554 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 particleXdecays at rest weakly as follows
X→π^0 +μ++νμ
Determine the following properties ofX
(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 X10.77 Theα-decay of an excited 2−state in^16 O to the ground 0+state of^12 Cis
found to have a widthTα∼= 1. 0 × 10 −^10 eV. Explain why this decay indicates
a parity-violating potential.
10.78 Given the mean life time ofμ+meson is 2. 197 μs and its branching fraction
forμ+→e++νe+νμis 100%, estimate the mean lifetime ofτ+if the
branching fractionBfor the decayτ+→e++νe+ντis 17.7%. The masses
of muon andτ-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 (JpI= 1 −^0 )
(b)η^0 (JpI= 0 −^0 )
(c) f^0 (JpI= 2 +^0 )
10.80 Why is the decayη→ 4 πnot observed?
10.81 Van Royen-Weisskopf proposed a formula for the partial width of the lep-
tonic decays of the vector mesons. For the vector mesonsρ^0 (765),ω^0 (785)
andΦ^0 (1,020) which have similar masses, the partial widthΓ∝Q^2 where
Q^2 =
∣
∣∑aiQi∣
∣^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)=cdmeson
as Cabibbo-allowed, Cabibbo-suppressed or forbidden in lowest order weak
interactions.
(a)D+→K++π−+e++νe
(b)D+→π++π−+e++νe