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Extra resources for High Energy Colliders
2. R. N. Mohapatra, Unification and supersymmetry, The frontiers of quark-lepton physics, Springer Verlag, Berlin (1986). 3. I. Hinchliffe, Ann. Rev. Nuclear and Particle Science, 36, 505 (1986). 4. M. B. J. H. Schwarz and E. Witten, Superstring theory I and 11, Cambridge University Press (1986). 5. L. Brink and M. Henneaux, Principles of String theory, Plenum (1987). 6. S. Dimopoulos, S. A. Raby and F. Wilczek, Unification of couplings, Physics Today, 44, 25 (1991). 7. R. E. Marshak, Conceptional foundations of modern particle physics, World Scientific, Singapore (1992).
In this frame: Pa = (EarP), Pb ( E c , ~ ,’ ) Pd pc = (Eb7-P) (Ed,-P’). 9a) Scattering and Particle Interaction 30 Figure 3 Two-body scattering in the centre of mass frame. 1l b ) Interaction Picture 31 and Ec lpl = lp’l 7 E d = Eb = Ea, -4p 2 sin2 6-. 13) 2 Thus we see that -t is the square of momentum transfer. Finally we derive a relation between the scattering angles 0 and OL using Lorentz transformation. Let us take p~ and p along z-axis. m. 15) E,” = y [E, + VP’COSO]. 2 +VEa] 1 VL = y[Ea + UP] 1 mb = y [Eb - tlP].
Lp’l [MI2 (PI 4T2 Consider a three-body decay m ml+m2+m3 K = Pl+P2+P3. The decay rate [cf. Eq. 93) Scattering and Particle Interaction 44 where for definiteness, we have taken all the particles to be fermions. We evaluate Eq. (94) in the rest frame of particle m. In this frame K = 0 and E = m. Hence we have P1 +P2+P3 El + & + I 3 3 = 0 = m. 95) From Eq. 97) -2 where IM1 is the value [MI2after the angular integration has been performed. In order to evaluate the integral in Eq. (97), it is convenient to define the invariants: In the rest frame of particle rn, we have s12 = m2+m:-2mE3 m2+mi-2mE2 = m2+m:-2mE1 = m2 rn?