Anomaly-matching and Higgs-less effective theories

Johannes Hirn, Jan Stern

Published 2004-03-01, updated 2004-10-20Version 2

We reconsider the low-energy effective theory for Higgs-less electroweak symmetry breaking: we study the anomaly-matching in the situation where all Goldstone fields disappear from the spectrum as a result of the Higgs mechanism. We find that the global SU(2)_L x SU(2)_R x U(1)_{B-L} symmetry of the underlying theory, which is spontaneously broken to SU(2)_{L+R} x U(1)_{B-L} has to be anomaly-free. For the sake of generality, we include the possibility of light spin-1/2 bound states resulting from the dynamics of the strongly-interacting symmetry-breaking sector, in addition to the Goldstone bosons. Such composite fermions may have non-standard couplings at the leading order, and an arbitrary total B-L charge. In order to perform the anomaly-matching in that case, we generalize the construction of the Wess-Zumino effective lagrangian. Composite fermions beyond the three known generations are theoretically allowed, and there are no restrictions from the anomaly-matching on their couplings nor on their U(1)_{B-L} charge. Absence of global anomalies for the composite sector as a whole does not preclude anomalous triple gauge boson couplings arising from composite fermion triangular diagrams. On the other hand, the trace of B-L over elementary fermions must vanish if all Goldstone modes are to disappear from the spectrum.