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− | === Proton-Reggeon vertex ===
| + | == Decay == |
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− | The amplitude for the emission of the exchange particle (Reggeon) at the baryon vertex can be described as the decay of the target proton into the final-state baryon plus the exchange particle. Following the prescription developed above, this amplitude is written as
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− | :<math>
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− | \langle \Omega_R ; J_R \lambda_R \epsilon_R; J_P \lambda_p | W | J_T m_T \rangle
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− | =
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− | \langle \Omega_R ; J_R \lambda_R \; \mp\epsilon; \textstyle{\frac{1}{2}}\;\lambda_p
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− | | \textstyle{\frac{1}{2}}\;m_T \lambda_R \lambda_p \rangle \langle \textstyle{\frac{1}{2}}\;m_T \lambda_R \lambda_p |
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− | W | \textstyle{\frac{1}{2}}\;m_T \rangle
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− | </math></td>
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− | <td>
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− | transition amplitude for <math>p \rightarrow R + p'</math>
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− | in the direction <math>\Omega_R</math> w.r.t. the coordinate
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− | system defined in the resonance RF.
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− | </td>
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− | </tr>
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− | <tr>
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− | <td><math>
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− | =\frac{1}{\sqrt{2\pi}} \left[
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− | D_{m_T (\lambda_R-\lambda_p)}^{\frac{1}{2} *} (\Omega_R,0) \; w_{\lambda_R\; \lambda_p}
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− | \mp
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− | \epsilon P_R (-1)^{J_R-\lambda_R}
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− | D_{m_T (-\lambda_R-\lambda_p)}^{\frac{1}{2} *} (\Omega_R,0) \; w_{\lambda_R\; -\lambda_p}
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− | \right]
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− | </math></td>
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− | <td>
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− | follows from relations given above
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− | </td>
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− | </tr>
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− | </table>
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− | === Decay ===
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| <math> | | <math> |