Abstract
In a recent paper we have shown how to optimally compute the differential and cumulative cross sections for massive event-shapes at mathcal{O}left({alpha}_sright) in full QCD. In the present article we complete our study by obtaining resummed expressions for non-recoil-sensitive observables to N2LL + mathcal{O}left({alpha}_sright) 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 far- tail of the distribution. The computation of the jet function cannot be cast as the dis- continuity of a forward-scattering matrix element, and involves phase space integrals in d = 4 − 2ε 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.
Highlights
Since the late 70s, a class of observables called event shapes has been used to test and determine fundamental properties of QCD, most notably to measure the strong coupling
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
When considering heavy quarks in the context of event shapes, depending on the scheme used in their definition the mass sensitivity of the cross section can vary significantly
Summary
Since the late 70s, a class of observables called event shapes has been used to test and determine fundamental properties of QCD (for a review see [1, 2]), most notably to measure the strong coupling. Some technical aspects of the computations are relegated to appendices A and B
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