Two-loop QED Bhabha scattering: Soft emission and numerical evaluation of the differential cross-section

Bonciani, Roberto; Ferroglia, Andrea; Mastrolia, Pierpaolo; Remiddi, E.; Bij, J.J. van der

doi:10.1016/j.nuclphysb.2005.03.010

Cited by 38 publications

(51 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These boxes become, as well as the reducible diagrams with one-loop vertices and boxes, infrared finite after adding real soft photon emission. The anatomy of that is nicely detailed in Section 2.2 of [7]. In order to construct an infrared-finite quantity, we combine: (i) Born diagrams interfering with the two-loop box diagrams [ Fig.…”

mentioning

confidence: 99%

Virtual Hadronic and Leptonic Contributions to Bhabha Scattering

et al. 2008

View full text Add to dashboard Cite

Using dispersion relations, we derive the complete virtual QED contributions to Bhabha scattering due to vacuum polarization effects. We apply our result to hadronic corrections and to heavy lepton and top quark loop insertions. We give the first complete estimate of their net numerical effects for both small and large angle scattering at typical beam energies of meson factories, the CERN Large Electron-Positron Collider, and the International Linear Collider. With a typical amount of 1-3 per mil they are of relevance for precision experiments. The determination of the luminosity at lepton and hadron colliders is a necessary task, since in many cases the normalization of the measured cross sections is an observable of direct phenomenological interest. In practice, this task can only be solved by selecting a particular reference process, which is expected to generate large statistics, be as free as possible of systematic ambiguities and predicted by the theory to suitable accuracy. As far as lepton colliders are concerned, the above criteria are fulfilled by Bhabha scattering, i.e., the e e ÿ ! e e ÿ process, where a precision under the per mil level can be achieved on both the theory and the experimental sides [1][2][3].In the last few years, there has been major progress in the evaluation of the corrections at the next-to-next-to-leading order accuracy. In fact, the two-loop QED corrections were first evaluated in the massless case in [4]. The photonic corrections to massive Bhabha scattering with enhancing powers of ln s=m 2 e were soon derived from that [5]. The missing constant term [6] plus the corrections with electron loop insertions [7,8] followed later. Recently, the heavy fermion (or N f 2) corrections were derived in the limit m 2 e m 2 s, jtj, juj [8,9], where m is the mass of the heavy fermion, and soon after also for arbitrary m, with m 2

show abstract

mentioning

confidence: 99%

Virtual Hadronic and Leptonic Contributions to Bhabha Scattering

et al. 2008

View full text Add to dashboard Cite

show abstract

“…Together with the result of Refs. [6,7] for the corrections with the closed fermion loop insertions our result gives a complete expression for the two-loop virtual corrections. It should be incorporated into the Monte Carlo event generators to reduce the theoretical error in the luminosity determination at present and future electron-positron colliders below 0.1%.…”

mentioning

confidence: 74%

“…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 corrections is a challenging problem at the limit of present computational techniques [8].…”

mentioning

confidence: 99%

Two-loop corrections to Bhabha scattering

Penin

2006

Nuclear Physics B - Proceedings Supplements

View full text Add to dashboard Cite

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...

show abstract

“…In this paper we concentrate exclusively on harmonic polylogarithms (HPL's) up to weight four, which since their introduction have found many applications in computations up to two-loop order in the perturbative expansion, e.g., [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]. In order to confront the theoretical next-to-next-to-leading order (NNLO) predictions to experiment, it is mandatory to be able to evaluate HPL's numerically in a fast and accurate way.…”

Section: Introductionmentioning

confidence: 99%