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The Higgs Transverse Momentum Distribution at NNLL and its Theoretical Errors

In this letter, we present the NNLL-NNLO transverse momentum Higgs distribution arising from gluon fusion. In the regime $p_\perp\ll m_H$ we include the resummation of the large logs at next to next-to leading order and then match on to the $α_s^2$ fixed order result near $p_\perp \sim m_h$. By utilizing the rapidity renormalization group (RRG) we are able to smoothly match between the resummed, small $p_\perp$ regime and the fixed order regime. We give a detailed discussion of the scale dependence of the result including an analysis of the rapidity scale dependence. Our central value differs from previous results, in the transition region as well as the tail, by an amount which is outside the error band. This difference is due to the fact that the RRG profile allows us to smoothly turn off the resummation.