4Status after the high precision tests at LEP1
It is interesting to discuss how far the high precision tests done at Z peak with fermionic
processes can be used to test the bosonic sector.In order to achieve this goal it is essential to use a description of the Z exchange processes which is su?ciently general in order to
account for possible NP e?ects but also to cover in an accurate way the SM radiative
correction e?ects(W,Z self-energies,vertex and box corrections).For this reason the usual description[45],[50]of the e?ective Z exchange amplitude in e+e?→f¯f has been somewhat generalized[24].
A)Formalism
We write it in the form
A Z=
√
q2?M2Z?iM ZΓZ(q2)[1+δs.e.][¯v eγµ([g V e+?g V e]?γ5[g Ae+?g Ae])u e]××[¯u fγµ([g V f+?g V f]?γ5[g Af+?g Af])v f](50)
The SM part at1-loop is fully taken into account through the three inputsα(0),Gµ, M Z,and through the shiftsδs.e.,?g V f and?g Af.From the inputs one derives
s21c21=πα(0)
2GµM2Z
(51)
and the basic g V f and g Af couplings
g V f=I3f?2s21Q f,g Af=I3f.(52) The shifts contain the SM radiative correction e?ects(in particular the large m t and M H dependent terms)and the NP contributions.We have already seen in Sect.3how Z?Z′mixing e?ects modify the Z couplings,i.e.addδg V f andδg Af for f=ν,l,u,d(assuming
universality).Non universal e?ects(i.e.b quark terms di?erent from s quark terms) already appear within SM because of large m2t e?ects in Zb¯b couplings[26].NP can add further non universal terms which can be described by eq(50).This leads us to separately discuss the various subsectors.
a)charged leptonic processes
2s21
(?g V l?(1?4s21)?g Al)(55)
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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
and can be experimentally measured through two ”good”observables
Γl =G µM 3Z 2[1+?l 1][1+(1?4¯s 2l )2](56)
and
A l =2(1?4¯s 2l )
4A 2l .
b)light quark processes
2s 2[δg V l ?vδg Al +32?4s 2)δg Au ](62)
δ′d =?14
A l A q but can only be measured with a su?cient accuracy through polarized e ±beams
with A pol (q )F B =3The only process available at Z peak is e +e ?→Z →b ¯b .It contains two additional parameters [25]that we identify through the departures from universality with the two ?rst families:δg V b =δg V d +δg Heavy V b
(64)δg Ab =δg Ad +δg Heavy Ab (65)
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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
that can be determined through the two new observables
Γb=Γd[1+δbV](66)
A b=A d[1+ηb](67) where the coe?cients correspond to
δbV=?
4
v d(1+v2d)[δg Heavy
V b?v dδg Heavy
Ab
](69)
with v d=1?4
Γhad
(70) and
A pol(b) F
B = 3
2
(72)
d)W mass
c2M2Z
=1+δξ(73)
δξ=?
s2
s2?1+2?2+
c2?s2
Ref.[45]Ref.[46]Ref.[47]Vac.pol.
αT A33(0)?A11(0)?2
4s2
c
?3
4s2
F11(M2W)?F33(M2Z)
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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
This table contains a dictionary for the various notations which had been introduced in the past for the leading vacuum polarization(universal or”oblique”)contributions written as
Πij(q2)=Aij(0)+q2F ij(q2)(76) Let us also recall the de?nition
?α=Fγγ(0)?Fγγ(M2Z)(77) and notice one recent notation[30]
?x=?1??2?y=??2?=??3(78) We emphazize that the inclusion of non universal SM or NP terms requires the use of the more general parametrization de?ned above with at least7+1free parameters.
Brief summary of LEP1constraints
[3δg V u+9δg Au?6δg V d+4δg V e+23δg Ae]≤0.008(83)
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and in the heavy sector[53]
δbV=0.0414±0.0110(84)
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