Extended gauge models and precision electroweak data

Physics Letters B 318 (1993) 139-147 North-Holland

PHYSICS LETTERS B

Extended gauge models and precision electroweak data -AG. A l t a r e l l i CERN, Geneva, Switzerland

R. Casalbuoni, S. D e C u r t i s Departamento di Fisica, Universititdi Firenze, Florence, Italy and INFN Sezione di Firenze, Florence, Italy N. D i B a r t o l o m e o , R . G a t t o Dbpartement de Physique Thborique, Universit~de Genbve, Geneva, Switzerland

and F. F e r u g l i o Departamento di Fisica, Universit~di Padova, Padua, Italy and INFN, Sezione di Padova, Padua, Italy Received 5 August 1993 Editor: R. Gatto

We consider the implications of precision electroweak data on extended gauge models. The cases of extended gauge models based on E~ ( for arbitrary orientation in group space of the new U ( 1) generator ) and of left-right models are discussed in detail. Fits of the data in terms of these extended gauge models are considered and limits on the mixing parameters are obtained. The relation with the epsilon parameter approach is discussed. We also consider a number of more particular models with specified Higgs structure, where limits on mz, can also be derived.

1. Introduction In this note we present an analysis o f the most recent LEP d a t a in the framework o f extended gauge models. The results o f the 1991 and, in p r e l i m i n a r y form, o f the 1992 runs at LEP have now b e c o m e available #~. The implications for extended gauge models o f these new d a t a on hadronic a n d leptonic partial widths a n d on asymmetries at the peak are important and make an update o f previous works [ 13] worthwhile. The present analysis also contains #r Partially supported by the Swiss National Foundation. #~ The present work is based on the latest LEP data presented at the European Physical Society Conference in Marseille, July 1993. Elsevier Science Publishers B.V.

some novel features with respect to previous similar studies where limits on mixing p a r a m e t e r s were derived. We consider in detail the question o f how the extended gauge models c o m p a r e with the experimental pattern o f results on the small p a r a m e t e r s that describe the deviations from the S t a n d a r d M o d e l plus pure Q E D corrections (in particular the epsilon parameters, introduced in ref. [4] ). We also describe the results o f a n u m b e r o f fits o f extended gauge models that contain two or three a d d i t i o n a l p a r a m e ters with respect to the S t a n d a r d Model. The extended gauge models that we shall discuss in detail are the left-fight m o d e l ( L R ) [ 5 ] a n d a set o f models with an extra U ( 1 ) contained in E6 for arbitrary defining angle 02 o f the corresponding generator in E6 space [ 6 ]. M o s t o f the results that we derive do 139

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not depend on assumptions on the detailed structure of the Higgs sector of the models. However, in some cases, for a number of particular schemes that have been explicitly considered in the literature, we describe additional constraints that follow for the specific structure of the Higgs sector of each model. In our analysis the standard model radiative corrections to the widths are taken into account at the full one-loop level, by using the Z F I T T E R programme [ 7 ].

25 November 1993

Standard Model relation between m w and m z is modified at tree level according to the equation m2 m 2 cos20w =Po.

(3)

In eq. (3) one has P0 = 1 + ApM + ApsB,

(4)

where

APM=r(mz'~2L\ m----~/ -- 1] sin2~°>~0 .

(5)

2. Widths and asymmetries in extended gauge models At LEP 1 the existence of an extended gauge sector can only cause departures from the standard predictions in that the observed mass eigenstate Z is in general a mixture of the standard gauge boson Zs and of a new one ZN. Given the ZN couplings as specified in each model (e.g. as functions of 02), the effects of such a mixing are completely described in terms of two parameters; the mixing angle ~o and the shift Apra in the p parameter due to the mixing. These two parameters are independent unless the Higgs structure of the model is specified. In this case it is possible that the mass of the heavy physical vector boson Z' is fixed as well as the relation between ~o and ApM. In models with an extra U ( 1 ), at tree level, before symmetry breaking, Zs and ZN are the states which are coupled to the ordinary neutral current J3L--sin20wJem and to the additional current JN, respectively: e Zs (J3L -- sin20wJem) LNC = sin 0w cos 0w

+gNZNJr~.

( 1)

Clearly, Zs has couplings which are formally identical to the neutral vector boson of the standard model in terms of an angle 0w whose relation to the basic input parameters of the theory is in general non standard and will be specified in the following. After symmetry breaking Zs and ZN are mixed. The physical vector bosons Z and Z ' ,

Z = cos ¢o Zs + sin ¢o Zr~ , Z' = - sin CoZs + cOs ¢oZN ,

(2)

are mass eigenstates with masses m z and mz,. The 140

ApM arises because the Z mass in absence of mixing is always larger than the observed Z mass: m2s = (1 + ~oM)m 2 (the lowest energy level is pushed down by the perturbation). For LR models there is in general an additional contribution to ApM from the charged sector (which is negligible if the new charged vector bosons are much heavier than the neutral Z' ). ApsB stands for a possible contribution from the symmetry breaking (SB) sector of the theory. For example ApsB could arise from the presence of non doublet Higgses. Beyond the tree level, the complete set of one-loop electroweak radiative corrections in the Standard Model has been taken into account, using ZFITTER [ 7 ] (the results have also been checked with TOPAZ0 [ 8 ] ). Loop effects due to the heavy gauge boson Z' are quite small for the relevant range of parameters and will be neglected here. Although we have included the full one-loop radiative corrections in the Standard Model, in the following, for the sole purpose of defining, for widths and asymmetries in the extended gauge models, the shifts from the Standard Model limit, it is sufficient to refer to the improved Born approximation [ 9 ]. This is because the small correction from additional radiative effects and from the extended gauge structure can be treated as independent in a linear approximation. In the Standard Model, the improved Born approximation correctly takes into account large logarithms (i.e. terms of order ( a / n ) log(m2/rn~ ) wherefl is a light fermion) and quadratic terms in the top mass (i.e. terms of order GFm ~ ). In the improved Born approximation the partial widths F ( Z - - , f f ) and the forward-backward asymmetry for the fermionfat the peak are given by ( f ~ b)

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r(z~ff)

=

PHYSICSLETTERSB

pN¢[ (~ff)2+ (afff)2] , e e Peffaeff

(6)

~ffafff

-4n3=3 (v~fr)2+ (a~ff)2 (~fr)2+ (a~ff)2.

(7)

Other asymmetries (e.g. the r polarisation asymmetry) can similarly be expressed in terms of ~ff/a~ff. Here No=3(1 +~QCD)(1 +~QEO) for quarks, Arc= (1 +t~QED) for leptons (JQEO is the correction from final state real and virtual photon radiation). The factor p also includes the large radiative corrections arising from the top quark loop as well as the logarithmic terms from the Higgs p = 1 + ApM -b APsB -t- Apt = 1 -b A p ,

(8)

where Ap~_-__3Gvm~/8n2x/~+..., where the dots stand for smaller terms in the large mt limit. The effective vector and axial vector couplings ~ff and a~ff are given by a superposition of the corresponding Zs and ZN couplings: ~ = C O S ~o~s +sin ~ o ~ , a~f~= cos ~oa:s + sin ~oa~.

(9)

In particular the Zs couplings are given by = T~L -- 2~'wQf

afs = - Tf3L,

(10)

where T:SL and Qrare the weak isospin (third component) and the electric charge of the fermion f The quantity ~w given by the relation g,2w= 1 _ m 2 pm2z

(11)

is the effective sin20w for the on-shell Z couplings. Because of the effect of ApM, it differs from the corresponding quantity g~ in the standard model, for fixed input parameter or, Gv, mz, my, mn, according to the relation

~=g~_

-2 -2 swcw -2 -z AOM .

Cw--Sw

25 November 1993

For the LR and the E6 models that we consider here and a~ are collected in table 1. The entries in table 1 correspond to gN (defined in eq. ( 1 ) ) given by gN=g' =gtan0w. This identification is clearly not necessary, but should be valid as an order of magnitude if grand unification occurs at a large scale. For a different choice for r=gN/g', with not too large a value, the consequence would be a rescaling of the results on ~o by a factor 1/r, while, in our approach, where mz, is not specified, the limits and the best fit values obtained for ApM are not affected. It is useful to consider the deviations from the corresponding standard model values of the predicted observables, mw/mz, the Z partial widths and asymmetries, linearised in ~o and ApM, expressed in the following form: 80 0 - (AoApM +Bo~o).

(13)

In eq. (13) the coefficients Ao are uniquely determined in terms of the standard model parameters, whereas Bo also depend on the couplings v~ and a~ [ 1 ]. Their expressions immediately follow from eqs. ( 6 ) - ( 12 ) and their numerical values are given in table 2, for all the relevant measured quantities. We have seen that at the Z peak all effects of extended gauge models are given in terms of ~PM and ~o, which are independent if the mass mz, of the heavy Table 1 Vector and axial couplings of fermions to the unmixed new vector boson ZN in the case of extra U ( 1 ) and LR models. Here 0=0,,. For left-right models, we have put in the text 2=gL/gR= 1. AS a consequence y = ~ 20. extra U ( 1 ) models

v~ = 0 a ~ = - ] sin 0cos 02 v a = ½sin 0(cos 02 + ~

sin 02)

a a = sin 0( - ~ cos 02 + ½ ~ sin 02) v~ = - ½ sin 0 ( cos 02 + ~ / ~ sin 02)

(12)

Note that the case F(Z--,b6) is exceptional because, as is well known, there are additional large terms of order Gym 2 from vertex diagrams, which are taken into account [ 9,10 ] by replacing 1 + Apt in p by l--]Apt and YEw by ~ w ( l + ] A p t ) in eqs. (6) and (10). The vector and axial vector couplings v~ and a~ of the new vector boson ZN depend on the model.

e d aNmaN

v~ = - s i n 0( ~ cos 02 + ½V/~ sin 02)

a~ =-v~ left-fight models /.~__ COS20(T3R__2~2 sin20~m) + 2 sin 20 ( T3R--2 sin 28 Qem) y cos20 2sin20 a~ = mZy T3RT3L Y 141

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25 November 1993

Table 2 Coefficients A and B defined in eq. ( 13 ). Quantity

Fz R tr~ Rbh

g~/go Mw/Mz

B

A

1.350 0.275 -0.030 --0.060 -- 17.556

O.715

for extra-U( 1) models

for the LR model

-0.130 cos 02+0.0044 sin 02 0.189 cos 02-1.158 sin 02 -0.045 cos 02+ 1.489 sin 02 -0.614 cos 02+0.087 sin 02 -6.547 cos 02-7.623 sin 02 0

-0.290 1,056 - 1.250 0.280 -2.098 0

more convenient to use ~o and Ap (given by eq. (8), or, more precisely by ~t0 = ~NI "~-~OM, with eN~ defined in ref. [ 1 1 ] ). The bounds on Ap are in fact almost independent on mt, contrary to those on Apra. The resulting constraints on Ap and Go for E6 models are plotted in figs. 1 and 2 for all values of 02. In figs. 1 and 2 the 90% CL upper and lower limits on Ap and ~o, respectively, are displayed for m n = 100 GeV, oq = 0. I 18 and mt = 100 and 200 GeV. As anticipated, for Ap, there is little dependence on mr. The residual dependence arises from logarithmic terms and also from the residual quadratic terms in the Z ~ b8 vertex (which is of only moderate importance for the fit because the error on Fb is still relatively large). With increasing mt less and less space is left for ApM because the standard term Apt is positive and increases quadratically. A typical value for the upper bound on Ap (at ors=0.1 18) o f about 0.006 is already saturated by the contribution from Apt with mt "" 175 GeV. The dependence on mt o f the limits on ~o is also very moderate, except in the region near 02 = 0. We have also studied the dependence on c~s in the range 0.111 < o q < 0 . 1 2 5 . It turns out that, for mn= 100 GeV, rot= 150 GeV, by increasing as o f 0.01 the allowed region for ApM is shifted down by about 0.0015. As for ~o the corresponding shift to the allowed region is at most o f about 0.004. The change is

vector boson Z ' , which appears in eq. (5), is not known. We now discuss the constraints imposed by the data on ApM and Go in E 6 models for all values o f 02 and in L R models.

3. The data and their implications The data on the widths and asymmetries that we use in the present analysis o f extended gauge models, together with the values o f m w / m z and o f ~ff and afff as obtained by the LEP experiments are collected in table 3. The Z mass was fixed at the value m z = 91.187 GeV. The Z 2 function minimized in the fit is the sum o f six terms: m w / m z , the total width Fz, the ratio of the hadronic and leptonic widths Rh=Fh/Ft, the hadronic cross section at the peak trh= 12n/m2['eFh/ F2z, the ratio Rbh=Fb/Fh o f Fb=F(Z--,br) and the total hadronic width Fh and the ratio vgff/agff. We have taken into account the main entries o f the correlation matrix, which, in the basis Fz, trh and Rh, are c12 = -- 0.07, c23 = 0.13 and Cl3 = 0.00. The theoretical expectation for the widths has been defined as the sum o f the full one-loop standard model prediction plus the corresponding deviation as given by eq. (13). Rather than deriving bounds on ~0 and ApM it is

Table 3 Experimental values from LEP and CDF/UA2 for the observables used for the fit. Fz (MeV)

R=/'h

2489 + 7

20.77 + 0.05

142

o'n (nb)

Rbh

1"1 41.55 _+0.14

0.220 + 0.0027

~

M.__.Ew

g,

Mz

0.0712 + 0.0028

0.8798 _+0.0028

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0 ~

30 i

60 i

90 0.010

0.005

0.005

0.000

0.000

-0.005

-0.005 mtop(GeV) = 100 mtop(GeV) = 200

-0.010 -90

I -60

i -30

I 0

i 30

I 60

-0,010 90

Oz(deg)

25 November 1993

of the extended gauge models. First we fix m u = 100 GeV, mt= 100 or 150 GeV and a, = 0.118 and we fit ~o and Ap (in E6 models we do the fit for a number of points on the 02 axis). The results are reported in table 5. Since the Standard Model fit, for the chosen values of the parameters, is already good, it is not too impressive that the extended gauge model fit, with two more parameters, is quite good for all values of 02, also for mt= 100 GeV. One can obtain a pictorial impression of the quality of the fit and a comparison with the Standard Model by using the epsilon variables of ref. [ 11 ]. As discussed in ref. [4 ], in extended gauge models end, eN2 and eN3 receive the additional contributions (with respect to the Standard Model) given by AeN~ = ApM + 4a~tg Go, Aes2 = --tg ~o(V~-- 3 a ~ ) ,

Fig. 1. Allowed range (90% CL) for Aq7versus 02, for m~-- 100 GeV, cq=0.118.

~0 -90 0.050

-60 I

-30 I

0 ~

30 I

60 I

90 0.050

0.025

0.025

0.000

..............

........... ~

~

.....

............. z

0.000

-0.025

-0.025

mtop(GeV) = 100 mtop(GeV) = 200 -0.050 -90

i -60

I -30

I 0

I 30

I 60

-0.050 90

02(deg)

Fig. 2. Allowedrange (90% CL) for ~ versus 02, for mn= 100

GeV, a,=0.118. upward for 02 > 0 and downward for 02 < 0. The corresponding results on the LR model are reported in table 4. The same pattern is found also in this case. The data set is by now sufficiently rich that we can attempt a fit of the six experimental entries in terms of the parameters of the Standard Model plus those

Ae~3=~tg~o [(l-2S~)v~+ (1+2~2)a~].

(14)

Note that, with respect to ref. [4], there is a sign change in front of the a~ terms. This is simply due to the fact that the opposite sign definition for a~ was adopted here, following eq. (10) for the axial couplings in the Standard Model. The variable eb is not particularly relevant in the present context because, in all extended gauge models we consider, all the couplings are family independent. Thus, whatever correction to the Z--. b6vertex would also affect all down quark vertices by the same amount. Since the accuracy of the data on Fb is relatively modest, we cannot adjust the value of Fb without at the same time spoil the agreement with the other hadronic observables. In figs. 3a and 3b, for mt-- 100 or 150 GeV, respectively, and m~t= 100 GeV, ors= 0.118, we plot a set of dots in the plane er~3versus eNl that correspond to the best fit for each 02 value obtained by considering the whole set of data given in table 3. The solid lines, for each dot, show the 1tr variation due to Ap, while the dashed lines span 1tr in ~o. The result for the LR model also appears in the figures, marked by a box symbol. The corresponding Standard Model point is also shown, together with the ellipse of the experimental data (with l a projections on both axes). The data correspond to a fit to the defining variables for end, eN2 and eN3, i.e. m w / m z , F~ and the ratio v~ff/a~r obtained by combining all the asymmetries. This cor143

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Table 4 LR Model. Best fit with 1a errors + 90% CL bounds.

(GeV)

( x 103 )

( x 103 )

( x 103 )

( x 103)

( x 103)

( x 103 )

100

0.Ill 0.118 0.125

0.4_+1.6 -0.8_+1.6 -2.1_+1.6

4.1_+1.4 3.4_+1.4 2.7_+1.4

-2.2 -3.5 -4.8

3.0 1.8 0.5

1.8 1.1 0.4

6.4 5.7 5.0

200

0.111 0.118 0.125

2.7±1.6 1.5_+1.6 0.2_+1.6

4.4_+1.4 3.7_+1.4 3.1_+1.4

0.1 -I.1 -2.4

5.3 4.1 2.8

2.1 1.4 0.8

6.7 6.0 5.4

Table 5 Best fit values for ~o and Ap with 1a errors for the various models and corresponding values for the observables. ~

mt (GeV)

ms (GeV)

~

~ ( × 103 )

Ap (Xl03 )

X2

Fz

Rh

as

R~

gv g,

Mw Mz

0.118

100

100

-90.00 -70.00 -50.00 -30.00 -10.00 0.00 10.00 30.00 50.00 70.00 90.00 LR

-1.1+1.4 -1.1_+1.4 -1.2+1.7 -1.6-+2.4 -1.6+4.2 0.2-+5.5 2.6-+5.0 2.1 +2.7 1.4+ 1.8 1.2_+ 1.5 -1.1+1.4 -0.8-+ 1.6

3.2_+1.4 3.3+ 1.4 3.4-+1.4 3.4+ 1.4 3.5+1.5 3.3-+1.6 2.9+1.6 3.0-+1.5 3.1-+1.4 3.2_+1.4 3.2+ 1.4 3.4-+1.4

1.1127 1.1403 1.1852 1.2806 1.5598 1.7053 1.4366 1.1104 1.0830 1.0933 1.1127 1.4222

2.4917 2.4920 2.4924 2.4929 2.4932 2.4919 2.4899 2.4903 2.4910 2.4914 2.4917 2.4928

20.7522 20.7522 20.7527 20.7549 20.7663 20.7790 20.7753 20.7584 20.7541 20.7527 20.7522 20.7600

41.5047 41.5025 41.4986 41.4895 41.4594 41.4388 41.4626 41.5004 41.5056 41.5058 41.5047 41.4828

0.2178 0.2179 0.2179 0.2180 0.2180 0.2178 0.2175 0.2176 0.2177 0.2178 0.2178 0.2177

0.0707 0.0706 0.0704 0.0701 0.0698 0.0703 0.0712 0.0712 0.0710 0.0708 0.0707 0.0701

0.8790 0.8791 0.8791 0.8792 0.8792 0.8791 0.8788 0.8789 0.8789 0.8790 0.8790 0.8791

0.118

150

100

-90.00 -70.00 -50.00 -30.00 -10.00 0.00 10.00 30.00 50.00 70.00 90.00 LR

0.0+1.4 0.0+1.4 -0.1+1.7 -0.2+2.4 -0.6_+4.2 -0.9_+5.5 -0.6_+5.0 -0.1+2.7 0.0-+1.8 0.0_+1.5 0.0+1.4 0.1-+1.6

3.5+ 1.4 3.5+ 1.4 3.5+ 1.4 3.5_+1.4 3.5_+1.5 3.5_+1.6 3.5+ 1.6 3.5-+1.5 3.5-+1.4 3.5+ 1.4 3.5-+1.4 3.5-+1.4

2.4384 2.4377 2.4364 2.4331 2.4218 2.4135 2.4217 2.4363 2.4385 2.4387 2.4384 2.4300

2.4897 2.4897 2.4898 2.4898 2.4901 2.4904 2.4903 2.4898 2.4898 2.4897 2.4897 2.4896

20.7425 20.7420 20.7414 20.7404 20.7390 20.7404 20.7439 20.7444 20.7436 20.7430 20.7425 20.7463

41.4710 41.4721 41.4735 41.4753 41.4763 41.4710 41.4636 41.4655 41.4682 41.4798 41.4710 41.4618

0.2163 0.2163 0.2163 0.2163 0.2164 0.2164 0.2164 0.2163 0.2163 0.2163 0.2163 0.2163

0.0711 0.0711 0.0711 0.0711 0.0710 0.0708 0.0709 0.0710 0.0711 0.0711 0.0711 0.0711

0.8801 0.8801 0.8801 0.8801 0.8801 0.8802 0.8802 0.8801 0.8801 0.8801 0.8801 0.8801

r e s p o n d s to t h e fit in c o l u m n 2 o f table 4 o f ref. [ 1 1 ]. We recall t h a t o t h e r o b s e r v a b l e s c a n n o t be u s e d to f u r t h e r c o n s t r a i n eN1, eN2 a n d 8N3 b e c a u s e the ext e n d e d gauge m o d e l s p r e s e r v e l e p t o n u n i v e r s a l i t y b u t a d d d i f f e r e n t v e r t e x c o r r e c t i o n s to leptons, d o w n a n d up quarks. Thus, as e x p l a i n e d in ref. [ 1 1 ], the m e n t i o n e d set o f d a t a is the largest t h a t can be u s e d for 144

eN1, 8N2 a n d 8N3 in the p r e s e n t context. S i m i l a r l y in figs. 4a a n d 4b we p r e s e n t the a n a l o g o u s p l o t in the p l a n e eN2 v e r s u s eN3. In general, for small v a l u e s o f rot t h e r e is a substantial i m p r o v e m e n t in g o i n g f r o m the S t a n d a r d M o d e l to the e x t e n d e d gauge models, m o s t l y d u e to the p r e s e n c e o f t w o a d d i t i o n a l p a r a m e t e r s a n d t h e fact that ApM increases Ap. T h i s is seen, for ex-

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E3N. 10 3

0

-2 12

I

4

2 '

6

E2N.10 3

8 12

I

(a) 10

10

8

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Fig. 3. In the 8Nt, eNS plane the lo ellipse corresponding to the experimental data on m w / m z , Fl and the ratio v ~ / a ~n obtained by combining all the asymmetries is shown together with the Standard Model point. The set of dots correspond to the best fit for the 02values listed in table 5. The box symbol correspondsto the LR model. The solid lines, for each dot, show the 1o variation due to Ap, while the dashed lines span 1o in ~o. Here we have assumed r a n = 100 GeV, a,=0.118, with mr= 100 GeV (a) or 150 GeV (b).

ample, from figs. 3a a n d 4a, which refer to m t = 100 GeV. For m r = 150 GeV a n d m H = 100 GeV, we see from figs. 3b a n d 4b that the Standard Model by itself provides a particularly good fit to the data. This is also confirmed by looking at the results of the fits displayed in table 5. We see that the best fit at all values of 02 is very close to ~o=0 a n d A p = 0 . 0 0 3 5 which is the Standard Model value for m r = 150 GeV. Leaving 0z also free the results of the fit are, for m r = 100 GeV,

-14

'

2

4

6

8

10

83N.103

~IN.103

83N.103 -2

2

,

(a)

8

6

25 November 1993

82N. 10 s 0 2 0

2

4

6

8

10 2

[ ' , , 1 ' ' ' 1 , , ' 1

(b)

0

-2

-2

-4

-4

-6

-6

-8

-8

-10

-10

-12

-12

-14

, 0

'

2

4

6

-14

'

8

10

E3N.| 03 Fig. 4. Same as fig. 3 for the eN2,8m plane. Note the absence of the solid lines through the dots, due to the independence of eN2 and em from ApM. ~0 ~ (

-I-5.2 1.5_6.2)X10 -3,

Ap=(3.1+I.6)X10 -3,

02(deg) = 40+41 -.'-139.

(15)

The m i n i m u m in 02 is very fiat so that the fit is not much sensitive to the physical structure of the new U ( 1 ) (see also table 5 ). The same situation also applies for m r = 150 GeV, where we find ~o=(-0.9+5.6)×10

-3,

Ap=(3.6+l.6)X10 -3, +89 2 02 (deg) = 0.8_9o:s •

(16)

The corresponding X2 values are given by 1.08 a n d 2.41, respectively (for three degrees of freedom). For comparison, the X: of the Standard Model fit, for the 145

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same values of m n and ors, is given by Z2= 7.26 for mt = 100 GeV and Z 2 = 2.41 for mr= 150 GeV (for six degrees of freedom). Similarly, for LR models, we obtain

m t = 100 GeV:

Ap= (3.37_+1.39) X10 - 3 , m t = 150 GeV: ~o=(0.15__1.58)×10 - 3 , (17)

with 22 values given by 1.42 and 2.43, respectively (for four degrees of freedom). We then let also mt and ors to vary. The results are ~o=(-1.2_+3.1)×10 -3, Z~/9~ (3.2_2.4) +2.6 X 10 -3 , + 180 02(deg) = -90_0.0 ,

o~s=0.118-+0.017, mt<153.8GeV

(atltr),

of m t mainly to find agreement with the ratio Rbh.

4. Special models We now consider the consequences of restricting the scalar structure of the model to a particular choice. We restrict ourselves to a Higgs structure that obeys the physical requirement of vanishing mixing for large mz,, i.e. we demand that, for large mz,,

?,o=(-0.84_+1.58)X10 -3,

Ap= (3.48_+ 1.39) × 10 -3 ,

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(18)

with a Z 2, for one degree of freedom, given by X2= 1.06. Again, for comparison, the Standard Model fit, for the same values of mH and oq gives mt = 143 + 18 GeV with Z 2= 2.27 (for five degrees of freedom). Leaving as also free we obtain practically the same value of m t together with ors= 0.120 -+0.006 with Z2=2.19 (for four degrees of freedom). The same fitting procedure for LR models leads to the result ~o = (-0.1___2.5) × 10 -3 ,

~o=c( mz ) 2 , \mz, /

(20)

with c a constant which depends on the Higgs structure and vacuum expectation values. Once c is given, in a particular model, then either ~o or ApM can be eliminated in favour of mz,. In this case a bound on mz, is directly obtained from the data. From the following illustrative cases we can appreciate the typical sensitivity of the present LEP data to the heavy vector boson mass. We have considered the so-called minimal left-right model, with Higgs particles transforming as complex (2, 2, 0), (3, 1, 0) and ( 1, 3, 0) representations of the gauge group SU (2) L× SU (2) R × U ( 1 ) B-L. In this case one has [ 5 ] c = ~ = 0.73. Assuming negligible additional mixing from the charged sector and Mz.(GeV) 100 2500

.

.

150 .i/

2000

1500

1500 /

1000

as = 0 . 1 1 3 + 0 . 0 1 2 , (atltr),

(19)

with a Z 2, for two degrees of freedom, given by Z2= 1.22. We recall that our fitting procedure is not sensitive to the strong m t dependence contained in the Ap parameter, so that the upper bound on mt that we obtain is a consequence of the quadratic mt dependence of the Z o b G vertex and of residual logarithmic behaviour. Indeed, as shown by the Z 2 values, the extended gauge model fit prefers low values 146

2500

2000

~ . ~ . ( 3 . 9 +2.0 _ L s ) × 10--3 ,

m/<147.1GeV

200

500

0

1000

i ..o..,-,-" '+. . . . . . . . . .

.---°'°

5O0 i

100

150

i

i

0

2O0 m~op(GeV) Fig. 5. Lower bounds on mz, (90% CL) as functions of mt obtained for MH= 100 GeV, ct.= 0.118 for LR models (dotted line), for the Z model (dash-dotted), for the r/ model with c=0.24 (dashed) and c = 0.63 (solid).

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PHYSICS LETTERSB

no further exotic c o n t r i b u t i o n to the p parameter one finds a lower b o u n d on m z , of about 1.5 TeV for a standard Higgs mass of 100 GeV and a top mass of 110 GeV. The lower b o u n d increases with mt as is seen from fig. 5 (all b o u n d s are given for as = 0.118 ). M o d e l s z [12] ( o r B [ 1 3 ] ) a n d r / [ 1 2 ] ( o r A [ 1 3 ] ) are also illustrated in fig. 5. The new gauge generator corresponds to 02 = 52.24 ° in the Z model and to 02 = 0 in the ~/model. For two Higgs doublets one finds [ 13 ] cz=0.39 a n d 0 . 2 4 < c , < 0 . 6 3 . One then obtains a lower b o u n d for mzx of about 900 GeV for rnh,= 100 GeV increasing with m t. Less stringent limits are obtained on m z , , corresponding to the smaller value allowed for c. For m r = 110 GeV the lower b o u n d is in the range 500-1000 GeV depending on the value o f c in the allowed range.

5. Conclusion The data collected at LEP on the Z peak were shown to impose very severe constraints on the mixings of a n o n standard Z ' , described by two parameters ~o and ApM, which in general are not related by the gauge structure of the model but only by the detailed structure of the Higgs sector. At present, the Standard Model is in such good agreement with the data that no indication for additional corrections is found, at least for unspecified mr. I n fact, only a very small a m o u n t of mixing is allowed, with G0always less than 1%. The fit of the data in terms o f extended gauge models is of comparable quality as that of the Standard Model, once that the existence of more parameters is properly taken into account.

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