Measurements of the Boson Mass and Trilinear Gauge Boson Couplings at the Tevatron John Ellison University of California, Riverside, USA Selection of and Z events Measurement of the mass Tests of the gauge boson self-couplings Summary XXXIInd Rencontres de Moriond Electroweak Interactions and Unified Theories Les Arcs, Savoie, France March 14-21 1998
and Z Candidate Events Run 1a 1992 93 15 pb 1 Run 1b 1994 95 85 pb 1 selection: high p T lepton, p T > 25 GeV missing E T > 25 GeV Z selection: two high p T charged leptons p 1 T > 25 GeV, second lepton loose DØ Run 1b data Events per GeV 25 2 15 DØ Preliminary eν 59579 candidates Lum ~ 76 pb-1 Events per GeV 8 7 6 5 DØ Preliminary Z ee 575 candidates Lum ~ 89 pb-1 4 1 3 5 2 1 3 4 5 6 7 8 9 1 11 12 Transverse Mass GeV 5 6 7 8 9 1 11 12 13 Z Invariant Mass GeV Transverse Mass M T = {p T p T ν ( 1 cos φ ν )}
Measurement of the Boson Mass Fundamental parameter of the SM, sensitive to top quark and Higgs boson radiative corrections: G F = p 2M 2 1, M 2 M 2 Z [1+r (; M ;M Z ;M H ;m t )] r = r () +r ( s) +r (2) + : : : t r M t 2 b H r ln M H Measured at the Tevatron via p p ν Latest results: DØ Run 1b ( eν) CDF Run 1b ( µν, preliminary)
Mass Measurement Technique Measure electron/muon momentum and p T of recoil system (includes underlying event) Neutrino p T given by p ν T = p T u T p T ν electron or muon p T l neutrino underlying event p a T recoil hadrons Calculate transverse mass / p T b M T = {p T E T ( 1 cos φ ν )} u T = p T a + p T b Use fast MC to model ν events Add backgrounds and model detector Generate M T spectra for various M values Fit MC M T spectra to data to obtain best fit M value using the maximum likelihood method
CDF Momentum Scale Normalize observed J/ψ µ + µ peak to the world average mass Μ µ + µ (MeV) Measured M J/ψ = 396.2 ± 1.5 MeV orld average M J/ψ = 396.88 ±.4 MeV Scale factor =.99977 ±.48 δm = 4 MeV/c 2 due to p scale uncertainty (1b) [ momentum resolution: δm = 25 MeV/c 2 (1b) ]
DØ Energy Scale Test beam measurements calorimeter energy response is linear to <.5% for E T e > 1 GeV Assume E obs = δ + α E true and use collider data to constrain δ and α α EM.96.958.956.954.952.95.948.946.944.942 J/ψ ee Combined 1σ contour π γγ Z ee.94 -.5 -.4 -.3 -.2 -.1.1.2.3.4.5 δ EM (GeV) Accounting for underlying event corrections and non-linearity at low E e T results in systematic errors on α and δ α =.9533 ±.8 +.3 δ = (.16 ) GeV δm = 7 MeV/c 2.21 energy scale (1b) [ δm = 25 MeV/c 2 energy resolution (1b) ]
DØ Recoil Response Recoil hadronic scale calibrated using transverse energy balance in Z ee decays Response R defined by ^ u T q T = R q T recoil response 1.9.8.7.6.5.4.3 HERIG + GEANT Z ee R = α + β ln (q T / GeV).2 5 1 15 2 25 3 q T (GeV) <p η (ee)+u η > (GeV) 6 5 4 3 2 1 Z ee data MC 5 1 15 2 25 3 p η (ee) (GeV) Determine α and β from η balance in Z ee data α =.693 ±.6 β =.4 ±.21 δm = 2 MeV/c 2 recoil response (1b) [ δm = 25 MeV/c 2 recoil resolution (1b) ]
Errors on M ( in MeV/c 2 ) DØ 1b CDF 1b prelim. statistics 7 1 E(e) or p(µ) scale 7 4 e or µ resolution 4 25 Recoil modeling 3 9 Selection bias 2 Backgrounds 1 25 width 1 1 production (incl. pdf s) 25 5 QCD / QED corrections 15 3 Total uncertainty 115 155
Mass Results Fit to M T Run 1b data number of events 7 6 5 4 DØ Ib χ 2 /dof = 79.5/6 ( eν) 3 2 1 # Events 5 4 3 5 55 6 65 7 75 8 85 9 95 1 m T (GeV) CDF(1B) Preliminary χ 2 /df = 158/139 (5 < M T < 12) χ 2 /df = 62/69 (65 < M T < 1) Mw = 8.43 +/-.1 (stat) GeV ( µν) 2 1 Fit region 5 6 7 8 9 1 11 12 Transverse Mass (GeV) DØ: M = 8.44 ±.1 (stat.) ±.7 (syst.) GeV/c 2 CDF: M = 8.43 ±.1 (stat.) ±.12 (syst.) GeV/c 2
Mass Measurements LEP, SLD Indirect Prediction UA2 D combined CDF combined (prelim) Hadron Collider Avg M = 8.37 ±.37 M = 8.43 ±.11 M = 8.38 ±.12 M = 8.4 ±.9 LEP2 Avg orld Avg M = 8.48 ±.14 M = 8.43 ±.8 79 79.5 8 8.5 81 81.5 M (GeV/c 2 )
Current Results: M vs M t Direct Measurements orld Averages: M = 8.43 ±.8 GeV/c 2 M t = 174.1 ± 5.4 GeV/c 2 (UA2, CDF, DØ, LEPII) (CDF, DØ) m (GeV) 8.7 8.6 DIRECT m : UA2+CDF+D+LEP2 m t : CDF+D MSSM 8.5 8.4 8.3 8.2 8.1 INDIRECT LEP + SLC 14 16 18 2 m t (GeV) 1 25 5 1 SM Higgs Mass (GeV) r in SM: see PDG Review of Particle Properties for a summary. r in MSSM: Chankowski et al., Nucl. Phys. B417:11 (1994); Garcia et al., Mod. Phys. Lett. A9:211 (1994).
Direct Measurement of the Gauge Boson Self-Couplings Standard model U(1) Y SU(2) L predicts existence of gauge boson self-interactions Direct measurement: Demonstrate agreement with SM Use as probe of new physics V (= γ or Z) L V =g V = ig V 1 y V, V y + i V y V + i V m y V 2 In the standard model at tree level: { g V 1 = 1 (g V 1 g V 1, 1 = ) V = 1 ( V V, 1 = ) V = magnetic dipole moment electric quadrupole moment e = (1 + + ) 2m Q e = e ( m 2, ) Form factors: a(^s) = a() (1 + ^s= 2 ) 2 where: ^ s = subprocess CM energy Λ = form factor scale (related to scale of new physics)
γ Production Results Number of candidate events = 127 (19) for DØ (CDF) Backgrounds ( + jet) 25 3%.4.2 -.2 -.4 95% CL allowed region from b sγ (CLEO + ALEPH) U(1) EM SM D 95% CL limits CDF (prelim.) 95% CL limits -3-2 -1 1 2 3 DØ Limits at 95% CL:.98 < κ γ < 1.1 (for λ = ).33 < λ γ <.31 (for κ = ) Implications: Independent of Z vertex (unlike production) First direct evidence of photon coupling to weak charge of the boson: U(1) EM -only coupling of photon to the boson (electric charge only) ruled out at the 88% CL (95% CL if assume λ = )
Zγ Production Results 3 Z( )γ candidates in each experiment Z(νν)γ channel (DØ only) most sensitive [Run 1a only, 1b analysis in progress] ZZγ described by four couplings {h 1 Z... h 4Z } h Z 4 1.75.5.25 -.25 -.5 -.75-1 DØ ννγ Λ=5 GeV CDF llγ prelim. Λ=5 GeV L3 ννγ Λ=75 GeV DØ ννγ Λ=75 GeV DØ combined Λ=75 GeV DØ llγ Λ=5 GeV -4-3 -2-1 1 2 3 4 h Z 3 DØ combined limits h 3,1 Z,γ <.36 (for h 4,2 Z,γ = ) Λ = 75 GeV h 4,2 Z,γ <.5 (for h 3,1 Z,γ = ) Most stringent direct limits on anomalous couplings to date from any experiment Tevatron is more sensitive than LEP due to higher ^ scattering energy s Contributions to amplitudes from h 3Z, h Z 4 terms rise ^ rapidly with energy as ~s 3 ^,~s 4
, Z ν qq, qq 1) Limits assuming κ Z = κ γ and λ Z = λ γ 95% CL limits Unitarity limits } DØ Limits.43 < κ <.59 Λ = 2 TeV.33 < λ <.36 } CDF prelim..49 < κ <.54 Λ = 2 TeV.34 < λ <.32 DØ Λ = 1.5 TeV 2) Assume SM γ couplings and derive limits on Z couplings κ Z =λ Z = point ruled out first direct evidence for Z coupling λ z 1.5 -.5-1 SM -1 -.5.5 1 κ z
ν ν ( = e, µ) Cross section: +6.3 CDF data: σ = (1.2 ± 1.6 ) pb 5.1 DØ data: σ < 37.1 pb (at the 95% CL) SM preciction: σ = (9.5 ± 1.) pb Limits on Anomalous Couplings: Different methods are used to obtain limits on anomalous couplings: (a) CDF fit to total number of events (b) DØ fit to the lepton p T spectrum, taking into account correlations (p T + = p T ) This method is more sensitive DØ : 95% CL limits for Λ = 2. TeV assuming κ γ = κ Z and λ γ = λ Z :.62 < κ <.77 (λ = ).52 < λ <.56 ( κ = )
DØ Simultaneous Fit DØ have performed a simultaneous fit to: photon p T spectrum in the γ data lepton p T distribution in ν ν p eν T distribution in, Z eν qq [Note: CDF and DØ analyses of latter two processes provide first direct evidence for the Z coupling] Results ( κ, λ, g 1 Z parametrization): Coupling FF =1:5 TeV FF =2: TeV = Z,.33,.46,.3,.43 = Z,.21,.21,.2,.2 (HISZ),.39,.61,.37,.56 (HISZ),.21,.21,.2,.2 g Z 1 (SM ),.56,.86,.52,.78 Z (SM ),.46,.64,.42,.59 Z (SM ),.33,.37,.31,.34 (SM Z),.63,.75,.59,.72 (SM Z),.27,.25,.26,.24
DØ Simultaneous Fit: α Bφ, α φ, α Parametrization LEP II results have used a Lagrangian with a different operator basis with parameters α Bφ, α φ, α, where g Z 1 = c 2 = Z = = + B Z =, s2 c 2 B New DØ limits on α Bφ, α φ, α : α 1 (a) Unitarity DØ 95% CL α 1 (b) DØ 95% CL -1-1 Unitarity -1 1 αbφ -1 1 αφ Coupling FF =1:5 TeV FF =2: TeV LEP combined B,.81,.61,.77,.58,.81, 1.5,.24,.46,.22,.44,.28,.33,.21,.21,.2,.2,.37,.68 g Z 1,.31,.6,.29,.57, * Summer 1997
Conclusions Measurement of M : M = 8.44 ±.11 GeV / c 2 (DØ) M = 8.38 ±.12 GeV / c 2 (CDF Prelim.) Future: Run II (2 fb 1 ) M 4 MeV/c 2 TeV33 (1 fb 1 ) M < 3 MeV/c 2 sensitive test of SM, M H (~ 8 1 6 eν events for 1 fb 1 ) Electroweak vector boson self couplings: γ : κ < 1. V:.3 < κ <.43 λ <.3 (combined fit) λ <.2 ZZγ : h Z,γ 3,1 <.36 h Z,γ 4,2 <.5 At the Tevatron (Run II and beyond) we will test the anomalous couplings to the level of 1 2 1 3 Important test of gauge symmetry of SM probe radiative corrections (Higgs, SUSY, )