Changes

where density matrices <math>\rho</math> represent the initial state particles' spin states. The unpolarized target presents an initial state with both reflectivities equally likely, resulting in  

where density matrices <math>\rho</math> represent the initial state particles' spin states. The unpolarized target presents an initial state with both reflectivities equally likely, resulting in  

<math>\rho_{\lambda_i \lambda_i'} = \frac{1}{2} \delta_{\lambda_i \lambda_i'}</math>. The same property holds for <math>\rho_{\lambda_f \lambda_f'}</math> by definition of the summation over the final states. As a result, the term characterizing the target proton's transition with the emission of the Reggeon factorizes, allowing us to drop indices for the proton states in the T matrix:

<math>\rho_{\lambda_i \lambda_i'} = \frac{1}{2} \delta_{\lambda_i \lambda_i'}</math>.  

 

 

 

 

As a result, the term characterizing the target proton's transition with the emission of the Reggeon factorizes, allowing us to drop indices for the proton states in the T matrix:

:<math>

:<math>

\langle \mathbf{q}_\pi 0 0 | U_\rho | J_\rho , \lambda_\rho \rangle

\langle \mathbf{q}_\pi 0 0 | U_\rho | J_\rho , \lambda_\rho \rangle

</math>

</math>

=== Mass dependence ===

=== Mass dependence ===