Confinement of Higgs bosons from hidden symmetry and convexity

In the full effective potential (EFP) approach, we find that the fact of spontaneous symmetry breaking (SSB) can, with the help of the rigorous convexity of the full EFP, lead to the prediction of the IR confinement of Higgs particles, adding difficulty for the experimental identification of Higgs particles unlike the electroweak gauge bosons. We do not specify the explicit form of the Higgs sector, merely suppose that it triggered SSB. In the meantime, we also discuss some subtle issues associated with the effective potential method and gave a simple but plausible proof of the convexity of the full EFP for any QFT where EFP can be consistently defined. The short distance behavior of the sector remain intact. The whole presentation is given in the understanding that any QFT should be an effective theory with underlying structures to take care of the various ill-definedness (like UV and/or IR divergences) according to a recently proposed natural