Abstract
We derive the hard functions for all 2->2 processes in massless QCD up to next-to-next-to-leading order (NNLO) in the strong coupling constant. By employing the known one- and two-loop helicity amplitudes for these processes, we obtain analytic expressions for the ultraviolet and infrared finite, minimally subtracted hard functions, which are matrices in color space. These hard functions will be useful in carrying out higher-order resummations in processes such as dijet and highly energetic top-quark pair production by means of soft-collinear effective theory methods.
Highlights
Account for virtual corrections to the underlying Born amplitudes
The next-to-leading order (NLO) hard functions for such QCD processes were extracted in [10]; these are a necessary ingredient for the resummation of any dijet hadronic process up to next-to-next-to-leading logarithmic (NNLL) accuracy
The goal of the current work is to build on previous results by presenting the complete set of next-to-next-to-leading order (NNLO) hard functions
Summary
A unique hard function is associated to each of the processes listed above These can all be extracted using the two-loop helicity amplitudes calculated in [11,12,13,14,15]. To describe the calculational procedure that goes into doing this, we first introduce some aspects of the color-space formalism of [17], which allows us to treat the different cases with a uniform notation In this formalism the UV-renormalized helicity amplitudes are considered vectors in color space, whose perturbative expansions we define as. We can evaluate (2.15) order-by-order in perturbation theory, defining renormalized amplitudes and expansion coefficients analogous to (2.12) and (2.14) With this notation it is a simple matter to write expressions for the hard functions to NNLO. We find agreement with the results in that work, after we account for differences in notation.
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