# Singlet Charge Quark hiding the Top:

Tevatron and LEP Implications

###### Abstract

If and quarks are strongly mixed with a weak singlet charge quark, could be suppressed via the mode, thereby the top quark could still hide below , whereas the heavy quark signal observed at the Tevatron is due to the dominantly singlet quark . This may occur without affecting the small value. Demanding GeV and , we find that cannot be too suppressed. The heavy quark decays via , and bosons. The latter can lead to -tagged jet events, while the strong – mixing is reflected in sizable fraction. decay occurs at tree level and may be at the order, leading to the signature of , all isolated and with large , at order.

###### pacs:

^{†}

^{†}preprint: NTUTH-94-18 August 1994

## I Introduction

Recently, the CDF collaboration has reported [1] some evidence for the production of heavy quarks with mass of order 174 GeV at the Tevatron. The most likely explanation is, of course, the standard model (SM) top quark. However, at present, in principle it is still possible [2] that the signal is due to some other heavy quark, whereas the actual top quark is hiding below . This is because the top quark semileptonic branching ratio (BR) has not yet been measured. If, for some reason, , the SM expected value, the top quark may have evaded detection. This can arise basically only through scalar induced interactions [2].

One such scenario was proposed [3] earlier by Mukhopadhyaya and Nandi (MN). Following a suggestion [4] by Barbieri and Hall (BH), MN considered the existence of singlet charge quark alongside SM fermions. Since GIM is broken, the mixing of with up-type quarks induce tree level flavor changing neutral couplings of the SM Higgs boson. If , transitions may trigger the aforementioned mechanism of suppressing . In a subsequent paper, facing criticisms of “naturalness” [5, 6] ( suppressions of heavy effects), MN retracted, and considered dominance to be not very likely [7]. In this letter we study the precise conditions that dominance can be realised. We find that this requires to be strongly mixed with both charm and top, which can occur even with a small eigenvalue. However, we find that although can be dominant, it is unlikely to be overwhelmingly dominant. Thus, should occur at reduced but still substantial fraction. This offers hope that, even if , the top quark can be uncovered at the Tevatron by a renewed study with existing data.

The heavy quark can decay both via and bosons [8], hence it could be the heavy quark observed by CDF. Although one could not explain the larger than expected cross section for 174 GeV quarks, one could plausibly account for the -tagged 4 jets events [1]. Eventually, events with 2 jets should start to emerge with increased luminosity [9]. Another point of great phenomenological interest is decays, first stressed in this context by BH [4]. These occur at tree level again because of GIM violation. Although widely known, the possibility apparently has not been studied with actual LEP data because of the standard expectation of a very heavy top. We estimate [4] that could occur at the level, but with of order a few percent. This results in a signal branching ratio of at the few level, and each LEP experiment could have a few tens of events at present. The background level can probably be managed, and LEP experiments are strongly urged to conduct such a search.

## Ii Singlet Quark Induced Couplings

Besides the standard -type quarks , (), we add a left-right singlet charge quark , . The left-handed singlet field can pair up with the four right-handed fields to form gauge invariant singlet masses, which we denote as and respectively. The right-handed singlet field introduces three extra Yukawa couplings, resulting in off-diagonal masses which we denote as . Thus, the -type quark mass matrix is

(1) |

where

(2) |

are Yukawa and singlet masses. is diagonalised by a biunitary transform,

(3) |

where, departing from the notation of MN [3],

(4) |

and is a matrix. The Yukawa matrix is not simultaneously diagonalised,

(5) |

and the off-diagonal term controls FCNC and couplings. The apparent freedom due to the presence of rotation matrix on right-handed fields led MN originally to conclude that coupling could easily be rather large. However, from eq. (3), simple algebra gives

(6) |

where is the diagonal mass matrix (see eq. (3)). We see that no reference to is left, and the off-diagonal couplings depend only on mass eigenvalues and -related mixing elements of [6, 7]. The relevant flavor changing Higgs couplings are [6] ()

(7) | |||||

(8) |

The FCNC couplings are [3]

(9) | |||

(10) |

which is simply related to the Higgs couplings. The charged current becomes

(11) | |||

(12) |

where

(13) |

The KM matrix is no longer unitary. Both and depend on the left-handed down quark rotation matrix .

## Iii Details

We wish to explore the range of parameter space where coupling could be sizable. To this end we make a special choice of basis to focus on the problem. First, we choose fields such that in . Second, we choose , , such that the matrix is diagonal, hence the KM matrix largely comes from the down-type quark sector (we have checked that it is not possible to generate the observed KM matrix structure just by introducing -type singlet quarks). Only the charged current is affected by the -type quark sector, the FCNC Higgs and couplings depend only on and .

The -type quark mass matrix is now in the form

(14) |

The relevant freedom introduced by the singlet quark is parametrized as 3 new off-diagonal Yukawa terms, plus the diagonal, gauge invariant Dirac mass . The parameters , and can be found by diagonalizing . Without loss of generality, we set so quark decouples from our discussion.

To illustrate the correlation between and , we set and plot, in Fig. 1, the mass eigenvalues , vs. for different values. Level repulsion is evident: and for , . For larger values, we adopt the convention that, if , the heavier state is defined as the top quark. Thus, Fig. 1 depicts both the mass eigenvalues and the label for and .

We are more interested in the effect of . With finite , but negligible , , , the heavy mass eigenvalues are

(15) |

where . For sake of discussion, we consider the case where (top lighter). Note that in Fig. 1 when is not too large, the top mass eigenvalue is close to the diagonal term . This is a generic feature. When other ’s can be ignored and is not too big, the mass eigenvalue and mixing are roughly

(16) |

These relations become affected only when there are two values that are sizable, which follows largely as a consequence of unitarity of the matrix . In Fig. 2 we plot , as a function of for and , , . Note the remarkable feature that is almost independent of , but is suppressed by large through unitarity. The physical reason for this can be traced back to the fact that is very small compared to 1, and that is small.

Thus, the eigenvalue could be made small by choosing a small value for , but this does not forbid from being sizable. This is precisely counter the “hierarchy principle” [10] advocated in ref. [6]. However, given that , are large, other than being a prejudice, there is really no reason why cannot be large, since it is an independent parameter. Of course, if , then the conclusions of ref. [6] would hold.

## Iv Phenomenology

Inspection of eq. (8) suggests that transitions are suppressed by [6], but transitions have the effective coupling . Since is not small, so long that is not too suppressed, the mode has good probability to be dominant over [3]. The necessary condition is therefore that both and are sizable and neither are suppressed. Hence, Q, t and c all become rather arbitarily mixed although the charm mass is fixed by . Such an unusual situation is bound to have unusual consequences beyond being sizable.

To illustrate the possibility of dominance, and at same time account for CDF’s apparent observation of a heavy quark of mass 174 GeV, we demand that the heavier quark (whether dominantly doublet or singlet) mass to be pinned to the CDF value. We then choose , GeV, vary (to get , etc.) and plot, in Fig. 3, vs. (the physical mass) up to 90 GeV, for 50–75 GeV. We allow for below the present LEP bound in case there are more than one Higgs doublet [12]. In producing Fig. 3, we compute the and decay width using the couplings of eqs. (8) and (12). We assume that amounts to a “small” rotation close to the “standard” KM matrix, ignoring all phases. We have also ignored decay as this is a three body process subdominant compared to . It is clear that, if the Higgs boson mass is sufficiently light, can be dominant. However, the combined demand of 174 GeV, and , dictates that the mode cannot be overwhelmingly dominant. Thus, although suppressed, should not be vanishingly small. For larger , dominance quickly fades, and the possibility is ruled out by CDF since is not drastically suppressed. In the following, we shall assume that one works in the domain where for the “top” (it could be the dominantly singlet quark, since we do not know the scale for ) is suppressed by or more. That is, .

Fig. 3 corresponds to , with GeV. The corresponding branching ratios are 0.51, 0.24, 0.04, 0.1, 0.02, 0.09, respectively. Note that, as a consequence of large , decay has a sizable rate! The modes and are suppressed by phase space, while and are suppressed by an extra power of . Thus, induced decays are still dominant, but the content in final state is diluted slightly by the mode. Although one cannot account for the large production cross section for the heavy quark (one could always add another singlet -type quark for this purpose), other features reported by CDF can be accounted for [8, 11], in particular, the appearance of -tagged 4 jet events. The boson comes from , , while a -tag could come from , or from or , etc., in subsequent decays. This could be at of the cross section, hence consistent to what is observed. On the other hand, single- with -tag is slightly depressed () compared to the standard top. We therefore conclude that the heavy quark observed by CDF may well be a doublet-singlet mixed state . The scenario offers many signatures and can be checked experimentally. The light top with not too suppressed can perhaps be probed with existing Tevatron data [2].

The scenario has a consequence that may be studied at LEP. As first pointed out by Barbieri and Hall [4], can be quite sizable with existence of charge 2/3 singlet quarks.Using eq. (10) and , values for the example above, we estimate that is of order a few , which is consistent with ref. [4]. Other phenomenological constraints are not particularly stringent, and can be found in ref. [4]. For example, – mixing constraint can be satisfied with small . Since does not vanish, we estimate that the potentially observable signal of 2 jet (where the jets contain and ) could have a branching ratio of order a few . Since the lepton and neutrino should be well isolated with sizable ( GeV) or missing energy (they are bona fide virtual decay events!), and that , and one jet should pair up to be the top mass, there should be sufficient handles for the suppression of background. The latter presumably comes from events with plus gluon bremsstrahlung.

###### Acknowledgements.

This work is supported in part by the National Science Council of the Republic of China under grant NSC-83-0208-M-002-023. WSH wishes to thank the CERN Theory Division for hospitality and a stimulating environment, and T. Ferguson for discussion.## References

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