Two-loop QED Corrections to Bhabha Scattering

Abstract

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 *

Matching perturbative and parton shower corrections to Bhabha process at flavour factories

“…a log s m 2 + bπ 2 σ 0 a = +2.656 ± 0.001 b = −1.391 ± 0.003 (19) showing that the missing two-loop photonic contributions in BABAYAGA are really of the order of α 2 L. The impact on the integrated cross section within the realistic set up of these terms will be shown in Tab. 6.…”

“…An exhaustive report of the status of the two-loop QED corrections to Bhabha scattering can be found in Ref. [19]. What is actually available is the complete two-loop virtual photonic correction in the approximation of neglecting O(m 2 /Q 2 ), where Q 2 stands for one of the Mandelstam invariants s, t and u [21].…”

“…Last but not least, precision measurements of R trough radiative return at high-luminosity e + e − storage rings KEK-B and PEP-II are already performed or foreseen in the near future, as previously mentioned. These facts are also among the motivations of the recent efforts in the direction of complete twoloop calculations to Bhabha scattering [19,20,21,22,23,24]. The need for keeping under control accurately radiative corrections to QED processes has been recently reinforced by the update of the e + e − → π + π − cross section by SND collaboration at VEPP-2M.…”

Planar two-loop master integrals for massive Bhabha scattering: N = 1 and N = 2

“…B5l2M2m ≡ B5l2M2m(1, 1, 1, 1, 1), B5l2M2md ≡ B5l2M2m(1, 2, 1, 1, 1), (20) and an expansion in the high-energy limit of the appropriate three-fold MB representations leads to the following results, …”

Extension of HPL to complex arguments

“…They are found in three-loop deeply inelastic splitting and coefficient functions [4][5][6][7], in two-loop massive vertex form factors [8][9][10][11][12][13][14][15], in two-loop Bhabha scattering [16][17][18][19][20][21][22], in multi-loop three-point and four-point functions [23][24][25][26][27][28][29][30][31][32][33], in 2-and 3-loop lepton g-2 [34,35], in the Higgs production and decay [36][37][38][39], heavy quark forward-backward asymmetry [40,41] and form factors [42], large-x limit of parton evolution [43] and various loop calculations [44][45][46] and in more formal developments [47].…”