[1208] | 1 | |
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| 2 | \section[Positron - Electron Annihilation into Hadrons]{Positron - Electron Annihilation into Hadrons} |
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| 3 | |
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| 4 | \subsection{Introduction} |
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| 5 | The process {\tt G4eeToHadrons} simulates the in-flight annihilation |
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| 6 | of a positron with an atomic electron into hadrons. It is assumed here |
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| 7 | that the atomic electron is initially free and at rest. Currently only |
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| 8 | two-pion production is available with a validity range up to 1 TeV. |
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| 9 | |
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| 10 | \subsection{Cross Section and Mean Free Path} |
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| 11 | The annihilation of positrons and target electrons producing pion pairs in |
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| 12 | the final state (${\rm e}^+{\rm e}^- \to \pi^+\pi^-$) may give an |
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| 13 | appreciable contribution to electron-jet conversion at the LHC, and |
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| 14 | for the increasing total number of muons produced in the beam pipe of |
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| 15 | the linear collider \cite{anniToHad.mu}. The threshold positron energy in the |
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| 16 | laboratory system for this process with the target electron at rest is |
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| 17 | \begin{equation}\label{he0} |
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| 18 | E_{\rm th}=2m_\pi^2/m_e-m_e\approx 70.35\:{\rm GeV}\,, |
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| 19 | \end{equation} |
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| 20 | where $m_\pi$ and $m_e$ are the pion and electron masses, respectively. |
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| 21 | The total cross section is dominated by the reaction |
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| 22 | \begin{equation}\label{he1} |
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| 23 | {\rm e}^+{\rm e}^- \to \rho\gamma\to\pi^+\pi^-\gamma, |
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| 24 | \end{equation} |
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| 25 | where $\gamma$ is a radiative photon and $\rho(770)$ is a well known vector |
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| 26 | meson. This radiative correction is essential, because it significantly |
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| 27 | modifies the shape of the resonance. Details of the theory are described in |
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| 28 | \cite{anniToHad.ben}, in which the main term and the leading $\alpha^2$ |
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| 29 | corrections are taken into account. |
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| 30 | |
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| 31 | \subsection {Sampling the final state} |
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| 32 | |
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| 33 | The final state of the $e+e-$ annihilation process \ref{he1} |
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| 34 | is simulated by first determining the kinematic limits of the photon energy |
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| 35 | in the center of mass system |
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| 36 | and then sampling the photon energy within those limits using the |
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| 37 | differential cross section. Conservation of energy-momentum is then used to |
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| 38 | determine the four-momentum of the pion final state. Then |
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| 39 | the backward transformation to the laboratory system is performed. |
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| 40 | |
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| 41 | |
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| 42 | \subsection{Status of this document} |
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| 43 | 09.12.05 created by V.Ivanchenko \\ |
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| 44 | |
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| 45 | \begin{latexonly} |
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| 46 | |
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| 47 | \begin{thebibliography}{99} |
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| 48 | \bibitem{anniToHad.mu} A.G. Bogdanov et al., IEEE-NSS-33-179 |
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| 49 | conference Record, 2004, accepted by IEEE Transaction. |
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| 50 | \bibitem{anniToHad.ben} M. Benayoun et al., Mod. Phys. Lett. A14, |
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| 51 | 2605 (1999). |
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| 52 | \end{thebibliography} |
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| 53 | |
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| 54 | \end{latexonly} |
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| 55 | |
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| 56 | \begin{htmlonly} |
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| 57 | |
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| 58 | \subsection{Bibliography} |
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| 59 | |
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| 60 | \begin{enumerate} |
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| 61 | \item A.G. Bogdanov et al., IEEE-NSS-33-179 |
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| 62 | conference Record, 2004, accepted by IEEE Transaction. |
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| 63 | \item M. Benayoun et al., Mod. Phys. Lett. A14, |
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| 64 | 2605 (1999). |
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| 65 | \end{enumerate} |
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| 66 | |
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| 67 | \end{htmlonly} |
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| 68 | |
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