Measurement of the W boson Mass at DØ

May 21, 1998

Why do we measure the mass of the W boson? To begin, we need to understand what is a W boson and how does it fit into our understanding of nature. The W boson is the charged mediator of the electroweak force. The electroweak force is responsible for one of the most important types of radioactivity, the decay of the neutron. It is known that a neutron decays into a proton, electron, and anti-electron neutrino. In this final list of particles we observe that there isn't a W boson. This is because the W boson appears as an intermediate particle in the reaction. The neutron decays into a proton and a virtual W boson. We say the W boson is virtual because it's mass, in this reaction, is much lower than it's true mass. The virtual W boson then decays into the electron and anti-electron neutrino.

Neutron Decay: A neutron decays into a proton, electron, and electron-neutrino through an intermediate W boson. Neutrons and protons are made up of up (u) and down (d) type quarks.

Our current theoretical understanding of electroweak interactions is called the Standard Model. From this theory, the W boson mass is predicted from three well known parameters; the electromagnetic coupling constant, the Fermi coupling constant, and the Z boson mass. Therefore, if we precisely measure the W boson mass we can compare with the prediction from theory and see if they are consistent.

In the Standard Model there is one additional particle, the Higgs boson, which hasn't been observed. The effect on the W boson mass due to the mass of Higgs boson can be calculated. Again, if we measure the W boson mass very precisely we can predict the Higgs boson mass. Now the Standard Model may not be the complete story and any new theory which includes particles that couple to the W boson may be confirmed or ruled out with a precise measurement of the W boson mass.

The W boson mass has been measured many times since it was discovered in 1983 at the CERN proton-antiproton collider. Each subsequent measurement tends to be more precise then the previous. The >DØ experiment at the Fermilab Tevatron currently has performed the most precise measurement ever of the W boson mass; the precision is 0.14%.

W Production: W bosons are produced in proton-antiproton collisions at Fermilab. A quark (d) from the proton and an antiquark (ubar) from the antiproton annihilate to produced the W boson. The W then decays in an electron and electron-neutrino pair.

The W bosons at the Tevatron are produced in proton-antiproton collisions at a center of mass energy of 1.8 TeV. A quark from the proton annihilates with an antiquark from the antiproton at the center of the DØ detector producing the W boson. The W boson decays into an electron and neutrino after only 10E-24 seconds. The electron is observed in the calorimeter of the DØ detector but the neutrino escapes. Neutrinos rarely interact with matter and so are not observed in the detector. In order to observe the neutrino we invoke momentum conservation. We add up the momenta of all the particles in the plane transverse to the beam direction. Since the neutrino's momentum is not observed, any imbalance is attributed to wayfaring particle. From the transverse momentum of the electron and neutrino, we calculate the transverse mass. The transverse mass is calculated in the same way as the invariant mass except only the vectors transverse to the beam direction are used. From the shape of the transverse mass distribution, the W boson mass is extracted.

Shown above and below are displays of W and Z boson events in the DØ detector. The top four plots are different views of the same W event. The left most plot is an end view of the DØ calorimeter and central tracking system. The red wedge indicates the energy from an electron and the purple spike is the missing transverse energy due to the neutrino. The middle left plot is a side view of the DØ calorimeter and the colored rectangles show the location and magnitude of the energy. The middle right plot is called a lego plot. A lego plot is made by cutting the calorimeter, which is the shape of a cylinder, lengthwise and unfolding it. The height of the rectangles in the lego plot indicates the magnitude of the transverse energy deposited in that region of the calorimeter. Again the red object in the plot is the energy of the electron and the open purple spike the missing transverse energy. The right most plot is also a lego plot where the distribution is in energy. The bottom four plots are a Z boson event. A Z boson decays into an electron and positron. The electron and positron are shown by the two high energy wedges in the end view (bottom left plot). The Z boson plots are the same order as the W plots.

A computer simulation, called a Monte Carlo, is used to generate transverse mass distributions as a function of an assumed W mass. Each of these distributions is compared to the data and the most likely distribution is the estimator of the W boson mass. The shape of the transverse mass distribution is sensitive to how the W boson is produced in the proton-antiproton collisions, to the resolutions from the detector, and to the momentum of the electron. The uncertainties on the measured W boson mass are due to how well we understand these different inputs to the Monte Carlo. We use the Z boson sample to calibrate the detector and provide input to the Monte Carlo simulation.

A plot of the transverse mass distribution along with the Monte Carlo simulation. The dots are the data and the solid line the Monte Carlo simulation.

The measured W boson mass from the DØ experiment is 80.43 +/- 0.11 GeV where the main uncertainty of 0.1% is due to the limited statistics of the of W and Z boson samples. This means that the error will be reduced when the experiment collects more data.

The following figure shows the W boson and top quark mass measurements along with the predicted bands for the indicated Standard Model Higgs boson mass. The MSSM (Minimal Supersymmetric Standard Model) band shown in green is an extension of the Standard Model which includes supersymmetric particles. We see at this time the data are compatible with either model.

A plot of the W boson and top quark mass measurements from the DØ and CDF experiments at the Tevatron and the recent W boson mass measurement from the LEP2 experiments. The black contour labeled Indirect is the predicted W boson and top quark mass values from a global fit to all other electroweak data. The blue contour labeled NuTeV is also a prediction of the W mass from a measurement of the weak mixing angle.

In the year 2000, the DØ experiment will begin collecting more W boson events with a significantly improved detector. The goal is to obtain a sample of 2,500,000 events which is 50 times the size of the current sample. This will result in a greatly improved measurement of the W boson mass. With this large sample, the experiment hopes to extend our understanding of the Standard Model (or maybe discover something new!).

The journal publications for the W boson mass measurements from the DØ experiment may be found in:

• Phys. Rev. Letters 77, 3309 (1996), FERMILAB Pub-96/177-E, hep-ex/9607011
• Phys. Rev. D 58, 012002 (1998), FERMILAB Pub-97/328-E, hep-ex/9710007
• Phys. Rev. D 58, 092003 (1998), FERMILAB Pub-97/422-E, hep-ex/9712029
• Phys. Rev. Letters 80, 3008 (1998), FERMILAB Pub-97/423-E, hep-ex/9712028

For further information contact: Dr. Eric Flattum (flattum@fnal.gov) or Dr. Ian Adam (imadam@slac. stanford.edu)

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