Tests of the Electroweak Theory

Transcription

1 Tests of the Electroweak Theory History/introduction Weak charged current QED Weak neutral current Precision tests Rare processes CP violation and B decays Neutrino mass FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 113

2 References (mainly weak neutral current/z-pole) E.D. Commins and P.H. Bucksbaum, Weak Interactions of Leptons and Quarks, (Cambridge Univ. Press, Cambridge, 1983) P. Renton, Electroweak Interactions, (Cambridge Univ. Press, Cambridge, 1990) P. Langacker, M.-X. Luo and A. K. Mann, High precision electroweak experiments, Rev. Mod. Phys. 64, 87 (1992) Precision Tests of the Standard Electroweak Model, ed. P. Langacker (World Scientific, Singapore, 1995) S. Eidelman et al. [Particle Data Group], Phys. Lett. B 592, 1 (2004) (Electroweak review, J. Erler and PL) LEP Electroweak Working Group: FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 114

3 The Z Lineshape Basic Observables: e + e f f (f = e, µ, τ, s, b, c, hadrons) (s = E 2 CM ) σ f (s) σ f sγ 2 Z (s M 2 Z )2 + s2 Γ 2 Z M 2 Z (plus initial state rad. corrections) M Z and Γ Z : from peak position and width Peak Cross Section: σ f = 12π M 2 Z Γ(e + e )Γ(f f) Γ 2 Z (Z model independent; γ and γ Z int. removed, (usually) assuming S.M.) FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 115

4 σ had [nb] ALEPH DELPHI L3 OPAL σ 0 20 Γ Z 10 measurements (error bars increased by factor 10) σ from fit QED corrected A FB (µ) M Z A FB from fit QED corrected average measurements E cm [GeV] (LEPEWWG, hep-ex/ ) ALEPH DELPHI L3 OPAL FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 116

5 Conventional (weakly correlated) observables: M Z, Γ Z, σ had, R l, R b, R c Derived σ had 12π M 2 Z Γ(e + e )Γ(Z hadrons) Γ 2 Z R qi Γ(q i q i ) Γ(had), q i = (b, c) R li Γ(had) Γ(l i l i ), l i = (e, µ, τ ) (lepton universality test: R e = R µ = R τ R l ) Γ(inv) = Γ Z Γ(had) i Γ(l i li ) N ν Γ(ν ν) (counts anything invisible in detector) FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 117

6 Z-Pole Asymmetries Effective axial and vector couplings of Z to fermion f ḡ Af = ρ f t 3f ḡ V f = ρ f [t 3f 2 s 2 f q f ] where s 2 f the effective weak angle, s 2 f = κ f s 2 W (on shell) = ˆκ f ŝ 2 Z ŝ2 Z (f = e) (MS ), ρ f, κ f, and ˆκ f are electroweak corrections, q f = electric charge, t 3f = weak isospin FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 118

7 A 0 = Born asymmetry (after removing γ, off-pole, box (small), P e ) forward backward : A 0f F B = 3 4 A ea f (A 0e F B = A0µ F B = A0τ F B A0l F B universality) τ polarization : P 0 τ = A 2z τ + A e 1+z 2 2z 1 + A τ A e 1+z 2 (z = cos θ, θ = scattering angle) e polarization (SLD) : A 0 LR = A e mixed (SLD) : A 0F B LR = σf LF σf LB σf RF + σf RB σ f LF + σf LB + σf RF + σf RB = 3 4 A f A f 2ḡ V fḡ Af ḡ 2 V f + ḡ2 Af ḡ V l s2 l (small) FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 119

8 Asymmetries depend on A f 2ḡ V f ḡ Af little sensitivity ḡ V 2 f +ḡ2 Af to m t, M H m t, M H enter in comparison with M Z and other lineshape A LR ḡ V l s2 l more sensitive to s 2 l than A0l F B ḡ2 V l Forward-Backward Pole Asymmetry Experiment A 0,l FB ALEPH ± DELPHI ± L ± OPAL ± # 2 / dof = 3.9 / 3 LEP ± common error A 0b F B = 3 4 A ea b much more sensitive to e vertex than b vertex assuming SM, but possible discrepancy M H [GeV] A 0,l FB!" (5) had = ± linearly added to M t = 172.7±2.9 GeV FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 120

9 A b F B, A l, and A b A b F B = (16) is 2.4σ below expectation of (8) Favors large M H. New physics or fluctuation/systematics lead to smaller M H A b F B = 3 4 A la b ; A b agrees with SM, A l (SLC) is 2.0σ high New physics in A b F B would require compensation of L and R couplings ( to preserve R b ) 5% effect, but 25% in κ probably tree level affecting third family New physics possibilities include Z with non-universal couplings, or b R mixing with B R in doublet with charge 4/3 Tension between leptonic (low M H ) and hadronic (high M H ) determinations of s 2 l FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 121

10 0,bb _ A FB ALEPH leptons DELPHI leptons L3 leptons OPAL leptons ALEPH inclusive DELPHI inclusive L3 jet-ch OPAL inclusive ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± A b SM LEP Winter mt [GeV] 0,bb _ <A > = ± FB Include Total Sys With Common Sys m H [GeV] 10 2 m t = ± 4.3 GeV α had = ± % CL _ ,bb A FB A l FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 122

11 A 0,l fb ± A l (P # ) ± A l (SLD) ± A 0,b fb ± A 0,c fb ± Q had fb ± Average ± " 2 /d.o.f.: 11.8 / 5 m H [GeV] 10 2 $% (5) had = ± m t = ± 2.9 GeV sin 2! lept eff FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 123

12 The Z Pole Observables: LEP and SLC (09/05) Quantity Group(s) Value Standard Model pull M Z [GeV] LEP ± ± Γ Z [GeV] LEP ± ± Γ(had) [GeV] LEP ± ± Γ(inv) [MeV] LEP ± ± 0.11 Γ(l + l ) [MeV] LEP ± ± σ had [nb] LEP ± ± R e LEP ± ± R µ LEP ± ± R τ LEP ± ± A F B (e) LEP ± ± A F B (µ) LEP ± A F B (τ ) LEP ± FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 124

13 Quantity Group(s) Value Standard Model pull R b LEP/SLD ± ± R c LEP/SLD ± ± A F B (b) LEP ± ± A F B (c) LEP ± ± A F B (s) DELPHI/OPAL ± ± A b SLD ± ± A c SLD ± ± A s SLD ± ± A LR (hadrons) SLD ± ± A LR (leptons) SLD ± A µ SLD ± A τ SLD ± A τ (P τ ) LEP ± A e (P τ ) LEP ± s 2 l (Q F B) LEP ± ± s 2 l (A F B(q)) CDF ± FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 125

14 LEP 2 e + e f f M W, Γ W, B (also Tevatron) M H limits (hint?) W W production (triple gauge vertex) Quartic vertex SUSY/exotics searches FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 126

15 Combined LEP 10 # hadron TOPAZ SM:!s " / " s " > 0.10 SM:!s " / " s " > !s " [GeV] FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 127

16 The triple gauge vertex for V =γ or Z: il V W W eff = g V W W [ g V 1 V µ ( W µν W +ν W + µν W ν) +κ V W + µ W ν V µν + λ V V µν W +ρ m 2 ν W ρµ W ( ) +ig V 5 ε µνρσ ( ρ W µ )W +ν W µ ( ρ W +ν ) V σ +ig V 4 W + µ W ν ( µ V ν + ν V µ ) κ V 2 W µ W + ν εµνρσ V ρσ λ V 2m 2 W W ρµ W +µ νε νραβ V αβ ] g γw W = e, g ZW W = e cot θ W ; F µν = µ F ν ν F µ Also ZZZ, ZZγ, Zγγ, quartic FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 128

17 CP T, CP, C, P, U(1) Q, custodial SU(2) reduce to g Z 1, κ γ, κ Z, λ γ, λ Z with κ Z = g Z 1 tan θ W (κ γ 1), λ Z = λ γ SM (tree): g Z 1 = κ γ = κ Z = 1; λ γ = λ Z = 0 W magnetic dipole moment: µ W = e(1 + κ γ + λ γ )/2M W W electric quadrupole moment: q W = e(κ γ λ γ )/M 2 W Measure at LEP II, Tevatron, e.g., in angular distribution in e + e W + W or e + e W eν Usually fix all but one to SM values PDG (g Z 1 = 1 + gz 1, κ γ = 1 + κ γ ) g Z 1 = κ γ = λ γ = (recent review: S. Mele, Phys. Rept , 255 (2004)) FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 129

18 20 LEP 02/03/2001 Preliminary! WW [pb] RacoonWW / YFSWW 1.14 no ZWW vertex (Gentle 2.1) only " e exchange (Gentle 2.1) E cm [GeV] FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 130

19 Other: atomic parity (Boulder, Paris); νe; νn (NuTeV); polarized Møller asymmetry (SLAC E158); M W, m t (Tevatron) Non-Z pole WNC experiments less precise but still extremely important Z-pole is blind to new physics that doesn t directly affect Z or its couplings to fermions (e.g., new box-diagrams, four-fermi operators) FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 131

20 Non-Z Pole Precision Observables (9/05) Quantity Group(s) Value Standard Model pull m t [GeV] Tevatron ± 2.7 ± ± M W [GeV] LEP ± ± M W [GeV] Tevatron /UA ± gl 2 NuTeV ± ± gr 2 NuTeV ± ± R ν CCFR ± ± ± R ν CDHS ± ± ± R ν CHARM ± ± R ν CDHS ± ± ± R ν CHARM ± ± R ν CDHS ± ± ± FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 132

21 Quantity Group(s) Value Standard Model pull A P V SLAC E ± ± gv νe CHARM II ± ± gv νe all ± ga νe CHARM II ± ± g νe A all ± Q W (Cs) Boulder/Paris ± ± Q W (Tl) Oxford/Seattle ± ± Γ(b sγ) Γ SL BaBar/Belle/CLEO ± τ τ [fs] direct/b e /B µ ± ± (a µ 2π α ) BNL/CERN ± ± FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 133

22 Measurement Fit O meas!o fit /" meas #$ (5) had (m Z ) ± m Z [GeV] ± % Z [GeV] ± " 0 had [nb] ± R l ± A 0,l fb ± A l (P & ) ± R b ± R c ± A 0,b fb ± A 0,c fb ± A b ± A c ± A l (SLD) ± sin 2 ' lept eff (Q fb ) ± m W [GeV] ± % W [GeV] ± m t [GeV] ± FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 134

23 Global Electroweak Fits much more information than individual experiments caveat: experimental/theoretical systematics, correlations PDG 04 review + 05 update (J. Erler and PL) Complete Z-pole and WNC (important beyond SM) MS radiative correction program (Erler) GAPP: Global Analysis of Particle Properties (J. Erler, hepph/ ) Fully MS (ZFITTER on-shell) Good agreement with LEPEWWG up to well-understood effects (WNC, HOT, α had ) despite different renormalization schemes FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 135

24 Global Standard Model Fit Results PDG 2006 (9/05) (Erler, PL) χ 2 /df = 47.5/42 Fully MS Good agreement with LEPEWWG up to known effects M H = GeV, m t = ± 2.8 GeV α s = ± ˆα(M Z ) 1 = ± ŝ 2 Z = ± s 2 l = ± s 2 W = ± α (5) had (M Z) = ± FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 136

25 Typeset by FoilT X m t = ± 2.8 GeV GeV from indirect (loops) only (direct: 172.7±2.9±0.6) t(b) t Z(γ) Z W W t(b) b Fit actually uses MS mass ˆm t ( ˆm t ) ( 10 GeV lower) and converts to pole mass at end H H Significant change from previous analysis due to lower m t from Run II H G mixed FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 137

26 Typeset by FoilT X α s = ± Higher than α s = (20) (PDG: 2004), because of τ lifetime G Z-pole alone: α s = (28) insensitive to oblique new physics very sensitive to non-universal new physics (e.g., Zb b vertex) FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 138

27 G Z(γ) Higgs mass M H = GeV LEPEWWG: direct limit (LEP 2): M H > (95%) GeV SM: 115 (vac. stab.) < M < H 750 (triviality) t(b) MSSM: M < H 130 GeV (150 t in extensions) indirect: ln MZ H Wbut significant W affected by new physics (S < 0, T > 0) t(b) b strong A F B (b) effect M H < 189 GeV at 95%, including direct H H H H FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 139

28 1000 all data (90% CL) M H [GeV] ! ", # had, R l, R q asymmetries low-energy M W m t excluded m t [GeV] FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 140

29 M W [GeV] direct (1!) indirect (1!) all data (90% CL) M = 100 GeV H M = 200 GeV H M = 400 GeV H M H = 800 GeV m t [GeV] FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 141

30 !" Theory uncertainty!# had =!# (5) ± ± incl. low Q 2 data m W [GeV] LEP1 and SLD LEP2 and Tevatron (prel.) 68% CL old 1 Excluded m H [GeV] 80.3!" m H [GeV] m t [GeV] FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 142

31 ! Z " 0 had R 0 l A 0,l fb A l (P # ) R 0 b R 0 c A 0,b fb A 0,c fb A b A c A l (SLD) sin 2 $ lept eff (Q fb ) m W *! W * Q W (Cs) sin 2 $%%(e % e % MS ) sin 2 $ W (&N) g 2 L (&N) g 2 R (&N) *preliminary M H [GeV] FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 143

32 Beyond the standard model Oblique corrections: γnew particlesγ which affect W, Z, γ propagators but not the fermion vertices l t had ρ 0 = 1 1 αt : physics which affects WNC/WCC and M W /M Z Splittings between non-degenerate fermion or scalar doublets (like t, b) ρ 0 1 = 3G F 8 2π 2 i C i 3 m2 i (C i = color factor) m 2 m m2 2 4m2 1 m2 2 m 2 1 m2 2 ln m 1 m 2 (m 1 m 2 ) 2 Higgs triplets with non-zero VEVs Typeset by FoilTEX FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 144

33 S affects Z propagator, relation between WNC and M Z Chiral (parity-violating) fermion doublets, even if degenerate (e.g., fourth family, mirror family, technifamilies) S = C 3π (t 3L (i) t 3R (i)) 2 i { 2 3π (family) 1.62 (QCD-like techni-generation) U similarly affects W propagator, usually small S, T, U have coefficient of α Varying conventions. PDG: ρ 0 1, S = T = U = 0 in SM (SM rad corrections treated separately) FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 145

34 ρ 0 ; S, T, U: Higgs triplets, nondegenerate fermions or scalars; chiral families (ETC) for M H = 117 (300) GeV S = 0.13 ± 0.10( 0.08) T = 0.13 ± 0.11(+0.09) U = 0.20 ± 0.12(+0.01) ρ αt = and GeV < M H < 191 GeV (for S = U = 0) i C i m 2 i /3 < (90 GeV)2 (95% cl) Can evade Higgs mass limit for S < 0, T > 0 (Higgs doublet/triplet loops, Majorana fermions) Degenerate heavy family excluded at % cl FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 146

35 ! Z, " had, R l, R q asymmetries M W # scattering Q W E 158 T S all: M H = 117 GeV all: M H = 340 GeV all: M H = 1000 GeV FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 147

36 Supersymmetry decoupling limit (M new > GeV): only precision effect is light SMlike Higgs little improvement on SM fit Supersymmetry parameters constrained FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 148

37 A TeV scale Z? Expected in many string theories, grand unification, dynamical symmetry breaking, little Higgs, large extra dimensions Natural solution to µ problem Implications Exotics FCNC (especially in string models) Non-standard Higgs masses, couplings (doublet-singlet mixing) Non-standard sparticle spectrum Neutrino mass, BBN, structure Enhanced possibility of EW baryogenesis Typically M Z > GeV (Tevatron, LEP 2, WNC), θ Z Z < few 10 3 (Z-pole) FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 149

38 M Z [GeV] Z χ 1500 X 1000 oo CDF excluded sin θ FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 150

39 Other Exotic fermion mixings Large extra dimensions New four-fermi operator Leptoquark bosons FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 151

40 Gauge unification: GUTs, string theories α + ŝ 2 Z α s = ± (MSSM) (non-susy: 0.073(1)) M G GeV Perturbative string: GeV (10% in ln M G ). Exotics: O(1) corrections.! i -1(µ)! i -1(µ) ! 1! 2 SM World Average! 3! S (M Z )=0.117±0.005 sin 2 " =0.2317± MS µ (GeV) 68% CL! 1 MSSM World Average 30! 2 20! U.A. W.d.B H.F µ (GeV) FNAL FNAL (December (December 13, 13, 2005) 2005) Paul Paul Langacker Langacker (Penn/FNAL) (Penn/FNAL)

41 Conclusions WNC, Z, W unification are primary predictions and test of electroweak SM correct and unique to first approx. representations) (gauge principle, group, SM correct at loop level (renorm gauge theory; m t, α s, M H ) Watershed: TeV physics severely constrained (unification vs compositeness) unification (decoupling): expect 0.1% TeV compositeness: expect several % unless decoupling Precise gauge couplings (gauge unification) FNAL (December 13, 2005) Paul Langacker (Penn/FNAL) 153