e+e− angularity distributions at NNLL′ accuracy

Abstract

We present predictions for the e + e − event shape angularities at NNLL resummed and O(α 2 s ) matched accuracy and compare them to LEP data at center-of-mass energies Q = 91.2 GeV and Q = 197 GeV. We perform the resummation within the framework of Soft-Collinear Effective Theory, and make use of recent results for the two-loop angularity soft function. We determine the remaining NNLL and O(α 2 s ) ingredients from a fit to the EVENT2 generator, and implement a shape function with a renormalon-free gap parameter to model non-perturbative effects. Using values of the strong coupling α s (m Z ) and the universal non-perturbative shift parameter Ω 1 that are consistent with those obtained in previous fits to the thrust and C-parameter distributions, we find excellent agreement between our predictions and the LEP data for all angularities with a ∈ [−1, 0.5]. This provides a robust test of the predictions of QCD, factorization, and the universal scaling of the non-perturbative shift across different angularities. Promisingly, our results indicate that current degeneracies in the {α s (m Z ), Ω 1 } parameter space could be alleviated upon fitting these parameters to experimental data for the angularity distributions.

Generic dijet soft functions at two-loop order: correlated emissions

“…According to the standard counting of logarithms for Sudakov problems (see Table 1), the two-loop expressions of γ S i and d i are needed at next-to-next-to-leading logarithmic (NNLL) accuracy, while the twoloop constants c S i and W S i enter at the NNLL level. SoftSERVE thus allows for increased logarithmic accuracy of SCET resummations, as was shown for the e + e − event-shape angularities in [41], where the improvement was from NLL to NNLL (using preliminary results for the angularity soft function that were published in [42]).…”

Analytic next-to-leading order calculation of energy-energy correlation in gluon-initiated Higgs decays

“…On the theory side, fixed-order numerical predictions at next-to-next-to-leading order (NNLO) accuracy are available for a wide range of event shape observables [24][25][26][27][28]. Regarding the resummation of endpoint divergences, many results at next-to-next-to-leading logarithmic (NNLL) and even NNNLL accuracy can be found in the literature [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43].…”

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“…(6.6) is carried out, retains a small, subleading µ dependence. See [92] for explanation and an alternative expansion that removes this residual µ dependence exactly at every order. ≥ z cut , (m/E J ) α , the resummation is turned off by setting µ = E J .…”