Tests of the standard electroweak model at the energy frontier

In this review, tests of standard electroweak (EW) theory at the highest available energies as a precursor to the Large Hadron Collider (LHC) era are summarized. The primary focus is on the published results (as of March 2010) from proton-antiproton collisions at $\sqrt{s}=1.96\mathrm{TeV}$ at the Fermilab Tevatron collected using the CDF and D0 detectors. After presenting an overview of the EW sector of the standard model, a summary of experimental tests of EW theory as of March 2010 is provided. These include gauge boson properties and self-couplings, tests of EW physics from the top-quark sector, and searches for the Higgs boson.

Figure 1

Leading-order (a) $W$ and (b) $Z$ boson production via quark-antiquark annihilation. The production is dominated by $q=u$, $d$ valence quarks. The ${\gamma }^{*}$ contribution interferes with the $Z$ diagram but is not shown.

Figure 2

Feynman diagrams showing corrections to the $W$ boson mass from (a) the top quark and (b) the SM Higgs boson.

Figure 3

The measured top quark and $W$ boson masses and a band of allowed Higgs-boson masses. This includes the recent results summarized in the text. From 82.

Figure 4

The $m_T$ distributions for (a) the CDF $W\to \mu \nu$ channel, (b) the CDF $W\to e\nu$ channel, and (c) the D0 $W\to e\nu$ channel.

Figure 5

Ideogram of previous measurements, the Run-II CDF and D0 measurements and the new world average. The reference is shown to the right of each measurement.

Figure 6

The $m_T$ distributions used for the ${\Gamma }_W$ measurement. (a) The CDF $W\to \mu \nu$ channel. (b) The CDF $W\to e\nu$ channel. (c) The D0 $W\to e\nu$ channel.

Figure 7

Summary of the ${\Gamma }_W$ measurements. The hadron collider average and world average results do not include the D0 result. From 47.

Figure 8

Dielectron forward-backward asymmetry as a function of dielectron mass (CDF).

Figure 9

Dielectron forward-backward asymmetry as a function of dielectron mass (D0).

Figure 10

Comparison of the Tevatron asymmetry results with those from other experiments. [a] 83; [b] 59; [c] 74; [d] 38.

Figure 11

The $Zuu$ and $Zdd$ coupling constants. From 74.

Figure 12

Leading-order diagram for diboson production via quark-antiquark annihilation involving the trilinear gauge coupling.

Figure 13

The (a) photon $E_T$ distribution for the D0 $W\gamma$ analysis. From 39. The photon $E_T$ distribution of events is used to constrain anomalous coupling parameters shown in (b).

Figure 14

(a) The background-subtracted charge-signed rapidity difference of events is shown along with the SM expectation from 39. Consideration of the full covariance matrix gives a 15% ${\chi }^2$ probability for compatibility between the data and the SM expectation. (b) Distributions of the $R$-test statistic for the SM (solid line) and “no-dip” (dashed line) hypothesis pseudoexperiments from 39. The data result is 0.64 shown by the vertical line where only 45 out of ${10}^4$ no-dip pseudoexperiments had a value smaller as small or smaller than 0.64. The $R$-test statistic is defined as the ratio of events in the “Dip Bin” to the “Small Max Bin,” as shown in the inset where the solid line is the SM expectation and the dashed line is for the no-dip hypothesis.

Figure 15

The three-body mass $M_{\ell \ell \gamma }$ vs the dilepton mass $M_{\ell \ell }$ for $Z\gamma$ candidate events in the D0 analysis. From 33.

Figure 16

The observed photon $E_T$ spectrum along with the SM expectation and possible anomalous TGC scenarios for (a) $Z\gamma \to \ell \ell \gamma$ (33) and (b) $Z\gamma \to \nu \nu \gamma$ (49) channels.

Figure 17

Two-dimensional bounds (ellipses) at 95% C.L. on $CP$-conserving (a) $Z\gamma \gamma$ and (b) $ZZ\gamma$ couplings. The crosses represent the one-dimensional bounds at the 95% C.L. setting all other couplings to zero. The dashed lines indicate the unitarity limits for $\Lambda =1.5\mathrm{TeV}$. From 49.

Figure 18

The $L{R}_{WW}$ distributions for the signal ($W^{+}{W}^{-}$) and background processes after a maximum likelihood fit to the data for the CDF $WW$ cross-section measurement. From 21.

Figure 19

Leading-lepton $p_T$ distribution for data compared to the SM expectation for the CDF $WW\to \ell \nu \ell \nu$ analysis (21). Also shown is how the expectation would be modified by anomalous couplings near the observed limits.

Figure 20

Distributions of the (a) leading and (b) trailing lepton $p_T$ for the D0 $WW\to \ell \nu \ell \nu$ analysis (50). Data are compared to the estimated signal $\sigma (WW)=12\mathrm{pb}$ and the background sum.

Figure 21

One- and two-dimensional 95% C.L. limits for the D0 $WW\to \ell \nu \ell \nu$ analysis (50) when enforcing $\mathrm{SU}(2{)}_L\otimes \mathrm{U}(1{)}_Y$ symmetry at $\Lambda =2\mathrm{TeV}$, for (a) $\Delta {\kappa }_{\gamma }$ vs ${\lambda }_{\gamma }$, (b) $\Delta {\kappa }_{\gamma }$ vs $\Delta g_1^Z$, and (c) ${\lambda }_{\gamma }$ vs $\Delta g_1^Z$, each when the third free coupling is set to its SM value; limits when enforcing the $WW\gamma =WWZ$ constraints are shown in (d). The curve represents the two-dimensional 95% C.L. contour and the ticks along the axes represent the one-dimensional 95% C.L. limits. An asterisk (*) marks the point with the highest likelihood in the two-dimensional plane.

Figure 22

Leading-order (a) $t$-channel and (b) $s$-channel diagrams for $WZ$ production at the Tevatron.

Figure 23

Distributions for $WZ$ candidates of (a) the ${\mathrm{E̸}}_T$, (b) the dilepton invariant mass for the same-flavor opposite-sign dilepton pair closest to the $Z$ mass, and (c) the $W$ transverse mass calculated from the remaining lepton and the ${\mathrm{E̸}}_T$, for the CDF $WZ\to \ell \ell \ell \nu$ analysis. In (a) and (b), the arrows indicate the signal region. From 70.

Figure 24

${\mathrm{E̸}}_T$ vs dilepton invariant mass of $WZ\to \ell \ell \ell \nu$ candidate events in the D0 $WZ$ analysis (34). The open boxes represent the expected $WZ$ signal. The filled boxes represent the sum of the estimated backgrounds. The stars are the data that survive all selection criteria. The open circles are data that either fail the dilepton invariant mass criterion or have ${\mathrm{E̸}}_T<20\mathrm{GeV}$.

Figure 25

The reconstructed $Z$ boson $p_T$ of the $WZ$ candidate events for the D0 $WZ\to \ell \ell \ell \nu$ analysis (34). The solid histogram is the expected sum of signal and background for the case of the $WWZ$ coupling parameters set to their SM values. The dotted and double-dotted histograms are the expected sums of signal and background for two different cases of anomalous $WWZ$ coupling parameter values.

Figure 26

Two-dimensional 95% C.L. contour limit in $\Delta g_1^Z=\Delta {\kappa }_Z$ vs $\Delta {\lambda }_Z$ space (inner contour) for the D0 $WZ\to \ell \ell \ell \nu$ analysis (34). The form factor scale for this contour is $\Lambda =2\mathrm{TeV}$. The physically allowed region (unitarity limit) is bounded by the outer contour. The cross hairs are the 95% C.L. one-dimensional limits.

Figure 27

Leading-order diagram for $ZZ$ production at the Tevatron. The $s$-channel diagram involving the neutral TGC is absent in the SM.

Figure 28

Limits on anomalous couplings for $\Lambda =1.2\mathrm{TeV}$ for the D0 $ZZ\to \ell \ell \ell \ell$ analysis (40): (a) $f_{40}^{\gamma }$ vs $f_{40}^Z$, (b) $f_{40}^{\gamma }$ vs $f_{50}^{\gamma }$, (c) $f_{40}^Z$ vs $f_{50}^Z$, and (d) $f_{50}^{\gamma }$ vs $f_{50}^Z$, assuming in each case that the other two couplings are zero. The inner and outer curves are the 95% C.L. 2 degree of freedom exclusion contour and the constraint from the unitarity condition, respectively. The inner cross hairs are the 95% C.L. 1 degree of freedom exclusion limits.

Figure 29

Distribution of the discriminating variable ${log}_{10}(1-LR)$ for the CDF $ZZ\to \ell \ell \nu \nu$ search. From 6.

Figure 30

Distribution of four lepton invariant mass in data, expected signal, and expected background for the D0 $ZZ\to \ell \ell \ell \ell$ analysis. From 41.

Figure 31

For the D0 analysis (51), (a) the RF output distribution from the combined $e\nu q\overline{q}$ and $\mu \nu q\overline{q}$ channels for data and simulated event predictions following the fit of simulation to data. (b) A comparison of the extracted signal (filled histogram) to background-subtracted data (points), along with the $\pm 1$ standard deviation (s.d.) systematic uncertainty on the background. The residual distance between the data points and the extracted signal, divided by the total uncertainty, is given at the bottom.

Figure 32

For the D0 analysis, (a) the dijet mass distribution from the combined $e\nu q\overline{q}$ and $\mu \nu q\overline{q}$ channels for data and simulated event predictions following the fit to the RF output. (b) A comparison of the extracted signal (filled histogram) to background-subtracted data (points), along with the $\pm 1$ standard deviation (s.d.) systematic uncertainty on the background. The residual distance between the data points and the extracted signal, divided by the total uncertainty, is given at the bottom. From 51.

Figure 33

For the CDF analysis, the (a) dijet invariant mass distribution of reconstructed $W/Z\to jj$ candidates compared to the fitted signal and background components, and (b) corresponding background-subtracted distribution. From 22.

Figure 34

Observed EPD distribution superimposed on distribution expected from simulated processes for the CDF analysis. From 22.

Figure 35

For the CDF analysis, $M_{jj}$ for events with (a) $\mathrm{EPD}<0.25$, (b) $0.25<\mathrm{EPD}<0.5$, (c) $0.5<\mathrm{EPD}<0.75$, and (d) $\mathrm{EPD}>0.75$. From 22.

Figure 36

The $p_T^W$ distribution used for setting the anomalous TGC limits in the CDF analysis. Shown are the SM expectation, data points, and one anomalous coupling scenario with $\lambda =\Delta \kappa =0.5$ and $\Lambda =1.5\mathrm{TeV}$. From 2.

Figure 37

For the D0 analysis, the (a) dijet $p_T$ distribution of combined ($\mathrm{\text{electron}}+\mathrm{\text{muon}}$) channels for data and SM predictions following the fit of simulated events to data, and (b) the difference between data and simulation divided by the uncertainty (statistical and systematic) for the dijet $p_T$ distribution. Also shown are the simulated signals for anomalous couplings corresponding to the 95% C.L. limits for $\Delta \kappa$ and $\lambda$ in the LEP parametrization scenario. The full error bars on the data points reflect the total (statistical and systematic) uncertainty, with the ticks indicating the contribution due only to the statistical uncertainty. From 52.

Figure 38

The 68% C.L. and 95% C.L. two-parameter limits on the $\gamma WW/ZWW$ coupling parameters $\Delta {\kappa }_{\gamma }$, $\lambda$, and $\Delta g_1^Z$, in the LEP parametrization scenario and ${\Lambda }_{NP}=2\mathrm{TeV}$ for the D0 analysis. The dots indicate the most probable values of anomalous couplings from the two-parameter combined ($\mathrm{\text{electron}}+\mathrm{\text{muon}}$) fit and the star markers denote the SM prediction. From 52.

Figure 39

The 68% C.L. and 95% C.L. two-parameter limits on the $\gamma WW/ZWW$ coupling parameters $\Delta \kappa$ and $\lambda$, in the equal couplings scenario and ${\Lambda }_{NP}=2\mathrm{TeV}$ for the D0 analysis. The dot indicates the most probable values of anomalous couplings from the two-parameter combined ($\mathrm{\text{electron}}+\mathrm{\text{muon}}$) fit and the star marker denotes the SM prediction. From 52.

Figure 40

Data compared with the sum of the predicted EW and multijet backgrounds for the $\Delta {\varphi }_{{\mathrm{E̸}}_T}^{\mathrm{jet}}$ variable in the CDF analysis. The band represents the total systematic uncertainty on the background. The measured signal is included here in the EW contribution. From 12.

Figure 41

Top: Comparison between data and fitted background only. The measured signal is shown unstacked. The band represents the systematic uncertainty due to the shape of EW background as described by 12. Bottom: Comparison of the diboson signal (solid line) with the background-subtracted data (points). The dashed lines represent the $\pm 1\sigma$ statistical variations on the extracted signal. The band represents the systematic uncertainty due the EW shape.

Figure 42

A graphical summary of EW gauge boson cross-section measurements and theory expectations during Run II and the Fermilab Tevatron.

Figure 43

Contours of constant-log(L) in the ${\Delta }_{\mathrm{jes}}\equiv k_{\mathrm{jes}}-1$ vs $M_t$ plane. A perfect a priori jet energy calibration used as input to this analysis results in $k_{\mathrm{jes}}=1$ corresponding to ${\Delta }_{\mathrm{jes}}=0$. From 15.

Figure 44

Published top mass measurements. For a given experiment and final state, the results from different methods have a significant correlation. [a]15; [b] 13; [c] 7; [d] 71; [e] 54; [f] 14; [g] 43; [h] 35; [i] 66; [j] 3; [k] 17. Also shown are the most recent Tevatron combination (153) and the PDG world average (83. Both of these include a subset of the measurements listed.

Figure 45

The $s$-channel (left) and $t$-channel (right) diagrams for single-top production.

Figure 46

The combined discriminant for the D0 analysis.

Figure 47

The combined discriminant for the CDF analysis.

Figure 48

Ideogram of the single-top cross-section measurements from D0 and CDF. [a] 45; [b] 8; [c] 151; [d] 143; 122; 100; 149; 103; 104; 113; 125; [e] 147.

Figure 49

The $\Delta {\chi }^2$ as a function of assumed Higgs mass resulting from fits to data assuming the SM. The exclusion regions from direct searches are also shown.

Figure 50

The NN output distributions for (a) single- ($\mathrm{ST}+\mathrm{NN}$) and (b) double-tagged ($\mathrm{ST}+\mathrm{ST}$, $\mathrm{ST}+\mathrm{JP}$) events from the CDF $2{\mathrm{fb}}^{-1}$ $WH$ search.

Figure 51

(a) The NN output for double-tagged dijet events and (b) the dijet mass for double-tagged three jet events from the D0 $WH$ search.

Figure 52

The cross-section limits from the CDF $WH$ search.

Figure 53

The cross-section limits from the D0 $WH$ search.

Figure 54

Dijet mass distribution for the D0 $1.0{\mathrm{fb}}^{-1}$ $ZH\to \ell \ell bb$ analysis.

Figure 55

NN distributions for the (a) single-tagged and (b) double-tagged samples from the CDF $1.0{\mathrm{fb}}^{-1}$ $ZH\to \ell \ell bb$ analysis. The 95% C.L. upper bound cross section is $19\times$ the SM prediction.

Figure 56

Expected and observed limits for the CDF $1.0{\mathrm{fb}}^{-1}$ $ZH\to \ell \ell bb$ analysis.

Figure 57

Expected and observed limits for the D0 $0.45{\mathrm{fb}}^{-1}$ $ZH\to \ell \ell bb$ analysis.

Figure 58

The dijet invariant mass distributions for the (a) single-tagged and (b) double-tagged CDF searches in the $VH\to {\mathrm{E̸}}_{T}bb$ final state.

Figure 59

Expected and observed 95% C.L. upper bounds on the $VH$ production cross section for the CDF ${\mathrm{E̸}}_T+bb$ search.

Figure 60

The outputs for the (a) MJ BDT, (b) the SM BDT for the single-tagged channel, and (c) the SM BDT for the double-tagged channel for the D0 $VH\to {\mathrm{E̸}}_{T}bb$ analysis.

Figure 61

The expected and observed 90% C.L. upper bounds on the Higgs-boson production cross section in the D0 $VH\to {\mathrm{E̸}}_{T}bb$ search.

Figure 62

(a) The dijet invariant mass distribution for the D0 $VH\to \tau \nu bb$ search, and (b) the NN output for the $VH\to \tau \tau jj$ search.

Figure 63

For the D0 $H\to W{W}^{(*)}$ analysis (58), the (a) dilepton invariant mass after preselection; (b) $\Delta \varphi (\ell ,\ell )$ angle after final selection; and (c) neural network output after final selection. The signal is shown for $m_H=165\mathrm{GeV}$. The systematic uncertainty is shown after the fit.

Figure 64

For the D0 $H\to W{W}^{(*)}$ analysis (58), the (a) data after subtracting the fitted background (points) and SM signal expectation (filled histogram) as a function of the NN output for $m_H=165\mathrm{GeV}/c^2$. Also shown is the $\pm 1$ standard deviation (s.d.) band on the total background after fitting. (b) Upper limit on Higgs-boson production cross section at 95% C.L. expressed as a ratio to the SM cross section. The 1 and 2 s.d. bands around the curve corresponding to the background-only hypothesis are also shown.

Figure 65

The combined distribution of NN scores for backgrounds and a $M_H=160\mathrm{GeV}/c^2$ Higgs boson compared to the observed data shown with statistical uncertainties for the CDF $H\to W{W}^{(*)}$ analysis. The Higgs-boson distribution is normalized to 10 times the SM expectation. From 23.

Figure 66

Expected and observed upper limits at the 95% C.L. on ${\sigma }_H$ presented as a ratio to the predicted SM values as a function of $M_H$ for the CDF $H\to W{W}^{(*)}$ analysis (23). The dashed line represents the median expected limits, the bands represent the estimated $1\sigma$ and $2\sigma$ probability bands for the distribution of expectations, and the solid line represents the observed limit.

Figure 67

The 95% C.L. upper bounds on the Higgs production cross section divided by the predicted cross section. This result includes both published and preliminary results from CDF and D0.