Dalitzplot                     (H. van Hees & J. Knoll)

         Equation for the boundary of 3-body phase-space in c.m. energies E1, E2:

sol = 
      Solve[4 (E1^2 - m1^2) (E3^2 - m3^2) == 
          (2 E1 E3  - 2 Sqrt[s] (E1 + E3) + s + m1^2 - m2^2 + m3^2)
              ^2, E3];

E3 /. Flatten[sol][[1]] // Simplify

Solution 1:

E31[E1_, m1_, m2_, m3_, s_] = 
      Simplify[E3 /. Flatten[sol][[1]]]

Solution 2:

E32[E1_, m1_, m2_, m3_, s_] = 
      Simplify[E3 /. Flatten[sol][[2]]]

Plot[{E31[E1, 0.14, 0.14, 0.14, 1], E32[E1, 0.14, 0.14, 0.14, 1], E1}, {
        E1, 0, 0.5}, AspectRatio -> 1, PlotRange -> {0, 0.5},  
      AxesLabel -> {"E1", "E2"}]

E1[s_, m1_, s23_] = (s + m1^2 - s23)/(2 Sqrt[s])

E3[s_, m1_, s12_] = E1[s, m3, s12]

s12[E3_, s_, m3_] = -2 Sqrt[s] E3 + m3^2 + s

Check:

s12[E3[s, m1, s12], s, m3]

Plot[{s12[E31[E1[1, 0.14, s23], 0.14, 0.14, 0.14, 1], 1, 0.14], 
        s12[E32[E1[1, 0.14, s23], 0.14, 0.14, 0.14, 1], 1, 0.14], 
        1 + 3*0.14^2 - s23}, {s23, 0, 1}, AspectRatio -> 1, 
      AxesLabel -> {"s12", "s23"}]