The Bosonic Sector of the Electroweak Interactions, Status a(5)

by the gauge coupling of the B?eld.This is why it is often discussed only in the limit g′→0.

Local symmetries

O DW=4 ([Dµ,Wµρ])([Dν,Wνρ]) ,(29)

O DB=(?µBνρ)(?µBνρ),(30)

O BW=Φ?BµνWµνΦ,(31)

OΦ1=(DµΦ)?ΦΦ?(DµΦ).(32) O W=13 WνλWλµWµν ,(33)

O UW=1

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

OΦ2=(?µ U U? )(?µ U U? ),(38)

OΦ3= U U? 3.(39) As presented in Table2,one can regroup the operators into sets which have basically di?erent physical consequences and behaviours under certain symmetries.The?rst four of them are called non-blind[34]because they involve2-point gauge boson functions.They would then directly a?ect the observables measured at LEP1.Consequently their coupling constants must have a strongly reduced strength in order to avoid direct observation.The next?ve ones are the”blind”ones in the sense that LEP1is blind to them at tree level. They can only a?ect the LEP1observables through1-loop.The resulting constraints are very mild and allow for large values of the coupling constants.The last two ones only involve Higgs?elds and has been dubbed”super-blind”[37]because they are almost unconstrainable by present and future machines.

Table2:Properties of the eleven bosonic operators

x

O DB

x

OΦ1

O UW x x

O WΦx

OΦ2x

x

Demanding a strict application of the custodial symmetry for the NP e?ects,strongly restricts the list of operators,see Table2.From the11above ones only?ve of them

13

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

are SU(2)c invariant namely,¯O DW,O W, O UW and the two superblind Oφ2and OΦ3. SU(2)c symmetry restricts the5blind ones to only two.Remember that one of them, O W was already obtained from the SU(2)L global symmetry which is for the pure W sector,a remnant of the full SU(2)c.The other one is O UW which also involves Higgs ?elds.The justi?cation for this strict use of custodial symmetry is that NP is supposed to be intimately related to the origin of the scalar sector and should therefore respects the same symmetries.

Chiral descriptions

v(40) E?ective lagrangians invariant under SU(2)×U(1)resulting from integrating out the e?ects of this sector can be constructed as combinations of gauge boson?elds,U matrices and their covariant derivatives.At present energies it is meaningful to make an expansion with respect to the number p of derivatives or of gauge?elds(U being dimensionless).At lowest(p2)order one?nds the SM part eq.(6).New couplings appear at order p4,p6,...etc. In this way one can again generate all possible bosonic operators.In the physical gauge, they produce the set of anomalous3-boson couplings listed above as well as higher multi-boson couplings.However the di?erence with the linear representation presented before is the absence of a physical Higgs?eld and a di?erent ordering in magnitude of the anomalous self-boson couplings.For exampleδZ,κγandκZ appear at order p4,through the operators called L9L and L9R and satisfy eq.(26)

L=?igL9L WµνDµUDνU? ?ig′L9R BµνDµUDνU? (41)

δZ=

e2

c xγ=?

e2

.

When operators with d>4are considered,they generally lead to boson-boson scat-tering amplitudes which grow fastly with the center of mass energy.For example d=6 terms lead to partial wave amplitudes growing like s or s2.This means that for a given value of the coupling constant the amplitudes reach the unitarity limit at a certain energy scale.At this point unitarity saturation e?ects(resonances or new particle creation,...)

14

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

must occur.So the unitarity relations which are obtained for each of the operators have two meanings.

1.For a given coupling constant one obtains a value for the scale at which unitarity saturation occurs(this can be considered as a practical de?nition of the NP scale),

2.For a given NP scale one can set upper limits for the coupling constants in order to satisfy unitarity in the whole s≤Λ2domain.

For the5blind operators the unitarity constraints read[39],[40]

|f B|≤98M2W s,|λW|<～19M2W

s

(45)

|d|<～17.6M2W√

s +1070

M3W

s?1123

M3W

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

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