Resummation properties of jet vetoes at the LHC

Abstract

Jet vetoes play an important role at the LHC in the search for the Higgs and ultimately in precise measurements of its properties. Many Higgs analyses divide the cross section into exclusive jet bins to maximize the sensitivity in different production and decay channels. For a given jet category, the veto on additional jets introduces sensitivity to soft and collinear emissions, which causes logarithms in the perturbative expansion that need to be resummed to obtain precise predictions. We study the higher-order resummation properties of several conceptually distinct kinematic variables that can be used to veto jets in hadronic collisions. We consider two inclusive variables, the scalar sum over ${p}_{T}$ and beam thrust, and two corresponding exclusive variables based on jet algorithms, namely, the largest ${p}_{T}$ and largest beam thrust of a jet. The inclusive variables can, in principle, be resummed to higher orders. We show that for the jet-based variables, there are dual effects due to clustering in the jet algorithm for both large and small jet radius $R$ that make a complete resummation at or beyond next-to-leading logarithmic order challenging. For $R\ensuremath{\sim}1$, the clustering of soft and collinear emissions gives $\mathcal{O}(1)$ contributions starting at next-to-next-to-leading logarithm that are not reproduced by an all-orders soft-collinear factorization formula and therefore are not automatically resummed by it. For $R\ensuremath{\ll}1$, clustering induces logarithms of $R$ that contribute at next-to-leading logarithm in the exponent of the cross section, which cannot be resummed with currently available methods. We explicitly compute the leading jet clustering effects at $\mathcal{O}({\ensuremath{\alpha}}_{s}^{2})$ and comment on their numerical size.