Physics 585 - Problem Set 4
1)
Consider a system of a positive and negative pion, with orbital angular momentum  in their centre of mass.
(a)
Determine the C-parity of this (+) system.
(5)
(b)
If  = 1, can the system decay into two photons ? Justify your answer.
(5)
2)
Show that a scalar meson cannot decay to three pseudo-scalar mesons in a parity conserving process.
(10)
3)
Pions are believed to satisfy Bose-Einstein statistics (this means that the wave function describing a pion
anti-pion pair must be symmetric under interchange of the pions when the wavefunction includes a ‘charge’
function). Show how this condition limits the possible values of the orbital angular momentum () and
isospin (I) of a pion anti-pion pair and make a classification of the allowed states.
(15)
4)
Two neutral meson resonances labelled A and B, with masses of less than 1 GeV/c 2, are assumed to have
spins and isospins of less than 2. They decay with the following partial widths,
 (A  +)
=
 (A  00)
125 MeV
Forbidden
 (B  0)
=
1.0 MeV
 (B  +)
=
0.1 MeV
 (B  +0) =
10 MeV
Deduce, giving reasons, the spin, parity, C-parity (JPC) and isospin, G-parity (IG) of the mesons A and B.
(20)
5)
Show that the reaction d  nn0 cannot occur for pions absorbed by the deuteron from an atomic s-state.
(20)