Large-angle Bhabha scattering and luminosity at flavour factories

TL;DR

Addresses the need for high-precision luminosity from LABH at low-energy $e^+e^-$ colliders by calculating QED radiative corrections with a Parton Shower approach, and benchmarks it against exact $O(\alpha)$ results. Introduces the BABAYAGA Monte Carlo generator for LABH with ISR/FSR, including photon kinematics, validated against a benchmark LABSPV calculation that includes higher-order LL terms. Finds that with a suitable $Q^2$ scale (≈ $st/u$) the PS reproduces exact results within about 0.5%, while higher-order LL terms contribute ~1–2% for tight cuts; $O(\alpha^2 L)$ corrections are negligible. Concludes that combining exact $O(\alpha)$ with LL resummation is essential for a few 0.1% precision and suggests future merging, plus extending PS to other QED processes and to B factories.

Abstract

The luminosity determination of electron-positron colliders operating in the region of low-lying hadronic resonances (E_cm ~ 1-10 GeV), such as BEPC/BES, DAPHNE, KEKB, PEP-II and VEPP-2M, requires the precision calculation of the Bhabha process at large scattering angles. In order to achieve a theoretical accuracy at a few 0.1% level, the inclusion of radiative corrections is mandatory. The phenomenologically relevant effect of QED corrections is taken into account in the framework of the Parton Shower (PS) method, which is employed both for cross section calculation and event generation. To test the reliability of the approach, a benchmark calculation, including exact O(alpha) corrections and higher-order leading logarithmic contributions, is developed as well and compared in detail with the PS predictions. The effect of O(alpha) next-to-leading and higher-order leading corrections is investigated in the presence of realistic event selections for the Bhabha process at the Phi-factories. A new Monte Carlo generator for data analysis (BABAYAGA) is presented, with an estimated accuracy of 0.5%. Possible developments aiming at improving its precision and range of applicability are discussed.

Figures (13)

• Figure 1: $x$ distribution of the electron SF at $\sqrt{s} = 190$ GeV. Solid line: numerical solution of DGLAP equation, by means of numerical inversion of Mellin transform. Histogram: result of the PS algorithm.
• Figure 2: Comparison for the Mellin moments of the electron SF at $\sqrt{s} = 190$ GeV. Solid line: exact analytical moments. Markers: results of the PS algorithm for $N=1,2,10,50,200$.
• Figure 3: QED corrected Bhabha cross section as a function of the infrared regulator $\epsilon$, at the peak of the $\Phi$ resonance. Cuts used are given in the text and correspond to a realistic event selection at DA$\Phi$NE.
• Figure 4: Comparison between the QED corrected LABH cross section and the Born one, in the c.m. energy range from 1 GeV to 10.5 GeV. Solid circles: Born approximation; solid triangles: QED corrected cross section. Cuts are given in the text.
• Figure 5: Relative effect of ISR and ISR+FSR on the integrated Bhabha cross section at the $\Phi$ factories. Open circles: ISR only; solid circles: ISR+FSR. Cuts used are given in the text.