Weak Interactions: W and Z bosons Particle Physics Weak interaction of hadrons. Weak interactions of hadrons: constituent quarks emit or absorb W bosons e- g W- W ν d gud e n d u u d p u Figure 93: Neutron β-decay. d π− d π− u u W- s d Λ u Λ s W- d u u d u p u p d u Figure 94: The dominant quark diagrams for Λ decay. Oxana Smirnova & Vincent Hedberg Lund University 193 Weak Interactions: W and Z bosons Particle Physics Lepton-quark symmetry: corresponding generations of quarks and leptons have identical weak interactions: ν ν ν µ c τ t e ↔ u ↔ ↔ e- d µ- s τ- b u d u d c s c s g ud gud gcs gcs ± ± ± ± W W W W Figure 95: The W-quark vertices obtained from lepton-quark symmetry if quark mixing is ignored. Examples of reactions allowed and not allowed in the lepton-quark symmetry scheme are pion and kaon decay: − − − π → µ + νµ du → µ + νµ allowed ! - − − K → µ + νµ su → µ + νµ not allowed ! Oxana Smirnova & Vincent Hedberg Lund University 194 Weak Interactions: W and Z bosons Particle Physics The kaon decay can be made allowed by introducing quark mixing (originally proposed by Cabibbo). According to the quark mixing scheme, d- and s-quarks participate in the weak interactions via the linear combinations: θ θ d' = dcos C + ssin C θ θ s' = –dsin C + scos C θ where the parameter C is called the Cabibbo angle. With quark mixing the quark-lepton symmetry applies to doublets like u and c d' s' u d’ u d u s gW gud gus ≡ + ± ± ± W W W θ θ gud=gWcos C gus=gWsin C Figure 96: The ud´W vertex can be interpreted as a sum of the udW and usW vertices. Oxana Smirnova & Vincent Hedberg Lund University 195 Weak Interactions: W and Z bosons Particle Physics With the quark mixing hypothesis some more W-quark vertices are allowed: u d u d c s c s g gud ud gcs gcs g cosθ g cosθ g cosθ g cosθ W C W C W C W C ± ± ± ± W W W W u s u s c d c d gus g us gcd gcd g sinθ W C g sinθ –g sinθ –g sinθ W C W C W C ± ± ± ± W W W W Figure 97: The basic W-quark vertices if quark mixing is taken into account. The top row of diagrams have couplings given by θ gud ==gcs gW cos C (102) while the bottom row diagrams have the couplings θ gus ==–gcd gW sin C (103) Oxana Smirnova & Vincent Hedberg Lund University 196 Weak Interactions: W and Z bosons Particle Physics The Cabibbo angle is measured experimentally by comparing decay rates like: Γ()- → µ-ν 2 K µ gus 2 ----------------------------------- ∝θ--------- = tan Γπ()- → µ-ν 2 C µ gud which give the result θ ° ± ° C = 12,7 0,1 (104) θ , gW cosC = 0 98gW θ , gW sinC = 0 22gW The charmed quark couplings gcd and gcs are measured in neutrino scattering experiments and this give the same result: θ ° ± ° C = 12 1 Oxana Smirnova & Vincent Hedberg Lund University 197 Weak Interactions: W and Z bosons Particle Physics Experimentally it has been observed that charmed hadrons almost always decays into strange hadrons. µ µ ν ν µ µ g g W W + W W+ θ c g cos g sinθ W C c W C s d Figure 98: Cabbibo-allowed and Cabbibo-suppressed semi-leptonic decay of a charmed quark. The ratio of semi-leptonic decays with Cabbibo-allowed and Cabibbo surpressed couplings are given by 2 g 2 1 --------cd ==tan θ ------ 2 C 20 gcs Oxana Smirnova & Vincent Hedberg Lund University 198 Weak Interactions: W and Z bosons Particle Physics The third generation The existence of the c-quark was first predicted from the lepton-quark symmetry. After the discovery of τ, ντ, and b, the sixth quark was predicted to complete the symmetry and the top-quark was discovered in 1994 with a mass of about 180 GeV/c2. The two generation quark mixing is conveniently written in matrix form as: cosθ sinθ d' = C C d (105) θ θ s' –sin C cos C s A third generation: gives rise to the Cabibbo-Kobayashi-Maskawa (CKM) matrix Vαβ : V V V d' ud us ub d = V V V s' cd cs cb s b' b (106) Vtd Vts Vtb Oxana Smirnova & Vincent Hedberg Lund University 199 Weak Interactions: W and Z bosons Particle Physics The coupling constants are then: α ,, β ,, ) gαβ ===gWVαβ ( uct; dsb (107) If the mixing between the b quark and (d,s) quarks can be neglected, the CKM matrix is reduced to V V V θ θ ud us ub cos C sinC 0 V V V ≈ θ θ (108) cd cs cb –sin C cosC 0 Vtd Vts Vtb 001 and hence b’=b. Since the two-generation mixing model agree well with data Vub, Vcb, Vtd and Vts must be small. Oxana Smirnova & Vincent Hedberg Lund University 200 Weak Interactions: W and Z bosons Particle Physics The b-quark is heavy (mass=4.5 GeV) and it can decay to the lighter u and c quarks as in the following decay: l- g W - W ν l V g b ub W gub u Figure 99: The semi-leptonic decay of the b-quark to a lighter quark. This decay modes has a rate proportional to the squared couplings: 2 2 2 gub = Vub gW (109) If Vub and Vcb are 0, b-quark must be stable. τ ≈ –12 Experimentally, b 10 s which is a long but not infinite lifetime. Oxana Smirnova & Vincent Hedberg Lund University 201 Weak Interactions: W and Z bosons Particle Physics The weak b-quark decay can be compared to that of the τ-lepton. l- g W - W ν l τ− g W ντ Figure 100: The decay of the τ-lepton. This decay should have decay rates 2 proportional to gW . If one assumes thatVub = 1 then one can predict what lifetime this would result in for the b-meson: 5 1 mτ τ ≈ ----------- τ ≈ –15 b . τ 10 s Nmb -13 where ττ≈3x10 s is the lifetime of the τ-lepton, N is the number of possible b-quark decays per τ analogous -decays (3 or 4) and mτ and mb are the masses of the τ and the b. Oxana Smirnova & Vincent Hedberg Lund University 202 Weak Interactions: W and Z bosons Particle Physics τ ≈ ∞ Vub ==Vcb 0 b Conclusion: τ ≈ –15 Vub = 1 b 10 s τ ≈ –12 Experimentally: b 10 s The most precise measurements at present yield ≈ , ≈ , Vub 0 004 and Vcb 004 (110) V V V θ θ , ud us ub cos C sin C 0004 V V V ≈ –sinθ cosθ 004, cd cs cb C C Vtd Vts Vtb ∼ 0 ∼ 0 ∼ 1 098, 022, 0004, ≈ , , , –022 098 004 ∼ 0 ∼ 0 ∼ 1 Oxana Smirnova & Vincent Hedberg Lund University 203 Weak Interactions: W and Z bosons Particle Physics The top-quark The top-quark is much heavier than even W bosons and can decay by W+ W+ W+ ≅ ≅ t gtd 0 t gts 0 t gts= gW d s b Figure 101: Weak interactions involving the top-quark. ≅ ≅ Since gtd 0 and gts 0 the only significant decay mode of the t-quark is t → W+ + b (111) with a rate proportional to α 2 ⁄ π ≈ × –3 W = gW 4 4,2 10 Γα∼ ∼ Estimation of the decay width: Wmt 1 GeV suggests a very short lifetime for the top-quark: τ ≈ × –25 t 4 10 s (112) Oxana Smirnova & Vincent Hedberg Lund University 204 Weak Interactions: W and Z bosons Particle Physics Discovery of the top quark. The top-quark was discovered in pp-collisions in the Collider Detector at Fermilab (CDF) in 1994. The Tevatron accelerator with a collision energy = 1.8 TeV was used. PRODUCTION: In proton colliders, pairs of top quarks are produced by the quark-antiquark annihilation process: q + q → g → t + t (113) p t q g q p t Figure 102: The production of top quarks in pp annihilation. Oxana Smirnova & Vincent Hedberg Lund University 205 Weak Interactions: W and Z bosons Particle Physics DECAY: The top quark decay in most cases to a b-quark and to a W which in turn decays to leptons or quarks: l+ q + W ν l W- q t b t b Figure 103: The decay of top quarks. The final state is a complex mix of jets and leptons: - ν ← l + l {q + q ← W - + b ← p + p t + t + X ← W + + b + ν ← l + l {q + q Figure 104: The production of tt-pairs in pp-collisions. Oxana Smirnova & Vincent Hedberg Lund University 206 Weak Interactions: W and Z bosons Particle Physics Figure 105: The CDF experiment which discovered the top quark. Oxana Smirnova & Vincent Hedberg Lund University 207 Weak Interactions: W and Z bosons Particle Physics The events that the CDF collaboration searched for were: t + t → b + l + ν + b + q + q where the lepton l was either an electron or a muon. SIGNATURE: Two b-jets Two light quark jets Missing energy from the neutrino Lepton with large transverse energy Figure 106: A top event in the CDF experiment. Oxana Smirnova & Vincent Hedberg Lund University 208 Weak Interactions: W and Z bosons Particle Physics The measured mass distribution (by the CDF experiment) of the events with the required signature was: Expected Signal Expected Background Figure 107: Mass distribution of top events.