Abstract
Large angle Bhabha scattering cross section and related processes are considered. Standard procedure of calculation of RC with emission of one and two real photons as well as lepton pairs are considered in details. Special attention is paid to the case of radiative large angle Bhabha scattering, where we show the validity of factorization theorem for one loop level RC. This is the basic assumption of the Drell-Yan form of the cross sections when hard particles are detected at large angles. The cases of collinear and semi-collinear kinematics for the final particles are considered explicitly. At the end of the review we consider some contributions to the large angles Bhabha elastic scattering cross section at two loop level. Among them, the emission of two hard photons in collinear and semi-collinear kinematics regions and the contribution of a set of gauge invariant FD of two loop level was calculated.
Similar content being viewed by others
References
V. N. Baier et al., “Inelastic Processes in Quantum Electrodynamics at High Energies,” Phys. Rep. 78, 293 (1981).
A. I. Akhiezer and V. B. Berestetskii, Quantum Electrodynamics (Nauka, Moscow, 1981).
V. B. Berestetskii et al., Quantum Electrodynamics (Nauka, Moscow, 1989).
F. A. Berends et al., “Multiple Bremsstrahlung in Gauge Theories at High Energies. 2. Single Bremsstrahlung,” Nucl. Phys. B 206, 61 (1982).
F. A. Berends et al., “Single Bremsstrahlung Processes in Gauge Theories,” Phys. Lett. B 103, 124 (1981).
V. N. Baier, V. S. Fadin, and V. A. Khoze, “Quasireal Electron Method in High-Energy Quantum Electrodynamics,” Nucl. Phys. B 65, 381 (1973).
P. Kessler, “Sur une Méthode Simplifée de Calcul pour les Processus Relativistes en Electrodynamique Quantique,” Nuovo Cimento 17, 809 (1960).
E. A. Kuraev, N. P. Merenkov, and V. S. Fadin, “The Compton Effect Tensor with Heavy Photon,” Yad. Fiz. 45, 82 (1987) [Sov. J. Nucl. Phys. 45, 486 (1987)]; E. A. Kuraev, N. P. Merenkov, and V. S. Fadin, “Compton Tensor with Heavy Photon,” Preprint INP 86-39 (Nobosibirsk, 1986).
V. N. Gribov et al., “On the Properties of Amplitudes with Logarithmically Increasing Interaction Radius,” Yad. Fiz. 13, 670 (1971) [Sov. J. Nucl. Phys. 13, 381 (1971)].
R. Barbieri, J. A. Mignaco, and E. Remiddi, “Electron Form Factors up to Fourth Order. 1,” Nuovo Cim. A 11, 824 (1972).
E. A. Kuraev and V. S. Fadin, “On Radiative Corrections to e + e − Single Photon Annihilation at High-Energy,” Yad. Fiz. 41, 733 (1985) [Sov. J. Nucl. Phys. 41, 466 (1985)].
A. B. Arbuzov, et al., “Table of Integrals: Asymptotical Expressions for Non-Collinear Kinematics,” arXiv:hep-ph/0703048.
J. Schwinger, Particles, Sources, and Fields, Vol. 2 (Westview, 1998).
B. F. L. Ward et al., “New Results on the Theoretical Precision of the LEP/SLC Luminosity,” Phys. Lett. B 450, 262 (1999), arXiv:hep-ph/9811245; G. Montagna et al., “Light Pair Correction to Bhabha Scattering at Small Angle,” Nucl. Phys. B 547, 39 (1999), arXiv:hep-ph/9811436; W. Beenakker, F. A. Berends, and S. C. van der Marck, “Large Angle Bhabha Scattering,” Nucl. Phys. B 349, 323 (1991); M. Caffo, R. Gatto, and E. Remiddi, “Hard Collinear Photons. High-Energy Radiative Corrections to Bhabha Scattering,” Nucl. Phys. B 252, 378 (1985).
A. B. Arbuzov, “Hard Pair Production in Large Angle Bhabha Scattering,” Nucl. Phys. B 474, 271 (1996).
A. B. Arbuzov, “Peripheral Processes in QED at High Energies,” Fiz. Elem. Chastits At. Yadra 41 (2010).
A. B. Arbuzov, “Structure Function Approach in QED for High Energy Processes,” Fiz. Elem. Chastits At. Yadra 41, 394 (2010); [Phys. Part. Nucl. 41, 394 (2010)].
S. I. Dolinsky et al., “Summary of Experiments with the Neutral Detector at the e + e − Storage Ring VEPP-2M,” Phys. Rep. C 202, 99 (1991).
A. Arbuzov et al., “Small Angle Bhabha Scattering for LEP,” arXiv:hep-ph/9506323.
G. Faldt and P. Osland, “Decorated Box Diagram Contributions to Bhabha Scattering. 1,” Nucl. Phys. B 413, 16 (1994); Nucl. Phys. B 419, 404(E) (1994); arXiv:hep-ph/9304212.
N. P. Merenkov, “Production of Hard e + e − Pairs in e p Collisions at High Energies,” Sov. J. Nucl. Phys. 50, 469 (1989); N. P. Merenkov, “A Study of the Process of Emission of Two Hard Photons in e p Collisions at High Energies,” Sov. J. Nucl. Phys. 48, 1073 (1988).
F. A. Berends et al. [CALKUL Collab.], “Multiple Bremsstrahlung in Gauge Theories at High Energies. 5. The Process e + e − → μ+μ−γγ,” Nucl. Phys. B 264, 243 (1986).
V. V. Sudakov, “Vertex Parts at Very High Energies in Quantum Electrodynamics,” Sov. Phys. JETP 3, 65 (1956).
G. ’t Hooft, and M. J. G. Veltman, “Regularization and Renormalization of Gauge Fields,” Nucl. Phys. B 44, 189 (1972).
A. B. Arbuzov, E. A. Kuraev, and B. G. Shaikhatdenov, “Violation of the Factorization Theorem in Large-Angle Radiative Bhabha Scattering,” Zh. Eksp. Teor. Fiz. 115, 392 (1999) [JETP 88, 213 (1999)]; arXiv:hep-ph/9805308]; JETP 97, 858(E) (2002).
A. Bassetto, M. Ciafaloni, and G. Marchesini, “Jet Structure and Infrared Sensitive Quantities in Perturbative QCD,” Phys. Rep. 100, 201 (1983).
A. B. Arbuzov, E. A. Kuraev, and B. G. Shaikhatdenov, “Second Order Contributions to the Elastic Large-Angle Bhabha Scattering Cross Section. I: All Except 2-Loop Box Diagrams,” Mod. Phys. Lett. A 13, 2305 (1998); arXiv:hep-ph/9806215.
V. A. Smirnov, “Analytical Result for Dimensionally Regularized Massive On-Shell Planar Double Box,” Phys. Lett. B 524, 129 (2002); arXiv:hep-ph/0111160; V. A. Smirnov and O. L. Veretin, “Analytical Results for Dimensionally Regularized Massless On-Shell Double Boxes with Arbitrary Indices and Numerators,” Nucl. Phys. B 566, 469 (2000); arXiv:hep-ph/9907385.
A. B. Arbuzov et al., “Emission of Two Hard Photons in Large-Angle Bhabha Scattering,” Nucl. Phys. B 483, 83 (1997); arXiv:hep-ph/9610228.
V. N. Baier and V. S. Fadin, “Pair Electroproduction Processes in Colliding-Beam Experiments,” Pis’ma Zh. Eksp. Teor. Fiz. 13, 293 (1971) [JETP Lett. 13, 208 (1971)].
W. L. van Neerven and J. A. M. Vermaseren, “Large Loop Integrals,” Phys. Lett. B 137, 241 (1984).
M. Greco et al., “QED Radiative Corrections and Radiative Bhabha Scattering at DAPHNE,” 2nd DAPHNE Physics Handbook (LNF Frascati, 1995), pp. 629–646.
A. B. Arbuzov et al., “Monte-Carlo Generator for e + e − Annihilation into Lepton and Hadron Pairs with Precise Radiative Corrections,” Eur. Phys. J. C 46, 689 (2006).
R. Bonciani and A. Ferroglia, “Two-Loop QED Heavy-Flavor Contribution to Bhabha Scattering,” Nucl. Phys. Proc. Suppl. 183, 181 (2008).
S. Actis et al., “Virtual Hadronic and Heavy-Fermion O(α2) Corrections to Bhabha Scattering,” Phys. Rev. D 78, 085019 (2008).
J. H. Kuhn and S. Uccirati, “Two-Loop QED Hadronic Corrections to Bhabha Scattering,” Nucl. Phys. B 806, 300 (2009); arXiv:0807.1284 [hep-ph].
R. Bonciani, A. Ferroglia, and A. A. Penin, “Calculation of the Two-Loop Heavy-Flavor Contribution to Bhabha Scattering,” JHEP 0802, 080 (2008); arXiv:0802.2215 [hep-ph].
R. Bonciani, “Two-Loop N(F) = 1 QED Bhabha Scattering: Soft Emission and Numerical Evaluation of the Differential Cross Section,” Nucl. Phys. B 716, 280 (2005); arXiv:hep-ph/0411321.
A. A. Penin, “Two-Loop Corrections to Bhabha Scattering,” Phys. Rev. Lett. 95, 010408 (2005).
E. W. N. Glover, J. B. Tausk, and J. J. van der Bij, Second Order Contributions to Elastic Large-Angle Bhabha Scattering, “Phys. Lett. B 516, 33 (2001), arXiv:hep-ph/0106052.
A. A. Penin, “Two-Loop Photonic Corrections to Massive Bhabha Scattering,” Nucl. Phys. B 734, 185 (2006); arXiv:hep-ph/0508127.
R. Bonciani and A. Ferroglia, “Two-Loop Bhabha Scattering in QED,” Phys. Rev. D 72, 056004 (2005); arXiv:hep-ph/0507047.
R. P. Feynman, “Space-Time Approach to Quantum Electrodynamics,” Phys. Rev. 76, 769 (1949).
Author information
Authors and Affiliations
Additional information
The article is published in the original.
Rights and permissions
About this article
Cite this article
Arbuzov, A.B., Bytev, V.V., Kuraev, E.A. et al. Radiative corrections to the Bhabha scattering. Phys. Part. Nuclei 41, 636–689 (2010). https://doi.org/10.1134/S1063779610050023
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063779610050023