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Quantum field theory Exercises 2.

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Quantum field theory Exercises 2.

2005-10-07

•Exercise 2.1. Mandelstam variables and Dalitz plot

Consider decay of a particle of massMand four-momentum pinto three different particles with masses m1, m2, m3 and momenta p1, p2, p3 respectively. Introduce the Mandelstam variables s,t,u

s= (p−p1)2, t= (p−p2)2, u= (p−p3)2.

1. Find the relation between these variables, i.e. find the value of

s+t+u.

2. Find the kinematically allowed region on thes−t plane. Analyze the case of generic masses, and the casesm1=m2=0 andm1=m2=m3=0.

The plot of the phase space region allowed by energy-momentum conservation is called Dalitz plot.

2

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