Mass generation for gauge fields in the Salam - Weinberg theory without Higgs

We consider the Salam-Weinberg theory by introducing tensor gauge fields. When these fields are coupled in a topological way with the vector ones, the resulting system constitutes an alternative mechanism of mass generation for vector fields without the presence of Higgs bosons. We show that these masses are in agreement with the ones obtained by means of the spontaneous symmetry breaking. 1 1. The origin of mass generation for gauge fields in the Salam-Weinberg (SW) theory has been an interesting and intriguing problem since its proposal. Nowadays, it is widely accepted that spontaneous symmetry breaking together with the Higgs mechanism is the most probable explanation for the origin of these masses. However, if this is actually true, the Higgs bosons must exist in nature. The point is that there is no precise theoretical prediction on the mass scale where these fields could be found and experiments till now have shown no evidence about them. More recently, it has been pointed out that a vector-tensor gauge theory [1], where vector and tensor fields are coupled in a topological way by a kind of a Chern-Simons term, constitutes an interesting mechanism of mass generation for vector fields that is not plagued with Higgs. The general idea of this mechanism resides in the following: Tensor gauge fields [2] are antisymmetric quantities and consequently in D = 4 they exhibit six degrees of freedom. By virtue of the massless condition, the number of degrees of freedom goes down to four. Since the gauge parameter is a vector quantity, this number would be zero if all of its components were independent. This is nonetheless the case because the system is reducible and we mention that the final number of physical degrees of freedom is one. When the Chern-Simons term is introduced, where vector and tensor field are coupled in a topological way, this remaining tensor degree of freedom can be absorbed by the vector one to acquire mass [1, 3]. We mention that this peculiar structure of constraints implies that quantization deserves some care and a reasonable amount of work has been done on this subject [4]. The purpose of our paper is to use this mechanism in the SW theory in order to generate mass for the weak gauge fields. 2. Let us first briefly show how these ideas work out in the Abelian case. We start from the well-known Lagrangian of the Maxwell …