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Associated production of the top-pions and single top at hadron colliders


Associated production of the top-pions and single top at hadron colliders
Chong-Xing Yue, Zheng-Jun Zong, Li-Li Xu, Jian-Xing Chen

arXiv:hep-ph/0601058v1 9 Jan 2006

Department of Physics, Liaoning Normal University, Dalian, 116029 P. R. China ?

February 7, 2008

Abstract In the context of topcolor assisted technicolor(TC2) models, we study the
0,± 0 p production of the top-pions πt with single top quark via the processes p? → tπt +X

± and p? → tπt + X, and discuss the possibility of detecting these new particles at p

Tevatron and LHC. We ?nd that it is very di?cult to observe the signals of these particles via these processes at Tevatron, while the neutral and charged top-pions
± 0 c πt and πt can be detecting via considering the same sign top pair tt? event and the

? tt? (or ttb) event at LHC, respectively. b

PACS number: 14.80.Cp, 12.60.Cn, 12.15.Lk

?

E-mail:cxyue@lnnu.edu.cn

1

I. Introducton The mechanism of electroweak symmetry breaking(EWSB) and origin of the fermion mass remain unknown in elementary particle physics in spite of the success of the standard model(SM) tested by high energy experimental data. Hadron colliders, such as Tevatron and Large Hadron Collider(LHC), are machines extremely well-suited to study these problems. The LHC is expected to directly probe possible new physics beyond the SM up to few T eV and provide some striking evidence of new physics, for instance of a light Higgs boson, in its ?rst months of operation[1]. Tevatron Run II has signi?cant potential to discover a light SM Higgs boson with mass up to about MH ≤ 130GeV [2]. The LHC will have considerably capability to discover and measure almost all the quantum properties of a SM Higgs boson of any mass[1]. However, if hadron colliders ?nd evidence for a new scalar state, it may not necessarily be the SM Higgs boson. Many alternative new physics theories, such as supersymmetry, topcolor, and little Higgs, predict the existence of new scalar or pseudo-scalar particles. These new particles may have cross sections and branching fractions that di?er from those of the SM Higgs boson. Thus, studying the production and decays of the new scalars at hadron colliders will be of special interest. Of particular interest to us is topcolor scenario[3], in which there is an explicit dynamical mechanism for breaking electroweak symmetry and generating the fermion masses including the heavy quark mass. Thus, it is very attractive kind of models beyond the SM.
0,± The presence of the physical top-pions πt in low energy spectrum is an inevitable fea-

ture of the topcolor scenario, regardless of the dynamics responsible for EWSB and other
0,± quark mass. One of the most interesting features of πt is that they have large Yukawa

couplings to the third-generation quarks and can induce the tree-level ?avor changing(FC) couplings[4].
0,± In this paper, we will study the associated production of the top-pions πt and single ± 0 top quark via the subprocesses gc → tπt and gb → tπt and further discuss the possible

signatures of these new particles at the Tevatron and LHC experiments. Our numerical results show that the top-pions can be signi?cant produced via these processes at LHC 2

and their cross sections are larger than those for the Higgs bosons H 0,± predicted by the minimal supersymmetric standard model(MSSM). These processes can be used to probe the top-pions and distinguish the Higgs bosons predicted by the MSSM from the top-pions predicted by the topcolor scenario. To completely avoid the problems arising from the elementary Higgs ?eld in the SM, various kinds of dynamical EWSB models have been proposed, among which the topcolor scenario is attractive because it can explain the large top quark mass and provide a possible EWSB mechanism[3]. The topcolor-assisted technicolor(TC2) models[5] are one kind of the phenomenologically viable models, which has all essential features of the topcolor scenario. So, in the rest of this paper, we will give our results in detail in the context of the TC2 models. This paper is organized as follows. Section II contains a short summary of the relevant
0,± couplings to ordinary particles of the top-pions πt in TC2 models. The anomalous top 0 quark coupling tqv has contributions to the process gq → tπt . Thus, the anomalous

top quark coupling tqv from the FC interactions in TC2 models is also discussed in this section. Sections III and IV are devoted to the computation of production cross sections
? 0 for the process p? → tπt + X and p? → tπt + X, respectively. Some phenomenological p p

analysis are also included in these sections. Our conclusions are given in Sec.V. II. The relevant couplings For TC2 models, the underlying interactions, topcolor interactions, are nonuniversal and therefore do not possess the Glashow-Iliopoulos-Maiani(GIM) mechanism. The nonuniversal gauge interactions result in the new FC coupling vertices when one writes
0,± the interactions in the mass eigen basis. Thus, the top-poins πt can induce the new FC 0,± coupling vertices. The couplings of πt to ordinary fermions, which are related to our

calculation, can be written as[4,5,6]: √ tt? bb mb ? m′b 5 0 tt tt? ? 0 ? [iKU R KU L tγ 5 tπt + 2KU R KDL?L tR πt + i bγ bπt b νW mt √ tc? bb ml ? 5 0 tc? tt 0 ? +iKU L KU R c? tR πt + 2KU R KDL?L cR πt + h.c.] + √ b lγ lπt , (1) L 2νW √ where νW = ν/ 2 = 174GeV , l represents the lepton τ or ?, and m′b ≈ 0.1εmt is the part m √ t 2Ft 3
2 νW ? Ft2

of the bottom-quark mass generated by extended technicolor(ETC) interactions. KU L(R) and KDL(R) are rotation matrices that diagonalize the up-quark and down-quark mass matrix MU and MD for which the Cabibbo-Kobayashi-Maskawa(CKM) matrix is de?ned
+ as V = KU L KDL . To yield a realistic form of the CKM matrix V, it has been shown that

their values can be taken as[4]: √ tt tc KU R = 1 ? ε, KU R ≤ 2ε ? ε2 . (2) √ tc In the following calculation, we will take KU R = 2ε ? ε2 and take ε as a free parameter,
tt bb KU L ≈ KDL ≈ 1,

which is assumed to be in the range of 0.01 ? 0.1[3,5].
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0 Figure 1: Feynman diagrams for the contributions of πt to the anomalous top quark

coupling tcg

In the context of the SM, the anomalous top quark couplings tqv (q=u- or c-quark and v = Z, γ or g gauge bosons), which are arised from the FC interactions, vanish at the tree-level but can be generated at one-loop level. However, they are strong suppressed by the GIM mechanism, which can not produce observable e?ects in the present and near future high energy experiments[7]. From Eqs.(1)and(2), we can see that the neutral top0 pion πt might generate the large top quark coupling tcg. The relevant Feynman diagrams

are shown in Fig.1. Similar to Ref.[8], we can give the e?ective form of the anomalous coupling vertex tcg: Λ? = igs tcg with F1g = 1 mt [√ 16π 2 2Ft
2 νW ? Ft2 2 tc tt? ′ ? ] KU R KU L (B0 + m2 t C0 ? 2C24 + m2 (C11 ? C12 ) ? B0 ? B1 ), π t νW (4)

λa ? [γ F1g + p? F2g + p? F3g ]. t c 2

(3)

4

F2g F3g

1 mt = 2mt [√ 2 16π 2Ft mt 1 [√ = 2mt 2 16π 2Ft

2 νW ? Ft2 2 tc tt? ] KU R KU L (C21 + C22 ? C23 ), νW 2 νW ? Ft2 2 tc tt? ] KU R KU L (C22 ? C23 + C12 ), νW

(5) (6)

where λa is the Gell-Mann matrix. The expressions of the two and three-point scalar integrals Bn and Cij are [9]: B0 = B0 (pg , mt , mt ),


? B0 = B0 (?pc , mπt , mt ),

(7) (8) (9) (10)

B1 = B1 (?pt , mπt , mt ), C24 = C24 (?pt , pg , mπt , mt , mt ), √ Cij = Cij (?pt , ? s, mπt , mt , mt ), i, j = 1, 2, 3. ?

0 Certainly, the neutral top-pion πt can also generate the anomalous top quark coupling 0 tug via the FC coupling πt tu. However, it has been argued that the maximum ?avor mix-

ing occurs between the third generation and the second generation, and the FC coupling
0? πt tu is very small which can be neglected[4]. Hence we will ignore the contributions of 0 the tug coupling to the process p? → tπt + X in the following discussions. p

± 0 Similar to the neutral top-pion πt , the charged top-pions πt can generate the anoma-

± lous top quark coupling tcg via the FC couplings πt bc. However, compared with those ± 0 of πt , the contributions of πt to the tcg coupling are approximately suppressed by the

factor mb /mt , which can be safely neglected.
0 III. Associated production of the neutral top-pion πt and single top quark

From above discussions, we can see that, due to the existence of the FC couplings, the
0 0 neutral top-pion πt can be generated via the subprocess gc → tπt at hadron colliders, 0? as shown in Fig.2. Fig.2(a) and Fig.2(b) come from the FC coupling πt tc, while Fig.2(c)

and Fig.2(d) come from the anomalous top quark coupling tcg. Although the strength of ? the coupling tcg is very smaller than that of the coupling gc? or gtt, we can not ignore c
0 ? the contributions of Fig.2(c) to the subprocess gc → tπt being large πt tt coupling. For

0 Fig.2(d), it is not this case. The πt c? coupling is very small and thus the contributions of c

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0 Figure 2: Feynman diagrams for the process gc → tπt

0 Fig.2(d) to the subprocess gc → tπt can be neglected. We have con?rmed this expectation

through explicit calculation. To obtain numerical results, we need to specify the relevant SM input parameters. These parameters are mt = 178GeV and αs (mt ) = 0.118[10]. Through out this paper, we neglect the charm quark mass and use CTEQ6L parton distribution functions with scale ? = 2mt [11]. The limits on the top-pion mass mπt can be obtained via studying its e?ects on various observables[3]. It has been shown that mπt is allowed to be in the range of a few hundred GeV depending on the models. As numerical estimation, we will assume √ 0 The production cross sections for the process p? → tπt +X at the Tevatron with s = p √ 1.96T eV and the LHC with s = 14T eV are plotted as functions of the top-pion mass mπt for three values of the free parameter ε in Fig.3(a) and Fig.3(b), respectively. From these
0 ?gures, we can see that the tπt production cross section at Tevatron is much smaller than

that the value of the top-pion mass mπt is in the range of 200GeV ? 500GeV.

that at LHC in all of the parameter space of the TC2 models. For 0.02 ≤ ε ≤ 0.08 and
0 200GeV ≤ mπt ≤ 500GeV , the tπt production cross sections at Tevatron and LHC are in

the ranges of 2.3 × 10?3 f b ? 4.1f b and 17f b ? 1.82 × 103 f b, respectively. If we assume √ the yearly integrated luminosity ?int = 2f b?1 for the Tevatron with s = 1.96T eV , then

0 the yearly production number of the tπt event is smaller than 8 in all of the parameter

space. Thus, it is very di?cult to detect the possible signals of the neutral top-pion 6

2.0

4.0

= 0.02
3.5

1.8

= 0.02 = 0.05 = 0.08

= 0.05 = 0.08

1.6

3.0

1.4

pb)
(s) (
250 300 350 400 450 500

fb)

2.5

1.2

(s) (

1.0

2.0

0.8

1.5
0.6

1.0
0.4

0.5

0.2

0.0 200

0.0 200 250 300 350 400 450 500

m
t

(GeV) (a)

m
t

(GeV) (b)

0 Figure 3: The cross section σ(s) of tπt production as function of mπt for three values of the parameter

ε at the Tevatron with

√ √ s = 1.96T eV (a) and the LHC with s = 14T eV (b).

0 0 πt via the process p? → tπt + X at the Tevatron experiments. However, there will be p √ 0 1.7 × 103 ? 1.8 × 105 tπt events to be generated per year at the LHC with s = 14T eV

and ?int = 100f b?1 .
0 ? ? c The possible decay modes of the neutral top-pion πt are tt, tc(t?), b? gg, γγ, τ τ , b, 0 ? c and ??. For mt < mπt ≤ 2mt , πt mainly decays to tc or t?. It has been shown that 0 ? the value of the branching ratio Br(πt → tc + t?) is larger than 90% for mπt = 250GeV c

0 and ε ≥ 0.02[12]. Thus, for mt < mπt ≤ 2mt , the associated production of πt with

single top quark can easily transfer to the same sign top pair event tt? at LHC. The c ?nal state of the same sign top pair is free from huge QCD background W+jets and ? also free from tt background[13], which can generate characteristic signatures at the LHC experiments. Thus, the same sign top pair can be used to prob new physics beyond the SM[14,15,16,17]. So, we further calculate the production cross section of the same sign top pair ?nal state at LHC. Our numerical results are shown in Fig.4, in which we have assumed mt < mπt ≤ 2mt and taken ε = 0.02, 0.05 and 0.08. From this ?gure, we can see that there will be several and up to ten thousands tt? events to be generated per year c at the LHC with ?int = 100f b?1. The signal of the same sign top pair event is same sign dileptons, two b-jets, one charm

7

1.8

1.6

= 0.02 = 0.05

1.4

= 0.08

pb)
(s) (

1.2

1.0

0.8

0.6

0.4

0.2

0.0 200 220 240 260 280 300 320 340

m
t

(GeV)

Figure 4: The production cross section σ(s) of the same sign top pair tt? as a function c √ of mπt for three values of the parameter ε at the LHC with s = 14T eV .

quark jet plus missing energy, i.e., llbbj+ E. The main background for this signal comes ? from the process pp → W ± tt → llbbj1 j2 + E with either j1 or j2 missing detection. It has been shown[13,14,15,16] that this background can be signi?cantly suppressed by applying appropriate cuts and so that the tt? event should be observed at the LHC experiments, c as long as its cross section is larger than several tens f b. Thus, in most of the parameter
0 space of TC2 models, the possible signals of the neutral top-pion πt with mt < mπt ≤ 2mt 0 can be detected via the process p? → tπt + X → tt? + X at the LHC experiments. p c

? ??
? ?

??
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? ?

??
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?? ·
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? ?

0 Figure 5: Feynman diagrams for the process qb → q ′ tπt .

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0 In all appearance, the ?nal state which is same as that of tπt can be reached by single 0 0 top production followed by πt bremsstrahlung i.e. the process qb → q ′ tπt , as shown in

Fig.5. However, due to the unitary constraint, there exists severe cancellation between Fig.5(a) and Fig.5(b) and so that its production cross section is highly suppressed, which
0 is much smaller than that of the subprocess cg → tπt [14,16,18]. Thus, this process can

0 not be taken as an e?ective process to detect the neutral top-pion πt at LHC.

0 ? For mπt > 2mt , the neutral top-pion πt mainly decays to tt and the associated pro0 ? duction of πt with single top quark can also produce the same sign top event ttt at LHC.

However, the signal of this kind of event is too di?cult to extract because of much large
0 background. Thus, if the neutral top-pion πt is indeed much heavy, we should consider

other processes to detect this type of new particles in the future high energy experiments.
± IV. Associated production of the charged top-pions πt with single top quark

? ?
? ? ?

?
? ?

?

? ?

? Figure 6: The Feynman diagrams for the process gb → tπt .

For TC2 models, the underlying interactions, topcolor interactions, are assumed to be chiral critically strong at the scale about 1TeV and coupled preferentially to the third
0,± generation. Thus, top-pions πt have large Yukawa couplings to the third family quarks. ± ± The charged top-pions πt should be abundantly produced via the subprocess gb → tπt

at LHC. The relevant Feynman diagrams are shown in Fig.6. Our numerical results are shown in Fig.7, in which we plot the production cross section √ ? σ(s) for the process p? → tπt + X at the Tevatron with s = 1.96T eV [Fig.7(a)] and the p √ LHC with s = 14T eV [Fig.7(b)] as a function of the top-pion mass mπt for three values of the free parameter ε. One can see from these ?gures that the cross section σ(s) is not sensitive to the free parameter ε and its value at LHC is much large, which is in the range 9

40

25

= 0.02 = 0.05 = 0.08
20

= 0.02 = 0.05 = 0.08

(s) (

pb)
20

fb)

(s) (

15

10

5

0 200 250 300 350 400 450 500

0 200 250 300 350 400 450 500

m
t

(GeV) (a)

m
t

(GeV) (b)

? Figure 7: The cross section σ(s) for tπt production as function of mπt for three values of the parameter

ε at the Tevatron with

√ √ s = 1.96T eV [Fig.7(a)] and the LHC with s = 14T eV [Fig.7(b)].

of 5.24 × 102 f b ? 2.5 × 104 f b for 0.02 ≤ ε ≤ 0.08 and 200GeV ≤ mπt ≤ 500GeV . The LHC has a good potential for discovery of a charged Higgs boson[19]. Thus, the associated production of the charged Higgs bosons predicted by the MSSM with single top quark has been extensively investigated in Refs.[20,21,22]. They have shown that, considering the complete NLO QCD corrections, the production cross section for the process p? → tH ± + X is smaller than 1pb in most of the parameter space of MSSM. p Compared with our numerical results, it is smaller than that for the charged top-pions
± ± πt . This is because the coupling strength of H ± tb is smaller than that of πt tb.

It has been shown that the heavy Higgs bosons H ± can be detected via the decay
± channels H ± → τ ντ , tb or W ± h0 at LHC[20,21]. For the charged top-pions πt , the

dominant decay mode is into tb channel and its branching ratio is larger than 95% in most of the parameter space of TC2 models. It is very di?cult to detect the possible
± ± ± signals of πt via the decay channel πt → τ ντ . Thus, the possible signals of πt can only ± be studied via the process pp → gb → tπt in the tb decay channel. According the analysis

results of Ref.[20,21], the 3 b-tags is better for detecting the signals of this process than
? ? the 4 b-tags. For 3 b-tags, the background of the subprocess gb → tπt → ttb comes from

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the NLO QCD processes: ?b gg → ttb? ? gb → ttb ? gg → ttg

? After the suitable cuts and the reconstruction of the πt mass, the value of the sig-

nal/background ratio is large than 5 in most parameter space of TC2 models. Thus, the
± charged top-pions πt should be observed in the near future LHC experiments.

V. Discussions and conclusions The SM predicts the existence of a neutral Higgs boson, while many popular models beyond the SM predict the existence of the neutral or charged scalar particles. These new particles might produce the observable signatures in the current or future high energy experiments, which is di?erent from that for the SM Higgs boson. Any visible signal from the new scalar particles will be evidence of new physics beyond the SM. Thus, studying the new scalar particle production at LHC is very interesting. Topcolor scenario is one of the important candidates for the mechanism of EWSB. A
0,± key feature of this kind of models is that they predict the existence of the top-pions πt 0,± in low-energy spectrum. In this paper, we study the associated production of πt with √ √ single top quark at the Tevatron with s = 1.96T eV and the LHC with s = 14T eV .

It is well known that the ?avor changing neutral current (FCNC) e?ects can be used to
0 look for the new physics beyond the SM. The neutral top-pion πt has large FC coupling to

top and charm quarks at tree-level. Thus, we ?rst calculate the production cross section
0 0 of the process p? → tπt + X at hadron colliders. We ?nd that the neutral top-pion πt can p √ 0 ? be signi?cant generated at the LHC with s = 14T eV . Due to πt mainly decay to tc or

t?, this process can produce a large number of the same sign top pair tt? events. While c c the production rates of this kind of events in the SM and the MSSM are far below the
0 observable level. Thus, we can use the process p? → tπt + X → tt? + X to look for the p c

0 neutral top-pion πt at LHC.

For a heavy charged scalar, the dominant production process at LHC is its associated production with a top quark via gluon bottom quark fusion. The LHC has good potential for discovering a heavy charged scalar through this process. In the context of the TC2 11

± models, we calculate the production cross sections of the process p? → tπt + X at hadron p

colliders. Our numerical results show that the production rates are larger than those for the charged Higgs bosons H ± from the MSSM. We can detect the possible signals of the
± ± charged top-pions πt at the near future LHC through the process p? → tπt + X in their p

tb decay channel. All of our numerical results are obtained with the scale chosen ? = 2mt for the CTEQ6L parton distribution function integration. Certainly, the numerical results would vary with the chosen value of the factorization scale varying. For example, if we chose
0 the scale ? = mt /2, then tπt production cross section at LHC is in the range of 8.4f b ?

1.8 × 103 f b for 0.02 ≤ ε ≤ 0.08 and 200GeV ≤ mπt ≤ 500GeV . Comparing with that for the scale chosen ? = 2mt , its value is decreased by 10% ? 50%, which is dependent on the value of the top-pion mass mπt . However, even in this case, there will be 8.4 × √ 0 102 ? 1.8 × 105 tπt events to be generated per year at the LHC with s = 14T eV and ?int = 100f b?1 , which might be detected in the near future LHC exprements. TC2 models also predict the neutral CP-even scalar, called the top-Higgs boson h0 , t ? which is a tt bound and analogous to the σ particle in low energy QCD. Similar to the
0 neutral top-pion πt , it also has large coupling to the top- and charm- quark at tree-level

and can give rise to the anomalous top quark coupling tcg. Thus, it can be abundant produced via the process p? → th0 + X at LHC. Our explicit calculation shows that the p t

signal of the top-Higgs h0 can also be detected through this process in the near future t LHC experiments. Acknowledgments This work was supported in part by Program for New Century Excellent Talents in University(NCET-04-0209), the National Natural Science Foundation of China under the Grants No.10475037.

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