10.2 Problems 547
π++p→π++p (1)
π−+p=π−+p (2)
π−+p=π^0 +n (3)
Show that ifa 1 / 2 a 3 / 2 thenσ 1 :σ 2 :σ 3 =9:1:2andifa 1 / 2 a 3 / 2 ,
thenσ 1 :σ 2 :σ 3 =0:2:110.19 Use the results ofπ-N scattering at the same energy,
σ+(π+p→π+p)=∣
∣a 3 / 2∣
∣^2
σ−(π−p→π−p)=1
9
∣
∣a 3 / 2 + 2 a 1 / 2∣
∣^2
σ^0 (π−p→π^0 n)=2
9
∣
∣a 3 / 2 −a 1 / 2∣
∣^2
to deduce the inequality√
σ++√
σ−−√
2 σ^0 ≥ 010.20 Calculate the branching ratio for the decay of the resonanceΔ+(1232) which
has two decay modes
Δ+→pπ^0
→nπ+
10.21 A resonance X+(1520) decays by the strong interaction to the final states nπ+
andpπ^0 with branching ratios of approximately 36 and 18% respectively.
What is its isospin?
10.22 Given that theρ-meson has a width of 158 MeV/C^2 in its mass, how would
you classify the interaction for its decay?
10.23 In which isospin states can (a)π+π−π^0 (b)π^0 π^0 π^0 exist?
10.24 The particlesXandYcan be produced by strong interaction
K−+p→K++X
K−+p→π^0 +Y
Identify the particlesX(1,321 MeV) andY(1,192 MeV) and deduce their
quark content. If their decay schemes areX→Λ+π−andY→Λ+γ,
give a rough estimate of their lifetime.10.25 The scattering of pions by proton shows evidence of a resonance at a centre
of mass system momentum of 230 MeV/c. At this momentum, the cross-
section for scattering of positive pions reaches a peak cross-section of 190 mb
while that of negative pions is only 70 mb. What can you deduce about the
properties of the resonance (a) from the ratio of the two cross-sections (b)
from the magnitude of the larger?
[University of Bristol]