part of the forward scattering amplitude. The second term is proportional to $\Delta n$ where the ratio of real to imaginary parts of Breit-Wigner amplitudes is taken into account $$\frac {{\rm Re} F(M, 0^o)}{{\rm Im} F(M, 0^o)}=\frac {m_{\rho }^2-M^2}{M\Gamma }
\label{reim}$$ so that $$\Delta n = \frac {N_s}{\Gamma }\sigma _{BW}\frac {m_{\rho }^2-M^2}{M^2},$$ where $\sigma _{BW}$ is the Breit-Wigner cross section.

This term vanishes for $M>m_{\rho }$ in Eq. (\[ll\]) because only positive $\Delta n$ lead to the Cherenkov effect. Namely it describes the distribution of masses of Cherenkov states. In these formulas, one should take into account the in-medium modification of the height of the peak and its width. In principle, one could consider $m_{\rho }$ as a free in-medium parameter as well. Let us rely on experimental findings that its shift in the medium is small. Theoretical estimates would ask for some dynamics to be known. In our approach, it is not determined. Therefore, first of all, one may just fit the parameters $A$ and $\Gamma $ by describing the shape of the mass spectrum at $0.75<M<0.9$ GeV measured in [@1a] and shown in Fig. 2. In this way any strong influence of the $\phi $-meson is avoided. Let 