

 14 Apr 1995

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

CERN-PPE/94-188

November 25, 1994

Limits on Extensions of the Minimal Standard Model from Combined LEP Lineshape Data

Andr'e Sopczak1

PPE Division, CERN

CH-1211 Geneva 23

Abstract The high statistics of the combined LEP lineshape data are used to derive constraints on hypothetical extensions of the Minimal Standard Model. The data comprises about eight million visible Z decays, recorded between 1989 and 1993. This letter gives limits for simple tests on models which predict additional Z boson decays or modified Z-couplings. As an application the two-doublet Higgs model is considered.

(In press Mod. Phys. Lett. A. Excerpt from invited talks at the Int. Workshop "Physics from Planck Scale to Electro-Weak Scale", Warsaw, Poland, Sep. 1994 and

"Beyond the Standard Model IV Conference", Granlibakken, USA, Dec. 1994)

1E-mail: andre@cernvm.cern.ch

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Introduction Severe limits on `New Physics' beyond the Minimal Standard Model (MSM) [1] can be obtained from precision measurements of the Z parameters. Any hypothetical Z decay into new particles Z ! X (Fig. 1a), radiative contributions from non-MSM virtual particles (Fig. 1b), or modifications to the MSM Z-couplings (Fig. 1c) are constrained by measurements of the total Z width \Gamma Z, the invisible Z width \Gamma invZ , the leptonic widths \Gamma eeZ , \Gamma __Z , \Gamma o/o/Z , or the ratio of the hadronic to leptonic Z decay width R. Thus, constraints on physics beyond the MSM can be expressed as limits on deviations from the MSM Z decay width predictions. In particular, such limits can be used to constrain the existence of Higgs bosons in models with more than one Higgs doublet; charginos, neutralinos and light gluinos in Supersymmetric Models with or without R-parity conservation; additional heavy charged or neutral leptons; or anomalous gauge boson couplings.

Figure 1: Illustration of possible effects in extensions of the MSM which can be constrained by a comparison of measured Z parameters with MSM predictions.

The present analysis includes 1992 data [2] and preliminary 1993 data collected by the four LEP experiments [3], corresponding to a total of about eight million visible Z decays. The Z parameters are obtained by fitting the lineshape of the Z decay into charged leptons and hadrons. All measurements are in agreement with the MSM predictions. Details of the experimental analysis and similar interpretations as presented here can be found in the corresponding publications of the four LEP experiments [2].

Measurement and Theory Table 1 summarizes the measured values of \Gamma Z, \Gamma invZ , \Gamma eeZ , \Gamma __Z , \Gamma o/o/Z , and R, as well as their MSM upper and lower bounds for one-sided 95% CL's. One-sided CL's are used because a new decay would always increase the Z width; they are derived assuming Gaussian errors by extending the 1 oe error to 1.64 oe [4]. The measured values are averages from the four LEP experiments taking into account common systematic errors [3]. Theoretical upper and lower bounds are obtained with an analytical program (ZFITTER version 4.6 [5]) by varying the strong coupling constant ffs, the top quark mass mt, and the MSM Higgs

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mass mh, independently within their one-sided 95% CL limits. The uncertainty in these values constitutes the dominant error on the MSM predictions.

For ffs the world average ffs(mZ) = 0:125 \Sigma 0:005 [3] is used. Note that this average is based on data from *N experiments, p_p colliders, the SLD measurement of the left-right asymmetry and the LEP experiments. For mt the limit implied by the recently reported CDF evidence for the top quark is used, i.e. mt = (174 \Sigma 10+13

\Gamma 12) GeV [6]. For mh a

combined lower mass limit [7], resulting from the data of the four LEP experiments [8],

and a theoretical upper mass bound following from consistency arguments in the MSM [9] is used. Thus, the ranges used for ffs, mt and mh are:

0:117 ! ffs(mZ) ! 0:133; (148 ! mt ! 201) GeV; (63:5 ! mh ! 1000) GeV: The central values of the MSM predictions are the arithmetic means of the upper and lower bounds.

Measurements Theory (MSM) Parameter Mean Lower Upper Lower Upper Mean

Value Bound Bound Bound Bound Value \Gamma Z 2497:4 \Sigma 3:8 2491.2 2503.6 2480.6 2512.3 2496.5 \Gamma invZ 499:8 \Sigma 3:5 494.1 505.5 499.7 503.4 501.6

\Gamma eeZ 83:85 \Sigma 0:21 83.51 84.19 83.56 84.33 83.95 \Gamma __Z 83:95 \Sigma 0:30 83.46 84.44 83.56 84.33 83.95

\Gamma o/o/Z 84:26 \Sigma 0:34 83.70 84.82 83.37 84.13 83.75

R 20:795 \Sigma 0:040 20.729 20.861 20.692 20.842 20.767

Table 1: Measured Z parameters, MSM predictions, and their lower and upper limits at one-sided 95% CL's. All decay widths are given in MeV.

In order to obtain a conservative limit on non-MSM effects from \Gamma Z, one considers the intervals:

(\Gamma Z)expmin \Gamma (\Gamma Z)thmax and (\Gamma Z)expmax \Gamma (\Gamma Z)thmin;

where both the experimental and theoretical limits are taken at the one-sided 95% CL. Similar intervals are defined for the other parameters listed in Table 1. If the value of the predicted mean value minus the measured mean value is negative (positive), it is added to the lower (upper) limit. This conservative approach avoids setting tighter constraints than allowed by the agreement between theory and measurement. Otherwise, e.g., a measurement of the central value of the total Z decay width significantly below the MSM expectation would naively lead to a too strong bound on physics processes beyond the MSM. Table 2 summarizes the intervals and differences obtained.

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Parameter Interval Difference Sum

(ffi\Gamma Z)min \Gamma 21:1 \Gamma 0:9 \Gamma 22:0 (ffi\Gamma Z)max 23.0 0 23.0 (ffi\Gamma invZ )min \Gamma 9:3 0 \Gamma 9:3 (ffi\Gamma invZ )max 5.8 1.8 7.6

(ffi\Gamma eeZ )min \Gamma 0:82 0 \Gamma 0:82 (ffi\Gamma eeZ )max 0.63 0.10 0.73 (ffi\Gamma __Z )min \Gamma 0:87 0 \Gamma 0:87 (ffi\Gamma __Z )max 0.88 0 0.88

(ffi\Gamma o/o/Z )min \Gamma 0:43 \Gamma 0:51 \Gamma 0:94 (ffi\Gamma o/o/Z )max 1.45 0 1:45

(ffiR)min \Gamma 0:113 \Gamma 0:028 \Gamma 0:141 (ffiR)max 0.169 0 0.169

Table 2: Allowed changes of \Gamma Z, \Gamma invZ , \Gamma eeZ , \Gamma __Z , \Gamma o/o/Z , and R due to non-MSM contributions, using twice one-sided 95% CL limits. Max indicates the maximum experimental value minus the minimum theoretical value, and min indicates the minimum experimental value minus the maximum theoretical value. The interval and difference are defined in the text. All decay widths are given in MeV.

Considering the new decay channel Z ! X, let the decay ratios of X be defined as xj j \Gamma (X ! j)=\Gamma (X ! anything); where j = h; l; i for hadrons, leptons and invisible particles, respectively. In this definition, xh + xl + xi = 1. Let the hadronic and leptonic branching ratios of the Z be bh and bl, respectively. In the definition of R, the hadronic Z decays are summed over all five quark types produced at LEP, while the leptonic Z decay width is given for a massless charged lepton pair assuming lepton universality. Let \Gamma XZ j \Gamma (Z ! X), then

1) The limit on \Gamma XZ from \Gamma Z is given by:

\Gamma XZ ^ (ffi\Gamma Z)max = 23:0 MeV: (1)

2) The limit on \Gamma XZ from \Gamma invZ is given by:

xi\Gamma XZ ^ (ffi\Gamma invZ )max = 7:6 MeV: (2)

3) A contribution from Z ! X decays would change the ratio R = bh=bl by:

ffiR = \Gamma Zbh + \Gamma

X Z xh\Gamma

Zbl + 13\Gamma XZ xl \Gamma

bhb

l ss R

\Gamma XZ

\Gamma Z ( x

hb

h \Gamma

xl3b

l ); (3)

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an approximation which is valid when \Gamma XZ o/ \Gamma Z. For xh = 1 and xl = 0, (ffiR)max leads to \Gamma XZ ^ 14 MeV. For xh = 0 and xl = 1, (ffiR)min results in \Gamma XZ ^ 1:7 MeV, however, this limit is weaker than those from \Gamma eeZ , \Gamma __Z , \Gamma o/o/Z . Recently, a lower limit on the gluino mass of 3:8 GeV derived from R-measurements has been reported at 90% CL [10].

Radiative contributions from non-MSM virtual particles or modifications to the MSM Z-couplings are constrained by the upper and lower limits given in Table 2.

Discussion and Example The most stringent limits on deviations from the non-MSM effects on the Z decay widths are summarized in Table 3. Both upper and lower limits are given at one-sided 95% CL. As a consequence, modified MSM Z-couplings or amplitudes of non-MSM radiative corrections are constrained to the interval at 90% CL. The limits on new decay modes obtained from \Gamma Z are independent of the decay branching fractions, while the limits from \Gamma invZ constrain only invisible Z decay modes. The limits from \Gamma eeZ , \Gamma __Z , \Gamma o/o/Z , and R constrain the corresponding leptonic and hadronic Z-couplings, respectively. The limits for unspecified and invisible decay modes are of most general use. The limits on \Gamma eeZ are tighter, since the Zee-coupling contributes both to Z production and decay. One should note that the charged leptonic and hadronic limits are not able to constrain Z decays if the resulting new particles subsequently decay; dedicated searches are necessary for such specific final states. This is due to the precise selection criteria applied for leptonic and hadronic Z decay event topologies. If a model predicts the invisible, charged leptonic and hadronic branching fractions of Z decays, a O/2-method allows setting tighter constraints.

Origin Decay Mode \Delta \Gamma (Z) (MeV) \Delta Br(Z) (in %)

\Gamma Z Z!anything \Gamma 22:0 23.0 0.92 \Gamma invZ Z!invisible \Gamma 9:3 7.6 0.30

\Gamma eeZ Z!e+e

\Gamma \Gamma 0:82 0.73 0.029

\Gamma __Z Z!_+_

\Gamma \Gamma 0:87 0.88 0.035

\Gamma o/o/Z Z!o/ +o/

\Gamma \Gamma 0:94 1.45 0.058

R Z!hadrons \Gamma 12 14 0.56

Table 3: One-sided 95% CL lower and upper limits on \Delta \Gamma (Z) for Z decaying into any, invisible, charged leptonic, and hadronic channel. The corresponding branching ratio upper limits on \Delta Br(Z) are also given.

The present study updates the analyses given in [11] which were based on 1990 and 1991 LEP data. Only slightly tighter limits are obtained by including the 1992 data as they were entirely taken on the Z pole. Including the 1993 data which contain both off

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and on peak results, limits are significantly improved: the experimental errors are reduced by about a factor two compared to those used in [11]. In this regard, little improvement is expected from the 1994 data as they are taken again on the Z-pole only. For unspecified Z decays, the 1993 improvement of \Delta \Gamma (Z) is mainly due to the increased predicted MSM lower bound on \Gamma Z following from the new top mass constraints of the CDF experiment.

As an example, a limit on cos2(fi \Gamma ff) in the general two-doublet Higgs model is derived. The definitions used are: tan fi the ratio of the vacuum expectation values of the Higgs doublets and ff the mixing angle between the neutral scalar Higgs fields. The Z decay width into neutral Higgs pairs in the general two-doublet Higgs model is given by [12]:

\Gamma (Z ! hA) = \Gamma (Z ! * _*) 12 cos2(fi \Gamma ff)*3=2( m

2 h

m2Z ;

m2A

m2Z ); (4) *(a; b) = (1 \Gamma a \Gamma b)2 \Gamma 4ab;

with \Gamma (Z ! * _*) derived from a combined Z lineshape fit: \Gamma (Z ! * _*) = 166:6 \Sigma 1:2 MeV [3]. Without any assumption on the Higgs decay modes, the constraint \Delta \Gamma (Z) ^ 23:0 MeV sets a limit on cos2(fi \Gamma ff) as a function of mh and mA:

cos2max(fi \Gamma ff) = 2\Gamma

X Z

\Gamma (Z ! * _*) *

\Gamma 3=2( m

2 h

m2Z ;

m2A

m2Z ): (5)

Figure 2 shows the excluded cos2(fi \Gamma ff) range at 95% CL as a function of mh for mA = 20 GeV. In conjunction with a constraint on sin2(fi \Gamma ff), derived from the search for the MSM Higgs boson, this limit leads to an exclusion of a large (mh; mA) parameter range [7]. Further constraints can result from an analysis of the one-loop vertex corrections to the Zbb-coupling involving additional neutral and charged Higgs bosons; such corrections could decrease \Gamma (Z ! bb) and thus the hadronic decay width, depending on the unknown parameters of the two-doublet Higgs model [13]. In this case the limit \Delta \Gamma (Z ! hadrons) * \Gamma 12 MeV applies.

Acknowledgments I would like to thank Sally Dawson, Wolfgang Hollik, Joachim Mnich, Stefan Pokorski, and Janusz Rosiek for fruitful discussions and I express my gratitude to the Institute of Theoretical Physics at the Warsaw University for their hospitality. For his advice on finalizing the manuscript I thank Remy Van de Walle.

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Figure 2: Limit on cos2(fi \Gamma ff) of the general two-doublet Higgs model as a function of mh for mA = 20 GeV. The limit is based on the constraint \Delta \Gamma (Z ! anything) ^ 23:0 MeV, set by the precision lineshape measurements. No assumptions on the decay branching ratios of the Higgs bosons are made.

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