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Register a new userMixed EW-QCD two-loop amplitudes for $qbar{q} to ell^+ell^-$ and $gamma_5$ scheme independence of multi-loop corrections
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We perform a dedicated study of the $q bar{q}$-initiated two-loop electroweak-QCD Drell-Yan scattering amplitude in dimensional regularization schemes for vanishing light quark and lepton masses. For the relative order $alpha$ and $alpha_s$ one-loop Standard Model corrections, details of our comparison to the original literature are given. The infrared pole terms of the mixed two-loop amplitude are governed by a known generalization of the dipole formula and we show explicitly that exactly the same two-loop polarized hard scattering functions are obtained in both the standard t Hooft-Veltman-Breitenlohner-Maison $gamma_5$ scheme and Kreimers anticommuting $gamma_5$ scheme.
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We compute the one-loop QCD amplitudes for the decay of an off-shell vector boson with vector couplings into a quark-antiquark pair accompanied by two gluons keeping, for the first time, all orders in the number of colours. Together with previous work this completes the calculation of the necessary one-loop amplitudes needed for the calculation of the next-to-leading order O(alpha_s^3) corrections to four jet production in electron-positron annihilation, the production of a gauge boson accompanied by two jets in hadron-hadron collisions and three jet production in deep inelastic scattering.
We calculate the long-distance effect generated by the four-quark operators with $c$-quarks in the $Bto K^{(*)} ell^+ell^-$ decays. At the lepton-pair invariant masses far below the $bar{c}c$-threshold, $q^2ll 4m_c^2$, we use OPE near the light-cone. The nonfactorizable soft-gluon emission from $c$-quarks is cast in the form of a nonlocal effective operator. The $Bto K^{(*)}$ matrix elements of this operator are calculated from the QCD light-cone sum rules with the $B$-meson distribution amplitudes. As a byproduct, we also predict the charm-loop contribution to $Bto K^*gamma$ beyond the local-operator approximation. To describe the charm-loop effect at large $q^2$, we employ the hadronic dispersion relation with $psi=J/psi,psi (2S), ...$ contributions, where the measured $ Bto K^{(*)}psi $ amplitudes are used as inputs. Matching this relation to the result of QCD calculation reveals a destructive interference between the $J/psi$ and $psi(2S)$ contributions. The resulting charm-loop effect is represented as a $q^2$-dependent correction $Delta C_9(q^2)$ to the Wilson coefficient $C_9$. Within uncertainties of our calculation, at $q^2$ below the charmonium region the predicted ratio $Delta C_9(q^2)/C_9$ is $leq 5% $ for $Bto K ell^+ell^-$, but can reach as much as 20% for $Bto K^*ell^+ell^-$, the difference being mainly caused by the soft-gluon contribution.
In this talk we review the recent computation of the five- and six-gluon two-loop amplitudes in Yang-Mills theory using local integrands which make the infrared pole structure manifest. We make some remarks on the connection with BCJ relations and the all-multiplicity structure.
Measurements of electroweak precision observables at future electron-positron colliders, such as the CEPC, FCC-ee, and ILC, will be sensitive to physics at multi-TeV scales. To achieve this sensitivity, precise predictions for the Standard Model expectations of these observables are needed, including corrections at the three- and four-loop level. In this article, results are presented for the calculation of a subset of three-loop mixed electroweak-QCD corrections, stemming from diagrams with a gluon exchange and two closed fermion loops. The numerical impact of these corrections is illustrated for a number of applications: the prediction of the W-boson mass from the Fermi constant, the effective weak mixing angle, and the partial and total widths of the Z boson. Two alternative renormalization schemes for the top-quark mass are considered, on-shell and $overline{mbox{MS}}$.
A summary is presented of the most recent matrix elements for massless 2 to 2 scattering processes calculated at two loops in QCD perturbation theory together with a brief review on the calculational methods and techniques used.
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