Now we are back in 1975. Steven Weinberg, one of the greatest physicists of all time, realizes there is a big problem in the standard model, and he calls this problem “The U(1) Problem”.
When you look at the equation that describes the way quantum chromodynamics acts – its Lagrangian – you find this global symmetry in the limit that all the quark masses go to zero. This global symmetry is composed of a vector symmetry (for isospin and baryon number) times what is called an “axial” symmetry (which basically just corresponds to rotating something about its axis). That is, if you are setting N flavors of quark masses to zero, this symmetry is U(N)v x U(N)a (where v = vector and a = axial).
In QCD, if we have this global symmetry, we need all of the strong interactions to be invariant under U(2)v x U(2)a. We’ve verified that strong interactions are invariant under U(2)v, but axial symmetries behave differently. In a nutshell, we see a U(2)a symmetry, but not a U(1)a symmetry! Weinberg pointed this problem out, in his paper “The U(1) Problem”, and said that there simply must be no axial U(1) symmetry in quantum chromodynamics.
Read: Weinberg’s original paper: http://link.aps.org/doi/10.1103/PhysRevD.11.3583