Z boson lends a hand to measure the W boson mass

By using the well-known Z boson as a standard candle to calibrate the detector response, scientists can measure the W boson mass to very high precision. The plot in this figure shows just how well the Z boson data (points) agree with the simulation (line) for the Z boson mass, even in the tricky ‘tails’ of the distribution, which are sensitive to many subtle detector effects.

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Last year, both CDF and DZero released their latest measurements of the W boson mass, a parameter of fundamental importance in testing the Standard Model of particle interactions. A previous column in this series discussed the motivation for this measurement and the significance of the results. Now the DZero collaboration has released more details of how they performed their measurement, highlighting exactly how meticulous each stage of the analysis has to be in order to achieve impressive precision exceeding one part in 3,000.

The standard way to measure a particle’s mass is to add up the contributions from all the decay products. However, for this analysis, the W boson decays into an electron and a neutrino. The neutrino passes unobserved through the detector, and so an unknown amount of energy is lost, preventing the direct extraction of the W mass. Instead, various properties of the event are compared to detailed simulations under different W mass hypotheses, allowing the W mass to be precisely inferred despite the missing neutrino.

The biggest challenge in this method is developing a simulation that can model the response of the detector with the required detail. Helpfully, the W boson has a partner, the Z boson, which often decays into a pair of electrons, and no missing neutrino. The Z mass is known to very high precision (one part in 50,000) and can therefore be used to develop and test the details of the simulation using the data itself.

In particular, the measured energy of an electron differs from the true energy because of losses incurred as the particle passes through the detector material and because the detector itself collects only a sample of the total energy. These effects need to be incorporated into the simulation, and the Z decays provide a “standard candle” with which to calibrate the simulation. Using the data like this also ensures that any residual detector effects not completely modeled by the simulation will largely cancel out, since they affect the W and Z boson masses in the same way.

This method of using Z bosons is so powerful that the final precision on the W mass measurement is just as limited by the Z boson sample size as it is by the number of W bosons detected. The good news is that the analysis currently uses only around half of the available data, so not only will the statistical precision improve as more W bosons are added, but the increased Z sample will also reduce the uncertainty. The next (final) updates of the W mass measurement from CDF and DZero will be the world’s best for many years to come, cementing the legacy of the Tevatron experiments in this field.

Mark Williams

These physicists all made major contributions to this publication.