Problems with putting mass on Yang-Mills theory by hand When Yang-Mills field theory was introduced, a problem is that the gauge invariance can not allow mass for the gauge field. Later people invented spontaneous symmetry breaking and Higgs mechanism to give the gauge field mass. The Higgs particle is almost confirmed at LHC.
My question is, since there is symmetry non-conservation (P/CP) in nature, why not simply put a mass on Yang-Mill's theory directly, got a non-abelian Proca action, say gauge symmetry breaking (although gauge may not be a symmetry actually Gauge symmetry is not a symmetry?; actually this point is more subtle, one can also take a Stueckelberg action then fixing the gauge, it leads to the same Lagrangian)? Is there any theoretical reason for not adding mass by hand on Yang-Mills theory? Or just because Higgs particle was found, it works, that's it.
My friend has a guess, that gauge invariance implies BRST symmetry, which restricts the possible form of Lagrangian. If one did a renormalization flow transformation to lower energy scale without BRST symmetry, there will be other coupling in the effective Lagrangian at lower energy scale. I am not sure about this reasoning, because BRST symmetry can restrict the possible counter terms, can it also restrict the possible terms in the effective Lagrangian?  
 A: In a quantum theory, gauge symmetry is an inevitable consequence of Poincare invariance and long range interactions at the classical level (the weak and strong interactions aren't long range because of quantum effects, such as confinement and the Higgs mechanism). If  one "breaks" a gauge symmetry (what it doesn't have much since since gauge symmetries are mathematical ambiguities rather than physical symmetries), the one has to give up either: 


*

*Poincare invariance.

*Existence of a normalizable vacuum state (or existence of states with negative norm). This prevents the probabilistic interpretation of quantum mechanics.


Note that breaking a gauge symmetry is different from formulating a theory without gauge invariance. For example, classical electrodynamics in terms of the electric and magnetic field doesn't have a gauge symmetry, but it doesn't break it.
A: In general Gauge Theories, abelian or non-abelian, mass terms are not by construction forbidden. If one has a chiral gauge symmetry, that is a gauge symmetry in which left and right handed particles transform differently under the gauge transformation, then mass terms will inevitably destroy the gauge symmetry and thus are forbidden. The most famous example is the SU(2)xU(1) symmetry of the electroweak symmetry, where on invokes the mechanism of spontaneous symmetry breaking (called Higgs Mechanism induced by the Higgs field) to allow mass terms for the fermions. Any other way to introduce mass terms in this chiral theory destroys the gauge symmetry! In QCD like QED there is a left-right symmetry under gauge transformation, so mass terms are allowed at least at what concerns the gauge symmetry.
In order to quantize a not spontaneously broken gauge symmetry where the gauge bosons remain massless, one is forced to fix the gauge of the lagrangian to get a physical and sensitive theory. This gauge fixed lagrangian, however has still the BRST-symmetry, which is, if one looks at the infinitesmal transformation properties of BRST-transformation, a special gauge transformation with a nilpotent transformation parameter. 
What this BRST-symmetry actually does in pertubative calculations is to ensure that only physical degrees of freedom appear in asymptotical particle states, i.e. particles that are created in in-and out-states of the S-matrix in some scattering process. The nilpotent BRST-symmetry operator sorts the states on which it acts into different state spaces, depending on whether they are physical or not.
If you are particlarly interested in BRST-symmetry, I can recommend you the textbooks by
1.Peskin & Schroeder (An Introduction to Quantum Field Theory).
2.Steven Weinberg (The quantum theory of fields, Volume II),
3.Mark Sredenicki (Quantum Field Theory, a more readible introduction than the books by Peskin and Weinberg in my opinion).
A: Because the basic concept of a gauge theory is its invariance under a gauge symmetry, which is realized in nature. Without a gauge symmetry gauge bosons would be useless and dispensible. But the crucial fact is that these gauge bosons are observed in nature and the way they interact with matter content build out of fermions has been experimentally proved throughoutly and confirmed with great accuracy. The great experimental success of the application of gauge theories to the strong and the electroweak interactions has established these gauge theories. In physics you may always choose out of different model that one that describe the phenomenological observations the best. And in the interactions between fundamental particle the model of interactions based of gauge theories one has found the best theory to fit the experimental data. 
The reason why we protect gauge symmetry is thus that it seems to be a fundamental ingredient in the building plan of nature which restricts together with renormalizability the possible terms in lagrangians describing the nature the way that we observe it experimentally. So nature itself gives you the most powerful alibi, which gauge symmetry should be preserved. 
A: Adding mass by hand results in loss of Unitarity beyond a certain energy level or at the very least breakdown of perturbation theory above the same energy scale, and more importantly loss of renormalizability.
We need gauge symmetry to be preserved since theories with such symmetry are in agreement with Unitarity and renormalizability.
Without t'hooft and Veltman proving the renormalizability of gauge theories that acquire mass via SSB, gauge theory and gauge symmetry would not be of much importance.
That's why gauge symmetry is the key in physics.
I also did not understand the point about CP.
