Lecture 16 - Electroweak Theory Electroweak Unification • W and Z Boson masses and widths • Z production at LEP • Forward-backward asymmetries • W production at colliders • Precision tests of Electroweak theory • 1 SU(2) Isospin and U(1) Hypercharge The combined groups SU(2)L U(1) describe electroweak symmetry × SU(2)L describes weak isospin (I3) couplings to left-handed fermions (or right-handed antifermions) U(1) describes weak hypercharge (Y) couplings The weak charged currents are described by SU(2) matrices τ ±: + 1 0 1 − 1 0 0 τ = (τ1 +iτ2)= τ = (τ1 iτ2)= 2 0 0 2 − 1 0 + µ + − µ − J =χ ¯νe γ τ χe J =χ ¯eγ τ χνe These are the currents associated with W + and W − exchange 2 Electroweak Neutral Currents The third component of weak isospin describes a weak neutral current: 3 µ 1 µ µ 1 0 J =χγ ¯ τ3χ =χ ¯νe γ χνe χ¯eγ χe τ3 = 2 − 0 1 − The electromagnetic current couples to charge Q: J EM =χγ ¯ µQχ This can be rewritten in terms of I3 and Y: Y EM 3 1 Y Q = I3 + J = J + J 2 2 The EM current is a sum of weak isospin and hypercharge 3 Electroweak Unification The combined electroweak interaction has a Lagrangian: = gJ.~ W~ + g′J Y B L W~ is a triplet of vector bosons W 1,2,3 coupling to weak isospin currents J 1,2,3 with strength g B0 is a singlet vector boson coupling to the weak hypercharge current J Y with strength g′ The physical vector bosons are: 1 W ± = (W 1 iW 2) r2 ∓ 0 3 0 0 3 0 Z = W cos θW B sin θW A = W sin θW + B cos θW − where the neutral W 3 and B0 mix to give Z0 and photon A0 4 The Weinberg Angle The mixing angle θW is measured to be: 2 sin θW = 0.2221 The weak isospin, hypercharge and EM couplings are related by: ′ g sin θW = g cos θW = e The electroweak Lagrangian can be written out in terms of the physical weak and electromagnetic currents: g − + + − g 3 2 EM 0 EM 0 (J W + J W )+ (J sin θW J )Z + eJ A √2 cos θW − The first terms describe W ± couplings with strength g The last term describes photon couplings with strength e The middle term describes the neutral Z0 coupling. It has pieces from both J 3 and J EM ! 5 Masses of W and Z Bosons The mass of the W boson can be related to sin θW : 2 2 GF g e √2 37.4 = 2 MW = 2 = GeV √2 8MW s8GF sin θW sin θW The mass of the Z boson is related to the mass of the W boson: MW 75 MZ = = GeV cos θW sin2θW These are now very accurately measured: MW = 80.425 0.038 GeV MZ = 91.1876 0.0021 GeV ± ± The large masses of the W and Z compared to the zero mass of the photon break electroweak symmetry Leads to introduction of Higgs mechanism - see next lecture 6 Neutral Current Couplings of Z The Z boson has left-handed couplings from J 3 and J EM and right-handed couplings from J EM : 2 2 gL = I3 Qsin θW gR = Qsin θW − − Usually expressed as vector and axial-vector couplings cV and cA: 2 cV = gL + gR = I3 2Qsin θW cA = gL gR = I3 − − Lepton 2cV 2cA Quark 2cV 2cA 8 2 νe, νµ, ντ 1 1 u,c,t 1 sin θW 1 − 3 2 4 2 e, µ, τ 1+4sin θW -1 d,s,b 1+ sin θW -1 − − 3 Electroweak theory predicts the weak neutral current couplings which depend on fermion type! 7 Z Production at LEP (1989-1995) ] σ0 nb 0 [ 40 Large samples of Z were + − had ALEPH collected in e e collisions σ DELPHI L3 at ECM MZ 30 OPAL ≈ Note interference between Γ 0 Z γ (QED) and Z diagrams 20 measurements, error bars increased by factor 10 Width of the Z0 boson: 10 σ from fit QED unfolded ΓZ = 2.4952 0.0023 GeV ± MZ 86 88 90 92 94 [ ] Ecm GeV 8 Z Couplings to fermions The couplings of the Z0 to ff¯ are: 2 0 ¯ g 2 2 Γ(Z ff)= 2 (cV + cA)f MZ → 48π cos θW The couplings to charged leptons are: 2 0 ¯ g Γ(Z ℓℓ)= 2 MZ = 84 MeV → 192π cos θW Sum of all quark couplings gives ratio of hadron jets to leptons: Γ(Z0 hadrons) R = → = 20.767 0.025 Γ(Z0 leptons) ± → The couplings to neutrinos give the invisible width: Γ(Z0 νν¯)=166MeV Γ(Z0 invisible) = 499 1.5 MeV → → ± The total width requires 2.988 0.023 neutrinos with mν < MZ /2 ± 9 Universality of Z couplings to leptons -0.032 -0.035 e+e−, µ+µ−, τ +τ − mH couplings are same Vl g mt Note the sensitivity -0.038 of these couplings + − ∆α l l to the Higgs mass! + − e e µ+µ− τ+τ− 68% CL -0.041 -0.503 -0.502 -0.501 -0.5 gAl 10 Interference between photon and Z e+e− ff¯ is described by sum of Z0 and photon diagrams: → 2 √2GF MZ f µ f µ e µ e µ Z = [g f¯Rγ fR + g f¯Lγ fL][g e¯Rγ eR + g e¯Lγ eL] M s M 2 R L R L − Z 2 e µ µ γ = [fγ¯ f][¯eγ e] M s The cross-sections depend on fermion helicities: 2 dσ − − α (e e+ µ µ+)= (1 + cos θ)2 1+ rgµge 2 dΩ L R → L R 4s | L L| 2 dσ − − α (e e+ µ µ+)= (1 cos θ)2 1+ rgµ ge 2 dΩ L R → R L 4s − | R L| where r is ratio of coefficients of Z0 and photon amplitudes 11 Forward-Backward Asymmetries Combining all four possible helicity combinations: 2 dσ + − + − α 2 (e e µ µ )= [A0(1 + cos θ)+ A1 cos θ] dΩ → 4s 2 2 2 2 2 2 2 2 2 A0 =1+2Re[r]c + r (c + c ) A1 = 4Re[r]c + 8 r c c V | | V A A | | V A The cos θ term gives a forward-backward asymmetry F B 1 dσ 0 dσ AF B = − F = dΩ B = dΩ F + B dΩ − dΩ Z0 Z 1 2 3A1 3 2 3cAGF s AF B = AF B(s MZ )= Re(r)cA = 8A0 ≪ 2 − √2e2 AF B is small at low s where r 1 and photon dominates | | ≪ 0 AF B 0 at √s = MZ where Z dominates ≈ 12 0.15 s) √ ( FB LEP A Forward-Backward 0.1 Asymmetries at √s MZ ≈ 0.05 The heavy quark AF B are sensitive to 0 virtual H, t diagrams Ab FB Ac FB -0.05 89 90 91 92 93 94 √s [GeV] Leptons AF B(MZ ) Quarks AF B(MZ ) e+e− e+e− (1.45 0.25)% e+e− ss¯ (9.8 1.1)% → ± → ± e+e− µ+µ− (1.69 0.13)% e+e− cc¯ (7.04 0.36)% → ± → ± e+e− τ +τ − (1.88 0.17)% e+e− b¯b (10.01 0.17)% → ± → ± 13 W Boson Production The W and Z bosons were discovered in pp¯ collisions at CERN W ℓν decays to high pT lepton and high missing ET of ν → CDF Experiment (2007) UA1 experiment (1983) MW = 80.493 0.048 GeV ± ΓW = 2.115 0.105 GeV ± 14 W +W − Pair Production at LEP-2 From 1996-2001 LEP-2 produced W pairs at √s 200 GeV. ≈ 30 02/08/2004 LEP (pb) PRELIMINARY Cross-section is a sum of: WW σ νe exchange 20 (t-channel) + virtual photon 10 (s-channel) 0 YFSWW/RacoonWW + Z with trilinear no ZWW vertex (Gentle) only ν exchange (Gentle) e gauge coupling − 0 Z0W +W 160 180 200 √s (GeV) 15 Measurement Fit |Omeas−Ofit|/σmeas 0 1 2 3 ∆α(5) ± had(mZ) 0.02758 0.00035 0.02767 Summary of m [GeV] 91.1875 ± 0.0021 91.1874 Z electroweak Γ [ ] ± Z GeV 2.4952 0.0023 2.4965 σ0 [ ] ± measurements had nb 41.540 0.037 41.481 R 20.767 ± 0.025 20.739 l http://lepewwg. 0,l ± Afb 0.01714 0.00095 0.01642 ± web.cern.ch/ Al(Pτ) 0.1465 0.0032 0.1480 ± Rb 0.21629 0.00066 0.21562 LEPEWWG/ ± Rc 0.1721 0.0030 0.1723 0,b ± Good agreement with Afb 0.0992 0.0016 0.1037 0,c ± Afb 0.0707 0.0035 0.0742 electroweak theory A 0.923 ± 0.020 0.935 b b (apart from AF B?) ± Ac 0.670 0.027 0.668 ± Al(SLD) 0.1513 0.0021 0.1480 2θlept ± sin eff (Qfb) 0.2324 0.0012 0.2314 [ ] ± mW GeV 80.425 0.034 80.389 Γ [ ] ± W GeV 2.133 0.069 2.093 [ ] ± mt GeV 178.0 4.3 178.5 0 1 2 3 16.