550
10 Particle Physics – II
(a) π
0
π
0
(b) π
+
π
+
(c) π
+
π
−
(d) Λπ
0
(e) Σ
0
π
0
(f) π
−
π
− ?
10.2.3 Quarks
10.44 Describe the phenomena when a quark is struck by a high energy electron
with a high enough momentum transfer.
10.45 The B
− meson is the lightest particle consisting of a b quark and u antiquark.
Which type of interaction causes its decay. Describe with explanation its
decay chain.
10.46 The 3γ decay of positronium (the bound state of e
+ e
− ) has a width that in
QED is predicted to be Γ(3γ ) = 2(π
2
− 9)α
6 m e c
2
/9π, where α is the fine
structure constant.
(a) If the hadronic decay of the c c bound state J/ψ (3,100) proceeds via an
analogous mechanism, but involving three gluons, use the experimental
hadronic width (fragmentation into hadrons occurring with probability
unity) Γ(3g) = 80 keV to estimate the effective strong interaction coupling constant α s .
(b) Determine α s from the radiative width Γ(ggγ) = 0.16 keV of the b b
bound state γ (9,460)
10.47 Calculate the ratio R of the cross section for e
+ e
−
→ QQ → hadrons to that
for the reaction e
+ e
−
→ μ
+
μ
− as a function of increasing CMS energy up
to 400 GeV. Assume the quark masses in GeV/c
2 up or down 0.31, strange
0.5, charm 1.6, bottom 4.6 and top 175.
10.48 Show that the quark model predicts the following cross-section relation
σ (Σ
− n) = σ( pp) + σ (K
− p) − σ (π
− p)
10.49 Using the additive quark model the total interaction cross-section is assumed
to result from the sum of the cross-sections of various pairs. Assuming that
σ (qq) = σ (qq) prove the relation σ (Λ p) = σ (pp) + σ (K
− n) − σ (π
+ p)
10.50 The coulomb self- energy of a hadron with charge +e or −e is about 1 MeV.
The quark content and rest energies (in MeV)of some hadrons are
n(udd)940, p(uud)938, Σ
− (dds)1197, Σ
0 (uds)1192, Σ
+ (uus)1189,
K
0 (ds)498, K
+ (us)494
The u and d quarks make different contribution to the rest energy. Estimate
this difference.
10 Particle Physics – II
(a) π
0
π
0
(b) π
+
π
+
(c) π
+
π
−
(d) Λπ
0
(e) Σ
0
π
0
(f) π
−
π
− ?
10.2.3 Quarks
10.44 Describe the phenomena when a quark is struck by a high energy electron
with a high enough momentum transfer.
10.45 The B
− meson is the lightest particle consisting of a b quark and u antiquark.
Which type of interaction causes its decay. Describe with explanation its
decay chain.
10.46 The 3γ decay of positronium (the bound state of e
+ e
− ) has a width that in
QED is predicted to be Γ(3γ ) = 2(π
2
− 9)α
6 m e c
2
/9π, where α is the fine
structure constant.
(a) If the hadronic decay of the c c bound state J/ψ (3,100) proceeds via an
analogous mechanism, but involving three gluons, use the experimental
hadronic width (fragmentation into hadrons occurring with probability
unity) Γ(3g) = 80 keV to estimate the effective strong interaction coupling constant α s .
(b) Determine α s from the radiative width Γ(ggγ) = 0.16 keV of the b b
bound state γ (9,460)
10.47 Calculate the ratio R of the cross section for e
+ e
−
→ QQ → hadrons to that
for the reaction e
+ e
−
→ μ
+
μ
− as a function of increasing CMS energy up
to 400 GeV. Assume the quark masses in GeV/c
2 up or down 0.31, strange
0.5, charm 1.6, bottom 4.6 and top 175.
10.48 Show that the quark model predicts the following cross-section relation
σ (Σ
− n) = σ( pp) + σ (K
− p) − σ (π
− p)
10.49 Using the additive quark model the total interaction cross-section is assumed
to result from the sum of the cross-sections of various pairs. Assuming that
σ (qq) = σ (qq) prove the relation σ (Λ p) = σ (pp) + σ (K
− n) − σ (π
+ p)
10.50 The coulomb self- energy of a hadron with charge +e or −e is about 1 MeV.
The quark content and rest energies (in MeV)of some hadrons are
n(udd)940, p(uud)938, Σ
− (dds)1197, Σ
0 (uds)1192, Σ
+ (uus)1189,
K
0 (ds)498, K
+ (us)494
The u and d quarks make different contribution to the rest energy. Estimate
this difference.