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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 00) 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 nn0 cannot occur for pions absorbed by the deuteron from an atomic s-state. (20)