Two-loop Bhabha scattering in QED: Vertex and one-loop by one-loop contributions

Journal Article · Thu Sep 01 04:00:00 EDT 2005 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.72.056004· OSTI ID:20711498

Bonciani, R; Ferroglia, A ^[1]

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1. Fakultaet fuer Mathematik und Physik, Albert-Ludwigs-Universitaet Freiburg, D-79104 Freiburg (Germany)

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 expansion 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.

• OSTI ID: 20711498
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 5 Vol. 72; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BHABHA SCATTERING
COMPARATIVE EVALUATIONS
CORRECTIONS
CROSS SECTIONS
ELECTRON-POSITRON INTERACTIONS
ELECTRONS
FEYNMAN DIAGRAM
INTERFERENCE
MOMENTUM TRANSFER
PHOTON EMISSION
POSITRONS
QUANTUM ELECTRODYNAMICS
RENORMALIZATION
REST MASS
ULTRAVIOLET DIVERGENCES