At a total centre-of-mass energy

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Particle Physics & Quantum Fields · Symmetry, groups and the quark model

Symmetry and Flavour, Ch Parity, charge conjugation and time reversal as operators, and the CPT theorem

Problem

\sqrt s=2130\,\mathrm{MeV}

, the proton momentum in the

pp

centre-of-mass frame is

p_p^*=504\,\mathrm{MeV}/c

and the pion momentum in the

\pi^+d

centre-of-mass frame is

p_\pi^*=200\,\mathrm{MeV}/c

. Take the cross sections at this energy to be

\sigma(pp\to\pi^+d) = 2.6\,\mathrm{mb}, \qquad \sigma(\pi^+d\to pp) = 11.0\,\mathrm{mb},

and take

s_p=\tfrac12

and

s_d=1

. ((a)) Write down the detailed-balance relation

\frac{\sigma(pp\to\pi^+d)}{\sigma(\pi^+d\to pp)} = 2\,\frac{(2s_\pi+1)(2s_d+1)}{(2s_p+1)^2}\,\frac{p_\pi^{*2}}{p_p^{*2}}

and rearrange it to solve for

2s_\pi+1

. ((b)) Evaluate

2s_\pi+1

and hence the pion's spin

s_\pi