Radiative corrections to Bhabha scattering at high energies: (II). Hard photon corrections and Monte Carlo treatment

doi:10.1016/0550-3213(88)90651-7

Nuclear Physics B

Volume 304, 1988, Pages 712-748

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Abstract

The cross section for single hard photon bremsstrahlung in Bhabha scattering is presented, and its main qualitative features are reviewed. Subsequently, the structure of a Monte Carlo event generator for Bhabha scattering at LEP/SLC energies, including all one-loop electroweak corrections, is discussed, in which the results on the virtual and soft photon corrections, given in the first paper of this set, are incorporated. Finally, a number of numerical results is presented.

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Cited by (196)

Bhabha scattering at NNLO with next-to-soft stabilisation
2021, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Citation Excerpt :
The one-loop corrections to the radiative matrix element were calculated in [17]. In addition to the work that has been put into the calculation of the matrix elements various Monte-Carlo event generators were developed, combining the matrix elements to physical observables such that non-trivial detector geometries and acceptances can be taken into account [4,18–27]. In particular, the BABAYAGA event generator that is based on the matching of the exact NLO results to a parton shower algorithm has achieved a precision of below 0.1% [28].
A critical subject in fully differential QED calculations originates from numerical instabilities due to small fermion masses that act as regulators of collinear singularities. At next-to-next-to-leading order (NNLO) a major challenge is therefore to find a stable implementation of numerically delicate real-virtual matrix elements. In the case of Bhabha scattering this has so far prevented the development of a fixed-order Monte Carlo at NNLO accuracy. In this paper we present a new method for stabilising the real-virtual matrix element. It is based on the expansion for soft photon energies including the non-universal subleading term calculated with the method of regions. We have applied this method to Bhabha scattering to obtain a stable and efficient implementation within the McMule framework. We therefore present for the first time fully differential results for the photonic NNLO corrections to Bhabha scattering.
Improved Bhabha cross section at LEP and the number of light neutrino species
2020, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
In $e^{+} e^{-}$ collisions, the integrated luminosity is generally measured from the rate of low-angle Bhabha interactions $e^{+} e^{-} \to e^{+} e^{-}$ . In the published LEP results, the inferred theoretical uncertainty of $\pm 0.061 %$ on the predicted rate is significantly larger than the reported experimental uncertainties. We present an updated and more accurate prediction of the Bhabha cross section in this letter, which is found to reduce the Bhabha cross section by about 0.048%, and its uncertainty to $\pm 0.037 %$ . When accounted for, these changes modify the number of light neutrino species (and its accuracy), as determined from the LEP measurement of the hadronic cross section at the Z peak, to $N_{ν} = 2.9963 \pm 0.0074$ . The 20-years-old 2σ tension with the Standard Model is gone.
The path to 0.01% theoretical luminosity precision for the FCC-ee
2019, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
The current status of the theoretical precision for the Bhabha luminometry is critically reviewed and pathways are outlined to the requirement targeted by the FCC-ee precision studies. Various components of the pertinent error budget are discussed in detail – starting from the context of the LEP experiments, through their current updates, up to prospects of their improvements for the sake of the FCC-ee. It is argued that, with an appropriate upgrade of the Monte Carlo event generator BHLUMI and/or other similar MC programs calculating QED effects in the low angle Bhabha process, the total theoretical error of 0.01% for the FCC-ee luminometry can be reached. A new study of the Z and s-channel γ exchanges within the angular range of the FCC-ee luminometer using the BHWIDE Monte Carlo was instrumental in obtaining the above result. Possible ways of BHLUMI upgrade are also discussed.
Full O(α) electroweak radiative corrections to e+e-→e+e-γ at the ILC with GRACE-Loop
2015, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
By using the GRACE-Loop system, we calculate the full $O (α)$ electroweak radiative corrections to the process $e^{+} e^{-} \to e^{+} e^{-} γ$ , which is important for future investigations at the International Linear Collider (ILC). With the GRACE-Loop system, the calculations are checked numerically by three consistency tests: ultraviolet finiteness, infrared finiteness, and gauge-parameter independence. The results show good numerical stability when quadruple precision is used. In the phenomenological results, we find that the electroweak corrections to the total cross section range from $\sim - 4 %$ to $\sim - 21 %$ when $\sqrt{s}$ varies from $250 GeV$ to $1 TeV$ . The corrections also significantly affect the differential cross sections, which are a function of energies and angles of the final state particles. Such corrections will play an important role in the high-precision program at the ILC.
Two-Loop QED Heavy-Flavor Contribution to Bhabha Scattering
2008, Nuclear Physics B - Proceedings Supplements
We briefly review the status of the calculation of next-to-next-to-leading order corrections to large angle Bhabha scattering in pure QED. In particular, we focus on the analytic calculation of the two-loop virtual corrections involving a heavy-flavor fermion loop, which was recently completed. We conclude by assessing the numerical impact of these corrections on the Bhabha scattering cross section at colliders operating at a center of mass energy of 1 GeV and at the future ILC.
Bhabha Scattering at NNLO
2008, Nuclear Physics B - Proceedings Supplements
We review the status of the calculation of next-to-next-to-leading order corrections to large angle Bhabha scattering in pure QED. After discussing the electron-loop and photonic corrections, we focus on the recently calculated two-loop virtual corrections involving an heavy-flavor fermion loop. We conclude by assessing the numerical impact of these corrections on the Bhabha scattering cross section at colliders operating at a center of mass energy of about 1-GeV.

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Nuclear Physics B

Abstract

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Cited by (196)

Bhabha scattering at NNLO with next-to-soft stabilisation

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Full O(α) electroweak radiative corrections to e<sup>+</sup>e<sup>-</sup>→e<sup>+</sup>e<sup>-</sup>γ at the ILC with GRACE-Loop

Two-Loop QED Heavy-Flavor Contribution to Bhabha Scattering

Bhabha Scattering at NNLO