Massive event-shape distributions at N<sup>2</sup>LL

Alejandro Bris, Vicent Mateu, Moritz Preisser

In a recent paper we have shown how to optimally compute the differential and cumulative cross sections for massive event-shapes at O(ffs) in full QCD. In the present article we complete our study by obtaining resummed expressions for non-recoil-sensitive observables to N2LL + O(ffs) precision. Our results can be used for thrust, heavy jet mass and C-parameter distributions in any massive scheme, and are easily generalized to angularities and other event shapes. We show that the so-called E- and P-schemes coincide in the collinear limit, and compute the missing pieces to achieve this level of accuracy: the P-scheme massive jet function in Soft-Collinear Effective Theory (SCET) and boosted Heavy Quark Effective Theory (bHQET). The resummed expression is subsequently matched into fixed-order QCD to extend its validity towards the tail and fartail of the distribution. The computation of the jet function cannot be cast as the discontinuity of a forward-scattering matrix element, and involves phase space integrals in d = 4 2" dimensions. We show how to analytically solve the renormalization group equation for the P-scheme SCET jet function, which is significantly more complicated than its 2-jettiness counterpart, and derive rapidly-convergent expansions in various kinematic regimes. Finally, we perform a numerical study to pin down when mass effects become more relevant.

Particle Physics
External organisation(s)
Universidad Autónoma de Madrid, Consejo Superior de Investigaciones Científicas (CSIC), Universidad de Salamanca
Journal of High Energy Physics
No. of pages
Publication date
Peer reviewed
Austrian Fields of Science 2012
103012 High energy physics
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