Abstract
We derive and solve renormalization group equations that allow for the resummation of subleading power rapidity logarithms. Our equations involve operator mixing into a new class of operators, which we term the “rapidity identity operators”, that will generically appear at subleading power in problems involving both rapidity and virtuality scales. To illustrate our formalism, we analytically solve these equations to resum the power suppressed logarithms appearing in the back-to-back (double light cone) limit of the Energy-Energy Correlator (EEC) in mathcal{N} = 4 super-Yang-Mills. These logarithms can also be extracted to mathcal{O}left({alpha}_s^3right) from a recent perturbative calculation, and we find perfect agreement to this order. Instead of the standard Sudakov exponential, our resummed result for the subleading power logarithms is expressed in terms of Dawson’s integral, with an argument related to the cusp anomalous dimension. We call this functional form “Dawson’s Sudakov”. Our formalism is widely applicable for the resummation of subleading power rapidity logarithms in other more phenomenologically relevant observables, such as the EEC in QCD, the pT spectrum for color singlet boson production at hadron colliders, and the resummation of power suppressed logarithms in the Regge limit.
Highlights
For the result including quarks in QCD was presented in [57]
While this expansion is an inefficient way to compute these subleading terms, which can much more be obtained by performing the full calculation and expanding the result, the ability to systematically compute the terms at each order in the power expansion will allow us to perform an all orders resummation by deriving renormalization group evolution equations in rapidity
In this paper we have shown how to resum subleading power rapidity logarithms using the rapidity renormalization group, and have taken a first step towards a systematic understanding of subleading power corrections to observables exhibiting hierarchies in rapidity scales
Summary
We introduce the EEC observable, and review its structure in the back-toback limit at leading power. For the leading power cross section, dσ(0)/dz, one can derive a factorization formula describing in a factorized manner the contributions of the soft and collinear modes to the EEC in the z → 1 limit [81]. The structure of the power corrections to the beam (jet) functions, and their matching to the parton distributions (fragmentation functions) is interesting, and will be presented in future work, since it is important for a complete understanding of pT at subleading powers These renormalization group evolution equations in both μ and ν allow for a derivation of the all orders structure of logarithms in the z → 1 limit, at leading order in the (1 − z) expansion.
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