556 10 Particle Physics – II
10.91 The neutral kaonsK^0 andK^0 are the charge conjugate of each other and are
distinguished by their strangeness. However, they decay similarly and mixing
can occur by a virtual process likeK^0 ⇔π++π−⇔K^0. Starting with a
pure beam ofK^0 ’s att=0 obtain the intensity ofK^0 ’s andK^0 ’s at timet,
in terms of the mean lifetimesτL(0. 9 × 10 −^10 s) andτs(0. 5 × 10 −^7 s)forthe
componentsKLandKs, long lived and short lived respectively.
10.92 Suppose one starts with a pure beam ofK^0 ’s which traverses in vacuum
for a time of the order of 100Ksmean lives so that all theKs- component
has decayed and one is left withKLonly. If now theKLtraverses a carbon
screen some of theKSstates are regenerated. Explain this phenomenon of
regeneration.
10.2.6 Electro-WeakInteractions...........................
10.93 The observation of the processνμe−→νμe−, signifies the presence of a
neutral current interaction. Similarly, why does the processνee− →νee−,
not indicate the presence of such an interaction?
10.94 From the data on the partial and full decay width ofZ^0 boson show that the
number of neutrino generations is 3 only.
Γz(total)= 2 .534 GeV,Γ(z^0 →hadrons)= 1 .797 GeV,
Γ(z^0 →l+l−)= 0 .084 GeV.Theoretical value forΓ(z^0 →νlνl)= 0 .166 GeV.
10.95 (a) What are the experimental signatures and with what detectors would one
measure (a)W→eνandW→μν(b)Z^0 →e+e−andZ^0 →μ+μ−
(b) The weak force is due toW,Zexchange, mass∼=100 GeV. Give the
range in meters.
[University of London 2000]
10.96 Using the results of electro-weak theory of Salam and Weinberg, calculate
the masses ofWandZbosons. Take the fine-structure constantα= 1 / 128
and Fermi’s constantGF/^3 c^3 = 1. 166 × 10 −^5 GeV−^2 and Weinberg angle
θW=^28.^17 ◦
10.2.7 FeynmanDiagrams ................................
10.97 Explain which force is responsible for the following particle interactions
and draw a Feynman diagram for each:
[University of Wales, Aberystwyth 2004]
(i)τ+→μ++νμ+ντ
(ii) K−+p→Ω−+K++K^0 (K−=su;K+=us;K^0 =ds;Ω−=sss)
(iii) D^0 →K++π− (D^0 =uc;K+=us;π−=du)