ELEMENTARY PARTICLE PHYSICS

The ratio of a particle’s magnetic moment to angular momentum gives the dimensionless constant g. A spinning ball with uniform charge has g = 1. Relativistic quantum mechanics predicts the muon has intrinsic spin which is is twice as effective at generating a magnetic moment as classical angular momentum, i.e., g_µ = 2.

A more complete description, quantum field theory, allows for the creation and annihilation of particle-antiparticle pairs. Interactions between the muon and a cloud of such pairs and force-carriers around it make g_µ = 2.002331 that we call the muon anomalous magnetic moment. 

Since the 1970s, the SM has explained experimental results with great success. However, the measured value of a_µ and the SM prediction differ¹ by Δa_µ = a_µ^exp − a_µ^SM = (288±80) x 10^-11. Does this difference, at the edge of statistical signicance, indicate a failure of the SM? Do unknown particles or forces contribute to a_µ?

The SM prediction a_µ^SM is the sum of contributions from electromagnetic (EM), electroweak (EW), and strong (QCD) interactions. Physicists represent the contributions with cartoons called Feynman diagrams. In the most important, Fig. 2, a muon encounters a photon γ from an external EM field, then departs with altered momentum. This diagram generates the "2.0" in g_µ = 2.002331. In the "1-loop" EM diagram, Fig. 3, the charged muon interacts with its own EM field. It first emits an "internal" γ, then reabsorbs it after meeting the external γ.

Fig. 4 shows the most important interaction involving QCD. The internal forming the loop in Fig. 3 interrupts its journey to briefly become a foam of gluons and quark-antiquark pairs, represented by the red blob. This interaction contributes only ~ 0.006% of a_µ, but more than 85% of the theoretical uncertainty Best estimates are phenomenological calculations using data from e⁺e⁻ collisions. Can lattice QCD do better?

With lattice QCD we calculate the importance of the QCD foam by inverting a large, sparse matrix (dimension ~ 10⁸). The matrix encodes simulated quark and gluon fields on a discretized block of spacetime. Its inverse describes the propagation of quarks or antiquarks in every permissible way from one end of the blob to the other.

Simulations at different quark masses and discretization scales help control systematic errors. Preliminary results2 (Fig. 5) are consistent with the e⁺ e⁻ data.

The goal is to further reduce the uncertainty to resolve if ∆a_µ is a signal of physics beyond the SM.