546
10 Particle Physics – II
10.10 Show that (a) ρ → η + π is forbidden as a decay through strong interaction.
(b) ω → η + π is forbidden as an electro-magnetic or strong decay.
10.11 (a) The ρ
0 and K
0 mesons both decay predominantly to π
+
+ π
− . Explain
why the mean lifetime of the ρ
0 is 10
−23 s, while that of K
0 is 0.89 ×
10
−10 s.
(b) The Δ
0 and the Λ both decay to proton and π
− meson. Explain why the
Δ
0 meson lifetime is ∼10
−23 s while that of Λ is 2.6 × 10
−10 s.
10.12 State and give reasons for the following decay modes of the ρ-meson
(J
p
= 1
−
, I = 1) which are allowed by the strong or electromagnetic interaction
(a) ρ
0
→ π
+
π
−
(b) ρ
0
→ π
0
π
0
(c) ρ
0
→ η
0
π
0
(d) ρ
0
→ π
0
γ
10.13 Conventionally nucleon is given positive parity. What does one say about
deuteron’s parity and the intrinsic parities of u and d-quarks?
10.14 Which of the following hyperon decays are allowed in lowest order weak
interactions?
(a) Ξ
0
→ Σ
−
+ e
+
+ ν e
(b) Ξ
0
→ p + π
−
+ π
0
(c) Ω
−
→ Ξ
0
+ e
−
+ ν e
(d) Ω
−
→ Ξ
−
+ π
+
+ π
−
10.15 Explain how the parity of K
− meson has been determined.
10.16 (a) Briefly define the following terms giving two examples of each:
(i) Hadron
(ii) Lepton
(iii) Baryon
(iv) Meson
(b) A π
0 meson at rest decays into two photons of equal energy. What is the
wavelength (in m) of the photons? [The mass of the π
0 is 135 MeV/c
2 ]
[University of London]
10.2.2 Strong Interactions
10.17 (a) The Δ
++ Resonance has a full width of Γ = 120 MeV. How far on average would such a particle of energy 200 GeV travel before decaying?
(b) Given that the width for W-boson decay is less than 6.5 MeV, estimate the
limit for the corresponding lifetime.
10.18 Analyze the pion – proton scattering data in terms of isospin amplitudes a 1/2
and a 3/2 for the reactions:
10 Particle Physics – II
10.10 Show that (a) ρ → η + π is forbidden as a decay through strong interaction.
(b) ω → η + π is forbidden as an electro-magnetic or strong decay.
10.11 (a) The ρ
0 and K
0 mesons both decay predominantly to π
+
+ π
− . Explain
why the mean lifetime of the ρ
0 is 10
−23 s, while that of K
0 is 0.89 ×
10
−10 s.
(b) The Δ
0 and the Λ both decay to proton and π
− meson. Explain why the
Δ
0 meson lifetime is ∼10
−23 s while that of Λ is 2.6 × 10
−10 s.
10.12 State and give reasons for the following decay modes of the ρ-meson
(J
p
= 1
−
, I = 1) which are allowed by the strong or electromagnetic interaction
(a) ρ
0
→ π
+
π
−
(b) ρ
0
→ π
0
π
0
(c) ρ
0
→ η
0
π
0
(d) ρ
0
→ π
0
γ
10.13 Conventionally nucleon is given positive parity. What does one say about
deuteron’s parity and the intrinsic parities of u and d-quarks?
10.14 Which of the following hyperon decays are allowed in lowest order weak
interactions?
(a) Ξ
0
→ Σ
−
+ e
+
+ ν e
(b) Ξ
0
→ p + π
−
+ π
0
(c) Ω
−
→ Ξ
0
+ e
−
+ ν e
(d) Ω
−
→ Ξ
−
+ π
+
+ π
−
10.15 Explain how the parity of K
− meson has been determined.
10.16 (a) Briefly define the following terms giving two examples of each:
(i) Hadron
(ii) Lepton
(iii) Baryon
(iv) Meson
(b) A π
0 meson at rest decays into two photons of equal energy. What is the
wavelength (in m) of the photons? [The mass of the π
0 is 135 MeV/c
2 ]
[University of London]
10.2.2 Strong Interactions
10.17 (a) The Δ
++ Resonance has a full width of Γ = 120 MeV. How far on average would such a particle of energy 200 GeV travel before decaying?
(b) Given that the width for W-boson decay is less than 6.5 MeV, estimate the
limit for the corresponding lifetime.
10.18 Analyze the pion – proton scattering data in terms of isospin amplitudes a 1/2
and a 3/2 for the reactions: