EPJ

2023 Impact factor 4.2
EPJ C - Particles and Fields
Particles and Fields
Eur. Phys. J. C 4, 631-639
DOI 10.1007/s100529800814

Helicity amplitudes for the small-angle lepton pair production
in e+e- or $\mu^+ \mu^-$ collisions

E.A. Kuraev1 - A. Schiller2 - V.G. Serbo3 - D.V. Serebryakova4

1 Joint Institute of Nuclear Research, 141980, Dubna, Russia (e-mail: kuraev@thsun1.jinr.dubna.su)
2 Institut für Theoretische Physik and Naturwissenschaftlich-Theoretisches Zentrum, Universität Leipzig,
D-04109 Leipzig, Germany (e-mail: schiller@tph204.physik.uni-leipzig.de)
3 Novosibirsk State University, 630090, Novosibirsk, Russia (e-mail: serbo@math.nsc.ru)
4 Institute of Mathematics, 630090, Novosibirsk, Russia

Received: 23 October 1997 / Published online: 24 March 1998

Abstract
The lepton pair production $e^- e^+ \!\! \to \! e^- e^+ l^- l^+$ or $\mu^- \mu^+ \to \mu^- \mu^+ l^- l^+ $is studied in the dominant cross section region of scattering angles ${m_j}/{E_j} lesssim \theta_j \ll 1$. An analytical expression is found for all 64 helicity amplitudes of these processes. The accuracy of the obtained formulae is given omitting only terms of the order of mj2/Ej2, $\theta_j^2$, and $ \theta_j {m_j}/{E_j}$. The result has a compact form convenient both for analytical and numerical calculations of various cross sections in this dominating scattering regime.

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