Even more serious are the following two problems concerning the Higgs sector.One is called”triviality”and expresses the fact that the renormalized coupling constant of theφ4 term of the Higgs potential tends to zero when one wants to get rid of the cut-o?introduced for regularization(as one usually does in renormalizable?eld theories).This would imply that SSB disappears in this limit.The second one is called”the naturalness problem”and corresponds to the fact that,at1-loop,the Higgs mass depends quadratically of the cut-o?and is no longer controlled by the tree level value M0H.Its value then only depends on an outside scale.This is opposite to what happens in the”natural”fermion mass case where the mass shift is proportional to the tree level mass term and only weakly (logarithmically)depends on the cut-o?.This seems to indicate that the description of the scalar sector of the SM is not in a fundamental stage but must be considered as an e?ective
The status of the Standard Model (SM) is reviewed. We emphazize the fact that in spite of the success of the SM for the descrition of the fermionic sector, the status of the bosonic sector (gauge and scalar) suffers from many theoretical deficiencies and f
2Questions to be asked about the bosonic sector The W±and Z bosons have been discovered in a range of mass which precisely agrees with the one expected from the properties of the weak interactions found in low energy experiments.The high precision tests which followed their discovery have con?rmed that their couplings to leptons and quarks agree up to a few permille with the SM predictions [1].Can one from that conclude that W and Z have exactly the gauge nature that the SM assumes for them?Does it also mean that the Higgs mechanism is necessarily responsible for mass generation?
Certainly not!In fact many options for non-standard(NP)models are still allowed by the presently limited empirical knowledge and one can ask the following questions, classi?ed into three types.
a)The nature of the W±,Z bosons.
Are they true gauge bosons?In that case what is the precise gauge group?SU(2)×U(1)or a larger one like SU(2)×SU(2)×U(1)or SU(2)×U(1)×U(1)?Such extensions like Left-Right symmetry,E6symmetry[4]are obtained on the way of a Grand Uni?ed Theory (GUT)[3]or in certain alternative mass generation mechanisms based on a strongly interacting sector[5],[6].
More drastically departing from the SM picture,W±and Z may be kind of massive vector states(hadron like)whose interactions respect some global symmetry.This is what happens in compositeness schemes where the global symmetry originates from the subconstituent structure.This ensures that the couplings to leptons and quarks are similar to the SM ones[9].Mass may here simply originate from con?nement e?ects.
b)The precise spectrum of weak bosons.
Vector bosons
.
Does the Higgs boson exist at all?This question arises because there exist alternative models without Higgs(Technicolour-like[8]or compositeness inspired[9]).If the Higgs exists,is it an elementary or a composite state[8]?.If it exists as an elementary state,mainly because of the naturalness problem[2],the question arises whether it is light(close to M Z)or heavy(close to the unitarity limit in the TeV range).If it is light,is it accompanied by other neutral H0states and charged H±states(as claimed by Supersymmetry in order to cancel the quadratic divergences)[2]?
One can also raise the question weather there exist higher spin(J≥2)bosonic states?
c)The precise structure of the bosonic interactions?
This question is motivated by the fact that any extension or modi?cation of the SM should lead to”anomalous”interactions among usual bosons.In the vector boson sub-sector,the basic W,Z,γself-interactions can be di?erent from the Yang-Mills ones.In
4
The status of the Standard Model (SM) is reviewed. We emphazize the fact that in spite of the success of the SM for the descrition of the fermionic sector, the status of the bosonic sector (gauge and scalar) suffers from many theoretical deficiencies and f
particular new forms and new multi-boson interactions could appear.Couplings involving longitudinal W L states may have special features related to the fact that they are created by the mass generation mechanism(MGM).This feature is a genuine one as compared to the QED or QCD cases where SSB does not occur.Within the SM structure it is already known that a very heavy Higgs is a source of strong W L W L interactions[7].New Physics structures may also introduce further di?erences between W T and W L interactions[10].
Obviously the Higgs sector should be directly a?ected by the existence of a di?erent MGM,especially Higgs self-interactions because they re?ect the structure of the potential. Scalar boson-Vector boson couplings would also be modi?ed if the origin of the scalar boson is non standard,for example like in TC[8]or in any other compositeness schemes[9].
In order to answer these questions,precision tests of the bosonic sectors(gauge and scalar)have to be performed.Because of the rich variety of possible NP schemes,the analyses of present and future experiments must be done in the most possible unbiased and model independent way.This is the aim of the phenomenological description presented in the next Section.