Two-loop QED Bhabha scattering differential cross section

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

doi:10.1016/j.nuclphysb.2004.09.015

Cited by 57 publications

(82 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By employing the results of [8,9], it was possible to complete the calculation of the virtual Bhabha scattering unpolarized differential cross-section, including the contribution of two-loop graphs involving a closed fermion loop (conventionally indicated as corrections of order α 4 (N F = 1), where α is the fine structure constant) [11]. The cross section presented in [11] is valid for arbitrary values of the squared center of mass energy s and momentum transfer t. The full dependence of the crosssection on the electron and positron mass m was retained.…”

Section: Introductionmentioning

confidence: 99%

“…The cross section presented in [11] is valid for arbitrary values of the squared center of mass energy s and momentum transfer t. The full dependence of the crosssection on the electron and positron mass m was retained. In calculating the Feynman diagrams, both UV and IR divergences were regularized with the continuous D-dimensional regularization scheme [12], while the diagrams were evaluated analytically in [8,9] by means of the Laporta algorithm [13] and the differential equations technique for the evaluation of the master integrals [14].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

et al. 2005

Self Cite

View full text Add to dashboard Cite

Recently, we evaluated the virtual cross-section for Bhabha scattering in pure QED, up to corrections of order α 4 (N F = 1). This calculation is valid for arbitrary values of the squared center of mass energy s and momentum transfer t; the electron and positron mass m was considered a finite, non vanishing quantity. In the present work, we supplement the previous calculation by considering the contribution of the soft photon emission diagrams to the differential cross-section, up to and including terms of order α 4 (N F = 1). Adding the contribution of the real corrections to the renormalized virtual ones, we obtain an UV and IR finite differential cross-section; we evaluate this quantity numerically for a significant set of values of the squared center of mass energy s.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2005

Self Cite

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: 71%

“…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

“…Therefore, it is reasonable to expect that it can be safely ignored except in the terms where it acts as a cut-off for collinear divergencies, as it was done in obtaining the results of [20]. For the set of corrections obtained in [21] and [30], for which unapproximated analytic results are available, it is possible to determine the numerical relevance of the terms suppressed by positive powers of the ratio m 2 /s as a function of the beam energy. This analysis is performed in [30].…”

Section: The Small Mass Limitmentioning

confidence: 99%

Two-loop QED Corrections to Bhabha Scattering

Bonciani

Ferroglia

2006

Nuclear Physics B - Proceedings Supplements

Self Cite

View full text Add to dashboard Cite

Recent developments in the calculation of the NNLO corrections to the Bhabha scattering differential cross section in pure QED are briefly reviewed and discussed. Status of the NNLO correctionsBhabha scattering, e + e − → e + e − , is a crucial process in the phenomenology of particle physics. Its relevance is mainly due to the fact that it is the process employed to determine the luminosity L at e + e − colliders: in fact, L = N Bhabha /σ th , where N Bhabha is the rate of Bhabha events and σ th is the Bhabha scattering cross section calculated from theory.Two kinematic regions are of special interest for the luminosity measurements, since in these regions the Bhabha scattering cross section is comparatively large and QED dominated. At colliders operating at c. m. energies of O(100 GeV), the relevant kinematic region is the one in which the angle between the outgoing particles and the beam line is of few degrees. This, for instance, was the case at LEP, where the luminometers were located between 50 and 100 mrad, and it will be also the case at the future ILC (luminometers between 25 and 80 mrad [1]). At machines operating at c. m. energies of the order of 1 − 10 GeV, the region of interest is instead the one in which the scattering angle is large; as an example, at KLOE, the luminosity measurement involves Bhabha scattering events that take place at angles between 55 • and 125 • [2]. Moreover, the large angle Bhabha scattering will be employed at the ILC in order to study the beam *

show abstract

Two-loop QED Bhabha scattering differential cross section

Cited by 57 publications

References 45 publications

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

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

Two-loop corrections to Bhabha scattering

Two-loop QED Corrections to Bhabha Scattering

Contact Info

Product

Resources

About