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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
3Phenomenological description of the bosonic sector Searches for NP e?ects can be divided into2classes:
(A)search for new particles which cannot?t into the SM classi?cation(not a new family of leptons and quarks,not a Higgs scalar),and
(B)search for anomalous interactions among usual particles due to residual e?ects of
NP.
In both cases we can look for direct as well as for indirect e?ects of these new particles
or interactions.The characteristic scale of NP is generally expected to lie in the TeV
range(following arguments based on unitarity,on the TC mechanism or simply on present experimental limits).If this is true,then new particles should more probably have masses
in this TeV range so that their direct production requires high energy colliders.It is however not excluded that some states have lower masses and can be found earlier.If
this is not the case one can nevertheless indirectly try,from their virtual e?ects in certain
processes(mixing e?ects with usual particles,e?ects through loop diagrams),to?nd hints of their existence.Similarly the existence of new interactions can be directly observed
in processes involving gauge bosons and Higgs bosons.But they could also be detected through indirect e?ects in fermionic processes(like loops involving self-boson couplings),
measured with a very high accuracy as it is the case at Z peak.
A1)Direct production of new particles
The rate for new particle production in a collider is essentially controlled by the productσ×B of the production cross section times the branching ratio of the new particle
decay mode into the channel that is detected.When no candidate event is observed a
mass limit for the new particle is given.This is signi?cant only if the coupling of the new particle to the initial and to the?nal states consisting of usual particles is su?ciently
strong so thatσ×B reaches the observability limit of the experiment.This is a very model dependent question and it explains why mass limits given in the literature are so strongly
process dependent and why the results are so largely spred out.As one essentially uses
fermionic processes,limits appear to be especially low for those states that are weakly coupled to usual leptons or quarks,i.e.M H≥60GeV from LEP1[11],M V≥250GeV for the V bosons generated by the strongly interacting sector[5],[6].On the opposite,in other cases they approach the TeV range[13].The low values quoted above illustrate the
fact that indeed,at present,the bosonic sector is still very weakly constrained.
A2)Indirect e?ects of new particles
As an example of indirect e?ect of heavier particles we shall treat the Z?Z′mixing case which has been extensively studied at LEP1[12].We shall?rst present a rather general model-independent description and then look at speci?c models.
If the Z0mixes with a higher Z′0vector boson with a mixing angleθM
Z=Z0cosθM+Z′0sinθM(1) its vector g V f and axial g Af couplings get modi?ed as follows
δg V f=G′θM c f+d f
2
(2)
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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
depending on the Z′0f¯f couplings de?ned as
?i eG′2c f+1+γ5
4A2l.
For the4parameters of the quark sector one can take the following two partial widths Γ4=Γu+Γd+Γc+Γs,Γb and the two asymmetries A c,A b.
OnlyΓ4is presently available with a high accuracy.It is in fact more convenient[12]
to use the combination[14]
D=Γ4
3
s2)A l(4)
The forward-backward asymmetries A F Bq=3
4A q for q=c,b
in order to get a meaningful result[12],[15],[16].
Application to speci?c models
M′
Z .In Sect.4we will see how LEP1results allow to give upper limits for
θM and hence to give lower mass limits for the Z′.
B)Residual bosonic interactions below New Physics threshold.
We now present the description of residual interactions among usual particles.We anticipate the discussion of results from Z peak physics which strongly constrain(at the permille level)all non SM e?ects involving light fermions.We restrict to couplings involving W±,Z,γand Higgses,avoiding those which involve lepton and quark?elds. The case of couplings involving a heavy top quark is still an opened question which is under study[17].Let us start by recalling the basic SM bosonic couplings.
SM self-couplings at tree level
2
<WµνWµν>(5)
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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