Yet Another Confusing Finding in Particle Physics

Non-compliant spin property measurements spell uncertainty for current standing theories. How exciting!

Recalling what we know about atoms, with electrons whizzing about in mysterious ways, we find that nestled deep in the center of the atom is an object known as its nucleus. The nucleus is comprised of a subset of hadrons called nucleons — namely, protons and neutrons.

An illustration of various hadrons. (Source, Illustration by Sandbox Studio, Chicago with Ana Kova)

Electrons, protons and neutrons: These particles all have intrinsic properties (of which the origins we are still unsure of). One of these properties is known as ‘spin’. Spin is synonymous with the angular momentum of the particle; however, this spin is not manifested in the typical physical sense of a rotating object. Rather, these particles simply “have” the property of spin. Despite its frustrating non-corporeality, particle spin is important in determining how particles interact, mainly involving the strong nuclear and electromagnetic forces. It is also possible to observe experimentally, albeit not in the way we would usually visualize a spinning object.

The haphazard nature and arbitrary number of particle families in the Standard Model makes it one of the most well put together mysteries known to man. (Source)

To be frank, the standard model of Particle Physics already feels like it has been duct-taped together, all the while still having a few plot holes.

One of these plot holes, in recent findings from the Jefferson Lab CLAS and E97–110 collaborations, which report some “measurements of observables probing both protons and neutrons”, some discrepancies were unearthed between their observations and current predictions from chiral effective field theories.

Chiral Effective Field Theories, or Chiral Perturbation Theories (ChPT) are theories that make good approximations of more complicated quantum theories. In this case, ChPT is used to describe Quantum Chromodynamics (QCD) — a theory that seeks to explain quarks, gluons and the Strong Nuclear Force which holds nuclei together— at relatively low energy levels, with the help of the chiral symmetry underneath QCD’s hood.

Chiral symmetry is a property of some theories (including QCD) that dictate an invariance of outcomes, regardless of any rotation applied to the phenomenon about the axis of importance.

At the energy levels described by ChPT, the observables of experiments are not quarks and gluons. Rather, ChPT aims to observe hadrons, which are composite particles made up of multiple quarks and gluons. The main culprits here are the aforementioned nucleons, piled together with a whole zoo of other particles like pions, kaons, eta mesons and so ons. Why we look at more composite particles is because, at low energy levels, the quarks and gluons are more stable and hence able to form hadrons that are not likely to decay too quickly.

A table that lists particles that arise from the Standard Model. Of note, are the Hadrons, like the Pions, Kaons Baryons and so ons. (Source)

Experiments were conducted at CLAS to obtain data of the proton’s spin structure, as well as its forward spin polarizability. The empirical data for the spin structure, when studied as a function of four-momentum exchange, sat quite nicely when compared to theoretical predictions. To study the spin structure as a function of four-momentum exchange (Q2) means that four-momentum exchange is a variable that can be manipulated by the experimenters.

The vector for four-momentum is near impossible to visualize due to its number of dimensions. Here, 3-dimensional space is abstracted and represented by the “Hypersurface of the Present”. This singular plane represents all of space in one instant of time. All possible events in the Universe can occur on a straight ‘world-line’ that always falls inside the ‘Light Cones’. (Source)

Four-momentum is a direct sibling of momentum, which is usually calculated in the three dimensions of space. The difference for four-momentum, is that there is an added dimension of time. Hence, four-momentum is a vector with four dimensions — those of spacetime. Four-momentum exchange (Q2), in this context, is the exchange of said momentum in spacetime between particles. prefixing the word ‘momentum’ with a number such as ‘four-’ is a ubiquitous practice in many fields of Mathematics and Physics that deal with variable numbers of dimensions. Writing ‘four-’ is synonymous with writing ‘4D’ or ‘4-dimensional’. Hence, in fields like Topology, it’s common to see discussions surrounding objects such as a ‘3-torus’ or a ‘4-sphere’.

It appears that at low Q2, nucleon spin polarizabilities have data values that do not corroborate well.

The forward spin polarizability, which simply put is a measure of the proton’s propensity to change course when encountering transverse electric and magnetic fields (that act perpendicularly to the particle’s motion), did not agree with hypothetical calculations. Similar experiments on neutrons at E97–110 had equally, if not more, dumbfounding results.

It appears that at low Q2, nucleon spin polarizabilities have data values that do not corroborate well, which is starkly dissimilar to the pretty, self-consistent picture that theoretical predictions seem to paint, with small uncertainties to boot. This keeps some eyebrows raised for sure.

In a bid to make heads or tails of these findings, experimentalists believe that current ChPTs are still not reliable methods of divulging comprehensive calculations of nucleon spin. While other theories, like lattice QCD, are in hot pursuit of this problem, this leaves theorists no choice but to go back to the drawing board and figure out what they’re missing.

This Medium story was written to help myself understand an article I read in Nature Physics, titled ‘Nuclear Spins Surprise’. I am most definitely not an expert on the topic (yet), and any corrections to my understanding are welcomed.