Bhabha scattering

Bhabha scattering is the elastic scattering process between an electron and its antiparticle, the positron. It is a fundamental QED process of significant historical and practical importance in particle physics. The process is named for the Indian physicist Homi J. Bhabha, who derived its cross section in 1935, providing an early test for QED and the existence of the positron.

Overview

Bhabha scattering is a quintessential example of lepton-antilepton interaction governed by the electromagnetic interaction. The process occurs via the exchange of a virtual photon, and its theoretical prediction was a major triumph for early quantum field theory. It played a crucial role in validating Dirac's theory of the electron and the concept of antimatter. The scattering is characterized by its angular distribution, which provides a sensitive probe of the underlying QED framework and possible deviations from the Standard Model.

Theoretical description

The full cross section for Bhabha scattering is calculated within the framework of QED using techniques like perturbation theory. The leading-order contribution involves two distinct Feynman diagrams: a t-channel diagram involving photon exchange and an s-channel diagram involving annihilation into a virtual photon. The interference between these amplitudes gives the scattering its distinctive angular dependence. Higher-order corrections involving virtual loops, such as vacuum polarization and vertex corrections, are required for precise predictions matching modern experimental accuracy. The calculation was historically significant, with contributions from figures like Werner Heisenberg and Wolfgang Pauli to the development of quantum field theory.

Experimental verification

Early experimental confirmation came from studies of cosmic rays using cloud chambers and later from experiments at particle accelerators like the Cornell Electron Storage Ring and the Large Electron–Positron Collider at CERN. These experiments meticulously measured the differential cross section and angular distributions, finding excellent agreement with QED predictions across a wide range of energies. The process served as a standard candle for luminosity monitoring in collider experiments, as its theoretical rate is precisely known. Discrepancies have been sought as potential signatures of new physics, such as contact interactions or the existence of a new Z′ boson.

Applications

The primary application of Bhabha scattering is as a precision tool for determining the integrated luminosity of electron–positron colliders, such as the former Large Electron–Positron Collider and current experiments like Belle II at KEK and BESIII at the Beijing Electron–Positron Collider. By comparing the measured event rate to the theoretically calculated cross section, experimenters can calibrate their detectors and normalize measurements of other processes. It is also used in tests of QED at high energies and in searches for phenomena beyond the Standard Model, including studies of possible compositeness of leptons or the effects of extra dimensions.

Relation to other processes

Bhabha scattering is closely related to other fundamental QED processes. It is the crossed-channel analogue of Møller scattering (electron-electron scattering) and positronium formation. Its annihilation diagram connects it to processes like electron–positron annihilation into muons or quarks, which were pivotal in the discovery of the J/ψ meson and the tau lepton. The theoretical structure shares deep similarities with Compton scattering via crossing symmetry. In the context of electroweak theory, it receives corrections from the exchange of the massive Z boson, especially at high energies near the Z pole, as precisely studied at the Stanford Linear Collider and the Large Electron–Positron Collider.

Category:Scattering Category:Quantum electrodynamics Category:Particle physics