Spinning tops and spinning top quarks

Spinless particles (such as Higgs bosons) decay in any direction with equal probability, but particles with spin (such as top quarks) prefer to decay along their axis of spin.

When I was asked to write an article on the CMS experiment’s measurement of the spin of the top quark, a metaphor immediately suggested itself: spinning tops. However, the more I thought of it, the more I realized how complex the relationship is between a toy top that you can spin with your fingers and a top quark, spinning on its own according to the rules of quantum mechanics.

A toy top is made of trillions of trillions of atoms, so its rotation is easy to define. It is rotating when the lattice of atoms orbit a central axis. If its surface were perfectly smooth and it were not made of granular pieces like atoms, then it would be harder to say that it is or is not rotating around its axis of symmetry — it would look exactly the same at all times. This is a problem when describing the rotation of black holes: All one can see is a knot of pure space-time, no surface wrinkles revolving like a carousel.

Angular momentum is a more fundamental concept than rotation, one that applies equally well to featureless objects like black holes. For an object with a well-defined rotation, angular momentum is proportional to the rate of rotation, but it is also proportional to the mass and diameter squared of the object in a way that depends on shape. If we shrink a top while maintaining its angular momentum, the rotation rate must increase, as it does when a spinning figure skater contracts his or her arms. If we shrink a toy top to an infinitesimal point, like a fundamental particle, the rotation rate would become infinite.

A top quark “spins” in the sense that it has angular momentum and it can transfer that angular momentum to other objects. If quarks are the indivisible, fundamental particles that they appear to be, then they have no parts to turn or rotate in the conventional sense.

Top quarks are too short-lived for their spins to be measured using macroscopic devices, but the spin’s influence can be seen in the quark’s pattern of decays. Imagine an exploding toy top: More pieces would fly out perpendicular to its axis of rotation than along it. If you only saw the trajectories of the debris, you could infer how much angular momentum the toy had before it exploded. Unfortunately for my metaphor, the top quark prefers to decay along its spin axis, rather than against it, because the mechanism has nothing to do with centrifugal forces.

With a huge sample of top quark decays observed by CMS, physicists selected the 9,000 cleanest events and successfully measured spin-related asymmetries in their decays. These measurements are sensitive to the details of the process that produces top quarks, which aligns the top spins before they decay. Ironically, the top quark’s short lifespan is essential for this inference — all other types of quarks lose the spin correlations that they were born with because they interact with each other before decaying.

Jim Pivarski

The physicists pictured above measured correlations in top quark spins using a new technique for this process: They unfolded uncertainties in the observed data, rather than mixing them into the theory prediction.
Professor Joe Incandela of the University of California, Santa Barbara, recently stepped down after two years heading the CMS experiment. During his tenure, CMS had tremendous success, most notably in the discovery of the Higgs boson.