Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://nuclphys.sinp.msu.ru/conf/lpp14/210809/Laperashvili.pdf Äàòà èçìåíåíèÿ: Wed Sep 16 16:30:21 2009 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 00:46:45 2012 Êîäèðîâêà: IBM-866

New Bound States of Heavy Quarks at LHC and Tevatron
C.D. Froggatt
Department of Physics and Astronomy, Glasgow University, Glasgow, Scotland

L.V. Lap erashvili
The Institute of Theoretical and Experimental Physics, Moscow, Russia

H.B. Nielsen
Niels Bohr Institute, Copenhagen, Denmark

14th Lomonosov Conference on Elementary Particle Physics, Moscow, 19 - 25 August, 2009

Sp eaker - Larisa Lap erashvili


The talk is based on the following papers: ï 1. The Production of 6t + 6t bound state at colliders.

C.D. Froggatt, L.V. Laperashvili, R.B.Nevzorov, H.B. Nielsen.
A talk given by Holger Bech Nielsen at CERN, 2008; preprint CERN-PH-TH/2008-051. 2. New Bound States of Heavy Quarks at LHC and Tevatron.

C.D. Froggatt, L.V. Laperashvili, H.B. Nielsen, C.R. Das,
to be published in Int.J.Mod.Phys.A 24,(2009); arXiv:0812.0828 [hepph]. 3. Trying to understand the Standard Model parameters.

Froggatt C.D. and Nielsen H.B.
Invited talk by H.B. Nielsen at the "XXXI ITEP Winter School of Physics", (February 18í26, 2003, Moscow, Russia), published in: Surveys High Energy Phys. 18, 55-75 (2003); ArXiv: hep-ph/0308144. 4. Remarkable coincidence for top Yukawa coupling, approximately massless bound states.

Froggatt C.D. and Nielsen H.B.,
to be published in Nucl.Phys.B (2009); arXiv: 0811.2089[hep-ph].

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5. Hierarchy-problem and a bound state of 6 t and 6 anti-t.

C.D. Froggatt, H.B. Nielsen, L.V. Laperashvili,
in: Proceedings of Coral Gables Conference on Launching of Belle Epoque in High-Energy Physics and Cosmology (CG 2003), Ft. Lauderdale, Florida, 17-21 Dec 2003. Published in: Int.J.Mod.Phys.A 20, 1268 (2005); ArXiv: hep-ph/0406110. 6. The Fundamental-weak scale hierarchy in the Standard Model.

C.D. Froggatt, L.V. Laperashvili, H.B. Nielsen,
Phys.Atom.Nucl. 69, 67 (2006) [Yad.Fiz. 69, 3 (2006)]; ArXiv: hep-ph/0407102. 7. A New bound state 6t + 6 anti-t and the fundamental-weak scale hierarchy in the Standard Model. C.D. Froggatt, L.V. Laperashvili, H.B. Nielsen, in: Proceedings of 13th International Seminar on High-Energy Physics: QUARKS-2004, Pushkinskie Gory, Russia, 24-30 May 2004; ArXiv: hep-ph/0410243.

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Contents:
1. Intro duction. 2. Higgs and gluon interactions of quarks. 3. T-balls' mass estimate. 4. Can we see T-balls at LHC or Tevatron? 5. CDF I I Detector exp eriment searching for heavy top-like quarks at the Tevatron. 6. Conclusions.

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1

Intro duction.

Although the Standard Model (SM) was confirmed by all experiments of the world accelerators, the mechanism of the Electroweak (EW) symmetry breaking (EWSB) has not yet been tested. According to the SM, the Higgs boson is responsible for generating the masses of the SM fermions due to the Higgs mechanism. However, the mass of the Higgs b oson is not predicted by theory. Direct searches in the previous experiments (mainly at LEP2) give a lowest limit for the Higgs boson mass MH: MH 114.4 GeV at 95% CL.

The recent Tevatron result is: 115 MH 160 GeV.

We hope that LHC will provide a solution of main puzzles of EWSB.

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The Higgs boson couples more strongly to the heavy top quarks than to the light ones. As a result, the Higgs exchanges between top quarks produce a whole spectroscopy of new bound states. The present talk is devoted to the following predictions: § There exists a scalar 1Síbound state of 6t + 6ï. t The forces which bind these top-quarks are so strong that almost completely compensate the mass of the 12 top-quarks forming this bound state. § There exists a new bound state 6t + 5ï, which is a fermion t similar to the quark of the fourth generation having quantum numbers of top quark. A new (earlier unknown) bound state 6t + 6ï, which is a color t singlet (that is, 'white' state), was first suggested by Froggatt and Nielsen in Ref. [3]. Now all these NBS are named T-balls, or T-fireballs.

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Fig. 1:

2

Higgs and gluon interactions of quarks.

If the Higgs particle exists, then between quarks qq, quarks and anti-quarks qq, and also between anti-quarks qq there exist virtual ï ïï exchanges by Higgs bosons (see Fig. 1). In all these three cases we have attractive forces.

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Fig. 2:

It is well-known that the bound state tï í so called top onium t í is obliged to the gluon virtual exchanges (see Fig. 2).

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In the case of the toponium the contributions of the Higgs scalar particles are essential, but less than gluon interactions. Toponium is very unstable due to the decay of the top quark itself. However, putting more and more top and anti-top quarks together in the lowest energy bound states, we notice that the attractive Higgs forces continue to increase. Simultaneously gluon (attractive and repulsive) forces first begin to compensate themselves, but then begin to decrease relatively to the Higgs effect, when we increase a number of top-anti-top constituents in the NBS.

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The maximum of the binding energy value corresponds to the 1S-wave state of the NBS 6t + 6ï . t The explanation is simple: top-quark has two spin states and three states of colors: 2 ½ 3 = 6 degrees of freedom. This means that, according to the Pauli principle, only 6 pairs of tï can simultaneously exist in the 'white' 1S-wave state. t ï If we try to add more tt-pairs , then some of them will turn out to the 2S-wave, and the NBS binding energy will decrease at least 4 times. For P-,D-, etc. wave states the NBS binding energy decreases more and more.

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3

T-ball mass estimate.

The kinetic energy term of the Higgs field and the top-quark Yukawa interaction are given by the following Lagrangian density: 1 gt L = D²HD²H + tLtRH + h.c., 2 2 (1)

where H and t are the Higgs and top-quark fields, respectively, and gt is the Yukawa coupling constant of their interaction. The VEV of the Higgs field in the EW-vacuum is: v =< |H| >= 246 GeV. According to the Salam-Weinberg theory the top-quark mass M and the Higgs mass MH are given by the following relations: gt Mt = v and M2 = v2, H 2 where is the Higgs selfinteraction coupling constant.
t

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According to the Particle Data Group, we have Mt 172.6 GeV, gt 0.93. Let us imagine now that the NBS is a bubble in the EW-vacuum and contains Nconst. top-like constituents. Insight this bubble (bag) we have the following VEV of the Higgs field: v0 =< |h| >, which is smaller than EW VEV value v: v0 < 1. v Then the effective masses insight the bubble are smaller than the corresponding experimental masses: v0 mt,h = Mt,H. v

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In this case the attraction between the two top (or anti-top) quarks is presented by the following potential:
2 gt /2 V(r) = - exp(-mhr). 4 r Assuming that the radius R0 of the bubble is small:

(2)

mhR0 << 1, we obtain the Coulomb-like potential:
2 gt /2 V ( r) - . (3) 4 r The attraction between any pairs tt, tï, ïï is described by the t tt same potential (3).

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Now we can estimate the binding energy of a single top-quark relatively to the nucleus having Z = Nconst. - 1. The total potential energy for the NBS with Nconst. = 12 is: V
tot 2 gt /2 (r) = -11 . 4 r

(4)

Considering a set of Feynman diagramms (the Bethe-Salpeter equation) and including the contributions of all (s-,t- and u-) channels for the Higgs and gluon exchange forces (see Ref. [4]), we obtain the following Taylor expansion: M2 = (N T
const. .

Mt)2½
2 12 2 gt + 6 gs 2

Nconst 1 - 2(Nconst. - 1) 12

+ .... .

Here the QCD coupling constant gs is given by its fine structure constant value at the EW-scale (Particle Data group):
2 s(MZ) = gs (MZ)/4 0.118.

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Now the value of the total binding energy for arbitrary N is equal to: ET = N
const.

const.

(N

const.

Nconst - 1) 12

.

2

12 2 gt + 6 gs

2

mt .

The mass of T-ball containing Nconst. top or anti-top quarks is: MT = Nconst.mt - ET. Approximately this dependence is described by the following expression: MT = Nconst.mt Nconst 1 - (Nconst. - 1) 12
. 2 12 2 gt + 6 gs 2

.

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Below we shall use the following notations: Ts-ball is a scalar NBS: 6t + 6ï t, having the spin S = 0, and Tf -ball presents the NBS: 6t + 5ï t, which is a fermion: Tf = 5t + 6ï, t Let us consider now the condition: 11 12 2 § (gt + gs )2 = 1. 2 6

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In this case the binding energy ET compensates the mass 12mt in the NBS so strongly that the mass of the scalar Ts-ball becomes zero: MTs = 11m
t

1-

11 12 2 § (gt + gs ) 2 6

2

= 0.

It is necessary to emphasize that the experimentally given values:
2 gt 2 0.86 and gs

1.48

are just very close to this limit. Fig. 3 shows the dependence of T-ball masses on the number of NBS constituents Nconst.. In the case when MTs = 0, we have: MT = Nconst.m
t

(Nconst. - 1) N2 const 1- 11 122

.

(5)

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2500 Bound state masses Mass-energy relation 2000

Mass in GeV

1500

1000

500

0 0 2 4 6 8 Number of third family (t and t)
-

10

12

14

Fig. 3: The dependence of T-ball masses on the number Nconst. of the NBS constituents.

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We easily see that the light scalar Higgs boson with mass mh < MH can bind the 12 top-like quarks so strongly that the mass MTs becomes almost zero, and even tachyonic: M2 s < 0. T In the last case we obtain the Bose-Einstein condensate of T-balls í a new vacuum at the EW-scale. This is very important for the solution of the hierarchy problem. We hope that the forthcoming numerical calculations of the masses of T-balls, using Monte-Carlo simulations on lattice, will give us a more exact answer.

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3.1

Tf -ball mass estimate

One of the main ideas of the present investigation is the Higgs interaction of the 11 top-anti-top quarks ball í a new fermionic bound state 6t + 5ï, which is t t -quark of the fourth generation. The estimate of the mass of Tf -ball 6t + 5ï by Eq. t M
Tf

to show that creates a Tf similar to the (5) gives : (6)

11mt § 0.236

300 GeV.

At present, a lot of physicists, theorists and experimentalists, are looking forward to the New Physics. However, it is quite possible that LHC will discover only the Salam-Weinberg Higgs boson and nothing more. Nevertheless, the T-balls considered in the framework of the SM could exist.

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4

Can we observe T-balls at LHC or Tevatron?

If our NBS are strongly bound and have very small radius, then they can be observed at colliders (Tevatron, LHC, etc.) in the following processes: 1) First of all, in the possible H-decay process: H 2Ts, if MTs < 1 MH. 2 Using limits given by Tevatron experiments 115 MH 160 GeV,

we obtain the requirement for the Higgs decay mechanism: MT
s

80 GeV.

Here we have argued that T-balls can explain why it is difficult to observe the Higgs boson H at colliders: T-balls can strongly enlarge the decay width of the Higgs particle.

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2) If MTs > 1 MH, then the first decay is absent in Nature, 2 and the Ts-balls fly away, forming jets, producing hadrons with a high multiplicity: Ts JETS. 3) Second, we can observe at Tevatron all processes given by Fig. 4 with the replacement tï t ï , Tf Tf . t t In the most optimistic cases the NBS 6t + 5ï (fermionic fireball) t plays a role of the fundamental quark of the fourth generation, say, with the mass MTf 300 GeV, given by our preliminary estimate. We exp ect that the Tevatron-LHC exp eriments should find either a fourth family t'-quark, or the fermionic NBS Tf , or b oth of them.

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Fig. 4: A typical process observed at the Tevatron in pp collisions. ï

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Fig. 5: Two gluon production of Ts -balls

The scalar NBS Ts cannot be produced simply in a pair by a gluon vertex, because it is a color singlet 1. But a pair Tf Tf can be produced by a gluon, because it is a color triplet 3. At LHC the pairs of Ts-balls or Tf -balls might be produced in pp collisions via the two gluon diagram with strong vertices (see Fig. 5).

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5

CDF I I Detector exp eriment at the Tevatron.

Recent experiments with CDF II Detector of the Tevatron search ing for heavy top-like quarks in pp-collisions with s ï 1.96 TeV: CDF Collaboration (T. Aaltonen et al.). FERMILAB-PUB-08017-E, Jan 2008. Phys.Rev.Lett. 100, 161803 (2008); arXiv: 0801.3877 [hep-ex]. CDF Collaboration (A. Lister et al.). Search for Heavy Top-like Quarks t W q Using Lepton Plus Jets Events in 1.96 TeV p - p Col lisions. FERMILAB-CONF-08-473-E, Oct 2008. Preï sented at 34th International Conference on High Energy Physics (ICHEP 2008), Philadelphia, Pennsylvania, 30 Jul - 5 Aug 2008; arXiv: 0810.3349 [hep-ex]. do not exclude the existence of T-balls with masses up to 500 GeV. 300 GeV,

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Here we can assume that the very strange events, observed at the Tevatron as a fourth family t , which decays into a W-boson and a presumed quark-jet, might in our model find another explanation: maybe it is a decay of T-balls into a W-boson and a gluon jet. Tevatron experiments exclude a fourth-generation t' quark with a mass below 300 GeV. Assuming that a fourth family t -quarks does not exist in Nature, but only the pairs of fermionic NBS Tf are produced at the Tevatron, we can give an explanation of the observed cross-section shown in Fig. 6. The curve for the cross-section t (p p t ï ) ï 0.1 pb

can correspond to the production of pairs of fermionic Tf -balls with mass MTf 300 GeV.

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CDF Run 2 (2.8 fb-1) Preliminary t'Wq, 4 jets HT vs Mreco

range of expected 95% CL upper limits theoretical prediction Bonciani et al.

observed

200

300

400

500

Fig. 6: Tevatron CDF-experiment: upper limit, at 95% CL, a fourth-generation t' quark with a mass below 300 GeV is excluded. Blue line presents a theoretical curve for the fourth-generation quarks cross-section.

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6

Conclusions 1. The present investigation is based on the following three assumptions: 1) there exists 1Síbound state of 6t + 6ï; 2) the t forces which bind these top-quarks are so strong that they almost completely compensate the mass of the 12 top-quarks forming this bound state; 3) such strong forces are produced by the interactions of top-quarks via the virtual exchange of the scalar Higgs bosons, when the top-quark Yukawa coupling constant is large: gt 1 . 2. Present theory also predicts the existence of the new bound state 6t + 5ï, which is a color triplet and a fermion similar to t the quark of the fourth generation. 3. We have estimated that the mass of the tachyonic: M2 s < T balls and formation masses of the lightest NBS and showed scalar T-balls MTs can be zero, and even 0, what leads to the condensation of Tof a new vacuum at the EW-scale.

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4. We have estimated masses of the fermionic T-balls predicted MTf 300 GeV. 5. It was shown that CDF II Detector experiments searching for heavy top-like quarks at the Tevatron in pp-collisions with ï s 1.96 GeV can observe Tf -balls up to 500 GeV. 6. We have considered all processes with T-balls, which can be observed at LHC, especially the decay H 2Ts and the production of Tf Tf together with t t , where t is a quark of the fourth generation. 7. We have argued that T-balls can explain why it is difficult to observe the Higgs boson H at colliders: T-balls can strongly enlarge the decay width of the Higgs particle.

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