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We review the past and current status of the extension of the standard model (SM) by a fourth generation of fermions. In particular the new results for Higgs boson searches at the LHC and at Tevatron exclude the possibility of having simply a perturbative fourth generation of fermions with one Higgs doublet (SM4). We also briefly mention more complicated extensions of the SM4, which are not yet excluded, like adding in addition another Higgs doublet to the SM4.

In the standard model [

Besides giving masses to the gauge bosons of the weak interaction and the fermions the Higgs mechanism predicts also in its simplest form the existence of one massive neutral scalar particle, the Higgs boson. The search for the Higgs boson was one of the primary goals of the LHC, which has probably been achieved in July 2012, when a new boson with a mass of about 125 GeV was observed by ATLAS and CMS [

At the LHC the dominant production mechanism of the Higgs boson is gluon fusion [

Gluon fusion with an internal top loop turns out to be the dominant Higgs production mechanism at the LHC.

At the LHC one is, however, also sensitive to subdominant production processes like associated vector boson-Higgs production/Higgs-Strahlung (

End of 2011 some hints for the existence of a Higgs-like boson at a mass of about 125 GeV have been presented by ATLAS [

We define the SM4 as the extension of the usual standard model simply by an additional chiral family of fermions. Its fermionic contents reads

Extending the SM by an additional fermion generation might change many observables directly, but also indirectly via loop processes. Thus, the SM4 is subjected to a number of constraints:

direct searches for the production of heavy quarks and leptons of the fourth generation at the LHC and at Tevatron;

flavor observables are affected by a fourth generation via a change of the values of the CKM elements and via loop processes;

electroweak precision observables are affected by a fourth generation via loop processes;

higgs production and decay are affected by a fourth generation via loop processes.

The first three classes of constraints will be discussed briefly and the last class in detail below.

The SM4 was already killed many times in the literature, however, until very recently the arguments for the exclusion of the SM4 relied always on some additional unjustified assumptions, which will be elaborated below. In the 1980s the idea of a fourth generation was relatively popular, see, for example, [

After LEP measured the number of light neutrinos to be very close to three,

Electroweak precision observables are also very sensitive to loop effects of the new heavy fermions. In the PDG article from Langacker and Erler [

1994: one heavy generation of ordinary fermions is allowed at 95% CL.

1998: an extra generation of ordinary fermions is now excluded at the 99.2% CL.

2002: an extra generation of ordinary fermions is excluded at the 99.8% CL on the basis of the

2010: An extra generation of SM fermions is excluded at the 6

Concerning some of the above statements one should keep in mind that there is no reason at all to consider the

So for quite some time it was an established prejudice; that the SM4 is excluded. This situation changed quite significantly with the paper of Kribs et al. from 2007 [

Similar arguments as the ones in [

There were, however, still some missing points in the investigation of the electroweak precision observables. First, treating the fourth generation lepton masses as free parameters allows, for example, easily also a degenerate fourth quark generation, see, for example, [

Allowed mass splitting of fourth generation fermions according to the constraints from electroweak precision observables. One clearly sees that mass degenerate quarks of the fourth family are not ruled out. Note, that for this result CKM mixing was neglected. Figure from [

Allowed mass splitting of fourth generation quarks according to the constraints from electroweak precision observables. (a) CKM mixing is forced to be zero, (b) it is allowed to an extent that does not violate any bound from flavor physics. For both pictures the lepton masses were fixed.

Allowed mass splitting of fourth generation fermions according to the constraints from electroweak precision observables, allowing for CKM mixing and free lepton masses.

A fourth generation of fermions can also have sizeable effects on flavor observables. First, the 3 times 3 CKM matrix will in general no longer be unitary—only the 4 times 4 CKM matrix has to fulfill unitarity. Thus, the current strong constraints on, for example,

To summarize the results of this section we make the following statement: the SM4 can easily accommodate all flavor and electroweak data and the previous claims on the exclusion of the SM4 relied on unjustified additional assumptions. One thing to keep in mind is the fact that currently two-loop electroweak corrections for the electroweak precision observables are still missing and these corrections might be sizeable.

Currently there are also stringent limits on the masses of the fourth generation quarks from direct searches [

Till now we found that the SM4 is resistant against all experimental attacks. In the next section we will, however, show that the SM4 cannot comply with the recent data from Higgs searches.

Concerning Higgs production and Higgs decay the common folklore reads as follows: gluon fusion is enhanced by a factor of nine (e.g., [

Despite these minor differences there is a common result: in the SM4 one expects more or at least as much Higgs events (depending on the channel) as in the SM. Hence, seeing nothing above the SM expectation rules out the SM4. These line of arguments can, for example, be found in the interpretation of the LHC Higgs searches presented at Lepton-Photon 2011, see also [

There are, however, two possible flaws in this argumentation, which have to be taken into account and which might actually revert the conclusions.

First, there is still the possibility that the heavy fourth neutrino is lighter than half of the Higgs mass. Current experimental bounds do not exclude a fourth neutrino with a mass larger than half of the

NLO-electroweak corrections to the Higgs production have already been determined in the midnineties [

Comparison of gluon fusion cross-section within the SM4 and the standard model. Depending on the value of the Higgs mass sizeable deviations of the naive expectation for ratio to be nine is possible. For Higgs masses in the region of 125 GeV this expectation works, however, very well. Figure from [

Also the decay rates of the Higgs boson are sizeably affected by NLO-electroweak corrections. In Figure

Comparison of Higgs decay rates within the SM4 and the standard model including NLO-electroweak corrections. In particular interesting is the strong reduction of the

With the results from Figures

There are however still some minor drawbacks, which should be kept in mind. First in the calculation of the NLO-electroweak corrections [

The complete NLO-electroweak corrections to Higgs production and decay and the possibility of an invisible Higgs decay were taken into account for the first time in [

Higgs branching ratios in dependence of the mass of the fourth neutrino for a Higgs mass of 125 GeV. Below

Due to the huge cancellations that arise now in the decay

A combined fit of electroweak precision observables and data for Higgs boson production and decay was presented in [

Pulls of the Higgs signal strengths with the data before ICHEP 2012. Figure from [

In Figure

Best fit results in dependence of the mass of the fourth neutrino. As soon as

On July 4, 2012 ATLAS and CMS announced new results for the Higgs boson search [

Both ATLAS and CMS see a

On July, 2012 also CDF and D0 updated their Higgs search [

In the SM4 one would expect a sizeable enhancement of the

In v2 of [

Before these new results the SM4 was excluded by 3.1 standard deviations; with the new data we expect the SM4 to be excluded by about five standard deviations [

The results, which were discussed here, relied strongly on the assumption of perturbativity of the heavy fermions and are also only valid for a minimal Higgs sector, that is, for only one Higgs doublet.

Investigations of a non-perturbative fourth generation can be found, for example, in [

The easiest way to avoid the above-discussed bounds on an additional fermion generation is to extend also the sector. A fourth generation in combination with a second Higgs doublet has been discussed in [

We reviewed the past and current status of the extension of the SM by an additional chiral generation of fermions. An amusing aspect thereby was the fact that the SM4 was declared dead many times. But all these declarations relied on some unjustified assumptions—giving them up the model was still viable. This clearly would be an interesting topic for a sociological study: why were there so many prejudices against the existence of this simple model? Nevertheless, it turned finally out that the SM4 is ruled out by experimental data (So unfortunately we did not learn the lesson that prejudices should be avoided in physics.): The SM4 cannot accommodate the new data for Higgs searches presented by LHC and Tevatron and thus, it is excluded.

There are still some missing ingredients like that the 2-loop corrections to the electroweak precision observables within the SM4 are still missing. Moreover the NLO-electroweak corrections to Higgs production and decay were calculated by neglecting CKM mixing.

Finally we commented very briefly that extending in addition the Higgs sector, for example, by an additional Higgs doublet might circumvent many of the above-discussed bounds.

The author thanks Markus Bobrowski, Otto Eberhardt, Abdelhak Djouadi, Geoffrey Herbert, Heiko Lacker, Andreas Menzel, Uli Nierste, Johann Riedl, Jürgen Rohrwild, Heinrich Päs [

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