Virtual Hadronic and Heavy-Fermion O(alpha^2) Corrections to Bhabha Scattering

Abstract

Effects of vacuum polarization by hadronic and heavy-fermion insertions were the last unknown two-loop QED corrections to high-energy Bhabha scattering and have been first announced in \cite{Actis:2007fs}. Here we describe the corrections in detail and explore their numerical influence. The hadronic contributions to the virtual O(alpha^2) QED corrections to the Bhabha-scattering cross-section are evaluated using dispersion relations and computing the convolution of hadronic data with perturbatively calculated kernel functions. The technique of dispersion integrals is also employed to derive the virtual O(alpha^2) corrections generated by muon-, tau- and top-quark loops in the small electron-mass limit for arbitrary values of the internal-fermion masses. At a meson factory with 1 GeV center-of-mass energy the complete effect of hadronic and heavy-fermion corrections amounts to less than 0.5 per mille and reaches, at 10 GeV, up to about 2 per mille. At the Z resonance it amounts to 2.3 per mille at 3 degrees; overall, hadronic corrections are less than 4 per mille. For ILC energies (500 GeV or above), the combined effect of hadrons and heavy-fermions becomes 6 per mille at 3 degrees; hadrons contribute less than 20 per mille in the whole angular region.

arXiv comment38 pages, LaTeX, 21 figures

References in corpus (87)

• The Cosmological Parameters 2006
• Big-Bang nucleosynthesis (Particle Data Group mini-review)
• The Precision Monte Carlo Event Generator KK For Two-Fermion Final States In e+e- Collisions
• JaxoDraw: A graphical user interface for drawing Feynman diagrams
• Numerical evaluation of multiple polylogarithms
• Automatized analytic continuation of Mellin-Barnes integrals
• HPL, a Mathematica implementation of the harmonic polylogarithms
• Hadronic contributions to $(g-2)$ of the leptons and to the effective fine structure constant $\alpha (M_Z^2)$
• Precise Prediction for the W-Boson Mass in the Standard Model
• BHWIDE 1.00: O(alpha) YFS Exponentiated Monte Carlo for Bhabha Scattering at Wide Angles for LEP1/SLC and LEP2
• Improved predictions for g-2 of the muon and α_{\rm QED}(M_Z^2)
• Confronting Spectral Functions from e+e- Annihilation and tau Decays: Consequences for the Muon Magnetic Moment
• ZFITTER v.6.21 - A Semi-Analytical Program for Fermion Pair Production in e+e- Annihilation
• Matching perturbative and Parton Shower corrections to Bhabha process at flavour factories
• Predictions for g-2 of the muon and alpha_QED(M_Z^2)
• AMBRE - a Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals
• The singular behavior of massive QCD amplitudes
• Extension of HPL to complex arguments
• ZFITTER: a semi-analytical program for fermion pair production in e+e- annihilation, from version 6.21 to version 6.42
• Two-loop QED corrections to Bhabha scattering
• Leptonic contribution to the effective electromagnetic coupling constant up to three loops
• Large-angle Bhabha scattering and luminosity at flavour factories
• Electroweak two-loop corrections to the effective weak mixing angle
• Two-Loop Correction to Bhabha Scattering
• Two-Loop Photonic Corrections to Massive Bhabha Scattering
• Analytical Result for Dimensionally Regularized Massive On-Shell Planar Double Box
• Large angle QED processes at e^+e^- colliders at energies below 3 GeV
• Monte-Carlo generator for e+e- annihilation into lepton and hadron pairs with precise radiative corrections
• Precision measurements of sigma_hadronic for alpha_eff(E) at ILC energies and (g-2)_mu
• Two-Loop Corrections to Bhabha Scattering
• Master integrals for massive two-loop Bhabha scattering in QED
• Rhad: A program for the evaluation of the hadronic R-ratio in the perturbative regime of QCD
• Precision calculation for e+ e- -> 2f: the KK MC project
• An Improved Parton Shower algorithm in QED
• Analytical Evaluation of Dimensionally Regularized Massive On-Shell Double Boxes
• QED vertex form factors at two loops
• Four-Fermion Production in Electron-Positron Collisions
• BHAGEN95: a Monte Carlo program for Bhabha scattering at LEP1/SLC and LEP2 energies
• ZFITTER -- An Analytical Program for Fermion Pair Production in e+e- Annihilation
• Planar box diagram for the (N_F = 1) 2-loop QED virtual corrections to Bhabha scattering
• Low energy hadronic contribution to the QED vacuum polarization
• Hadronic Contributions to the Muon Lifetime
• BHAGENE3, a Monte Carlo Event Generator for Lepton Pair Production and Wide Angle Bhabha Scattering in $e^{+}{e}^{-}$ Collisions Near the Z-Peak
• Two-Loop N_F=1 QED Bhabha Scattering Differential Cross Section
• Small-Angle Electron-Positron Scattering with a Per Mille Accuracy
• The planar four-point master integrals for massive two-loop Bhabha scattering
• Virtual Hadronic and Leptonic Contributions to Bhabha Scattering
• Two-Loop Fermionic Corrections to Massive Bhabha Scattering
• Two-Loop Heavy-Flavor Contribution to Bhabha Scattering
• Elektroweak one-loop corrections for e^+e^- annihilation into t\bar{t} including hard bremsstrahlung
• Second order contributions to elastic large-angle Bhabha scattering
• Two-Loop N_F =1 QED Bhabha Scattering: Soft Emission and Numerical Evaluation of the Differential Cross-section
• Two-Loop Bhabha Scattering in QED
• The running of the electromagnetic coupling alpha in small-angle Bhabha scattering
• The Monte Carlo Program KORALZ, for the Lepton or Quark Pair Production at LEP/SLC Energies -- From version 4.0 to version 4.04
• Calculation of the Two-Loop Heavy-Flavor Contribution to Bhabha Scattering
• Second order contributions to elastic large-angle Bhabha scattering cross-section
• A complete set of scalar master integrals for massive 2-loop Bhabha scattering: where we are
• Light Pair Correction to Bhabha Scattering at Small Angle
• Exact O(alpha) Corrections to the Single Hard Bremsstrahlung Process in Low Angle Bhabha Scattering in the SLC/LEP Energy Regime
• SABSPV - A Monte Carlo Integrator for Small-Angle Bhabha Scattering
• First order radiative corrections to Bhabha scattering in $d$ dimensions
• Large-Angle Bhabha Scattering at LEP 1
• Matrix elements and Parton Shower in the event generator BABAYAGA
• Next-to-leading order corrections to Bhabha scattering in renormalization group approach (I). Soft and virtual photonic contributions
• Automated calculations for massive fermion production with aITALC
• Precision Calculation of Bhabha Scattering at LEP
• Automated use of DIANA for two-fermion production at colliders
• Emission of Two Hard Photons in Large-Angle Bhabha Scattering
• Pentagon diagrams of Bhabha scattering
• Planar two-loop master integrals for massive Bhabha scattering: N_f=1 and N_f=2
• Small-Angle Bhabha Scattering
• Small-Angle Electron-Positron Scattering
• BHAGEN-1PH: A Monte Carlo event generator for radiative Bhabha scattering
• Small-Angle Bhabha Scattering at LEP1. Analytical Results for Wide-Narrow Angular Acceptance
• Investigation of vacuum polarization in t-channel radiative Bhabha scattering
• Simulation of the process $e^{+}{e}^{-}\mapsto e^{+}{e}^{-}\gamma$ within electroweak theory with longitudinally polarized initial electrons
• LABSMC: Monte Carlo event generator for large-angle Bhabha scattering
• Virtual Hadronic Corrections to Massive Bhabha Scattering
• Two-loop QED Corrections to Bhabha Scattering
• Bhabha Process at LEP - Theoretical Calculations
• Exact Results on O(alpha^2) Single Bremsstrahlung Corrections to Low Angle Bhabha Scattering at LEP/SLC Energies
• Violation of the factorization theorem in large angle radiative Bhabha scattering
• On Large-Angle Bhabha Scattering at LEP
• Small Angle Bhabha Scattering for LEP
• Large-angle Bhabha scattering and luminosity at Daphne
• Radiative large-angle Bhabha scattering in collinear kinematics

Cited by in corpus (15)

• Quest for precision in hadronic cross sections at low energy: Monte Carlo tools vs. experimental data
• Two-Loop Planar Corrections to Heavy-Quark Pair Production in the Quark-Antiquark Channel
• Improved Bhabha cross section at LEP and the number of light neutrino species
• Revisiting Neutrino Self-Interaction Constraints from $Z$ and $\tau$ decays
• Numerical Evaluation of Tensor Feynman Integrals in Euclidean Kinematics
• The QCD form factor of heavy quarks at NNLO
• The Path to $0.01\%$ Theoretical Luminosity Precision for the FCC-ee
• Numerical multi-loop integrals and applications
• NLO QED Corrections to Hard-Bremsstrahlung Emission in Bhabha Scattering
• Efficient Evaluation of Massive Mellin--Barnes Integrals
• NNLO leptonic and hadronic corrections to Bhabha scattering and luminosity monitoring at meson factories
• NNLO massive corrections to Bhabha scattering and theoretical precision of BabaYaga@NLO
• Discriminating the HTM and MLRSM models in collider studies via doubly charged Higgs boson pair production and the subsequent leptonic decays
• Full $\mathcal{O}(\alpha )$ electroweak radiative corrections to $e^{+}{e}^{-}\to e^{+}{e}^{-}\gamma$ at the ILC with GRACE-Loop
• Analytic results for two-loop planar master integrals for Bhabha scattering