Vector Meson Dominance

Summary

I’m only now learning about ‘vector meson dominance’—a big idea put forth by Sakurai and others around 1960. Here’s a family of 9 mesons called the ‘vector nonet’. Each one is made of an up, down or strange quark and an antiup, antidown or antistrange antiquark. That’s 3 × 3 = 9 choices. In this chart, S is strangeness (the number of strange quarks minus the number of antistrange antiquarks in the particle) and Q is electric charge. I’ll focus on the neutral rho meson, the ρ⁰, which has no strangeness and no charge. But why are these called ‘vector’ mesons? It’s because the quark and antiquark have spin 1/2, and in this kind of meson their spins are lined up, so together they have spin 1. A spin-1/2 particle is described by a spinor, which is a bit weird, but spin-1 particle is described by something more familiar: a vector! The most familiar spin-1 particle is a photon. And in fact, the photons around us are slightly contaminated by neutral rho mesons! That in fact is the point of vector meson dominance. But more on that later. First, if you’ve read a bit about mesons, you may wonder why your friends the pion and kaon weren’t on that last chart. Don’t worry: they’re on this chart! This is the ‘pseudoscalar nonet’. In these mesons, the spins of the quark and antiquark point in opposite directions, so the overall spin of these mesons is 0. That means they don’t change when you rotate them, like a ‘scalar’. But these mesons do change sign when you reflect them, because then you’re switching the quark and antiquark, and those are fermions so you get a minus sign whenever you switch two of them. So these mesons are ‘pseudoscalars’. If you don’t get that, don’t worry. I’m going to tell the tale of rho mesons and especially the neutral one, the ρ⁰. A photon will sometimes momentarily split into a quark-antiquark pair. Since the neutral rho meson is the lightest meson with the same charge, spin and other quantum numbers as a photon, this quark-antiquark pair will usually b...