S-matrix Approach to the $Z$ Resonance

Riemann, T.

doi:10.5506/aphyspolb.46.2235

Cited by 6 publications

(5 citation statements)

References 14 publications

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“…[1,2,106]. The correct unfolding framework for extracting 2 → 2 observables at accuracies amounting to about 1/20 of the LEP era certainly has to rely on the correct treatment of Laurent series for the Z line shape as is discussed e. g. in [107][108][109][110].…”

Section: Discussionmentioning

confidence: 99%

Complete electroweak two-loop corrections to Z boson production and decay

et al. 2018

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This article presents results for the last unknown two-loop contributions to the Z-boson partial widths and Z-peak cross-section. These are the so-called bosonic electroweak two-loop corrections, where "bosonic" refers to diagrams without closed fermion loops. Together with the corresponding results for the Z-pole asymmetries A l , A b , which have been presented earlier, this completes the theoretical description of Z-boson precision observables at full two-loop precision within the Standard Model. The calculation has been achieved through a combination of different methods: (a) numerical integration of Mellin-Barnes representations with contour rotations and contour shifts to improve convergence; (b) sector decomposition with numerical integration over Feynman parameters; (c) dispersion relations for sub-loop insertions. Numerical results are presented in the form of simple parameterization formulae for the total width, Γ Z , partial decay widths Γ e,µ , Γ τ , Γ ν , Γ u , Γ c , Γ d,s , Γ b , branching ratios R l , R c , R b and the hadronic peak cross-section, σ 0 had . Theoretical intrinsic uncertainties from missing higher orders are also discussed.

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Section: Discussionmentioning

confidence: 99%

Complete electroweak two-loop corrections to Z boson production and decay

et al. 2018

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“…It was first studied in Refs. [38][39][40][41], but its extension beyond two-loop level will require more work [8,42,43]. The numerically relevant two-loop and partial higher-order corrections were included in the final analysis of LEP 1 data [44].…”

Section: Introductionmentioning

confidence: 99%

Electroweak pseudo-observables and Z-boson form factors at two-loop accuracy

Dubovyk

Freitas

Gluza

et al. 2019

J. High Energ. Phys.

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We present Standard Model predictions for the complete set of phenomenologically relevant electroweak precision pseudo-observables related to the Zboson: the leptonic and bottom-quark effective weak mixing angles sin 2 θ eff , sin 2 θ b eff , the Z-boson partial decay widths Γ f , where f indicates any charged lepton, neutrino and quark flavor (except for the top quark), as well as the total Z decay width Γ Z , the branching ratios R , R c , R b , and the hadronic cross section σ 0 had . The input parameters are the masses M Z , M H and m t , and the couplings α s , α. The scheme dependence due to the choice of M W or its alternative G µ as a last input parameter is also discussed. Recent substantial technical progress in the calculation of Minkowskian massive higher-order Feynman integrals allows the calculation of the complete electroweak two-loop radiative corrections to all the observables mentioned. QCD contributions are included appropriately. Results are provided in terms of simple and convenient parameterization formulae whose coefficients have been determined from the full numerical multi-loop calculation. The size of the missing electroweak three-loop or QCD higher-order corrections is estimated. We briefly comment on the prospects for their calculation. Finally, direct predictions for the Zf f vector and axial-vector form-factors are given, including a discussion of separate order-by-order contributions.

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“…In general, it might be more consistent to work with only one amplitude and to understand photonic corrections a a part of background. Then, nevertheless it makes sense to calculate those parts of the photonic backgound with a precision needed by experiment, and to separate this from the unknown parts of the background, as was discussed in [17].…”

Section: Pos(ll2016)075mentioning

confidence: 99%

“…A relatively simple version was offered with the interface ZUSMAT of ZFIT-TER. This interface was finally replaced by a call to the independent Fortran package SMATASY [13,14,30,31,32,33,17]. It is not the intention here to describe details of the approach.…”

Section: Pos(ll2016)075mentioning

confidence: 99%

30 years, 750 integrals, and 1 desert

Dubovyk¹,

Freitas²,

Gluza³

et al. 2016

Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2016)

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The one-loop corrections to the weak mixing angle sin 2 θ b eff , derived from the Zbb vertex, are known since 1985. It took another 30 years to calculate the complete electroweak two-loop corrections to sin 2 θ b eff . The main obstacle was the calculation of the O(700) bosonic two-loop vertex integrals with up to three mass scales, at s = M 2 Z . We did not perform the usual integral reduction and master evaluation, but chose a completely numerical approach, using two different calculational chains. One method relies on publicly available sector decomposition implementations. Further, we derived Mellin-Barnes (MB) representations, exploring the publicly available MB suite. We had to supplement the MB suite by two new packages: AMBRE 3, a Mathematica program, for the efficient treatment of non-planar integrals and MBnumerics for advanced numerics in the Minkowskian space-time. Our preliminary result for LL2016, the "dessert", for the electroweak bosonic two-loop contributions to sin 2 θ b eff is:This contribution is about a quarter of the corresponding fermionic corrections and of about the same magnitude as several of the known higher-order QCD corrections. The sin 2 θ b eff is now predicited in the Standard Model with a relative error of 10 −4 [1].

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S-matrix Approach to the $Z$ Resonance

Cited by 6 publications

References 14 publications

Complete electroweak two-loop corrections to Z boson production and decay

Complete electroweak two-loop corrections to Z boson production and decay

Electroweak pseudo-observables and Z-boson form factors at two-loop accuracy

30 years, 750 integrals, and 1 desert

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