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10 Particle Physics – II
neutrino energy was spread between 5 and 15 MeV over a period of 4 s.
Estimate the upper limit for the mass of neutrino.
10.76 A particle X decays at rest weakly as follows
X → π
0
+ μ
+
+ ν μ
Determine the following properties of X
(a) Charge
(b) baryon number
(c) Lepton number
(d) Isospin
(e) Strangeness
(f) spin
(g) boson or fermion
(h) lower limit on its mass in MeV/c
2
(i) Identity of X
10.77 The α-decay of an excited 2
− state in
16 O to the ground 0
+ state of
12 C is
found to have a width T α ∼ = 1.0×10
−10 eV . Explain why this decay indicates
a parity-violating potential.
10.78 Given the mean life time of μ
+ meson is 2.197 μs and its branching fraction
for μ
+
→ e
+
+ ν e + ν μ is 100%, estimate the mean lifetime of τ
+ if the
branching fraction B for the decay τ
+
→ e
+
+ ν e + ν τ is 17.7%. The masses
of muon and τ -lepton are 105.658 and 1,784 MeV.
10.79 State with reasoning which of the following particles may undergo two-pion
decay?
(a) ω
0 (J
pI
= 1
−0 )
(b) η
0 (J
pI
= 0
−0 )
(c) f
0 (J
pI
= 2
+0 )
10.80 Why is the decay η → 4π not observed?
10.81 Van Royen-Weisskopf proposed a formula for the partial width of the leptonic decays of the vector mesons. For the vector mesons ρ
0 (765), ω
0 (785)
and Φ
0 (1,020) which have similar masses, the partial width Γ ∝ Q
2 where
Q
2
=
a i Q i
2 is the squared sum of the charges of the quarks in the
meson. Show that
Γ(ρ
0 ) : Γ(ω
0 ) : Γ(Φ
0 ) = 9 : 1 : 2
[Courtesy D.H. Perkins, Introduction to High Energy Physics, University of
Cambridge Press]
10.82 Classify the following semi-leptonic decays of the D
+ (1,869) = cd meson
as Cabibbo-allowed, Cabibbo-suppressed or forbidden in lowest order weak
interactions.
(a) D
+
→ K
+
+ π
−
+ e
+
+ ν e
(b) D
+
→ π
+
+ π
−
+ e
+
+ ν e