1000 Solved Problems in Modern Physics

552 10 Particle Physics – II

dσ

dΩ

=

α^2 ^2 c^2

4 E^2 CM

(1+cos^2 θ)

whereECMis the total centre of mass energy andθis the scattering angle

with respect to the beam direction. Calculate the total cross-section at this

energy.

10.60 (a) TheΣ^0 hyperon decays toΛ+γwith a mean lifetime of 7. 4 × 10 −^20 s.
Estimate its width.
(b) Explain why the absence of the decayK+→π++γcan be considered
an argument in favor of spin zero forK+meson.
10.61 Positronium is the bound state of positron and electron. It is found either in
the singlet s-state (para-positronium) or in a triplet s-state (ortho-positronium).
Show how the C-invariance restricts the number of photons into which the
positronium can annihilate for these two types of systems
10.62 Which of the following processes are allowed in electro-magnetic interac-
tions, and which are allowed in weak interactions via the exchange of a single
W±orZ^0?

(a)K+→π^0 +e++νe

(b)Σ^0 →Λ+νe+νe

10.2.5 WeakInteractions..................................

10.63 Estimate the rate of decay for D+(1,869)→e++anything, D^0 (1,864)→

e++anything. Given the branching fractionsB=19%, and 8% respectively,

τD+= 10. 6 × 10 −^13 s,τD^0 = 4. 2 × 10 −^13 s

10.64 It is observed that the cross section for neutrino-electron scattering falls by

20% as the momentum transfer increases from very small values to 30 GeV/c.

Deduce the mass of the exchanged boson.

10.65 Estimate the number ofW+→e+νeevents produced in 10^9 pp−interactions

[The cross-sectionsσ(pp−→W+)= 1 .8 nb andσ(pp−→anything)=

70 mb]

(University of Cambridge, Tripos 2004)

10.66 Use Cabibbo theory to explain the difference in the decaysD+→K^0 μ+νμ

andD+→π^0 μ+νμ. Given that theD+consists of a c quark anddantiquark.

10.67 Show that the ratio of decay rates

R≡

Γ(Σ−→n+e−+νe)

Γ(Σ−→Λ+e−+νe)

∼= 17