Boosted Higgs Shapes

The inclusive Higgs production rate through gluon fusion has been measured to be in agreement with the Standard Model (SM). We show that even if the inclusive Higgs production rate is very SM-like, a precise determination of the boosted Higgs transverse momentum shape offers the opportunity to see effects of natural new physics. These measurements are generically motivated by effective field theory arguments and specifically in extensions of the SM with a natural weak scale, like composite Higgs models and natural supersymmetry. We show in detail how a measurement at high transverse momentum of $H\to 2\ell+\mathbf{p}\!\!/_T$ via $H\to \tau\tau$ and $H\to WW^*$ could be performed and demonstrate that it offers a compelling alternative to the $t\bar t H$ channel. We discuss the sensitivity to new physics in the most challenging scenario of an exactly SM-like inclusive Higgs cross-section.