W + W - The Z pole. e + e hadrons SLC. Cross-section (pb) Centre-of-mass energy (GeV) P529 Spring,

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1 The Z pole Cross-section (pb) Z e + e hadrons CESR DORIS PEP W + W - 10 KEKB PEP-II PETRA TRISTAN SLC LEP I LEP II Centre-of-mass energy (GeV) P529 Spring,

2 The LEP/SLC Era Z Pole: e + e Z l + l, q q, ν ν LEP (CERN), Z s, unpolarized (ALEPH, DELPHI, L3, OPAL); SLC (SLAC), , P e 75 % (SLD) Z pole observables lineshape: M Z, Γ Z, σ branching ratios e + e, µ + µ, τ + τ q q, c c, b b, s s ν ν N ν = ± if m ν < M Z /2 asymmetries: FB, polarization, P τ, mixed lepton family universality P529 Spring,

3 Combined LEP 10 # hadron TOPAZ SM:!s " / " s " > 0.10 SM:!s " / " s " > !s " [GeV] P529 Spring,

4 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.) P529 Spring,

5 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 P529 Spring,

6 The Z width and partial widths Γ(f f) C fg F M 3 Z 6 2π [ }{{} ˆρ ḡv f 2 + ḡ Af 2] only MS (plus fermion mass, QED (2 loop), QCD (3 loop), mixed QED-QCD (2 loop) corrections; C l = 1, C q = 3) ḡ Af = ρ f t f 3L ḡ V f = ) ρ f (t f 3L 2 s2 f q f s 2 f = κ fs 2 W = ˆκ fŝ 2 Z Standard model (m t = 173.2(1.3) GeV, M H = 117 GeV) Γ(f f) ± 0.06 MeV(uū), ± 0.02 MeV(ν ν) ± 0.06 MeV(d d), ± 0.01 MeV(e + e ) MeV(b b) P529 Spring,

7 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 li ), 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) P529 Spring,

8 A 0,l fb %$ m t m H 68% CL l + l " e + e " µ + µ " # + # " $ s Ratio of Hadronic to Leptonic Width Experiment R l = " had / " l ALEPH ± DELPHI ± L ± OPAL ± # 2 / dof = 3.5 / 3 LEP ± common error R 0 l=! had /! ll M H [GeV] 10 2! S = 0.118±0.003 linearly added to M t = 172.7±2.9 GeV R l P529 Spring,

9 N ν = 3 + N ν = ± N ν = 1 for fourth family ν with m ν M Z /2 N ν = 1, light ν in supersymmetry 2 N ν = 2, Majoron + scalar in triplet model of m ν with spontaneous L violation rom the ALEPH, DELPHI, L3, and OPAL Collaborations for the cross section in e + e annihilation into of the center-of-mass energy near the Z pole. The curves show the predictions of the Standard Model with t neutrinos. The asymmetry of the curve is produced by initial-state radiation. Note that the error bars have display purposes. References: r. Phys. J. C14, 1 (2000). r. Phys. J. C16, 371 (2000). P529 hys. J. C16, 1 (2000). r. Phys. J. C19, 587 (2001). Collaborations (ALEPH, DELPHI, L3, OPAL) Spring,

10 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 P529 Spring,

11 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) P529 Spring,

12 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 W,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 P529 Spring,

13 g V f Τ Τ l l e e Μ Μ A P529 Spring,

14 and (iii) from the angular distribution of the τ polarization at LEP 1. The two A τ values are from SLD and the total τ polarization, respectively. Quantity Value Standard Model Pull Dev. M Z [GeV] ± ± Γ Z [GeV] ± ± Γ(had) [GeV] ± ± Γ(inv) [MeV] ± ± 0.07 Γ(l + l ) [MeV] ± ± σ had [nb] ± ± R e ± ± R µ ± ± R τ ± ± R b ± ± R c ± ± A (0,e) FB ± ± A (0,µ) FB ± A (0,τ) FB ± A (0,b) FB ± ± A (0,c) FB ± ± A (0,s) FB ± ± s 2 l (A(0,q) FB ) ± ± ± A e ± ± ± ± A µ ± A τ ± ± A b ± ± A c ± ± A s ± ± P529 Spring, May 5, :41

15 LEP 2 e + e f f M W, Γ W, B (also Tevatron) M H limits (hint?) W µ + W µ + p q p q r γν r Wσ Wσ iecµνσ(p, q, r) e i Cµνσ(p, q, r) tan θ W W W production (triple gauge vertex) Quartic vertex SUSY/exotics searches W µ + W ν + W µ + Zν Wρ Wσ Wρ e 2 i sin 2 Qµνρσ θ W e 2 i Qµρνσ tan θ W C µνσ (p, q, r) g µν (q p) σ + g µσ (p r) ν + g νσ (r q) µ Zν W µ + γσ Wρ e 2 i tan 2 Qµρνσ θ W Q µνρσ 2g µν g ρσ g µρ g νσ g µσ g νρ Zν W µ + Zσ Wρ ie 2 Qµρνσ γν γσ Typeset by FoilTEX P529 Spring,

16 Gauge Self-Interactions Three and four-point interactions predicted by gauge invariance Indirectly verified by radiative corrections, α s running in QCD, etc. Strong cancellations in high energy amplitudes would be upset by anomalous couplings W W + W W + W W + ν e γ Z e e + e e + e e + (Tree-level diagrams contributing to e + e W + W ) P529 Spring,

17 " WW (pb) 30 LEP PRELIMINARY 17/02/ YFSWW/RacoonWW no ZWW vertex (Gentle) only # e exchange (Gentle) !s (GeV) P529 Spring,

18 Non-Z Pole Experiments 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) P529 Spring,

19 the leptonic branching ratios [5]; in this case, the theory uncertainty is included in the SM prediction. In all other SM predictions, the uncertainty is from M Z, M H, m t, m b, m c, α(m Z ), and α s, and their correlations have been accounted for. The column denoted Pull gives the standard deviations for the principal fit with M H free, while the column denoted Dev. (Deviation) is for M H = 117 GeV fixed. Quantity Value Standard Model Pull Dev. m t [GeV] ± ± M W [GeV] ± ± ± gl ± ± gr ± ± gv νe ± ± ga νe ± ± Q W (e) ± ± Q W (Cs) ± ± Q W (Tl) ± ± τ τ [fs] ( ± 0.48 ) ± (3.11 ± 0.07) Γ(b sγ) Γ(b Xeν) (g µ 2 α π ) ( ± 0.77) 10 9 ( ± 0.08) P529 Spring,

20 Global Electroweak Fits much more information than individual experiments caveat: experimental/theoretical systematics, correlations PDG 12 review ((J. Erler and PL)) Complete Z-pole and WNC (important beyond SM) M S radiative correction program (Erler) GAPP: Global Analysis of Particle Properties (J. Erler, hep-ph/ ) Fully MS (ZFITTER on-shell) Good agreement with LEPEWWG up to well-understood effects (WNC, HOT, α had ) despite different renormalization schemes P529 Spring,

21 Global Standard Model Fit Results PDG 2012 (11/11) (Erler, PL) χ 2 /df = 45.0/42 Fully MS Good agreement with LEPEWWG up to known effects M H = GeV, m t = ± 1.0 GeV α s = ± ŝ 2 Z = ± s 2 l = ± s 2 W = ± (1) P529 Spring,

22 m t = ± 1.0 GeV GeV from indirect (loops) only (direct: ± 1.0) 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 H G mixed P529 Spring, Typeset by FoilTEX

23 Typeset by FoilT X α s = ± Excellent agreement with other determinations (e.g., quarkonia/lattice, jets) G World average: α s = (7)) Z-pole alone: α s = (28) insensitive to oblique new physics very sensitive to non-universal new physics (e.g., Zb b vertex) P529 Spring,

24 Higgs mass M H = direct limit (LEP 2): M H self-energy (95%) GeV LHC (2012): M H GeV SM: 85 (vac. stab.) M H 700 (triviality) MSSM: M H 130 GeV (150 in extensions) indirect: lnt(b) M H but significant t affected by new physics (S < 0, T > 0) Z(γ) strong A F B (b) effect Z W M H < 150 t(b) GeV at 95%, includingb direct LEP 2 vertex (quadratic) m t and (logarithmic) M H depen WW, ZZ, Zγ self-energies (SU(2)-breaking); W b t W t b H H Z P529 Spring, STIAS (January, 2011)

25 M H [GeV] Γ Z, σ had, R l, R q (1σ) Z pole asymmetries (1σ) M W (1σ) m t (1σ) low energy precision data (90% CL) allowed by searches excl. by 1 experiment excl. by > 1 experiment m t [GeV] P529 Spring,

26 M W [GeV] direct (1σ) indirect (1σ) all precision data (90% CL) allowed by Higgs searches excluded by 1 experiment excluded by > 1 experiment m t [GeV] P529 Spring,

27 6 5 4 March 2012 Theory uncertainty α had = α (5) ± ± incl. low Q 2 data m Limit = 152 GeV χ LEP excluded m H [GeV] LHC excluded P529 Spring,

28 The precision program: SM correct and unique to zeroth approx. (gauge principle, group, representations) SM correct at loop level (renorm gauge theory; m t, α s, M H ) TeV physics severely constrained (unification vs compositeness) Consistent with light elementary Higgs Precise gauge couplings (SUSY gauge unification) Measurement Fit O meas O fit /σ meas α (5) had (m Z ) ± m Z [GeV] ± Γ Z [GeV] ± σ 0 had [nb] ± R l ± A 0,l fb ± A l (P τ ) ± R b ± R c ± A 0,b fb ± A 0,c fb ± A b ± A c ± A l (SLD) ± sin 2 θ lept eff (Q fb ) ± m W [GeV] ± Γ W [GeV] ± m t [GeV] ± July P529 Spring,