---
abstract: |
    We present electroweak physics results from the 0 and CDF experiments using data from $p \bar p$ collisions at $\sqrt{s} =
    1.8$ . Measurements of the cross sections times branching ratios for  and  production, the inclusive width of the boson and the  boson mass are presented. Direct tests of the  and  trilinear gauge boson couplings are also presented based on studies of diboson production.
address: |
    Physics Department,\
    University of California,\
    Riverside, CA 92521, USA
author:
- JOHN ELLISON
title: '-3cm W BOSON PHYSICS AT THE FERMILAB TEVATRON[^1] '
---

0[DØ]{} 0[DØ]{} \#1[\#1$#1$]{}

Introduction
============

The CDF and 0 detectors at the Fermilab Tevatron collider collected data during the 1992-93 run (“run 1a”) corresponding to integrated luminosities of $\approx$15 pb$^{-1}$ and $\approx$20 pb$^{-1}$ for 0 and CDF respectively. In the 1994-95 run (“run 1b”) data sets of $\approx$80 pb$^{-1}$ ([0]{}) and $\approx$90 pb$^{-1}$ (CDF) were collected. The large Tevatron data sets allow precise measurements of the  boson properties, such as its mass and width, and new studies of the physics of electroweak boson pair production.

In this paper we present selected recent results on  boson physics from the analysis of a subset of these data, concentrating mainly on electroweak physics. Theoretical aspects of  production at hadron colliders are covered in the talk by Stirling at this conference.

W and Z Production and the Inclusive Width of the W Boson
=========================================================

The measurement of the production cross-sections times branching ratios ($\sigma \cdot B$) for the  and  bosons allows a determination of the width of the  boson and a comparison of and  boson production with QCD predictions. The latter are calculated to order $\alpha_s^2$ and therefore, precision measurements of the cross sections are a test of radiative processes in QCD.

Measurements of the cross sections were made by 0 and CDF using the $W~\to~e \nu$, $Z~\to~e e$, $W~\to~\mu \nu$ and $Z~\to~\mu \mu$ decay channels. Events were selected from single lepton triggers and offline were required to contain a high  isolated lepton plus missing transverse energy ( events) or two high  isolated leptons ( events). The 0 and CDF run 1a analyses are described in [@d0_xsec; @cdf_xsec].

Figure \[fig:mtev-mee\] shows the 0 preliminary run 1b transverse mass spectra for $W~\to~\ell \nu$ candidate events and the invariant mass spectra for $Z~\to~\ell \ell$ candidate events.

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The values of $\sigma \cdot B$ were calculated by subtracting the background from the number of observed events and dividing by the acceptance, efficiency and integrated luminosity. The results are shown in Table \[table:xsec\] and are plotted in Fig. \[fig:xsec\]. The measurements agree well with the order $\alpha_s^2$ QCD predictions (van Neerven  [@vanNeerven]) of $\sigma_W \cdot B(W~\to~\ell \nu) =
2.42^{+0.13}_{-0.11}$ nb and $\sigma_Z \cdot B(W~\to~\ell \nu) =
0.226^{+0.011}_{-0.009}$ nb, shown as the shaded bands in Fig. \[fig:xsec\]. The CTEQ2M parton distribution functions [@cteq], and the values $m_W = 80.23 \pm 0.18$ and $m_Z = 91.188 \pm 0.002$  were used to calculate the central values.

  ----------------------------- ---------------- ---------------- ---------------- ----------------
                                      $e$             $\mu$             $e$             $\mu$
  $W$ cand.                          59579             4472            13796             6222
  A$_W$ (%)                      43.4 $\pm$ 1.5   20.1 $\pm$ 0.7   34.2 $\pm$ 0.8   16.3 $\pm$ 0.4
  $\epsilon_W$ (%)               70.0 $\pm$ 1.2   24.7 $\pm$ 1.5   72.0 $\pm$ 1.1   74.2 $\pm$ 2.7
  Bkg (%)                        8.1 $\pm$ 0.9    18.6 $\pm$ 2.0   14.1 $\pm$ 1.3   15.1 $\pm$ 2.2
  $\int {\cal L}$ (pb$^{-1}$)    75.9 $\pm$ 6.4   32.0 $\pm$ 2.7   19.7 $\pm$ 0.7   18.0 $\pm$ 0.7
  $Z$ cand.                           5702             173              1312             423
  A$_Z$ (%)                      34.2 $\pm$ 0.5   5.7 $\pm$ 0.5    40.9 $\pm$ 0.5   15.9 $\pm$ 0.3
  $\epsilon_Z$ (%)               75.9 $\pm$ 1.2   43.2 $\pm$ 3.0   69.6 $\pm$ 1.7   74.7 $\pm$ 2.7
  Bkg (%)                        4.8 $\pm$ 0.5    8.0 $\pm$ 2.1    1.6 $\pm$ 0.7    0.4 $\pm$ 0.2
  $\int {\cal L}$ (pb$^{-1}$)    89.1 $\pm$ 7.5   32.0 $\pm$ 2.7   19.7 $\pm$ 0.7   18.0 $\pm$ 0.7
                                                                                   
  ----------------------------- ---------------- ---------------- ---------------- ----------------

  : Summary of 0 and CDF analyses and production cross section times branching ratio results for  and  bosons. The symbols A, $\epsilon$ and Bkg are the acceptance, detection efficiency and background, respectively.[]{data-label="table:xsec"}

The inclusive width of the  boson is calculated using the measured ratio ($R$) of the  and  $\sigma \cdot B$ values: $$R=\frac{\sigma_W \cdot B(W~\to~\ell \nu)}{\sigma_Z \cdot B(Z~\to~\ell \ell)}~\rm{~~with~~}~ B(W~\to~\ell \nu) = \frac{\Gamma(W~\to~\ell \nu)}{\Gamma(W)}$$

Many common sources of error cancel in $R$, including the uncertainty in the integrated luminosity and parts of the errors in the acceptance and event selection efficiency. The theoretical calculation $\sigma_W
/ \sigma_Z = 3.33 \pm 0.03$ [@vanNeerven] and the LEP measurement $B(Z~\to~\ell \ell) = (3.367 \pm 0.0006)\%$ [@pdg] are used to obtain $B(W~\to~\ell \nu)$. This measurement of $B(W~\to~\ell \nu)$ is then combined with a theoretical calculation [@d0_xsec; @Wwidth] of $\Gamma(W~\to~\ell \nu) = 225.2 \pm 1.5$  to obtain an indirect measurement of the  inclusive width.

Figure 3 summarizes the measurements to date. The world average (excluding the preliminary 0 run 1b results) is $\Gamma(W) = 2.062
\pm 0.059$ . This can be compared with the Standard Model (SM) prediction of $2.077 \pm 0.014$  [@d0_xsec; @Wwidth] to set limits on non-standard decays of the . At the 95% confidence level, the upper limit on the width due to non-standard decays ( decays to heavy quarks or to SUSY particles such as charginos and neutralinos) is 109  ( approximately 5% of the  width).

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The  width directly affects the shape of the transverse mass distribution in  events. The effect is most prominent at high values of $m_T$ where the Breit-Wigner line shape dominates over the detector resolutions. CDF have utilized this fact to determine the width from a binned likelihood fit to the transverse mass distribution in the region $m_T > 110~\GeVcc$ [@cdf_width_direct]. The result is $\Gamma_W = 2.11 \pm 0.28 \pm 0.16~\GeV$. This method is currently less precise than the indirect method described above but is relatively independent of SM assumptions.

Diboson Production and the Gauge Boson Couplings
================================================

The production of electroweak boson pairs at hadron colliders is particularly interesting since these processes probe the nature of the non-Abelian gauge boson self-couplings of the Standard Model ( the  and  couplings). These processes are also sensitive to deviations from the tree level SM couplings, which may arise due to compositeness of the  and  bosons or radiative loop corrections to the vertex factors as shown in the examples of Fig. \[fig:wwgvertex\].

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To test the agreement with the SM and to evaluate the sensitivity to anomalous couplings the  $(V=\gamma,Z)$ vertex is parametrized using the phenomenological effective Lagrangian of reference [@wwvLagrangian]. Assuming electromagnetic gauge invariance, and invariance under Lorentz and CP transformations the effective Lagrangian is reduced to a function of five dimensionless coupling parameters $g_1^Z, \kappa_V$, and $\lambda_V$. In the SM at tree level $g_1^Z = 1, \kappa_V = 1$ and $\lambda_V = 0$. Assuming that the coupling parameters for the  and  vertices are equal, only two parameters remain:

$\kappa_\gamma = \kappa_Z = \kappa~({\rm or}~\Delta\kappa
\equiv \kappa - 1)$

$\lambda_\gamma = \lambda_Z = \lambda.$

The coupling parameters are related to the lowest order terms in a multipole expansion of photon interactions with the  boson, the  magnetic dipole moment is given by $\mu_W =
(e/2m_W)(1 + \kappa_\gamma + \lambda_\gamma)$.

All interaction Lagrangians with constant anomalous couplings violate unitarity at high energy. In the SM delicate cancelations ensure that unitarity is satisfied and anomalous couplings would destroy these cancellations leading to violation of unitarity. Therefore, all the coupling parameters must be modified to include form factors, $$\Delta\kappa(\hat s) = \frac{\Delta\kappa^0}{(1 + \hat s / \Lambda^2)^n}$$ where $\Delta\kappa^0 =$ value of coupling parameter at $\hat s = 0$, $\hat s =$ square of the invariant mass of the partonic subprocess, $n
= 2$ for a dipole form factor and $\Lambda =$ form factor scale (a function of the scale of new physics).

 Production and the  Coupling
-----------------------------

The study of  production at the Tevatron can be used to probe the  coupling [@Wg]. The $u$- and $t$-channel Feynman diagrams for $p \bar p~\to~\ell \nu \gamma$ correspond to photon bremsstrahlung from an initial state quark, whereas the $s$-channel diagram is sensitive to the  vertex. Events in which a photon is radiated from the final state lepton from single  decay also result in the same $\ell \nu \gamma$ final state, but are suppressed by imposing a cut on the photon-lepton angular separation. Non-SM values of the  coupling result in an increase in the total cross-section and an enhancement of events with high- photons. This is the experimental signature which is used by 0 [@d0_wg] and CDF [@cdf_wg] to test for anomalous couplings.

In addition to the  selection criteria, a high- isolated photon with $p_T > 10$ (7)  is required in the 0 (CDF) analyses, separated from the lepton by $\Delta R_{\ell \nu} > 0.7$ units in $\eta
- \phi$ space. Photons are detected in the pseudorapidity range $|\eta| < 1.1$ for CDF and $|\eta| < 1.1$ or $1.5 < |\eta| < 2.5$ for 0.

The numbers of signal events after background subtraction are compared with the SM predictions in Table \[table:wg\]. Note that the number of events is on the order of 100 for each experiment. The 0measured cross section times branching ratio (with $E_T^\gamma >
10~\GeV$ and $\Delta R_{\ell \nu} > 0.7)$ is $\sigma (W \gamma) \times
B(W~\to~\ell \nu) = 11.3^{+1.7}_{-1.5}~{\rm (stat)} \pm 1.5$ (sys) pb compared with the SM prediction of $\sigma (W \gamma) \times B(W \to
\ell \nu) = 12.5 \pm 1.0$ pb. Figure \[fig:wgpt\] shows the 0$p_T^\gamma$ distribution for the observed candidate events together with the SM signal prediction plus the sum of the estimated backgrounds. The number of observed events and the shapes of the distributions show no deviations from the expectations. The SM predictions for the number of events observed was obtained using the leading order  event generator of Baur and Zeppenfeld [@wgmc] (using a K-factor of 1.34 to approximate higher order QCD effects) combined with Monte Carlo simulations of the 0 and CDF detectors.

  ---------------- ---------------------------------- ------------------------------------ ---------------------------------- ------------------------------------
                                                                                                                              
                                                                                                                              
                    $W\gamma\rightarrow e\nu\gamma $   $W\gamma\rightarrow \mu\nu\gamma $   $W\gamma\rightarrow e\nu\gamma $   $W\gamma\rightarrow \mu\nu\gamma $
  $N_{\rm data}$                   57                                  70                                  75                                  34
  $N_{\rm bkg}$              15.2 $\pm$ 2.5                      27.7 $\pm$ 4.7                      16.1 $\pm$ 2.4                      10.3 $\pm$ 1.2
  $N_{\rm sig}$           $41.8^{+8.8}_{-7.5}$                $42.3^{+9.7}_{-8.3}$              $58.9 \pm 9.0 \pm 2.6 $             $23.7 \pm 5.9 \pm 1.1 $
  $N_{\rm SM}$               43.6 $\pm$ 3.1                      38.2 $\pm$ 2.8                      $53.5 \pm 6.8$                     $21.8 \pm 4.3  $
  ---------------- ---------------------------------- ------------------------------------ ---------------------------------- ------------------------------------

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In both experiments, limits on the  vertex coupling parameters are obtained from a binned maximum likelihood fit to the photon distribution. In the electron channel run 1b analysis, 0 require the electron-photon-neutrino transverse cluster mass to be $>90~\GeVcc$. This cut suppresses radiative  decays and increases the sensitivity to anomalous couplings by about 10%. Figure \[fig:wglimits\] shows the 95% confidence level (CL) limits in the $\Delta \kappa - \lambda$ plane, for a form factor scale of $\Lambda = 1.5~\TeV$. Varying only one coupling at a time, the following limits are obtained at the 95% CL:

[0]{}:            =$-0.9 < \Delta \kappa < 0.9~~({\rm for}~\lambda = 0)$\
$-0.3 < \lambda < 0.3~~({\rm for}~\Delta \kappa = 0)$\
\
CDF: $-1.8 < \Delta \kappa  < 2.0~~({\rm for}~\lambda = 0)$\
$-0.7 < \lambda < 0.6~~({\rm for}~\Delta \kappa  = 0)$

The possibility of a minimal U(1)-only coupling ($\kappa =
\lambda = 0$) indicated by the star in Fig. \[fig:wglimits\] is ruled out at the 88% CL by the 0 measurement. This shows that the photon couples not only to the  electric charge but also to its weak isospin.

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 and  Production
----------------

0 and CDF have searched for  and  production using two decay modes: (a) the “dilepton” mode and (b) the “lepton plus jets” mode.

Both experiments have searched for  production in the dilepton decay modes $e \nu e \nu$, $e \nu \mu \nu$ and $\mu \nu \mu
\nu$ [@d0_wwdilep; @cdf_wwdilep]. In the preliminary 0 run 1b analysis, based on an integrated luminosity of 78.5 pb$^{-1}$, four events pass the event selection criteria. 0 set an upper limit on the cross section for $p \bar
p \to WW$ of 41 pb at the 95% CL, estimated based on four candidate events and a total estimated background of $2.6 \pm 0.4$ events.

In the CDF analysis based on 108 pb$^{-1}$ of data, a SM  signal is observed above background. The event selection yields 5 events with a background of $1.2 \pm 0.3$ events. The measured  cross section is $\sigma (p \bar p \to WW) =
10.2^{+6.3}_{-5.1} \pm 1.6$ pb. The cross section for this process has been calculated to next to leading order by Ohnemus [@wwxs_nlo] with the result $\sigma_{SM} (p \bar p \to WW) = 9.5 \pm 1.0$ pb.

The  pair production process is sensitive to the  and couplings, since the $s$-channel propagator can be a $\gamma$ or . Anomalous couplings result in a higher cross section and an enhancement of events with high   bosons. Due to the low statistics in this channel, only the total cross section is used in setting limits. Assuming $\Delta \kappa_Z = \Delta
\kappa_\gamma$ and $\lambda_Z = \lambda_\gamma$, the limits obtained on $\Delta \kappa$ and $\lambda$ are shown in Fig. 7.

  --------- ---------
   = 5.5cm   = 5.5cm
  --------- ---------

\[fig:wwvlim\]

In the lepton plus jets analyses 0 and CDF search for candidate events containing a high- lepton, missing  and two jets with invariant mass consistent with the  or  mass. CDF also accept events with two charged leptons and two jets resulting from $p \bar
p \to WZ \to \ell^+ \ell^- jj$. The data are dominated by background, mainly from $W~+$ jets events with $W \to e \nu$ and multijet production where one jet was misidentified as an electron and there was significant (mismeasured) missing . The data are in good agreement with the expectations.

At large values of $p_T^W$ the backgrounds are relatively small and it is in this region where anomalous couplings would enhance the cross section. CDF make a cut at $p_T^W > 200~\GeV$, where $p_T^W$ is calculated from the  of the dijet system. Limits on anomalous couplings are then derived by comparing the number of surviving events with the predicted number of events as a function of the anomalous coupling parameters, determined from the leading order calculation by Hagiwara, Woodside and Zeppenfeld [@wwxs_lo] with a K-factor of 1.34.

0 use a binned likelihood fit to the $p_T^W$ spectrum above $p_T^W
> 25~\GeV$, where $p_T^W$ is calculated from the  of the $e \nu$ system. The results, assuming the  and  coupling parameters are equal, are shown in Fig. 7. At the 95% CL for $\Lambda = 2.0~\TeV$, assuming $\Delta \kappa_Z = \Delta \kappa_\gamma, \lambda_Z = \lambda_\gamma$ the following limits are obtained:

[0]{}:            =$-0.4 < \Delta \kappa  < 0.6~~({\rm for}~\lambda = 0)$\
$-0.3 < \lambda < 0.4~~({\rm for}~\Delta \kappa  = 0)$\
\
CDF: $-0.5 < \Delta \kappa  < 0.6~~({\rm for}~\lambda = 0)$\
$-0.4 < \lambda < 0.3~~({\rm for}~\Delta \kappa  = 0)$

Assuming SM  couplings and fixing $\lambda_Z = 0$, both experiments exclude the point $\kappa_Z = g_1^Z = 0$ at $>99\%$ CL. This is direct evidence for a nonzero  coupling.

Measurement of the W Boson Mass
===============================

The mass of the  boson $m_W$ is one of the fundamental parameters of the SM. From the relation among the parameters of the SM we can write $m_W$ in terms of $\alpha$, $G$, $m_Z$ and $\Delta r$. Radiative corrections associated with the SM are contained in the $\Delta r$ term, the largest contributions to $\Delta r$ being proportional to $m_t^2$ and ${\rm ln} m_H$. Therefore, a precise determination of the and top masses can be used to constrain the Higgs mass.

In $p \bar p \to W \to \ell \nu$ events at the Tevatron, the longitudinal component of the neutrino cannot be determined and therefore $m_W$ is measured using the transverse mass defined by $$m_T =  \sqrt{ 2\, p_T^\ell \, p_T^\nu \, 
                     (1 - \cos\varphi^{\ell\nu}) }$$ where $\varphi^{\ell\nu}$ is the angle between the lepton and neutrino in the transverse plane. The experimentally measured quantities are the lepton momentum and the transverse momentum of the recoil system $
{\vec p}_T^{\,had}$. The transverse momentum of the neutrino is then inferred from these two observables: $$\begin{aligned}
    \etmisv = - {\vec p}_T^{\,e} -  {\vec p}_T^{\,had} 
            = - {\vec p}_T^{\,e} - {\vec p}_T^{\,rec} - {\vec u}_T({\cal L})\end{aligned}$$ The  of the recoil system is given by ${\vec p}_T^{\,had} = {\vec p}_T^{\,rec} + {\vec u}_T({\cal L})$, where ${\vec p}_T^{\,rec}$ is the transverse momentum of the  recoil and ${\vec u}_T({\cal L})$ is the transverse energy flow of the underlying event, which depends on the luminosity. The latter two quantities are experimentally inseparable for  events.

The  mass is determined by generating Monte Carlo  events and fitting to the transverse mass distribution observed in the data. To correctly model the $m_T$ distribution a precise knowledge of the response and resolution of the detector to charged leptons and the recoil particles is required. The response determines the position of the peak of the $m_T$ distribution, while the resolution determines its width.

In CDF the momentum scale is determined by normalizing the measured $J/\psi \to \mu^+ \mu^-$ mass peak to the world average value. The calorimeter energy scale is then determined from a comparison of the observed $E/p$ distribution with a detailed Monte Carlo simulation. At 0 only $W \to e \nu$ events are used to measure $m_W$. The electromagnetic calorimeter energy scale is established using $Z \to e^+e^-$ events and calibrating against the LEP measurement of $m_Z$, with additional constraints from $J/\psi\to e^+e^-$ and $\pi^0 \to \gamma \gamma$ events.

In CDF the   is modeled in the Monte carlo using the distribution of  events observed in the data. The recoil system is also taken from the  data. The 0 experiment generates the  using the double differential  production cross section in and rapidity calculated to next to leading order by Ladinsky and Yuan [@Wprod_resum]. Minimum bias events are used to model the underlying event. The response of the calorimeter to the hadronic recoil is determined from the balance in transverse momentum in events.

Figure 8 shows the transverse mass distributions for the data together with the best fit of the Monte Carlo for the muon and electron channel run 1a data (CDF) and the run 1b electron data (0).

  --------- ---------
   = 5.5cm   = 5.5cm
  --------- ---------

\[fig:mt\_d0\_cdf\]

The  mass results are:

[0 1a]{}:   =$m_W^e = 80.350 \pm 0.140 {\rm (stat)}
\pm 0.165 {\rm (syst)} \pm 0.160 {\rm (scale)}~\GeVcc$\
[0 1b]{}: $m_W^e = 80.380 \pm 0.070 {\rm (stat)}
\pm 0.130 {\rm (syst)} \pm 0.080 {\rm (scale)}~\GeVcc$\

[CDF 1a $W \to e \nu$]{}:   =$m_W^e = 80.490 \pm 0.145 {\rm (stat)} \pm
0.175 {\rm (sys)}~\GeVcc$\
[CDF 1a $W \to \mu \nu$]{}: $m_W^\mu = 80.310 \pm 0.205 {\rm (stat)}
\pm 0.130 {\rm (sys)}~\GeVcc$\

Table \[table:mw\_sys\] lists the systematic errors on the individual measurements and the common errors.

  -------------------------- ----- ----- ----- ----- ----- ----
                                                           
  Statistical                  145   205     —   140    70    —
  Energy scale                 120    50    50   160    80   25
  Angle scale                    —     —     —    50    40   40
  $E$ or $p$ resolution         80    60     —    70    25   10
  $p_T^W$ and recoil model      80    75    65   110    95 
  PDF’s                         50    50    50    65    65   65
  QCD/QED corr’s                30    30    30    20    20   20
  $W$-width                     20    20    20    20    10   10
  Backgrounds                   10    25     —    35    15    —
  Efficiencies                   0    25     —    30    25    —
  Fitting procedure             10    10     —     5     5    —
  Total                        230   240   100   270   170   80
  Combined                                                 
  -------------------------- ----- ----- ----- ----- ----- ----

Using the above results and combining with previous  mass measurements [@mw_previous], a world average of $m_W = 80.356 \pm
0.125~\GeVcc$ is obtained. The world average values of $m_W$ and $m_t$ are shown in Fig. \[fig:mtmw\]. Also shown are the results from the indirect measurements from LEP and SLC and the predictions of the SM for various Higgs masses. The errors in the latter predictions are indicated by the width of the bands and are primarily due to the uncertainty in $\alpha(m_Z^2)$, the electromagnetic coupling strength at the  mass scale. Although only small improvements to the indirect results from LEP/SLC data are expected, the direct measurements of $m_W$ and $m_t$ are expected to improve by factors of $3-5$ from future measurements [@Tev2000] at the Tevatron. This would lead to a prediction of the Higgs mass at the level of $\delta m_H / m_H \approx 20\%$.

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Charge Asymmetry in $W \to \ell \nu$ Events
-------------------------------------------

On average $u$ valence quarks in the proton have higher momentum than $d$ valence quarks. Therefore, $W^+$ bosons produced via $u \bar d \to
W^+$ are boosted predominantly along the proton direction and $W^-$ bosons from $\bar u d \to W^+$ are boosted predominantly along the antiproton direction. This results in an asymmetry in the charged lepton rapidity distribution in $W \to \ell \nu$ events, defined as $$A(y_\ell) =  
              { dN^+ (y_\ell) / dy_\ell \,-\, dN^- (y_\ell) / dy_\ell \over 
                dN^+ (y_\ell) / dy_\ell \,+\, dN^- (y_\ell) / dy_\ell }$$ where $N^{+(-)}$ is the number of positively (negatively) charged leptons with rapidity $y_\ell$. The $(1 \pm {\rm cos}\theta)^2$ decay asymmetry from the $V-A$ decay of the  must also be accounted for when studying $A(y_\ell)$. The importance of this measurement is that it is sensitive to the difference in the $u$ and $d$ quark distribution functions at very high $Q^2$ ($\approx m_W^2$) and low $x$ ($0.007 < x < 0.25$). The measurements therefore constrain the parton distribution functions (PDF’s) and are used to reduce the error in $m_W$ due to the uncertainty in the PDF’s.

The most recent measurements of this asymmetry from CDF are shown in Figure \[fig:cdf\_wasym\]. The data include the run 1a+1b results with a total integrated luminosity of 111 pb$^{-1}$, utilizing the forward muon toroids and the end plug electromagnetic calorimeter to extend the coverage in rapidity. Also shown are the predictions of the DYRAD NLO Monte Carlo [@dyrad] using various parton distribution functions. The uncertainty in the measurement of $m_W$ due to the choice of PDF in the modeling of  events is constrained by selecting only PDF’s which show good agreement with the asymmetry data,  those for which $| \zeta | < 2$, where $$\zeta = { \overline{A}_{\,PDF} \,-\, \overline{A}_{\,data} \over 
                  \sigma(\overline{A}_{\,data})  }$$ and $\overline{A}$ is the weighted mean of the asymmetries $A(y_\ell)$. The resulting uncertainty on $m_W$ is $50~\MeVcc$ in the CDF analysis (see Table \[table:mw\_sys\]).

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Conclusions
===========

Recent analyses of data based on the production of  bosons at the Fermilab Tevatron have resulted in precision measurement of the properies of the . The indirect measurement of the  boson width is $\Gamma(W) = 2.062 \pm 0.059$  (world average, excluding the preliminary run 1b results), corresponding to a precision of 3%. The new world average value of the  mass is $m_W = 80.356 \pm
0.125~\GeVcc$, corresponding to a precision of 0.15%.

New studies of the trilinear gauge boson couplings have also been undertaken. The production of  and  events is in agreement with the prediction of the SM, within the experimental sensitivity. The current 95% CL limits on the trilinear coupling parameters are (approximately) $| \Delta \kappa | < 0.9 (0.5)$ and $| \lambda | < 0.3 (0.3)$ for the  coupling assuming $\Lambda = 1.5~\TeV$ ( coupling assuming $\Lambda = 2.0~\TeV$). The measurements provide direct evidence for the existence of the $WWZ$ coupling and show that the photon couples to the SU(2) weak isospin of the  boson as well as to its U(1) electric charge.

The upgraded 0 and CDF detectors will begin running at the Tevatron in 1999. Improvements in the precision in the measurement of the properties of the  boson, coupled with improved measurements of the top quark mass, will yield predictions for the Higgs mass and may provide crucial self consistency tests of the SM.

****

Acknowledgments

I would like to thank all my colleagues from the 0 and CDF collaborations who helped in preparing my talk and this paper. Particular thanks to Darien Wood for his useful comments.

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[^1]: Presented at the Cracow Epiphany Conference on the  Boson, 4-6 January 1997, Kraków, Poland.
