Weak angles

Studying the angles at which muons are emitted during the decay of a Z boson is an important study of particle physics. The precision studies that CMS researchers intend to do over the next few years require this being understood in great detail.

Particle physics research involves many different approaches, whether it is looking for undiscovered particles of proposed theories or searching for something entirely new. It is also about revisiting familiar topics in unfamiliar environs to see if something unexpected presents itself. Just like tugging a loose thread can unravel an entire sweater, digging into an unexplained measurement on a familiar topic has occasionally occasioned a rewrite of the textbooks.

In today’s measurement, CMS physicists took a hard look at the Z boson, which is one of the best studied of the subatomic particles. Z bosons decay in many ways, but one of the cleanest and easiest to study is when it decays into two muons, which are heavy cousins of electrons.

You can do an analysis in any reference frame, from one in which the particle is moving to one that is stationary. If you do your analysis properly, you will draw the same conclusions in any frame. So CMS scientists picked the easiest frame, specifically one in which the Z boson was stationary. In such a frame, only a few properties define the particle. The Z boson is electrically neutral and massive. It also decays only via the weak nuclear force. Given the measured mass of the Z boson and decay muons, many of the details of how the muons are emitted are determined completely via energy and momentum conservation. The muons are emitted back to back and with a specific energy.

The one thing that is not predetermined is the angle at which the muon pair is emitted. That angle is related to the spin of the Z boson. The Z boson has spin (which has a complex meaning in the quantum world). Also, the angle is influenced by the nature of the weak force, which prefers certain spins over others.

To simplify the analysis, the experimenters expressed the various possible angular distributions using trigonometric functions. It turns out that you can describe the expected distribution using five functions, and the analysis reduces to five simple numbers that say just how much of each function is needed to describe the data.

The analyzers then determined these five numbers and plotted how they changed as a function of the momentum and angle of the Z boson in the reference frame of the LHC collision. They found minor discrepancies between data and theory and ascribe the difference not to a discovery, but rather to insufficiently precise theoretical calculations. Analyses of this kind are a crucial precursor to doing precision measurements at the LHC, and theoretical physicists are studying this measurement with great interest.

Don Lincoln

These U.S. CMS scientists made important contributions to this analysis.
These U.S. researchers have taken leadership roles in the design, commissioning, operation and upgrades of the CMS forward pixel detector. This detector is a crucial component for nearly every CMS analysis.