Extra generations and discrepancies of electroweak precision data

V.A. Novikov, L.B. Okun, ITEP, Moscow, Russia A.N. Rozanov,

CPPM, IN2P3, CNRS, Univ. Mediteranee, Marseilles, France

and ITEP, Moscow, Russia M.I. Vysotsky ITEP, Moscow, Russia

Abstract It is shown that additional chiral generations are not excluded by the latest electroweak precision data if one assumes that there is no mixing with the known three generations. In the case of “heavy extra generations”, when all four new particles are heavier than Z boson, quality of the fit for the one new generation is as good as for zero new generations (Standard Model). In the case of neutral leptons with masses around 50 GeV (“partially heavy extra generations”) the minimum of χ^{2} is between one and two extra generations.

Two years ago in paper [1] we analyzed bounds from the electroweak precision data on the non-decoupled New Physics in a form of additional heavy quark-lepton generations. It was shown that while the case of all four new fermions (U and D quarks, neutral lepton N and charged lepton E) heavier than Z boson was excluded at 2.5 σ level, existence of new generations with relativity light neutral lepton N (m_{N} ≈ 50 GeV) was allowed. At that time quality of Standard Model (SM) fit of the data was very good, χ^{2}/n_{d.o.f.} = 15/14. At the time of Osaka Conference, summer 2000, nothing radical happened but χ^{2} became 21/14 and the level at which one extra heavy generation was excluded went down to 2σ [2]. However the latest precision data announced summer 2001 [3] has changed the situation: the fit is still bad, 24/13, but now the presence of one heavy generation does not make the fit worse as compared with SM.

In Table 1 LEPTOP fit of summer 2001 data is presented. There are two significant changes in comparison with previous data presented in Table 2:

1. Due to precision measurement of the cross-section of e^{+}e^{−} annihilation into hadrons in the interval 2-5 GeV at BES the error in ᾱ ≡ α(M_{Z}) is now two times smaller. (Following Electroweak Working Group (EWWG) we use result [4] though other estimates can be found in the literature as well);

2. Central value of M_{W} is now bigger by a half of σ.

Table 1: LEPTOP fit to electroweak observables. Year 2001. By italics we designate calculated (not measured) quantities.

Source  Observable  Exp. data LEPTOP fit Pull
Γ_{Z} [GeV]  2.4952(23)  2.4966(16) -0.6
σ_{h} [nb]  41.540(37)  41.480(14) 1.6
A_{F B}^{l}  0.0171(10)  0.0165(3) 0.7
R_{l}  20.767(25)  20.738(18) 1.1
LEP I  A_{τ}, A_{e}  0.1465(33)  0.1483(11) -0.5
R_{b}  0.2165(7)  0.2157(1) 1.2
R_{c}  0.1719(31)  0.1723(1) -0.1
A_{F B}^{b}  0.0990(17)  0.1040(8) -2.9
A_{F B}^{c}  0.0685(34)  0.0743(6) -1.7
s_{l}^{2}(Q_{F B})  0.2324(12)  0.2314(1) 0.9
A_{LR}  0.1513(21)  0.1483(11) 1.4
SLC  s_{l}^{2} (A_{LR})  0.2310(3)  0.2314(1) -1.4
A_{b}  0.9220(200)  0.9349(1) -0.6
A_{c}  0.6700(260)  0.6684(5) 0.1
LEP II, Tevatron m_{W} [GeV]  80.451(33)  80.392(20) 1.8
s_{W}^{2} (m_{W})  0.2216(6)
Tevatron s_{W}^{2} (νN) 0.2255(21) 0.2230(3) 1.2
m_{W} (νN) [GeV] 80.250(109)
m_{t} [GeV]  174.3(5.1)  175.0(4.4) -0.1
Fit  m_{H} [GeV]  79_{−29}^{+47}
α̂_{s}  0.1182(27)
e^{+}e^{−} → hadrons ᾱ^{−1}  128.936(49) 128.918(45) 0.4
χ^{2}/n_{d.o.f.}  23.8/13

The latter is the main cause for the relaxation of the bound on heavy extra generations.

Exclusion plot for the number N_{g} of extra heavy generations is presented in Fig. 1.

To produce this plot we take m_{D} = 130 GeV – the Tevatron lower bound on new quark mass; we use experimental 95% C.L. bound on higgs mass m_{H} > 113 GeV [3] and vary Δm = \sqrt{m_{U}^{2} − m_{D}^{2}} and number of extra generations N_{g}. (In order to have two-dimensional plot we arbitrary assumed that m_{N} = m_{U} and m_{E} = m_{D}; other choices do not change the obtained results drastically); χ^{2} minimum corresponds to unphysical point N_{g} = 0.5. For 170 GeV < m_{U} < 200 GeV we get the same quality of fit in the case N_{g} = 1 as that for the SM (N_{g} = 0). In ref. [5] one can find a statement that extra heavy generations are excluded by the precision electroweak data. However, analysis performed in [5] refers to upper and lower parts of Fig. 1, Δm > 200 GeV and Δm = 0, where

Table 2: LEPTOP fit to electroweak observables. Year 2000.

Source  Observable  Exp. data LEPTOP fit Pull
Γ_{Z} [GeV]  2.4952(23)  2.4964(16) -0.5
σ_{h} [nb]  41.541(37)  41.479(15) 1.7
A_{F B}^{l}  0.0171(10)  0.0164(3) 0.7
R_{l}  20.767(25)  20.739(18) 1.1
LEP I  A_{τ}, A_{e}  0.1467(32)  0.1480(13) -0.4
R_{b}  0.2165(7)  0.2157(1) 1.2
R_{c}  0.1709(34)  0.1723(1) -0.4
A_{F B}^{b}  0.0990(20)  0.1038(9) -2.4
A_{F B}^{c}  0.0689(35)  0.0742(7) -1.5
s_{l}^{2}(Q_{F B})  0.2321(10)  0.2314(2) 0.7
A_{LR}  0.1514(22)  0.1480(16) 1.5
SLC  s_{l}^{2} (A_{LR})  0.2310(3)  0.2314(2) -1.5
A_{b}  0.9110(250)  0.9349(1) -1.0
A_{c}  0.6300(260)  0.6683(6) -1.5
LEP II, Tevatron m_{W} [GeV]  80.434(37)  80.397(23) 1.0
s_{W}^{2} (m_{W})  0.2219(7)
Tevatron s_{W}^{2} (νN) 0.2255(21) 0.2231(2) 1.1
m_{W} (νN) [GeV] 80.250(109)
m_{t} [GeV]  174.3(5.1)  174.0(4.2) 0.1
Fit  m_{H} [GeV]  55_{−26}^{+45}
α̂_{s}  0.1183(27)
e^{+}e^{−} → hadrons ᾱ^{−1}  128.878(90) 128.850(90) 0.3
χ^{2}/n_{d.o.f.}  21.4/14

the existence of new heavy generations is really strongly suppressed. This is not the case for the central part of Fig. 1 (Δm ≈ 150 GeV).

Two heavy generations are excluded at more than 3σ level. Nevertheless, two and even three “partially heavy” generations are allowed when neutral fermions are relatively light, m_{N} ≃ 55 GeV (see Fig. 2). Using all existing LEP II statistics on the reactions e^{+}e^{−} → γ + νν̄, γ + NN̄ in dedicated search one can exclude 3 “partially heavy” generations which contain such a light N at a level of 3σ (see [6]), while one or even two such generations may exist.

The cause of disappearance of the suppression of extra heavy generations which existed in the early data is the contradiction in description of modern data on M_{W} and s_{l}^{2} in the framework of SM. The point is that the higgs mass, a free parameter of the SM, has the following values being extracted from these observables:

(m_{W})_{LEPII,Tevatron,NuTeV} = 80.428(32) GeV ⇒
⇒ m_{H} = 50_{−35}^{+50} GeV ,  (1)

Figure 1: Exclusion plot for heavy extra generations. χ^{2} minimum is shown by cross; borders of regions show domains allowed at the level 1σ, 2σ, etc. N_{g} is the number of extra generations.

(s_{l}^{2})_{LEPI,SLAC} = 0.23140(15) ⇒
⇒ m_{H} = 150_{−50}^{+75} GeV .  (2)

N_{g} = 0.5 reduces the contradiction between the two values of m_{H}. Nevertheless the resulting χ^{2} does not improve drastically and this is due to another “defect” of precision data: the discrepancy between the average value of s_{l}^{2} extracted from pure leptonic measurements and its value from events with hadrons in final state [3]:

s_{l}^{2}
Leptons 0.23113(21)
Hadrons 0.23230(29)  (3)

These 3.3 σ difference is the root of poor quality of the SM fit. The value of hadronic contribution to s_{l}^{2} in (3) is dominated by very small uncertainty of the forward-backward asymmetry in reaction e^{+}e^{−} → Z → bb̄. According to Figure 2: Exclusion plot for the number of partially heavy extra generations with light neutral lepton N. On horizontal axis the number of extra generations N_{g}, on vertical axis – the mass of the neutral lepton m_{N}. The input: m_{U} = 220 GeV,m_{D} = 200 GeV, m_{E} = 100 GeV Table 1

(A_{F B}^{b})_{exp} = 0.0990(17) .  (4)

One can question whether such a good accuracy can be obtained in the analysis of hadronic jets production. Another value of A_{F B}^{b} can be obtained by multiplying measured at SLAC beauty asymmetry A_{b} and leptonic asymmetry A_{l}. Then

A_{F B}^{b} = \frac{3}{4}A_{b}A_{l} = 0.1038(25) .  (5)

The number (5) differs from (4), but nicely coincides with the SM fit: 0.1040(8) (see Table 1).

Let us assume following Chanowitz [7] that A_{F B}^{b} has larger uncertainty than given in Eq. (4) and look to what consequences with respect to extra generations this hypothesis will lead.^{1} If we multiply experimental uncertainties of A_{F B}^{b} and A_{F B}^{c}, which are strongly correlated, by a factor 10, the quality of SM fit improves drastically: χ^{2}/n_{d.o.f.} shifts from 23.8/13 to 10.9/13 and simultaneously one heavy extra generation becomes excluded at the level of 2.5σ (see Fig. 3).

However, a serious problem arises: it is just A_{F B}^{b} given by Eq. (4) which pushes m_{H} to larger values. With our modification of experimental results on A_{F B}^{b} and A_{F B}^{c} the SM fit gives:

m_{H} = 42_{−18}^{+30} GeV ,  (6)

well below modern LEP II bound: m_{H} > 113 GeV, a substantial trouble for the SM.

What concerns partially heavy extra generations, they nicely fit the data even with ten times enlarged uncertainties of A_{F B}^{b} and A_{F B}^{c}, see Fig. 4. At both minima in this Figure χ^{2}/n_{d.o.f.} ≈ 13/11, while m_{H} ≈ 116 GeV.

In the recent paper [9] it was noted that SUSY extension of Standard Model with light sneutrinos with masses in the range 55- 80 GeV is allowed by precision data and pushes higgs mass to larger values. (A_{F B}^{b} was neglected there as well). This might be a strong indication in favor of light SUSY particles.

The presence of new particles is important for production and decay of higgs. New heavy quarks considerably enhance higgs production at Tevatron and LHC through gluon fusion which should help to discover this particle [10]. If the decay of higgs into a pair of neutral leptons is kinematically allowed it will dominate, so that a moderately heavy higgs will decay invisibly [11]. At LEP II the invisibly decaying higgs is excluded almost at the same level as the SM higgs by missing Figure 3: Exclusion plot for heavy extra generations with 10 times enlarged errors in A_{F B}^{b} and A_{F B}^{c}. χ^{2} minimum is at the upper border of the Fig.

1Another way to resolve situation with A_{F B}^{b} is to assume that there exist New Physics contributions to Zbb̄ couplings g_{V}^{b} and g_{A}^{b}. Since in the expression for A_{F B}^{b} the corrections to g_{V}^{b} and g_{A}^{b} are multiplied by small factor g_{V}^{e} they should be large, so they must appear at the tree level. Also Z → bb̄ width proportional to (g_{A}^{b})^{2} + (g_{V}^{b} )^{2} should not noticeably change since R_{b} ≡ Γ_{Z→bb̄}/Γ_{Z} is at present in good agreement with SM fit, see Table 1. In recent paper [8] inclusion of additional bottom-like heavy quarks with vector currents is suggested to resolve the discrepancy (3).

Figure 4: Exclusion plot for partially heavy extra generations with 10 times enlarged errors in A_{F B}^{b} and A_{F B}^{c}. Two local χ^{2} minima are shown (see upper left corner of the plot).

mass method [12]. Contrary to that the LHC will look for visible decay modes of higgs. If the branching ratios of the latter are small the search will be not easy.

We are grateful to A. Olshevsky for providing ref. [3] and to P.S. Bambade and M. Stanitzki for providing ref. [12].

L.O., A.R. and M.V. are grateful to CERN EP and TH for hospitality; L.O., V.N. and M.V. were partly supported by RFBR grant No. 00-15-96562.

P.S. After this paper had been completed a new result for s_{W}^{2} (νN) and hence for m_{W} (νN) was published by NuTeV collaboration [13]:

s_{W}^{2} (νN) = 0.2277(17) ,
m_{W} (νN) = 80.140(80) .

The new value of m_{W} (νN) differs from m_{W} measured by LEP II and Tevatron by 3.7 σ and leads to a pull of 2.8 instead of 1.2 (see Table 1) aggravating the discrepancy. Using the same procedure as for Table 1 we get:

m_{H} = 86_{−32}^{+51} GeV ,
χ^{2}/n_{d.o.f.} = 30.3/13 .

The influence of the new NuTeV data on the limits on extra generations, as well as the change of LEPTOP code accounting for the new NuTeV procedure of extracting s_{W}^{2} (νN) will be discussed elsewhere.

We are grateful to V.Rubakov for providing ref. [13]

P.P.S.

As a response to the appearance of this article on hep/ph H.-J.He suggested to us to cite ref. [14], in which the problem of extra generations has been considered in a framework of the models with two and one Higgs doublets. In latter case the results of ref.[14] drastically differ from ours. First, their results are the same for the data of 2000 and 2001. Second, they claim that 500 GeV higgs accompanied by fourth generation fits the electroweak precision data. In order to check this statement we made special LEPTOP runs assuming m_{H} = 500GeV for N_{g} = 0 and N_{g} = 1. In both cases the probability that such models describe the data is of the order of 10^{−5}, while our fits for light higgs are at least three orders of magnitude better. One of the possible causes of this difference is the reliance of [14] on S, T, U parametrization of New Physics. This parameters being well suited for heavy oblique corrections are not valid for new fermions with masses of the order of M_{Z}.

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