Kinematical limits on Higgs boson production via gluon fusion in association with jets

In this paper, we analyze the high-energy limits for Higgs boson $+$ two jet production. We consider two high-energy limits, corresponding to two different kinematic regions: (a) the Higgs boson is centrally located in rapidity between the two jets, and very far from either jet; (b) the Higgs boson is close to one jet in rapidity, and both of these are very far from the other jet. In both cases the amplitudes factorize into impact factors or coefficient functions connected by gluons exchanged in the t channel. Accordingly, we compute the coefficient function for the production of a Higgs boson from two off-shell gluons, and the impact factors for the production of a Higgs boson in association with a gluon or a quark jet. We include the full top quark mass dependence and compare this with the result obtained in the large top-mass limit.