Positron Annihilation into Hadrons in Media
Introduction
The process G4eeToHadrons simulates the in-flight annihilation of a positron with an atomic electron into hadrons [eal06]. It is assumed here that the atomic electron is initially free and at rest. Currently accurate cross section is available with a validity range up to 1 TeV.
Cross Section
The annihilation of positrons and target electrons producing pion pairs in the final state (\(e^+e^- \to \pi^+\pi^-\)) may give an appreciable contribution to electron-jet conversion at the LHC, and for the increasing total number of muons produced in the beam pipe of the linear collider [eal06]. The threshold positron energy in the laboratory system for this process with the target electron at rest is
where \(m_\pi\) and \(m_e\) are the pion and electron masses, respectively. The total cross section is dominated by the reaction
where \(\gamma\) is a radiative photon and \(\rho(770)\) is a well known vector meson. This radiative correction is essential, because it significantly modifies the shape of the resonance. Details of the theory are described in [BEIS99], in which the main term and the leading \(\alpha^2\) corrections are taken into account.
Additional contribution to the hadron production cross section come from \(\omega(783)\) and \(\phi(1020)\) resonances with \(\pi^+\pi^-\pi^0\), \(K^+K^-\), \(K_LK_S\), \(\eta\gamma\), and \(\pi^0\gamma\) final states.
Sampling the final state
The final state of the \(e^+e^-\) annihilation process is simulated by first sampling of radiative gamma using a sum of all hadronic cross sections in the center of mass system. Photon energy is used to define new differential cross section. After that, hadronic channel is randomly selected according to it partial cross section. Final state is sampled and final particles transformed to the laboratory system.
Bibliography
- BEIS99
M. Benayoun, S. I. Eidelman, V. N. Ivanchenko, and Z. K. Silagadze. Spectroscopy at b-Factories using hard photon emission. Modern Physics Letters A, 14(37):2605–2614, dec 1999. URL: https://doi.org/10.1142/S021773239900273X, doi:10.1142/s021773239900273x.
- eal06(1,2)
A.G. Bogdanov et al. Geant4 simulation of production and interaction of muons. IEEE Trans. Nucl. Sci., 2006.