Gauge Hierarchy, Decoupling, and Heavy Particle Effects

Abstract

We deal with the problems of a large gauge hierarchy and decoupling in theories with spontaneously broken symmetry. They are relevant to the current developments of grand unification, in which several vacuum expectation values of scalar fields are introduced, with one of them (V) much larger than all the others. We shall show to all orders in the loop expansion that: (1) Once we make a proper identification of the light particles and of the heavy particles at the tree level, then such a division will be maintained order by order in the loop expansion without the necessity of fine tuning. The correction to the light masses in each order is only logarithmic in V. (2) To v(1) accuracy, there is a local renormalizable effective Lagrangian, composed of light fields only, which can be used to reproduce all the one light particle irreducible Green’s functions for external momenta ≪ V. (3) A set of renormalization group equations can be written down, wherein one stays in the lower energy region to correlate the two sets of parameters in the full and the effective light theories.