Low Energy Tests of Chiral Symmetry

When I was a student back in the 1960’s, the goal of particle and nuclear physicists was to seek the fundamental laws of nature, and one of the requirements of such a “fundamental” law was that it be renormalizable. Well now it’s 1996 and we’ve learned a few things in these three decades. One is that nonrenormalizable effective field theories can be just as if not more useful than their renormalizable siblings in certain situations. One of these is the case of QCD, where we have what we feel is a correct model of nature. However, it is written in terms of the “wrong” degrees of freedom (quarks and gluons rather than hadrons) and is impossible to solve because of its strong coupling and inherent nonlinearity. Much more useful in the arena of low energy physics is an effective Lagrangian, which is written in terms of experimental degrees of freedom—mesons and baryons—and which encodes the symmetries of the underlying QCD interaction—specifically for our purposes chiral symmetry, which exists in the limit in which the quark mass can be taken as vanishing. This is a program which was begun in the 60’s with the effective two-derivative Lagrangian[1]