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Title: Two-loop QED corrections to Bhabha scattering

Authors:
; ; ;
Publication Date:
Research Org.:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
910193
Report Number(s):
FERMILAB-PUB-07-060-T
arXiv eprint number arXiv:0704.3582
DOE Contract Number:
AC02-07CH11359
Resource Type:
Journal Article
Resource Relation:
Journal Name: JHEP 0706:084,2007
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Phenomenology-HEP

Citation Formats

Becher, Thomas, /Fermilab, Melnikov, Kirill, and /Hawaii U. Two-loop QED corrections to Bhabha scattering. United States: N. p., 2007. Web. doi:10.1088/1126-6708/2007/06/084.
Becher, Thomas, /Fermilab, Melnikov, Kirill, & /Hawaii U. Two-loop QED corrections to Bhabha scattering. United States. doi:10.1088/1126-6708/2007/06/084.
Becher, Thomas, /Fermilab, Melnikov, Kirill, and /Hawaii U. Sun . "Two-loop QED corrections to Bhabha scattering". United States. doi:10.1088/1126-6708/2007/06/084.
@article{osti_910193,
title = {Two-loop QED corrections to Bhabha scattering},
author = {Becher, Thomas and /Fermilab and Melnikov, Kirill and /Hawaii U.},
abstractNote = {},
doi = {10.1088/1126-6708/2007/06/084},
journal = {JHEP 0706:084,2007},
number = ,
volume = ,
place = {United States},
year = {Sun Apr 01 00:00:00 EDT 2007},
month = {Sun Apr 01 00:00:00 EDT 2007}
}
  • In the context of pure QED, we obtain analytic expressions for the contributions to the Bhabha scattering differential cross section at order {alpha}{sup 4}, which originate from the interference of two-loop photonic vertices with tree-level diagrams and from the interference of one-loop photonic diagrams amongst themselves. The ultraviolet renormalization is carried out. The IR-divergent soft-photon emission corrections are evaluated and added to the virtual cross section. The cross section obtained in this manner is valid for on-shell electrons and positrons of finite mass and for arbitrary values of the center of mass energy and momentum transfer. We provide the expansionmore » of our results in powers of the electron mass, and we compare them with the corresponding expansion of the complete order {alpha}{sup 4} photonic cross section, recently obtained by A. A. Penin [Phys. Rev. Lett. 95, 010408 (2005).]. As a by-product, we obtain the contribution to the Bhabha scattering differential cross section of the interference of the two-loop photonic boxes with the tree-level diagrams, up to terms suppressed by positive powers of the electron mass. We evaluate numerically the various contributions to the cross section, paying particular attention to the comparison between exact and expanded results.« less
  • We present a set of scalar master integrals (MIs) needed for a complete treatment of massive two-loop corrections to Bhabha scattering in QED, including integrals with arbitrary fermionic loops. The status of analytical solutions for the MIs is reviewed and examples of some methods to solve MIs analytically are worked out in more detail. Analytical results for the pole terms in {epsilon} of so far unknown box MIs with five internal lines are given.
  • The two-loop radiative photonic corrections to Bhabha scattering are computed in the leading order of the small electron mass expansion up to the nonlogarithmic term. After including the soft photon bremsstrahlung, we obtain the infrared-finite result for the differential cross section, which can directly be applied to a precise luminosity determination of the present and future e{sup +}e{sup -} colliders.
  • We present the two-loop virtual QED corrections to e{sup +}e{sup -}{yields}{mu}{sup +}{mu}{sup -} and Bhabha scattering in dimensional regularization. The results are expressed in terms of polylogarithms. The form of the infrared divergences agrees with previous expectations. These results are a crucial ingredient in the complete next-to-next-to-leading order QED corrections to these processes. A future application will be to reduce theoretical uncertainties associated with luminosity measurements at e{sup +}e{sup -} colliders. The calculation also tests methods that may be applied to analogous QCD processes.