakov-shoulder singularity problem, present in
fixed-order calculations.
