Two-loop corrections to Bhabha scattering

Abstract

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 + e − colliders.PACS numbers: 11.15. Bt, 12.20.Ds Electron-positron Bhabha scattering plays a special role in particle phenomenology. It is crucial for extracting physics from experiments at electron-positron colliders since it provides a very efficient tool for luminosity determination. The small angle Bhabha scattering has been particularly effective as a luminosity monitor in the LEP and SLC energy range because its cross section is large and QED dominated [1]. At a future International Linear Collider the luminosity spectrum is not monochromatic due to beam-beam effects. Therefore measuring the cross section of the small angle Bhabha scattering alone is not sufficient, and the angular distribution of the large angle Bhabha scattering has been suggested for disentangling the luminosity spectrum [2]. The large angle Bhabha scattering is important also at colliders operating at a center of mass energy √ s of a few GeV, such as BABAR, BELLE, BEPC/BES, DAΦNE, KEKB, PEP-II, and VEPP-2M, where it is used to measure the integrated luminosity [3]. Since the accuracy of the theoretical evaluation of the Bhabha cross section directly affects the luminosity determination, remarkable efforts have been devoted to the study of the radiative corrections to this process (see [1] for an extensive list of references). Pure QED contributions are particularly important because they dominate the radiative corrections to the large angle scattering at intermediate energies 1-10 GeV and to the small angle scattering also at higher energies. The calculation of the QED radiative corrections to the Bhabha cross section is among the classical problems of perturbative quantum field theory with a long history. The first order corrections are well known (see [4] and references therein). To match the impressive experimental accuracy the complete second order QED effects have to be included on the theoretical side. The evaluation of the two-loop virtual corrections constitutes the main problem of the second order analysis. The complete two-loop virtual corrections to the scattering amplitudes in the massless electron approximation have been computed in Ref. [5], where dimensional regularization has been used for infrared divergences. However, this approximation is not sufficient since one has to keep a nonvanishing electron mass to make the result compatible with available Monte Carlo event generators [1]. Recently an important class of the two-loop corrections, which include at least one closed fermion loop, has been obtained for a finite electron mass [6] including the soft photon bremsstrahlung [7]. A similar evaluation of the purely photonic two-loop correcti...