The cross section for a b R in the medium

GiBUU

Next: Reactions of the type Up: Resonance production: Previous: The cross section for Contents

The cross section for a b $\longrightarrow$ R in the medium

Now we want to consider a resonance with a potential. Our philosphy will be to evaluate the mass $\mu$ of the produced resonance as described above in equation (1.1), and to treat hereafter the process like a vacuum collision at $s=\mu$ . Therefore we exchange in a first step

by $\mu$

$\begin{eqnarray*} \sigma_{a\,b \rightarrow R}(s)\sim \frac{1}{p^{2}_{ab}(\mu(s))... ...{\left(\mu(s)^2-M_R^2\right)^2+\mu(s)\Gamma_{tot}^2(\mu(s))} \ . \end{eqnarray*}$

As a next step we need to consider a correction due to the relative velocities of the colliding particles which was introduced by Effenberger [Eff99]^1.1. The flux-factor in the cross section is proportional to $\frac{1}{v_{rel}}$ . Therefore we correct by setting

$\begin{displaymath} \sigma(s)=\frac{v_{rel}\left(\mu(s)\right)}{v_{rel}(s)}\, \sigma\left(\mu(s)\right) \ . \end{displaymath}$

Hence the cross section in the case of a resonance being produced in a potential is given by

$\displaystyle \sigma_{a\,b \rightarrow R}(s)=$		$\displaystyle \frac{v^{ab}_{rel}\left(\mu(s)\right)}{v^{ab}_{rel}(s)} F_I \frac{2J_R+1}{\left(2J_a+1\right)\left(2J_b+1\right)} \frac{1}{\mathcal{S}_{ab}} \,$
		$\displaystyle \frac{4\pi}{p^{2}_{ab}(\mu(s))} \, \frac{\mu(s)\, \Gamma_{R\right... ..._{tot}(\mu(s))}{\left(\mu(s)^2-M_R^2\right)^2+\mu(s)\Gamma_{tot}^2(\mu(s))} \ .$	(1.4)

Next: Reactions of the type Up: Resonance production: Previous: The cross section for Contents

Oliver Buss 2005-03-16