pi N -> pi pi N with rho meson in final state
												                                       7.6.2000 B.Friman

Off[General::"spell1"]

λ[x_, y_, z_] := 
      x^2 + y^2 + z^2 - 2*x*y - 2*x*z - 2*y*z

Pion momentum in pi pi rest frame

k[s_] := Sqrt[λ[s, mpi^2, mpi^2]]/(2*(Sqrt[s]))

Rho-meson propagator

drho[s_] := 1/(s - mrho^2 + I*(Sqrt[s])*gamrho)

mn = 940; mpi = 140; mrho = 770; gamrho = 150;

Mass distribution

f[s_, sππ_] := 
      1/s*(Sqrt[λ])[s, sππ, mn^2]/
          sππ^2*(λ[sππ, mpi^2, mpi^2])^1.5*
        Re[drho[sππ]*Conjugate[drho[sππ]]]

mnorm[mrho_, s_] := Min[mrho, (Sqrt[s]) - mn - 100]

Rho-meson spectral function with appropriate normalization, so that it can be compared to the mass distribution f.

g[s_, sππ_] := 
      1/s*(Sqrt[λ])[s, mnorm[mrho, s]^2, mn^2]/
          sππ^2*(λ[sππ, mpi^2, mpi^2])^1.5*
        Re[drho[sππ]*Conjugate[drho[sππ]]]

Choose the total cm  energy

s1 = 1700^2

phasespace = 
      Plot[f[s1, e^2], {e, 2*mpi, ((Sqrt[s1]) - mn)}, 
        PlotStyle -> {{RGBColor[0, 0, 1]}}]

pipispectr = 
      Plot[g[s1, e^2], {e, 2*mpi, 1200}, 
        PlotStyle -> {{RGBColor[1, 0, 0]}}]

Show[pipispectr, phasespace]