Abstract
In this work we complete the investigation of the recently introduced energy-energy correlation (EEC) function in hadronic Higgs decays at next-to-leading order (NLO) in fixed-order perturbation theory in the limit of vanishing light quark masses. The full analytic NLO result for the previously unknown EEC in the H → qoverline{q} + X channel is given in terms of classical polylogarithms and cross-checked against a numerical calculation. In addition to that, we discuss further corrections to predictions of the Higgs EEC event shape variable, including quark mass corrections, effects of parton shower and hadronization. We also estimate the statistical error on the measurements of the Higgs EEC at future Higgs factories and compare with the current perturbative uncertainty.
Highlights
Worth noting that by making use of the AdS/CFT duality in N = 4 SYM one can obtain a strong-coupling limit result for the EEC [26, 27]
The existence of numerical NNLO results [36, 46] as well as the availability of public codes (e.g. Event 2 [50, 51], NLOJet++ [52, 53], Eerad3 [54]) capable of evaluating the EEC numerically greatly facilitate the cross-checks of new analytic results
In [18] it was suggested that a new event shape variable, denoted as the Higgs EEC, could provide an intriguing connection between the strong and the Higgs sectors by defining an observable accessible to experimentalists analyzing the data from a future Higgs factory and to theorists calculating the corresponding predictions
Summary
Our calculation essentially follows the path that has already been outlined in [17] and explained in details in [18], so that we keep the following description short. We need to obtain matrix elements squared |M(H → qq + X)|2 for real, double-real and real-virtual corrections to the Higgs decaying into a quark-antiquark pair. The real and double-real contributions follow directly from squaring the corresponding tree-level amplitudes with 3- or 4-parton final states respectively. The real-virtual piece follows from the interference of the tree-level and 1-loop 3-parton final states. In the case of a 4-parton final state, one subtopology gives rise to 6 integral families, stemming from the parton pairs (1, 2), 1The IR safety of the EEC observable guarantees the absence of 1/εIR poles in the final result but not in the intermediate results. The most complicated double-real piece stemming from the qqgg final state involves 3 following subtopologies. Upon adding all contributions together and carrying out the UV-renormalization of the real-virtual contribution, we end up with a manifestly finite result, as expected from the IR-safe property of the EEC event shape variables
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