1000 Solved Problems in Modern Physics

584 10 Particle Physics – II Meson Quark wave function |ΣaiQi|^2 ρ^0 (uu−dd)/ √ 2 [ √^1 2 ( 2 3 − ( −^13 ))]^2 =^12 ω^0 (uu+dd)/ ...

10.3 Solutions 585 νμ=ν 1 cosθ+ν 2 sinθ (1) andνe=−ν 1 sinθ+ν 2 cosθ (2) which form a set of ortho normal states.νμandνeare the ...

586 10 Particle Physics – II 10.87 (a)Pe(t)= 1 −Pμ(t)=sin^22 θsin^2 [ (E 2 −E 1 ) 2 t ] (b)Pμ(t)=Pe(t) 1 −sin^22 θsin^2 [ (E 2 − ...

10.3 Solutions 587 Fig. 10.12 10.89 The reaction (a) can go via the mechanism of the diagram shown in Fig. 10.12a. However, no d ...

588 10 Particle Physics – II 10.91 Let aK^0 beam be formed through a strong interaction likeπ−+p→K^0 +Λ. Neither ∣ ∣K^0 〉nor ∣ ∣ ...

10.3 Solutions 589 |Ks〉= 1 √ 2 (∣ ∣K^0 〉 + ∣ ∣ ∣K^0 〉) |KL〉= 1 √ 2 (∣ ∣K^0 〉− ∣ ∣ ∣K^0 〉) ψ(t)= 1 2 e−imsc (^2) t/[ e−t/^2 τs ( ...

590 10 Particle Physics – II Since f =f, we conclude that some of theKS-state has regenerated. The regeneration of the short li ...

10.3 Solutions 591 However, forνe+e−→νe+e−, there are two diagrams shown in Fig. 10.13b and Fig. 10.13c. Thus the reaction can b ...

592 10 Particle Physics – II (b)R∼ c mc^2 = 197 MeV−fm 100 × 103 MeV = 2 × 10 −^3 fm 10.96 MW^2 = 4 πα 8sin^2 θW · √ 2 (c)^3 G ...

10.3 Solutions 593 Diagram is the same as in Problem 10.2(iii) (ii) τ−→μ−+l+l Fig. 10.16(a)Decay ofτ− τ−→ντ+μ−+νμ (iii)l=νμ Fig. ...

594 10 Particle Physics – II (b)Ω−→ΛK− Fig. 10.17 (b) 10.100 (a) e+e−→νμνμ Fig. 10.18 (a) (b) D^0 →K−π+ Fig. 10.18 (b) ...

10.3 Solutions 595 10.101 (a) Fig. 10.19(a)Moller scattering (b) Fig. 10.19(b)Bhabha scattering 10.102 (a)Λ→p+e−+νe Fig. 10.20(a ...

596 10 Particle Physics – II (b) Fig. 10.20(b) 10.103 (a) Fig. 10.21(a) (b) Fig. 10.21(b) 10.104 The Feynman diagram is Fig. 10. ...

10.3 Solutions 597 The two vertices 1 and 2 where the W boson couples pertain to weak interactions and have strengths √ αw. Vert ...

598 10 Particle Physics – II For the neutral pion there are two vertices of strength √ αembut the propa- gator term is absent be ...

10.3 Solutions 599 10.108 (a) Fig. 10.26(a)Photo electric effect (b) Fig. 10.26(b)Lowest order Feynman diagrams for the Compton ...

600 10 Particle Physics – II 10.110 Fig. 10.28(a) Fig. 10.28(b) The decayK+→π+π+π−. In all hadrons, gluon interactions keep the ...

10.3 Solutions 601 where the combinations (1,2) are (e+,νe)or(μ+,νμ)or(d ̄,u), the last one three times for three colors. The co ...

602 10 Particle Physics – II 10.113 Fig. 10.31 Λ→pπ− Λ=uds;p=udu;π−=ud ̄ ...

Appendix: Problem Index........................................... Chapter 1 Mathematical Physics 1.2.1 Vector Calculus Ifφ= 1 / ...