An indirect road to the W mass taken by CDF

The vertical line, drawn at the value of the Z boson mass, is where the asymmetry measurement is most sensitive to the electroweak mixing parameter sin<sup>2</sup>&theta;<sub>W</sub> of the Standard Model. Two expectations, calculated using the PYTHIA and POWHEG-BOX proton-antiproton collision simulations, are also shown.

The vertical line, drawn at the value of the Z boson mass, is where the asymmetry measurement is most sensitive to the electroweak mixing parameter sin2θW of the Standard Model. Two expectations, calculated using the PYTHIA and POWHEG-BOX proton-antiproton collision simulations, are also shown.

In the Standard Model of particle physics, the W and Z boson particles are the carriers of the weak force, similar to the way the photon mediates electromagnetic forces. W bosons mediate beta decays of radioactive nuclei and nuclear reactions that power our sun. Z boson effects have been observed only at particle accelerators such as the Tevatron. Collider experiments have focused heavily on measuring the masses the W boson, Higgs boson and top quark. These masses are related to each other by the Standard Model, and deviations from the expectation may be a signature of unexpected new physics.

The Tevatron led the way in the precise, direct measurements of the W boson and top quark masses. The LHC has added to the precision of the top quark mass measurement, and on July 4, 2012, the discovery of a Higgs-like particle was announced. Evidence to date indicates that it is the Standard Model Higgs boson, and its mass is accurately known.

Fermilab scientists have put forth great effort to measure the W boson mass, and a recent column documents CDF’s effort on the single most precise direct measurement. Similar efforts by both CDF and DZero have gone into the indirect determination of the W mass because it is an independent cross check of the Standard Model.

In the current experiment, we observe the Drell-Yan process, in which quark-antiquark pairs (up and down) annihilate via the electromagnetic and weak interactions to produce electron-positron pairs. Z bosons mediate the weak interaction in this process.

The indirect measurement from the electron-positron collider experiments is labeled LEP-1 and SLD. Our previous measurement is labeled CDF μμ 9 fb-1 (red); our most recent measurement CDF ee 9 fb-1 (blue), and the combination of the two results CDF ee+µµ 9 fb-1 (purple).

The indirect measurement from the electron-positron collider experiments is labeled LEP-1 and SLD. Our previous measurement is labeled CDF μμ 9 fb-1 (red); our most recent measurement CDF ee 9 fb-1 (blue), and the combination of the two results CDF ee+µµ 9 fb-1 (purple).

The indirect determination is from the relationship of the W boson mass to the electroweak mixing parameter sin2θW from the unification of the electromagnetic and weak forces, known as the electroweak interaction. This measurement is truly indirect as no W particle is involved in our measurement.

At CDF, we have updated our indirect determination of the W boson mass using all of our Tevatron Run II data samples. We use Z bosons, which decay into electrons or muons and their antiparticles. On average, the negatively charged electron or muon from the decay of the Z boson has a slight preference for being emitted in the direction of the collision proton over that of the antiproton in the opposite direction. The strength of this preference is related to the value of the electroweak mixing parameter sin2θW. Consequently, the W boson mass can be inferred from the measurement of this asymmetry.

Our previous indirect measurement of W boson mass uses the asymmetry measured with muon-antimuon pairs from Z boson decays. CDF’s last word on the indirect measurement of the W boson mass is the combination of the muon-antimuon (denoted as µµ in the figure) results and new results from the asymmetry measured with electron-positron (denoted as ee in the figure) pairs.

Both results use the full Run II Tevatron data sample of 9 inverse femtobarns.

The precise measurement of the asymmetries and robustness of the W boson mass inferences were challenging but interesting problems for us. In addition to the necessary attention to details, we developed and implemented new methods with better precision to calibrate the CDF detector and to measure the asymmetry. We also adopted the theoretical approach used by LEP experiments at CERN and the SLAC Large Detector electron-positron collider experiments to connect asymmetry measurements with the electroweak mixing parameter sin2θW of the Standard Model.

These physicists were responsible for this analysis. From left: Arie Bodek, Jiyeon Han and Willis Sakumoto, all from the University of Rochester.

These physicists were responsible for this analysis. From left: Arie Bodek, Jiyeon Han and Willis Sakumoto, all from the University of Rochester.

The electron-positron pairs we observe are from an admixture of the production and decay of Z bosons and pairs produced by electromagnetic interactions. Z boson decays are intrinsically asymmetric. While electromagnetic interactions produce no asymmetry, its interference with the production and decay of Z bosons result in pairs that are also asymmetric.

The figure above shows our measurement of the asymmetry using electron-positron pairs as a function of the mass of the pairs.

The second figure shows a comparison of the world average of the combined direct measurements of the W mass from CDF, DZero and LEP-2 (labeled TeV and LEP-2) with indirect measurements.

Stay tuned as CDF and DZero physicists are combining their full Tevatron Run II data sets for the Tevatron legacy measurement.

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