Adding a mass term for gauge bosons without the Higgs mechanism violates gauge invariance and unitarity.
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Standard particle physics literature confirms that introducing a naive mass term for gauge bosons without a Higgs mechanism breaks gauge invariance and leads to unrenormalizability and violation of physical principles.
Higgs mechanism, gives a rest mass to all massive elementary particles of the Standard Model, including the Higgs boson itself. The existence of the Higgs
The Higgs boson, sometimes called the Higgs particle, is an elementary particle in the Standard Model of particle physics produced by the quantum excitation of the Higgs field, one of the fields in particle physics theory. In the Standard Model, the Higgs particle is a massive scalar boson that couples to (interacts with) particles whose mass arises from their interactions with the Higgs field, ha
Gauge invariance is an important property of modern particle theories such as the Standard Model, partly due to its success in other areas of fundamental physics such as electromagnetism and the strong interaction (quantum chromodynamics). However, before Sheldon Glashow extended the electroweak unification models in 1961, there were great difficulties in developing gauge theories for the weak nuclear force or a possible unified electroweak interaction. Fermions with a mass term would violate gauge symmetry and therefore cannot be gauge invariant. (This can be seen by examining the Dirac Lagrangian for a fermion in terms of left and right handed components; we find none of the spin-half particles could ever flip helicity as required for mass, so they must be massless.)
W and Z bosons are observed to have mass, but a boson mass term contains terms which clearly depend on the choice of gauge, and therefore these masses too cannot be gauge invariant. Therefore, it seems that none of the standard model fermions or bosons could "begin" with mass as an inbuilt property except by abandoning gauge invariance. If gauge invariance were to be retained, then these particles had to be acquiring their mass by some other mechanism or interaction.
Additionally, solutions based on spontaneous symmetry breaking appeared to fail, seemingly an inevitable result of Goldstone's theorem. Because there is no potential energy cost to moving around the complex plane's "circular valley" responsible for spontaneous symmetry breaking, the resulting quantum excitation is pure kinetic energy, and therefore a massless boson ("Goldstone boson"), which in turn implies a new long range force. But no new long range forces or massless particles were detected either. So whatever was giving these particles their mass had to not "break" gauge invariance as the basis for other parts of the theories where it worked well, and had to not require or predict unexpected massless particles or long-range forces which did not actually seem to exist in nature.
A solution to all of these overlapping problems came from the discovery of a previously unnoticed borderline case hidden in the mathematics of…
According to the conventional concept of the gauge field theory, the local gauge invariance excludes the possibility of giving a mass to the gauge boson without resorting to the Higgs mechanism because the Lagrangian constructed by adding a mass term to the Yang-Mills Lagrangian is not only gauge-non-invariant, but also unrenormalizable. On the contrary, we argue that the principle of gauge invariance actually allows a mass term to enter the Lagrangian if the Lorentz constraint condition is taken into account at the same time. The Lorentz condition, which implies vanishing of the unphysical longitudinal field, defines a gauge-invariant physical space for the massive gauge field. The quantum massive gauge field theory without Higgs mechanism may well be established by using a BRST-invariant action which is constructed by the Lagrange undetermined multiplier procedure of incorporating the Lorentz condition and another condition constraining the gauge group into the original massive Yang-Mills action. The quantum theory established in this way shows good renormalizability.
Abstract In order to understand the confining decoupling solution of the Yang–Mills theory in the Landau gauge, we consider the massive Yang–Mills model which is defined by just adding a gluon mass term to the Yang–Mills theory with the Lorentz-covariant gauge fixing term and the associated Faddeev–Popov ghost term. First of all, we show that massive Yang–Mills model is obtained as a gauge-fixed version of the gauge-invariantly extended theory which is identified with the gauge-scalar model with a single fixed-modulus scalar field in the fundamental representation of the gauge group. This equivalence is obtained through the gauge-independent description of the Brout–Englert–Higgs mechanism proposed recently by one of the authors. Then, we reconfirm that the Euclidean gluon and ghost propagators in the Landau gauge obtained by numerical simulations on the lattice are reproduced with good accuracy from the massive Yang–Mills model by taking into account one-loop quantum corrections. Moreover, we demonstrate in a numerical way that the Schwinger function calculated from the gluon propagator in the Euclidean region exhibits violation of the reflection positivity at the physical point of the parameters. In addition, we perform the analytic continuation of the gluon propagator from the Euclidean region to the complex momentum plane towards the Minkowski region. We give an analytical proof that the reflection positivity is violated for any choice of the parameters in the massive Yan
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