23.1. Decay processes Consider the decay processes of the higher particles in the spectrum of 4 theory, Bk→rB1 +sB2 where r and s are all those integers which satisfy mk ≥ rm1 +sm2, r +s = n.

Take as an explicit example ξ < 15

. The decay width of these processes is given by the Fermi golden rule

 = (2π)2 δ2(P −p1−· · ·−pn) | Tfi |2 1 2E n



i=1 dpi

(2π)2Ei

, where P denotes the 2-momentum of the decay particle whereas the amplitude Tfi is given by the matrix element Tfi = Bk(P) | B1(p1) . . .B1(ps)B2(ps+1) . . .B2(pn) .

a. Assuming Tfi to be of the same order of magnitude for the various processes, use the phase space expressions discussed in Appendix 17.C to estimate the decay rates

5 11

· · · · · · B5→B1 +B1

5 12

· · · · · · B5→B1 +B2

5 22

· · · · · · B5→B2 +B2 with respect to the decay rate 3 11 of the process B3→B1 +B1.

b. Show that there exists a critical value ξc where the particle B5 has its mass exactly equal to 2m2 and discuss the consequences of this critical value for the decay processes.