We show that the Laurent series of the two-loop kite integral in D = 4 − 2ε space-time dimensions can be expressed in each order of the series expansion in terms of elliptic generalisations of (multiple) polylogarithms. Using differential equations we present an iterative method to compute any desired order. As an example, we give the first three orders explicitly.
We study the analytic continuation of Feynman integrals from the kite family, expressed in terms of elliptic generalisations of (multiple) polylogarithms. Expressed in this way, the Feynman integrals are functions of two periods of an elliptic curve. We show that all what is required is just the analytic continuation of these two periods. We present an explicit formula for the two periods for all values of t ∈ R. Furthermore, the nome q of the elliptic curve satisfies over the complete range in t the inequality |q| ≤ 1, where |q| = 1 is attained only at the singular points t ∈ {m 2 , 9m 2 , ∞}. This ensures the convergence of the q-series expansion of the ELi-functions and provides a fast and efficient evaluation of these Feynman integrals.
We compute the mixed QCD-electroweak corrections to the cross section for the production of a Higgs boson via gluon fusion, in the limit of a small mass of the electroweak gauge bosons. This limit is regular and we calculate it by setting the W, Z masses to zero in the Feynman rules for their propagators. Our analytic results provide an independent check, in a non-trivial limit, of a recent exact computation for the three-loop mixed QCD and electroweak virtual corrections [1] and the corresponding contribution to the cross section in the soft-virtual approximation [2]. From our calculation in the small mass approximation, we can infer the second term in the expansion of the cross section around the threshold limit with its exact dependence on the masses of the W, Z bosons. Furthermore we find that in the small mass approximation the non-factorizable contributions from the real radiation, so far unknown for full gauge boson mass dependence, are modest in comparison to the known factorizable and virtual contributions to the full O(α 3 s α 2 ) mixed QCD and electroweak cross-section. This furnishes a new phenomenological test of estimates [3] for the mixed QCD and electroweak corrections, which were based on the hypothesis of factorization of QCD and electroweak corrections.
We compute mixed QCD-weak corrections to inclusive Higgs production at the LHC from the partonic process gg → Hqq. We start from the UV-and IR-finite one-loop weak amplitude and consider its interference with the corresponding one-loop QCD amplitude. This contribution is a O(α s α) correction to the leading-order gluon-fusion cross section, and was not numerically assessed in previous works. We also compute the cross section from the square of this weak amplitude, suppressed by O(α 2 ). Finally, we consider contributions from the partonic process gq → Hq, which are one order lower in α s , as a reference for the size of terms which are not enhanced by the large gluon luminosity. We find that, given the magnitude of the uncertainties on current state-of-the-art predictions for Higgs production, all contributions computed in this work can be safely ignored, both fully inclusively and in the boosted Higgs regime. This result supports the approximate factorisation of QCD and weak corrections to that process.
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