QED radiative corrections to low-energy Møller and Bhabha scattering

Abstract

We present a treatment of the next-to-leading-order radiative corrections to unpolarized Møller and Bhabha scattering without resorting to ultrarelativistic approximations. We extend existing softphoton radiative corrections with new hard-photon bremsstrahlung calculations so that the effect of photon emission is taken into account for any photon energy. This formulation is intended for application in the OLYMPUS experiment and the upcoming DarkLight experiment but is applicable to a broad range of experiments at energies where QED is a sufficient description. DOI: 10.1103/PhysRevD.94.033004 I. MOTIVATIONWith the development of new precision physics experiments on the intensity frontier using lepton beams on targets containing atomic electrons, interest has been renewed in Møller and Bhabha scattering as important signal, background, and luminosity-monitoring processes. Two such experiments are the subject of current attention at the MIT Laboratory for Nuclear Science: DarkLight [1] and OLYMPUS [2]. These experiments require calculations of the Møller and Bhabha processes including next-toleading-order radiative effects.The DarkLight experiment aims to search for a massive dark-sector boson by precisely measuring the process e − p → e − pe þ e − . It will use the 100 MeV electron beam at the Jefferson Lab Low Energy Recirculator Facility incident on a gaseous hydrogen target. DarkLight aims to measure all four final-state particles in a fourfold coincidence. At the design luminosity of ∼10 36 cm −2 s −1 and at such low energies, Møller electrons and associated radiated photons induce an enormous background of secondary particles. Careful study is necessary to understand and minimize the backgrounds masking the comparatively rare signal process.The OLYMPUS experiment aims to measure the ratio of positron-proton to electron-proton elastic scattering cross sections in the effort to quantify the contribution of two-photon exchange. OLYMPUS acquired data with 2 GeV alternating electron and positron beams incident on a hydrogen target [3] at the DORIS storage ring at the Deutsches Elektronen-Synchrotron (DESY). Møller/ Bhabha calorimeters placed at the symmetric angle (90°c .m. ¼ 1.29°l ab ) were used as one of the luminosity monitors. Precise luminosity monitoring is important to normalize the separate electron and positron data sets and form the cross section ratio. Since electron-electron and positron-electron scattering are the only processes in the experiment that can be fully described by QED, they are the most suitable choices for normalization. As a result, knowledge of their cross sections including radiative corrections is essential to forming the final result.A Monte Carlo approach has been identified as the preferred method of treating the radiative corrections for both of these experiments. This approach stands in contrast with traditional soft-photon radiative corrections, which are typically included as a multiplicative factor to the Born cross section,with δ ¼ δðΔE; ΩÞ. This traditional method requ...

Measurement of Møller scattering at 2.5 MeV

“…This is seen dramatically in Fig. 1 of [7]: neglecting the electron mass leads to a prediction of increasing cross section in decreasing energy window size. This is clearly unphysical.…”

“…Figures 3-5 show a comparison between the extracted Møller spectra and that reconstructed from a complete radiative simulation based on [7]. The data have been scaled vertically to match.…”

“…At low energies, the electron mass must not be neglected in calculating the Møller cross section, and we have calculated next-to-leading-order radiative corrections to unpolarized Møller and Bhabha scattering without resorting to ultrarelativistic approximations [7]. To briefly summarize the results of our previous paper, neglecting the electron mass results not in a changed numerical result but in a complete breakdown of the radiative correction formalism.…”

Design and performance of a lead fluoride detector as a luminosity monitor

“…Simple event generators that produce final states (i.e., pairs of particles) for Møller scattering, Bhabha scattering, and pair annihilation have been written using tree level cross section formulas. A more advanced set of generators, including next-toleading order radiative corrections, has also been developed and is intended for use in the full OLYMPUS analysis [17]. Based on the input beam species and energy, a kinematically allowed result is selected randomly according to a sampling distribution that approximates the cross section as a function of the scattering angle.…”

Realization of a large-acceptance Faraday Cup for 3 MeV electrons

“…It is important to quantify radiative Møller scattering as it has not yet been measured precisely at these energies [5] and is an experimental concern for other proposed experiments [6]. Recently, the experiment has measured the radiative Møller electron momentum spectrum at three different spectrometer angles between 30°and 40° [6].…”