a clean signal for a top-like isosinglet fermion at the large hadron collider

PRAMANA c© Indian Academy of Sciences Vol. 81, No. 6— journal of December 2013

physics pp. 975–986

A clean signal for a top-like isosinglet fermionat the Large Hadron Collider

AARTI GIRDHARRegional Centre for Accelerator-based Particle Physics, Harish-Chandra Research Institute,Chatnaag Road, Jhunsi, Allahabad 211 019, India and Department of Physics,Dr B R Ambedkar National Institute of Technology, Jalandhar 144 011, IndiaE-mail: [email protected]

MS received 20 March 2013; revised 26 July 2013; accepted 29 August 2013DOI: 10.1007/s12043-013-0618-0; ePublication: 8 November 2013

Abstract. We predict a clean signal at the Large Hadron Collider (√

s = 14 TeV) for a scenariowhere there is a top-like, charge +2/3 vector-like isosinglet fermion. Such a quark, via mixingwith the standard model top, can undergo decays via both flavour-changing Z -boson coupling andflavour-changing Yukawa interactions. We concentrate on the latter channel, and study the situa-tion where, following its pair production, the heavy quark pair gives rise to two tops and two Higgsbosons. We show that when each Higgs decays in the bb channel, there can be a rather distinct andbackground-free signal that can unveil the existence of the vector-like isosinglet quark of this kind.

Keywords. Top-like; vector-like; isosinglet; flavour changing neutral current.

PACS Nos 14.65.Jk; 14.65.Ha

1. Introduction

Our present knowledge about elementary particles and their interactions upto the energyscale of several hundred GeVs are encapsulated in the theory called the Standard Model(SM). The SM, a renormalizable gauge theory of strong and electroweak interactionsbased on the gauge group SU(3)C × SU(2)L × U(1)Y, gives successful explanations formost of the phenomena governing fundamental processes, and is in excellent agreementwith the experimental data to date. However, there are a number of unanswered questionswhich motivate us to think beyond the SM. These include, just to name a few, the flavourand naturalness problems, the absence of a cold dark matter candidate in the spectrum, andthe origin of neutrino masses and mixing [1]. They have led to a plethora of conjecturesextending the SM.

On the experimental side, a golden opportunity to test many of these conjectures hascome through the Large Hadron Collider (LHC). So far, the most spectacular achievement

Pramana – J. Phys., Vol. 81, No. 6, December 2013 975

Aarti Girdhar

of the LHC has been the discovery of what is believed to be a scalar particle withmass in the range of 125–126 GeV, with properties consistent with the Standard ModelHiggs boson [2]. This ‘discovery’ can in turn be used, whenever appropriate, to look forsignatures of physics beyond the SM.

One of the many new physics ideas is to extend the fermionic sector of the SM by pos-tulating the existence of either a sequential fourth generation [3] or vector-like fermions.The electroweak precision data strongly constrain the existence of extra chiral fermions.On the other hand, vector-like fermions have left- and right-handed components with thesame transformation property under SU(2), and are considerably free from the aforemen-tioned constraints. They can have gauge invariant mass terms of the form t ′

Lt ′R, which

do not arise from the electroweak symmetry breaking mechanism, and should be tracedto some new physics scale. Thus, their signature is of immediate interest if that scale isaccessible to the LHC, with the fond hope that they might contain some clue to the flavourproblem.

Vector-like fermions appear as singlets, doublets or triplets under SU(2), in manyoptions beyond the Standard Model (BSM) like Little Higgs Model [4,5], compositeHiggs model [6] and extra dimensional models [7]. They also appear in some grandunified theories like E6 [8], which once got impetus from considerations underlyingsuperstring theories. In particular, vector-like isosinglets also play a role in the �F = 2effective Lagrangian analysis studies [9]. Also, it has been pointed out that models withsuch an extended quark sector can give rise to quark electric dipole moment at the two-loop level due to the lack of Glashow–Illiopoulos–Maiani (GIM) suppression, therebyimplying constraints on the model parameter space(s) [10]. The collider phenomenologyof such an isosinglet vector fermion has been studied from various angles [9–43].

Here we focus on an SU(2) singlet, charge 2/3 vector-like quark. It should be notedthat down-type vector-like isosinglets, too, have been considered extensively in [10–15].The vector-like quark is pair-produced at the LHC in the same way as the top quark,subject, of course, to the inevitable kinematical suppression if its mass is higher. Sucha quark, however, has additional decay channels, which can make it distinct. The mainfeatures responsible for such a distinction are its isosinglet character, and its capacity tomix with the top, once SU (2) × U (1) is broken. As a result of doublet–singlet mixing inthe left chiral sector, such a quark, named t ′ here, has flavour changing interactions bothwith the Higgs boson (H ) and the Z -boson. We propose to utilize the resulting decaychannels, namely t ′→ t H and t ′→ t Z . In particular, we find that the former channelleads to a rather unique and background-free signature arising from a t t H H state.

On account of mixing between the SM fermions and their SU(2) singlet counterparts,many observables are expected to be different from the Standard Model predictions,specially in the sector involving third family. Our search strategy is buttressed by theavailable information on the Higgs mass. We use such a Higgs as an instrument to inves-tigate the production and decay of exotic top-like quark into channels which hardly haveStandard Model backgrounds. Our claim is that using this information on the Higgsmass enables one to have a high search limit even in the all-hadron channel, through thereconstruction of two b-pairs to a Higgs each.

In order to maximize our signal rates, we let the Higgs decay in each case into thefinal state with maximum branching ratio, namely H → bb. We show that, using theconsequent 6b final states (including decays of the top quarks as well), one can construct

976 Pramana – J. Phys., Vol. 81, No. 6, December 2013

A clean signal for a top-like isosinglet fermion

signals with very little SM backgrounds. Tagging five bs out of six in each case, withappropriate event selection criteria, proves to be sufficient for this purpose. We demon-strate that such a signal can allow us to probe in a discriminating fashion a large part ofthe parameter space consisting of the t ′ mass and its mixing with the t .

The rest of the paper is organized as follows. Section 2 contains an outline of thescenario, statements on the signal looked for, a reminder of the constraints on variousparameters, and a resume of the methodology adopted. The results are presented in §3.We summarize and conclude in §4.

2. The scenario, the signal, and the methodology

2.1 The scenario and its signals

As has been said already, we consider a minimal extension of the SM with the inclusionof a top-like vector isosinglet, t ′

L (3,1,+ 43 ), t ′

R (3,1,+ 43 ) to the matter content of the SM.

The gauge boson and the Higgs sector remain unchanged.t ′ can be produced in pair via the strong interactions [16–18] or singly via electroweak

processes [19]. We concentrate here on the former channel, which at the parton levelcorresponds to gg → t ′ t ′ and qq → t ′ t ′ essentially arising from the gluon coupling ofthe heavy quark:

LQCD = −ιgs t ′γμt ′Gμ. (1)

Neglecting the small contribution from electroweak diagrams, the pair production cross-section for an isosinglet fermion and a chiral fourth-generation fermion is the same[44,45]. The production cross-section depends only upon the mass of t ′ and goes downwith increase in the mass.

Once the SU (2) × U (1) symmetry is broken, the most substantial mixing of t ′ cantake place with the top, as there are rather stringent bounds on mixing with the first twogenerations [20]. It must be remarked that there have been studies which considered themixing with the lighter generations, which can affect, for example, the single productionof vector-like quarks through the electroweak channels [21]. As a result of such mix-ing, the four charge 2/3 quarks in the weak basis are related to the corresponding masseigenstates by

⎡⎢⎢⎢⎣

u0

c0

t0t ′0

⎤⎥⎥⎥⎦

L

= U

⎡⎢⎢⎢⎣

u

c

t

t ′

⎤⎥⎥⎥⎦

L

, U =[

V †3×3 W3×1

X1×3 v1×1

]=

⎡⎢⎢⎢⎣

V ∗ud V ∗

cd V ∗td Wdt ′

V ∗us V ∗

cs V ∗ts Wst ′

V ∗ub V ∗

cb V ∗tb Wbt ′

Xu4 Xc4 Xt4 v4t ′

⎤⎥⎥⎥⎦ , (2)

where V is the Standard Model CKM matrix. In such a basis the mass matrix for thedown-type quarks is diagonal. The mass matrix (Mu) for the up-type quarks is

Mu =[

MqLqR MqLt ′R

Mt ′LqR

Mt ′Lt ′

R

], (3)

where qL,R = (u, c, t)L,R, MqLqR is 3 × 3 mass matrix of the SM particles, MqLt ′R

is 3 × 1,MqLt ′

Ris 1 × 3 and Mt ′

Lt ′R

is the mass term for t ′. Mt ′LqR

and Mt ′Lt ′

Rdo not arise from the


Aarti Girdhar

Yukawa couplings. Mu is diagonalized by the bi-unitary transformation: U † MuU ′ =Mu

diag, where U ′ is the analogous mixing matrix for right-handed charge +2/3 quarks.With the structure of the mixing matrix being what is shown in eq. (2), the Standard

Model CKM matrix is no longer unitary, and instead forms a block in the unitary 4 × 4mixing matrix U . The V and W together form the 3 × 4 charged current mixing matrix.The violation of CKM unitarity leads to a breakdown of the Glashow–Illiopolous–Maiani(GIM) mechanism, and leads to the flavour changing neutral current (FCNC) processes(t → cZ ) and (t → cH ) in the top sector [20,22,23]. As mentioned above, t ′ decays tothe SM fermions along with either the electroweak gauge bosons (W ±, Z ) or Higgs boson(H ) at the tree level. The charged current interaction (t ′→ bW +) is given by

Lcc = gWbt ′√2

t ′LγμbLW +

μ + h.c. (4)

On account of mixing with the top quark we have FCNC interactions with Z bosongiven by

Lneutral = gX∗t4v4t ′

2 cosWt ′LγμtL Zμ + h.c., (5)

and the interaction of t ′ with Higgs boson and the flavour changing Yukawa coupling is

Lyukawa = yt ′ qLi H ct ′R + h.c., (6)

where yt ′ in this is −(g/2MW)X∗t4v4t ′ Mt ′ . In addition to the above Yukawa coupling there

are terms proportional to t ′LqR and t ′

Lt ′R which arise because it is not possible to diagonalize

the mass and Yukawa matrices simultaneously.Following the simplified version of the mixing matrix used in [23], we describe all the

interactions of t ′ by the following mixing matrix:

U =

⎡⎢⎢⎢⎣

1 0 0 0

0 1 0 0

0 0 cos θ sin θ

0 0 −sin θ cos θ

⎤⎥⎥⎥⎦ , (7)

where its interactions with all the quarks of the first two generations are neglected. Wealso neglect the interactions of the SM quarks across the generations. The elements ofthe mixing matrix are chosen with the motivation to have considerable flavour changingdecay modes in addition to the charge changing decay modes.

We concentrate on one of the decay process of t ′, namely, (t ′ → t H) with MH = 125.5GeV. This particular decay channel has already been used as a tool to study the discov-ery potential of Higgs [16,24–26] but with a different final state. It must be remarkedthat when t–t ′ mixing takes place, both the resulting eigenstates contribute to the loopsinvolved in Higgs production via gluon fusion. The gluon fusion is sensitive to the contri-bution from new physics and may deviate from the SM values [27,28]. While the presentuncertainties in Higgs data allow for such contribution, they may potentially constraintmt ′ − θ parameter space. In [5] though the final decay of H considered is also to bb butit is in the context of ‘Little Higgs model’ where there are extra gauge and Higgs bosons



along with t ′. The decay chain we consider further is where both the tops decay to bWand both the Higgs to bb. i.e

pp → t ′ t ′ → Ht Ht → bbbW +bbbW −. (8)

The final state consists of 6bs and 2W s, out of which we attempt to identify 5bs andpredict the signal for 5b+ X final state. As we show in this work, this turns out to be arather clean signal with very low SM background.

Direct and indirect searches for the vector fermions put constraints on the mass andcouplings of t ′ and the mixing angle θ , between t and t ′. Among them, direct searchesimply the following bounds:

• Considering t ′ → W +q as the only possible decay chain, the lower limit on themass of t ′ is 358 GeV at 95% CL by the CDF Collaboration [44] at the centre ofmass energy,

√s = 1.96 TeV.

• The DO Collaboration puts the lower limit in the channel of W+jets decay, at 95%CL to be 285 GeV [45] at

√s = 1.96 TeV.

• The latest study by ATLAS set the lower limit on the mass of t ′ at mt ′ < 404 GeVat 95% CL assuming 100% decay through bW + mode [46] at the centre of massenergy,

√s = 7 TeV.

• Assuming 100% branching fraction for the decay t ′→ t Z , t ′ with any mass less than475 GeV is excluded at 95% CL by CMS detector at the LHC [47] at

√s = 7 TeV.

• The Rb ratio given by,

Rb = �(Z → bb)

�(Z → hadrons),

gives a strong constraint on the t–t ′ mixing angle, θ to be θ ≤ 25◦ [29].

For the purpose of our current work, we consider the lowest mass to be 350 GeV, andmake no specific assumption about branching ratios in the three decay channels.

2.2 Methodology

For numerical calculations, we have used CalcHEP v2.5.6 [48,49] and a CalcHEP-PYTHIA interface program [50] along with PYTHIA-6.4.24 [51]. The production cross-section of the isosinglet quark pair and the decay of t ′, t ′ are calculated using CalcHEPv2.5.6 [48,49]. In order to do so, a new model with the new interactions based on the mix-ing matrix considered, was added to the existing list of CalcHEP models. We have takenmt = 172 GeV, and used CTEQ6L parton distribution functions (PDF), for the centre-of-mass energy

√s = 14 TeV. The renormalization scale, Q2 is s = Mi j

2 = (pi + p j )2.

We chose the following benchmark points for our calculation (table 1).After calculating the production cross-section and branching fractions for all the bench-

mark points by CalcHEP, the output is interfaced with PYTHIA through the LHE (LesHouches Event) interface [50]. Taking into account the initial state radiation (ISR), finalstate radiation (FSR) and multiple interactions, hadronization is done in PYTHIA toobtain rates in the desired final state of 5b + X . We use b quarks at the parton level


Aarti Girdhar

Table 1. Benchmark points.

Parameter Value

Mt ′ (GeV) 350, 400, 500Mixing angle t − t ′, θ 5◦, 10◦, 15◦MH (GeV) 125.5

but a conservative identification efficiency of 50% has been folded in, which holds for bswith pT in the range of 40–150 GeV.

The SM background in this case is calculated at the parton level for the signal pp →H Htt using CalcHEP v2.5.6 [48,49]. The only on-shell process which gives rise to thissignal in the SM is pp → t t → H Htt , and as a result the background is very small. Otherbackgrounds, for example Zbb with Z decaying Z → bb, t t H, t t Z , bbbb j , are not foundto be of serious concern. Explicit calculation using ALPGEN v2.14 [52], for example,reveals that σ(Zbb) is of the order of 10−2 pb, which on being folded with the jet fakingprobability and imposing the restriction that two b pairs peak at mbb, 124 ≤ mbb ≤ 127GeV reduces the background to very low level. We have not taken into account the effectof, for example, charm-induced jets faking bs.

We reconstruct the invariant mass of all the bb pairs which survive the first three selec-tion cuts listed below, and follow the criteria explained there. We have used the followingselection criteria on the minimum of five bs required in our stipulated final state:

(a) Each of the identified b should have ET > 40.0 GeV.(b) Each b jet should be central, with pseudorapidity, |η |<2.5.(c) We implement b-tagging efficiency of 50%, i.e. εb ∼ 0.5.(d) As a final step, we calculate the invariant mass for all the possible combinations of

b pairs. We impose the following restriction on the calculated invariant mass (mbb)for two of the b-pairs in the final state: 124 ≤ mbb ≤ 127 GeV.We get our final numbers by counting all the events (NH) which have at least twosuch b pairs with their calculated invariant mass falling in the above limit. Wepredict our signal using this number.This kind of h pair identification is beset with a combinatorial background whichhas been included in our analysis. The Minv distributions include contributions fromcombinatorial backgrounds which cause a broadening of the peak in each case.Some background events may have added to the signals through combinatorics, butthat is not expected to yield any substantial overestimation, since the 5b background(∼10−5pb) is quite small, and the probability of non b jets faking as b jets does notmake it much higher, once the invariant mass cut is imposed.

3. Results

We are presenting the results at the leading order (LO), and thus our estimate can be calledconservative. Our final state consists of six bs and two W s. A similar use of the final statecomprising six bs has been considered in [24,35]. However, the suggested signal, clean



1000900800700600500400300

12

10

8

6

4

2

0

Figure 1. Production cross-section of t ′ t ′, plotted against the t ′-mass for√

s = 14TeV.

as it is, has suppressed rates due to the requirement of the simultaneous tagging of anisolated lepton. We, in contrast, give up the lepton tagging requirement. Moreover, wesuggest identifying only five out of the six bs, with the proviso that four out of themdisplay two individual peak, each at the observed Higgs mass. The avowed discovery ofthe Higgs has thus allowed us to suppress backgrounds even without any leptonic tag, afact that is responsible for higher event rates. As is clear from figure 1, the pair productioncross-section of t ′ decreases with Mt ′ since it depends only on the mass. We find that theproduction of signal at the parton level, H Htt in the SM, is weaker by at least 103 orderof magnitude in comparison to the lowest signal (for M ′

t = 500 GeV, MH = 125.5 GeVand θ = 15) in our model as can be seen in tables 2 and 3.

We present our results as the cut-flow chart for all the considered benchmark points andthe invariant mass distributions of bb pairs. We compute our results for different valuesof m ′

t and mixing angle θ . In spite of a substantial reduction of the signal due to taggingefficiency of 50% per b, our predicted signal is still good enough to be observed at theLHC at the integrated luminosity of 30 fb−1. We find the following trends in our resultsas can be seen from table 4.

(a) For a given value of M ′t , change in θ does not make much of a difference (.2 fb)

(figure 2), a fact that is well-known in the study of vector-like exotics.

Table 2. Production cross-section in the StandardModel for the signal pp → H Htt at

√s = 14 TeV.

MH (GeV) Cross-section (pb)

125.5 0.00053


Aarti Girdhar

Table 3. The rate for pp → t t H H via t ′ pairs for√

s = 14 TeV.

Cross-section (pb)

Mt ′ MH (GeV) θ = 5◦ θ = 10◦ θ = 15◦

350 125.5 1.446 1.431 1.367400 125.5 0.828 0.814 0.771500 125.5 0.249 0.244 0.231

Table 4. Cut-flow table for various benchmark points for MH = 125.5 GeV.

MH = 125.5 GeV

Cross-section (pb)

Mt ′ (GeV) Cut θ = 5◦ θ = 10◦ θ = 15◦

350 EbT > 40.0 GeV 0.453 0.437 0.421|ηb |< 2.5 0.418 0.437 0.388εb ∼ 0.5 0.0237 0.0223 0.0220

NH at least 2 0.011 0.010 0.009400 Eb

T > 40.0 GeV 0.270 0.259 0.248|ηb |< 2.5 0.251 0.240 0.229εb ∼ 0.5 0.014 0.014 0.0134

NH at least 2 0.007 0.006 0.006500 Eb

T > 40.0 GeV 0.088 0.086 0.061|ηb |< 2.5 0.082 0.081 0.058εb ∼ 0.5 0.005 0.005 0.003

NH at least 2 0.002 0.002 0.002

=15=10=5

500450400350300

0.011

0.01

0.009

0.008

0.007

0.006

0.005

0.004

0.003

0.002

0.001

Figure 2. Cross-section for the final state (5b + X ) with the mass of t ′ for variousvalues of mixing angle θ and MH = 125.5 GeV at

√s = 14 TeV.



150145140135130125120115110

180

160

140

120

100

80

60

40

20

0

Figure 3. Invariant mass distribution of bb for mt ′ = 350 GeV, mixing angle θ = 5◦and MH = 125.5 GeV for

√s = 14 TeV.

(b) For a given value of θ dependence on M ′t is the strongest. It changes the cross-

section for the signal by 7–9 fb.(c) Also as M ′

t goes from 350 to 500 GeV, the change in θ hardly makes any differenceon the signal cross-section.

We plot the invariant mass distribution of all the combinations of b pairs for the eventswhich survive the first three selection criteria. We find that this distribution has two peakscorresponding to the reconstructed Higgs mass within the required mass range (124 ≤mbb ≤ 127) GeV, as in figures 3 and 4, satisfying our fourth selection criterion, for all ourbenchmark points. We present here the distribution for two points only, i.e. figures 3 and 4.

150145140135130125120115110

60

50

40

30

20

10

0

Figure 4. Invariant mass distribution of bb for mt ′ = 500 GeV, mixing angle θ = 15◦and MH = 125.5 GeV for

√s = 14 TeV.


Aarti Girdhar

Let us now compare the results of table 4 with the results of ref. [24], where thet t H H channel yields about 23 reconstructed events for M ′

t = 500 GeV with an integratedluminosity of 30 fb−1. In our case, we have used to our advantage the currently availableinformation on the Higgs mass, whereby the backgrounds are rather effectively elim-inated. On the other hand, for the same M ′

t , we have about 60 events with 30 fb−1

with the final states chosen using our criteria, including the Higgs mass information.Even with some potential reduction in the number of events due to detector effects etc.,this marks an improvement over earlier works, and a higher search limit for a top -likevector singlet.

4. Summary and conclusions

We have calculated the particular signal (5b+ X ), in the framework of a model with atop-like (+2/3) vector fermion, (t ′), in addition to the SM particles. We assume thatit mixes only with the top quark. We ignore not only the interactions of t ′with first twogenerations but also the interactions of the SM quarks across the generations in the mixingmatrix, U in eq. (7). As a result of the mixing with the top, t ′ has flavour changing neutralinteractions with Z and H bosons. We make use of the interaction with Higgs boson andfollow a particular decay mode (t ′ → Ht) of t ′ and further consider the decay of Higgsto bb. Using CalcHEP, PYTHIA and CalcHEP–PYTHIA interface programs, we predictan observable signal of 5b+X from a final-state signal of 6bs and 2W s, at the LHC at thecentre-of-mass energy,

√s = 14 TeV. We consider the situation when the Higgs boson is

already discovered, so that its mass is a known quantity, and can be used to identify two b-pairs with invariant mass around the mass of the Higgs, that is to say, 125.5 GeV. We findthat in spite of the rather ambitious proposal of tagging five bs, we get, after all the cuts,a signal of the order of a few fb which is at least two orders of magnitude higher than theSM background. Since all our results are at the leading order, the predictions we makeabout the signal are rather conservative. We conclude that an integrated luminosity of30 fb−1 should be sufficient to either find out or rule out the existence of t ′ in the massrange 350–500 GeV.

Acknowledgement

The author is grateful to Prof. Biswarup Mukhopadhyaya for suggesting the problemconsidered here and for constant support throughout the course of this work and to Prof.Asesh Krishna Datta for useful discussions. The author acknowledges technical help fromSatyanarayan Mukhopadhaya and Nishita Desai, help from Sanjoy Biswas in writing thecode and Monalisa Patra for pointing out an important fact. The author also appreci-ates the constant support and encouragement from D S Ramana. This work is supportedby a grant (SR/WOS-A/PS-04/2009) from the Department of Science and Technology,Government of India, New Delhi, under the WOS-A scheme and partially by funds avail-able for Regional Centre for Accelerator-based Particle Physics, from the Department ofAtomic Energy, Government of India.



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http://arxiv.org/abs/hep-ex/9807003

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a clean signal for a top-like isosinglet fermion at the large hadron collider

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