Interactions... + similar terms for µ and τ Feynman rule: gauge-boson propagator: ig 2 2 γ λ(1 γ 5 ) = i(g µν k µ k ν /M 2 W ) k 2 M 2 W

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1 Interactions... L W-l = g [ νγµ (1 γ 5 )ew µ + +ēγ µ (1 γ 5 )νwµ ] + similar terms for µ and τ Feynman rule: e λ ig γ λ(1 γ 5 ) ν gauge-boson propagator: W = i(g µν k µ k ν /M W ) k M W. Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

2 Compute ν µ e µν e σ(ν µ e µν e ) = g4 m e E ν 16πM 4 W [1 (m µ m e)/m e E ν ] (1 + m e E ν /M W ) Reproduces 4-fermion result at low energies if g 4 16M 4 W = G F g 4 = 3(G F M W ) = 64 ( GF MW ) g ( GF M ) 1 W = Using M W = gv/, determine v = (G F ) 1 46 GeV the electroweak scale φ 0 0 = (G F 8) GeV Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

3 W-propagator modifies HE behavior σ(ν µ e µν e ) = g4 m e E ν 16πM 4 W [1 (m µ m e)/m e E ν ] (1 + m e E ν /M W ) lim σ(ν µe µν e ) = E ν g 4 3πM W = G F M W independent of energy! partial-wave unitarity respected for s < M W[exp(π /G F M W) 1] Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

4 W-boson properties No prediction yet for M W (haven t determined g) Leptonic decay W e ν e e(p) p ( MW ; M W sin θ, 0, M ) W cos θ W ν e (q) q ( MW ; M W sin θ, 0, M ) W cosθ M = i G F MW 1 ū(e, p)γ µ (1 γ 5 )v(ν, q) ε µ ε µ = (0; ˆε): W polarization vector in its rest frame M = G F M W tr [/ε(1 γ 5 )q/(1 + γ 5 )/ε p/] ; tr[ ] = [ε q ε p ε ε q p + ε p ε q + iɛ µνρσ ε µ q ν ε ρ p σ ] decay rate is independent of W polarization; look first at longitudinal pol. ε µ = (0; 0,0,1) = ε µ, eliminate ɛ µνρσ M = 4G F M 4 W sin θ Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

5 dγ 0 dω = M 64π S 1 M 3 W S 1 = and [M W (m e + m ν ) ][M W (m e m ν ) ] = M W dγ 0 dω = G F M 3 W 16π sin θ Γ(W eν) = G F M 3 W 6π Other helicities: ε µ ±1 = (0; 1, i, 0)/ dγ ±1 dω = G F MW 3 3π (1 cosθ) Extinctions at cos θ = ±1 are consequences of angular momentum conservation: e ν e W (θ =0) forbidden (θ = π) allowed ν e e (situation reversed for W + e + ν e ) e + follows polarization direction of W + e avoids polarization direction of W important for discovery of W ± in pp ( qq) C violation Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

6 Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

7 Interactions... L A-l = gg g + g ēγµ ea µ...vector interaction; A µ as γ, provided gg / g + g e Define g = g tanθ W θ W : weak mixing angle g = e/sin θ W e g = e/cos θ W e Z µ = b 3 µ cos θ W A µ sinθ W A µ = A µ cosθ W + b 3 µ sinθ W L Z e = L Z ν = g νγ µ (1 γ 5 )ν Z µ 4cos θ W g ē [L e γ µ (1 γ 5 ) + R e γ µ (1 + γ 5 )] ez µ 4cos θ W L e = sin θ W 1 = x W + τ 3 R e = sin θ W = x W Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

8 Z-boson properties Decay calculation analogous to W ± Γ(Z ν ν) = G FMZ 3 1π Γ(Z e + e ) = Γ(Z ν ν) [ L e + ] R e Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

9 Z-boson properties Decay calculation analogous to W ± Γ(Z ν ν) = G FMZ 3 1π Γ(Z e + e ) = Γ(Z ν ν) [ L e + ] R e Neutral-current interactions New νe reaction, not present in V A ν µ e ν µ e σ(ν µ e ν µ e) = G F m ee ν π σ( ν µ e ν µ e) = G F m ee ν π σ(ν e e ν e e) = G F m ee ν π σ( ν e e ν e e) = G F m ee ν π L e + R e /3 L e/3 + R e (L e + ) + R e/3 (L e + ) /3 + R e Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

10 Gargamelle ν µ e Event Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

11 Model-independent analysis Measure all cross sections to determine chiral couplings L e and R e or traditional vector and axial couplings v and a a = 1 (L e R e ) v = 1 (L e R e ) L e = v + a R e = v a model-independent in V, A framework Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

12 Neutrino electron scattering Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

13 Twofold ambiguity remains even after measuring all four cross sections: same cross sections result if we interchange R e R e (v a) Consider e + e µ + µ M = ie ū(µ, q )γ λ Q µ v(µ, q + ) gλν s v(e, p +)γ ν u(e.p ) + i G F M Z ū(µ, q )γ λ [R µ (1 + γ 5 ) + L µ (1 γ 5 )]v(µ, q + ) gλν s M Z v(e, p + )γ ν [R e (1 + γ 5 ) + L e (1 γ 5 )]u(e, p ) muon charge Q µ = 1 dσ dz = πα Q µ s (1 + z ) αq µg F M Z (s M Z ) 8 [(s M Z ) + M Z Γ ] [(R e + L e )(R µ + L µ )(1 + z ) + (R e L e )(R µ L µ )z] G F + M4 Z s 64π[(s MZ ) + MZ Γ ] [(R e + L e )(R µ + L µ )(1 + z ) + (R e L e )(R µ L µ )z] Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

14 F-B asymmetry A dz dσ/dz 0 1 dz dσ/dz dz dσ/dz lim A = s/m Z 1 3G F s 16παQ µ (R e L e )(R µ L µ ) s 1 GeV (R e L e )(R µ L µ ) = 3G F sa /4πα A FB 1 SPEAR MARK I PEP HRS PETRA CELLO TRISTAN AMY LEP L MAC JADE TOPAZ 0.5 MARK II MARK J PLUTO VENUS 0.5 TASSO e + e - µ + µ s [GeV] J. Mnich Phys. Rep. 71, (1996) Measuring A resolves ambiguity Validate EW theory, measure sin θ W Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

15 Neutrino electron scattering Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

16 With a measurement of sin θ W, predict M W = g v /4 = e /4G F sin θ W (37.3 GeV/c ) / sin θ W M Z = M W / cos θ W Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

17 UA1 Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

18 10-31 σ [cm ] E ν [GeV] At low energies: σ( ν e e hadrons) > σ(ν µ e µν e ) > σ(ν e e ν e e) > σ( (ν e e ν µ µ) > σ( ν e e ν e e) > σ(ν µ e ν µ e) > σ( ν µ e ν µ e) Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

19 EW interactions of quarks Left-handed doublet L q = u d L I 3 Q Y = (Q I 3 ) two right-handed singlets I 3 Q Y = (Q I 3 ) R u = u R R d = d R CC interaction L W-q = g ūeγ µ (1 γ 5 )d W + µ + dγ µ (1 γ 5 )u W µ identical in form to L W-l: universality weak isospin NC interaction L Z-q = g 4 cosθ W i=u,d q i γ µ [L i (1 γ 5 ) + R i (1 + γ 5 )] q i Z µ L i = τ 3 Q i sin θ W R i = Q i sin θ W equivalent in form (not numbers) to L Z-l Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

20 Trouble in Paradise Universal u d, ν e e not quite right Good: u d L Better: u d θ d θ d cosθ C + s sin θ C cosθ C = ± L Cabibbo-rotated doublet perfects CC interaction (up to small third-generation effects) but serious trouble for NC L Z-q = g 4cos θ W Z µ {ūγ µ [L u (1 γ 5 ) + R u (1 + γ 5 )] u + dγ µ [L d (1 γ 5 ) + R d (1 + γ 5 )] d cos θ C + sγ µ [L d (1 γ 5 ) + R d (1 + γ 5 )] s sin θ C + dγ µ [L d (1 γ 5 ) + R d (1 + γ 5 )] s sin θ C cosθ C + sγ µ [L d (1 γ 5 ) + R d (1 + γ 5 )] d sin θ C cosθ C } Strangeness-changing NC interactions highly suppressed! ν ν BNL E-787/E-949 has three s d K + π + ν ν candidates, K + π+ with B(K + π + ν ν) = u (SM: 0.8 ± 0.3) Phys. Rev. Lett. 93, (004) Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

21 Glashow Iliopoulos Maiani two left-handed doublets ν e e L ν µ µ L u d θ L c s θ L (s θ = s cos θ C d sinθ C ) + right-handed singlets, e R, µ R, u R, d R, c R, s R Required new charmed quark, c Cross terms vanish in L Z-q, q i λ ig 4cosθ W γ λ [(1 γ 5 )L i +(1+γ 5 )R i ], q i L i = τ 3 Q i sin θ W R i = Q i sin θ W flavor-diagonal interaction! Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

22 Straightforward generalization to n quark doublets composite Ψ = L W-q = g Weak-isospin part: u c. d s. Ψγ µ (1 γ 5 )OΨ W + µ + h.c. L iso Z-q = Since O, O = I 0 flavor structure O = 0 U 0 0 U: unitary quark mixing matrix g Ψγ µ (1 γ 5 ) O, O Ψ 4 cosθ W τ 3 0 I NC interaction is flavor-diagonal General n n quark-mixing matrix U: n(n 1)/ real, (n 1)(n )/ complex phases 3 3 (Cabibbo Kobayashi-Maskawa): phase CP violation Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

23 Qualitative successes of SU() L U(1) Y theory: neutral-current interactions necessity of charm existence and properties of W ± and Z 0 Decade of precision tests EW (one-per-mille) M Z ±.1 MeV/c Γ Z σhadronic 0 Γ hadronic Γ leptonic Γ invisible 495. ±.3 MeV ± nb ±.0 MeV ± MeV ± 1.5 MeV where Γ invisible Γ Z Γ hadronic 3Γ leptonic light neutrinos N ν = Γ invisible /Γ SM (Z ν i ν i ) Current value: N ν =.994 ± excellent agreement with ν e, ν µ, and ν τ Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

24 Three light neutrinos Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

25 Two families The top quark must exist u d L c s don t account for CP violation. Need a third family... or another answer. Given the existence of b, (τ) top is needed for an anomaly-free EW theory absence of FCNC in b decay (b sl + l, etc.) b has weak isospin I 3L = 1 ; needs partner t e b L Z 0 L b =I 3L Q b sin θ W L e R b =I 3R Q b sin θ W Chris Quigg Electroweak Theory Fermilab Academic Lectures bis

26 Measure I (b) 3L = I(b) 3R = 0.08 ± Needed: top with I 3L = + 1 D. Schaile & P. Zerwas, Phys. Rev. D45, 36 (199) Chris Quigg Electroweak Theory Fermilab Academic Lectures bis