Chiral Perturbation Theory,Weak Interactions and the Nuclear Two-body Axial Vector Current

Abstract

In this thesis I give a practical introduction to chiral perturbation theory. This is an effective field theory of pions and nucleons. It is governed by the chiral symmetry stemming from the lightness of the up- and down quarks in quantum chromodynamics. The validity region comprises energies up to the rho meson mass. The theory is expressed as an infinite series of chiral invariant interactions, whose strengths are expressed in an infinite number of low energy constants. The interactions can be ordered and I identify the most important ones. Special care has to be taken when including nucleons in chiral perturbation theory because of the scale introduced by the nucleon mass. To facilitate straightforward calculations I work in heavy-baryon chiral perturbation theory. In this formalismthe nucleons are considered to be very heavy and the nucleon mass only appears in next-to-leading order corrections. The pions and nucleons are coupled to the charged vector bosons of the weak interactions. This interaction is determined entirely by the chiral symmetry. As an example, I compute the decay rate of charged pions. Experimental data for this observable can be used to fix one low energy constant. Finally, I compute the two-body axial vector current of nucleons in heavybaryon chiral perturbation theory with the long wavelength approximation. This current complements the leading order one-body current operator and gives the first correction to the Gamow-Teller operator from the nuclear environment. I provide both a detailed derivation and an explicit expressions for this two-body current operator.