1 | |
---|
2 | \section[Positron - Electron Annihilation into Hadrons]{Positron - Electron Annihilation into Hadrons} |
---|
3 | |
---|
4 | \subsection{Introduction} |
---|
5 | The process {\tt G4eeToHadrons} simulates the in-flight annihilation |
---|
6 | of a positron with an atomic electron into hadrons. It is assumed here |
---|
7 | that the atomic electron is initially free and at rest. Currently only |
---|
8 | two-pion production is available with a validity range up to 1 TeV. |
---|
9 | |
---|
10 | \subsection{Cross Section and Mean Free Path} |
---|
11 | The annihilation of positrons and target electrons producing pion pairs in |
---|
12 | the final state (${\rm e}^+{\rm e}^- \to \pi^+\pi^-$) may give an |
---|
13 | appreciable contribution to electron-jet conversion at the LHC, and |
---|
14 | for the increasing total number of muons produced in the beam pipe of |
---|
15 | the linear collider \cite{anniToHad.mu}. The threshold positron energy in the |
---|
16 | laboratory system for this process with the target electron at rest is |
---|
17 | \begin{equation}\label{he0} |
---|
18 | E_{\rm th}=2m_\pi^2/m_e-m_e\approx 70.35\:{\rm GeV}\,, |
---|
19 | \end{equation} |
---|
20 | where $m_\pi$ and $m_e$ are the pion and electron masses, respectively. |
---|
21 | The total cross section is dominated by the reaction |
---|
22 | \begin{equation}\label{he1} |
---|
23 | {\rm e}^+{\rm e}^- \to \rho\gamma\to\pi^+\pi^-\gamma, |
---|
24 | \end{equation} |
---|
25 | where $\gamma$ is a radiative photon and $\rho(770)$ is a well known vector |
---|
26 | meson. This radiative correction is essential, because it significantly |
---|
27 | modifies the shape of the resonance. Details of the theory are described in |
---|
28 | \cite{anniToHad.ben}, in which the main term and the leading $\alpha^2$ |
---|
29 | corrections are taken into account. |
---|
30 | |
---|
31 | \subsection {Sampling the final state} |
---|
32 | |
---|
33 | The final state of the $e+e-$ annihilation process \ref{he1} |
---|
34 | is simulated by first determining the kinematic limits of the photon energy |
---|
35 | in the center of mass system |
---|
36 | and then sampling the photon energy within those limits using the |
---|
37 | differential cross section. Conservation of energy-momentum is then used to |
---|
38 | determine the four-momentum of the pion final state. Then |
---|
39 | the backward transformation to the laboratory system is performed. |
---|
40 | |
---|
41 | |
---|
42 | \subsection{Status of this document} |
---|
43 | 09.12.05 created by V.Ivanchenko \\ |
---|
44 | |
---|
45 | \begin{latexonly} |
---|
46 | |
---|
47 | \begin{thebibliography}{99} |
---|
48 | \bibitem{anniToHad.mu} A.G. Bogdanov et al., IEEE-NSS-33-179 |
---|
49 | conference Record, 2004, accepted by IEEE Transaction. |
---|
50 | \bibitem{anniToHad.ben} M. Benayoun et al., Mod. Phys. Lett. A14, |
---|
51 | 2605 (1999). |
---|
52 | \end{thebibliography} |
---|
53 | |
---|
54 | \end{latexonly} |
---|
55 | |
---|
56 | \begin{htmlonly} |
---|
57 | |
---|
58 | \subsection{Bibliography} |
---|
59 | |
---|
60 | \begin{enumerate} |
---|
61 | \item A.G. Bogdanov et al., IEEE-NSS-33-179 |
---|
62 | conference Record, 2004, accepted by IEEE Transaction. |
---|
63 | \item M. Benayoun et al., Mod. Phys. Lett. A14, |
---|
64 | 2605 (1999). |
---|
65 | \end{enumerate} |
---|
66 | |
---|
67 | \end{htmlonly} |
---|
68 | |
---|