  We investigate the QCD resummation for the Higgs boson plus a high $P_T$ jet
production with large rapidity separations in proton-proton collisions at the
LHC. The relevant Balitsky-Fadin-Kuraev-Lipatov (BFKL) and Sudakov logs are
identified and resummed. In particular, we apply recent developments of the
transverse momentum dependent factorization formalism in the impact factors,
which provides a systematic framework to incorporate both the BFKL and Sudakov
resummations.
