THE NONTRIVIAL EFFECTIVE POTENTIAL OF THE TRIVIAL LAMBDA-PHI(4)- THEORY - A LATTICE TEST

The strong evidence for the 'triviality' of (lambdaPHI4)4 theory is no t incompatible with spontaneous symmetry breaking. Indeed, for a 'triv ial' theory the effective potential should be given exactly by the cla ssical potential plus the free-field zero-point energy of the shifted field; i.e., by the one-loop effective potential. When this is renorma lized in a simple, but nonperturbative way, one finds, self-consistent ly, that the shifted field does become noninteracting in the continuum limit. For a classically scale-invariant (CSI) lambdaPHI4 theory one finds m(h)2 = 8pi2v2, predicting a 2.2 TeV Higgs boson. Here we extend our earlier work in three ways: (i) we discuss the analogy with the h ard-sphere Bose gas; (ii) we extend the analysis from the CSI case to the general case; and (iii) we propose a test of the predicted shape o f the effective potential that could be tested in a lattice simulation .