Measuring the "direction" of the Standard Model

The weak mixing angle, recently measured by the DZero collaboration, expresses the relation between the observed photon and Z boson, and the more fundamental bosons of the unified electroweak interaction. This is analogous to expressing earthly directions in terms of the cardinal points of a compass. The angle is extracted by examining the variations in the forward-backward asymmetry of electron-positron pairs as a function of their combined mass.

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For some time, we’ve known that the apparently fundamental forces of electromagnetism and the weak interaction are actually just the low-energy manifestations of a single unified electroweak interaction. This beautiful concept was developed by theorists in the 1960s and has been confirmed resoundingly by years of rigorous experimentation, including the discovery of the W, Z and Higgs bosons. This theory has only a handful of parameters; measuring them with the highest possible precision is crucial to test the unification mechanism and search for possible hints of new physics signatures.

One such fundamental parameter is the weak mixing angle (or Weinberg angle, after one of the pioneers of the electroweak theory). By analogy with a compass, where any particular direction can be expressed in terms of north-south and east-west components, the mixing angle represents the “direction” of the weak and electromagnetic forces, within the overarching framework of the electroweak interaction. In technical terms, the observed electromagnetic (photon) and weak (Z0) neutral force carriers are actually formed from some blend of the more fundamental electroweak bosons, denoted B0 and W0.

These DZero members all made significant contributions to this publication.

The DZero collaboration has recently performed a new measurement of the weak mixing angle. According to the Standard Model, electroweak production of electron-positron pairs from the original proton-antiproton collision has an inherent directional asymmetry (electrons are more likely to follow the original proton direction and vice versa for positrons). This asymmetry is a function of the mass of the electron-positron system, and the details of this mass dependence are highly sensitive to the weak mixing angle, allowing it to be extracted from the data.

This latest measurement makes several improvements compared to previous DZero publications. The data set itself is doubled, but in addition, the analysis is expanded in scope to include events not previously considered, giving a total increase in the sample size of more than 400 percent and a corresponding halving of the statistical uncertainty. Scientists also used a new technique to ensure an accurate determination of the electron energy scale, which is a crucial input to the mass dependence. In this method, the measured electron energies are corrected using a calibration database derived from the well-known Z boson mass.

The DZero authorship committee keeps track of all members of the collaboration, ensuring that everyone does their fair share of service work before they are rewarded with a place on the author list for new publications. Service work covers a wide range of essential activities, including building or maintaining parts of the detector, designing and implementing essential software tools, and reviewing and editing the papers themselves.

The final measurement of the weak mixing angle, with all improvements taken into account, is expressed as the quantity sin2θleff, which we measure to be 0.23106 ± 0.00053, corresponding to an angle of around 29 degrees. This is the most precise determination of this parameter ever made at a hadron collider and is consistent with previous measurements made at the SLC and LEP colliders. It is also the most precise instance of extracting the weak angle using this inclusive electron-positron asymmetry method. As such, it provides an important input for global tests of the electroweak theory.