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1. Mixed EW-QCD two-loop amplitudes for $$ q\overline{q}\to {\mathrm{\ell}}^{+}{\mathrm{\ell}}^{-} $$ and γ5 scheme independence of multi-loop corrections

   https://doi.org/10.1007/JHEP05(2021)213  

   Heller, Matthias ; von Manteuffel, Andreas ; Schabinger, Robert M. ; Spiesberger, Hubert ( May 2021 , Journal of High Energy Physics)

   null (Ed.)

   A bstract We perform a dedicated study of the $$ q\overline{q} $$ q 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 α and α 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 γ 5 scheme and Kreimer’s anticommuting γ 5 scheme. 

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2. Power expansion for heavy quarkonium production at next-to-leading order in e+e− annihilation

   https://doi.org/10.1007/JHEP09(2020)046  

   Lee, Kyle ; Sterman, George ( September 2020 , Journal of High Energy Physics)

   null (Ed.)

   A bstract We study heavy quarkonium production associated with gluons in e + e − annihilation as an illustration of the perturbative QCD (pQCD) factorization approach, which incorporates the first nonleading power in the energy of the produced heavy quark pair. We show how the renormalization of the four-quark operators that define the heavy quark pair fragmentation functions using dimensional regularization induces “evanescent” operators that are absent in four dimensions. We derive closed forms for short-distance coefficients for quark pair production to next-to-leading order ( $$ {\alpha}_s^2 $$ α s 2 ) in the relevant color singlet and octet channels. Using non-relativistic QCD (NRQCD) to calculate the heavy quark pair fragmentation functions up to v 4 in the velocity expansion, we derive analytical results for the differential energy fraction distribution of the heavy quarkonium. Calculations for $$ {}^3{S}_1^{\left[1\right]} $$ 3 S 1 1 and $$ {}^1{S}_0^{\left[8\right]} $$ 1 S 0 8 channels agree with analogous NRQCD analytical results available in the literature, while several color-octet calculations of energy fraction distributions are new. We show that the remaining corrections due to the heavy quark mass fall off rapidly in the energy of the produced state. To explore the importance of evolution at energies much larger than the mass of the heavy quark, we solve the renormalization group equation perturbatively to two-loop order for the $$ {}^1{S}_0^{\left[8\right]} $$ 1 S 0 8 case. 

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3. Locally finite two-loop QCD amplitudes from IR universality for electroweak production

   https://doi.org/10.1007/JHEP05(2023)242  

   Anastasiou, Charalampos ; Sterman, George ( June 2023 , Journal of High Energy Physics)

   A bstract We describe the implementation of infrared subtractions for two-loop QCD corrections to quark-antiquark annihilation to electroweak final states. The subtractions are given as form-factor integrands whose integrals are known. The resulting subtracted amplitudes are amenable to efficient numerical integration. Our procedure is based on the universality of infrared singularities and requires a relatively limited set of subtractions, whose number grows as the number of two-loop diagrams, rather than with the number of singular regions of integration. 

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4. Two-loop helicity amplitudes for gg → ZZ with full top-quark mass effects

   https://doi.org/10.1007/JHEP05(2021)256  

   Agarwal, Bakul ; Jones, Stephen P. ; von Manteuffel, Andreas ( May 2021 , Journal of High Energy Physics)

   null (Ed.)

   A bstract We calculate the two-loop QCD corrections to gg → ZZ involving a closed top-quark loop. We present a new method to systematically construct linear combinations of Feynman integrals with a convergent parametric representation, where we also allow for irreducible numerators, higher powers of propagators, dimensionally shifted integrals, and subsector integrals. The amplitude is expressed in terms of such finite integrals by employing syzygies derived with linear algebra and finite field techniques. Evaluating the amplitude using numerical integration, we find agreement with previous expansions in asymptotic limits and provide ab initio results also for intermediate partonic energies and non-central scattering at higher energies. 

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5. Mixed EW-QCD leading fermionic three-loop corrections at $$ \mathcal{O} $$(αsα2) to electroweak precision observables

   https://doi.org/10.1007/JHEP03(2021)215  

   Chen, Lisong ; Freitas, Ayres ( March 2021 , Journal of High Energy Physics)

   null (Ed.)

   A bstract Measurements of electroweak precision observables at future electron-position 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 $$ \overline{\mathrm{MS}} $$ MS ¯ . 

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