###### Abstract

We consider the implications of an extended color group, , spontaneously broken to at a TeV or lower scale, for the hadronic colliders. The associated massive color octet gauge bosons (the colorons) can enhance the pair production at the Tevatron collider. At the LHC, the colorons can be pair produced, each decaying to a pair. This gives rise to anomalous multi W production: a clear signature of physics beyond the Standard Model. We calculate the associated multijet and multilepton final states at the Tevatron and the LHC energies, and compare these with the expectations from the Standard Model.

OSU-292

DOE-ER 40757-059

CPP-94-36-059

TOP QUARK SIGNATURE IN

EXTENDED COLOR THEORIES

D.A.Dicus, B.Dutta and S.Nandi

Center for Particle Physics

The University of Texas at Austin

Austin, Texas 78712

Department of Physics

Oklahoma State University

Stillwater, OK 74078

## 1 Introduction

The CDF collaboration at the Fermilab Tevatron has reported [1] the observation of two charged dilepton and ten single lepton+ jet events which are in excess of those expected in the Standard model (SM) excluding production. A detailed analysis of seven of these events (which have at least one b-tag and a 4 jet) yields the central value for top quark mass of 174 GeV and cross section of 13.9 pb at the Tevatron energy ( . This cross section is about three times larger than expected in the Standard Model [2] although the error [1] is large. It is entirely possible that with larger statistics, the values of the mass and the cross section will change to be in agreement with the SM. However, it is also possible that we are seeing the first glimpse of new physics beyond the SM at this TeV scale which is being explored directly for the first time. Several ideas have been proposed for new physics. One is to assume that the color group at high energy is bigger, namely SUSU [3]. The color I is coupled to the first two families of fermions while the color II is coupled to the third family. This group breaks spontaneously to the usual SU at a TeV scale or below giving rise to eight massive color octet gauge bosons, called colorons. Due to mixing, these colorons couple to both the ordinary light quarks and to . These colorons are then produced from the ordinary light as resonances which then decay to , thus enhancing the production. The second idea assumes the multiscale models of walking technicolor[4]. The color octet technipion, is produced as a resonance in the gluon gluon channel and decay dominantly to , thus increasing the production to the level observed by CDF. In the third scenario, a singlet vector like, charge quark is assumed with a mass comparable to the top quark [5]. This singlet quark mixes with the top. Their production and the subsequent decay then effectively double the standard top signals [5]. Another idea proposed is that the top quark may have anomalous chromomagnetic moment type tree level coupling with the gluons [6]. A small value of the chromomagnetic moment, can produce a cross section of the level observed by the CDF Collaboration[6].

In this work, we discuss the hadronic collider implications of the first idea above, an extended color model, , where the first two families of quarks couple to the whereas the third family couples to , as proposed in reference (3) .We calculate the multijet and / or multilepton final state cross sections arising from production and the subsequent decay of the coloron at the Fermilab Tevatron and Large Hadron Collider(LHC) energies, and compare those with the expectations from the Standrad Model. Hill and Parke have studied the coloron procuction at the Fermilab Tevatron energy. At the Tevatron, the coloron is singly produced by annihilation. There is no contribution from gluon-gluon fusion, since there is no gluon-gluon-coloron coupling in this model. Hill and Parke showed that for the extended color symmerty breaking scale at a TeV or less, the resonant enhancement of the coloron production and their subsequent decay to is enough to produce the large cross section observed by the CDF collaboration. They also study the W and top quark distributions and the mass distributions and note that the larger in this model can be used to distinguish it from the Standard Model. In this work we go further by looking at the decay products of the W’s and making some simple visiblity cuts to test the extent to which the distributions as they would be observed, are really different. However, the main part of our work is to study the implications of the model at the LHC energy (. Here, the colorons can be pair produced via gluon-gluon fusion. Each coloron decays to a or pair. If we look at the tops, we get two top quarks and two top antiquarks whose decays give rise to four W bosons in the final state. The cross sections for these four W final states are much larger than those in the Standard model. This anomalous W productions will be very clean signal for physics beyond the Standard Model at high energy hadronic colliders such as LHC. We also calculate the branching ratios for the various mutijet and/or multilepton final state arising from the subsequent decays of these final state W’s.

We present our work as follows. In Sec.II, we give the formalism for the extended color model and write down the relevent interactions. In Sec.III, we discuss our results for the Fermilab Tevatron. Sec.IV contains the main part of our work. In part A, we calculate the differential and total cross sections for coloron + coloron+ anything at various center of mass energies. In part B, we discuss the topology of the events and calculate the branching ratios of the multijet and/or multilepton final states by applying appropriate cuts. Here we discuss our results and point out the inportant channels for clear signals beyond the Standard Model. SectionV contains our conclusions.

## 2 Formalism for the Color Model

The gauge part of the of the extended color model is

(1) |

where

and similarly for with replaced by . and are the two color gauge coupling constants. The symmetry is broken spontaneously to the usual at some scale M at or below a TeV. This is achieved by using a Higgs field, which fransform like (1,3, under ( with VEV=diag.(M,M,M). At low energy, we are left with eight massless gluons (A) and eight massive colorons (B defined as

(2) |

where is the mixing angle, and

(3) |

The mass of the coloron is

(4) |

In terms of the gluon (A) and the coloron field (B), we can write the gauge part of the interaction schematically as

(5) |

In Eq.(5), A and represent schematically the usual three and four point gauge interactions, namaly,

and

(6) |

We see from Eq.(5) that a single coloron does not couple to two or three gluons. Thus, a single coloron or a coloron in association with a gluon can not be produced in hadronic colliders from gluon-gluon fusion.

The fermion representations under ( are

(7) |

Note that the first two families of quarks couple to the color I while the third family of quarks couples to color II. This assignment is anomaly free. With the above assignment, the intersctions of all the quark with the gluons are same as in the usual QCD. The interactions of the colorons are given by

(8) |

where the sum i is over u, d, s and c quarks.

(9) |

so that zz

## 3 Results for Fermilab Tevatron

In this section, we discuss production and the resulting multijet and/or multilepton final states at the collider at the Fermilab Tevatron, TeV. The dominant subprocess is the annihilation of ordinary pair to produce via coloron exchange in the s-channel, in addition to the usual standard model processes. (The contribution of gg subprocess producing two colorons is either kinematically not allowed or negligible). The total cross sections depends on the coloron mass as well as the coloron width. We use Eq. (8) for our calculations, and following Hill and Parke, present our results for the coloron model, zz (Eq. 9), as well as for another model which is like the coloron model except the value of zz. [The value of zz can be obtained in a color singlet vector resonance model with an extra U(1) [7]]. For parton distributions, we use those produced by the CTEQ collaboration[8].

Hill and Parke note that in their models the top quark and the W boson have larger than in the Standard Model and that this could be used to distinguish these models from the standard model with only a relatively small number of top events. Here we go slightly further by looking at the decay products of the Ws and making some simple visibility cuts.

In particular we keep the matrix element for top decay into bl or so as to include the coherent polarization sum of the Ws. We then combine the quarks into jets by requiring that final state quarks be in the same jet if their angular seperation is less than with the standard definition of . We next require that jets and the charged leptons from the Ws be visible by requiring that their be larger than some and that their rapidity be less than some . We also require that these leptons be seperated from the jets, and from each other, if there is more than one, by

Using these criteria, we find the branching ratios for n jets and m charged leptons where n=0,1,2,3,4,5,6 and m=0,1,2. We do this for the standard model and for the following four models of Hill and Parke: (a) zz M M zzM M zz M M and (d) zz M M

As can be seen from Fig.1, these four models each have a total cross section near 14 pb. Table I gives the branching ratios if yis and is 35 GeV. Clearly there is very little difference between these models and the standard model (which is the top number in each set of five) so far as BR’s are concerned. Table II gives the same cases for GeV. Here the new models do show some behavior (except for model (a)) but the branching ratios for the interesting topologies, four jets and one lepton for example, are quite small. If the detector efficiency is 10% and we have 1000 pb of integrated luminosity then the standard model gives 2.4 events of 4 jet, 1 lepton type, while the new models give 4.2 to 23 events. Of course a large part of the extra events in the new models is still just the larger cross section- 14 pb vs 5 pb for the standard model.

We have also investigated other values of M and and found similar results. For the additional p inherent in these models is of only modest help in increasing the branching ratios of the interesting topologies. For the additional p is a big help but the branching ratios themselves are quite small.

We note that when we talk about charged leptons we mean electrons or muons. We include the tau lepton by assuming it decays immmediately after production into a muon or electron plus neutrinos (35.5% of the time) or into a quark pair plus a neutrino (64.5% of the time). Thus the visible final states of a W decay through a tau have the same particle content as other W decays: an electron, a muon, or a pair of quarks. The possible energies of the visible particles are, of course, different if the decay is through a tau, and that has been included.

## 4 Coloron Signal at Lhc Energy

In this section, we discuss the coloron pair productions in hadronic collisions in the spontaneously broken extended color model. We consider only the case where each coloron decays to top quarks, . Decays of these t(or ) to a W give rise to four W bosons in the final state. The cross section for these four W productions is much larger than that expected in the Standard model. This anomalous W productions will be a very clean signal for physics beyond the Standard Model. In section IVA, we calculate the differential and total cross sections for the coloron pair production. In IVB, we discuss the multijet and/or multilepton cross sections resulting from the decays of the four tops produced from the coloron pairs.

###
4.1 Cross Sections for Coloron Pair

Productions

The dominant contribution to the coloron pair production at the LHC enengy comes from the subprocess

(10) |

The corresponding Feyman diagrams obtained from (5) are shown in Fig. 2. The contribution of the other subprocess (Eq. 8) is very small at the LHC energy because of the low q luminosity.

The differential cross section for the subprocess (10) is obtained to be

(11) |

where

(12) |

Here, is the total center of mass (CM) energy squared for the subprocess, z is the cosine of the CM angle, M is the mass of the coloron, B, is the QCD coupling constant squared over 4, and

(13) |

From Eq. (11), we obtain the total subprocess cross section to be

(14) |

The total cross section for the process

(15) |

is obtained by folding in the gluon distributions with the above cross section. We have used the distribution produced by the CTEQ collaboration [8] evaluated at .

###
4.2 Multijet-Multilepton Final States

From Coloron
Pair Decays

Using the production cross section above, and assuming the branching ratio for each final states of W decay to be , we find the branching ratio for n jets and m charged leptons where n = 0, and m = 0,. These results depend on the mass of the coloron, the visibility cuts, and the mixing with light quarks (z and z in (8) above). To isolate the combinations which can not be produced in lowest order of the SM we consider only the final state.

As in the Fermilab results above, we combine the quarks into jets using the condition that a quark belongs in an adjacent jet if the angular seperation between them is less than which we take to be 0.5. Once the jets are formed, we requires that their transverse momentum be larger than 30 GeV and their rapidity be less 2. For the leptons (electron or muon) we require a tranverse momentum of 20 GeV and a maximum rapidity of 2.5. The leptons must be seperated from the jets, and from each other by which is also taken to be 0.5. Thus, for example, if two leptons each satisfy the transverse momentum and rapidity cuts but have less than 0.5 then they are counted as only one lepton.

If the final state of a W decay is a tau lepton, then we assume the tau has decayed and use its decay products in forming jets and applying the visibility cuts. In other words in case of a tau, we go one level further in the decay chain to find the particles we treat as the final state.

We keep a coherent sum over the polarizations of the Ws from the top decays but not for the Ws in the tau decays. We do not keep a coherent spin sum for the tops.

Our results are given in Tables 3-5 for a coloron mass of 400, 600, and 800 GeV. We give results only for the branching ratios for events with more jets or leptons than can be straight -forwardlẏ produced in the SM, or by other final states of the colorons, for example. To include mixing with the lighter quarks each branching ratio should be miltiplied by

where I is given by

These branching ratios are rather small; fortunately the production cross sections are large so the actual number of events with these topologies can be large.

## 5 Conclusion

At Fermilab energies we have calculated the branching ratios for the various final states possible from a pair produced through resonant coloron. This is quite model dependent; however, the motivation for these model is that they can give a larger cross section than the SM. Thus we choose sets of parameters which give a production cross section of about three times the SM cross section. Our results are shown in Table 1 and 2. We see that the branching ratios for the interesting final states are not very different from those of the standard model unless we take a large value for the minimum p. This seems to be in agreement with Ref. 3. We have chosen to require a large transverse momentum for the jets and leptons because it was hoped that these models would be distinguished by larger branching ratios for large transverse momentum.

The only check we have on the accuracy of the numbers in any of the tables is to rerun the Monte Carlo integral which generates the histograms with different sets of random numbers. When we do this the branching ratios, even those whose values are very small, remain very stable; nevertheless we feel the very small numbers should not be trusted.

At LHC energies we have calculated the branching ratios for the various final states of coloron-coloron production. These are given in Tables 3, 4 and 5. Here we have many final states that are only possible in higher order in the SM; if n is the number of jets and m is the number of electron or muons these final states are if if if . Even when the branching ratios for these states are rather small, this is compensated by a large production cross section if the coloron mass is not too large. Detection of these states would be a very strong signal for the coloron.

## 6 Acknowledgements

This work was supported in part by the U.S. Department of Energy Grants DE-F603-93ER 40757 and DE-FGO2-94ER 40852.

## References

- [1] F. Abe et. al, Phys. Rev. Lett. 73, 225(1994); ibid, Phys. Rev. D 50, 2966 (1994).
- [2] E. Laenen, J. Smith, and W.L.Van Neerven, Phys. Lett. B321, 254(1994).
- [3] C.T. Hill, S.J. Parke, Phys. Rev. D 49, 4454 (1994); C.T. Hill, Phys. Lett. B266, 419 (1991).
- [4] E. Eichten and K. Lane. FERMILAB-PUB-94/007-T/BUHEP-94-1(1994); T.Appelquist and G.Triantaphyllou, Phys. Rev. Lett. 69, 2750 (1992); E. Eichten, I. Hinchcliffe, K. Lane and C. Quigg, Phys. Rev. D 34, 1547 (1986).
- [5] V. Barger and R.J.N. Phillips. University of Wisconsin Preprint, MAD/PH/830 (1994), hep-ph 9405224; W. S. Hou and H. Huang, National Taiwan University Preprint, NTUTH-94-18(1994) (hep-ph 9409227); W. S. Hou, Phys. Rev. Lett. 72, 3945 (1994); B. Mukhopadhyaya and S.Nandi, Phys. Rev. Lett. 66, 285 (1991); ibid; Phys. Rev.D.46, 5098 (1992); T.P.Cheng and L.-F. Li, Phys. Rev D45, 1708 (1992) W.S. Hou, Phys. Rev. Lett. 69, 3587(1992); B. Mukhopadhyaya and S. Nandi, Phys. Rev. Lett. 24, 3588 (1992).
- [6] D. Atwood, A. Kagan and T.G. Rizzo, SLAC-PUB-6580, July, 1994; G. L. Kane, G.A. Ladinsky and C.P. Yuan, Phys. Rev. D 45, 124 (1992).
- [7] M. Lindner and D. Ross, Nucl. Phys. B 370, 30 (1992).
- [8] R. Brock et. al. (CTEQ Collaboration), ”Handbook of Perturbative QCD, Version 1.0”, Fermilab-Pub-93-094 (1993).

FIGURE CAPTION

Figure 1. Feynman diagrams for the process gluon+gluon coloron+coloron.

Figure 2. Cross sections (in pb) for the pair productions at the Tevatron ( and are the mass and the width of the coloron. The solid curves are for = -1 white the dotted curves are = 1 as discussed in Section III. The numbers indicated with the curves are the coloron masses in GeV. The four models discussed in the text are indicated by (a), (b),(c) and (d). The experimental value of the cross section, as measured by CDF collaboration, is shown by the arrow.

TABLE CAPTION

Table 1.

Branching ratios for the various multijet and multilepton final states with each jet and charged lepton (e or having GeV and with other cuts as discussed in the text. The decays of to e, or quarks have been included. The results are for the Tevatron energy, =1.8 TeV. SM stands for the Standard Model and (a), (b), (c) and (d) are the four different models discussed in Section 3.

Table 2.

Same as in table 1 except for GeV.

Table 3.

Branching ratios for the various multijet and multilepton (e or final states at the LHC energy, =14 TeV for the coloron model with coloron mass = 400 GeV. The cuts are , y 2.0, y 2.5, and = 0.5 everywhere as discussed section 4.2. The top mass has been taken to be 175 GeV. The decays of to e, or quarks have been included. Each branching ratio in the table should be multiplied by

Table 4.

Same as in table 3, except for = 600 GeV. Each branching ratio in the table should be multiplied by .

Table 5.

Same as in table 3 except for = 800 GeV. Each branching ratio in the table should be multiplied by

jets leptons | 0 | 1 | 2 | |
---|---|---|---|---|

(SM) | 1.81E-3 | 2.32E-3 | 9.09E-4 | |

(a) | 2.17E-3 | 2.14E-3 | 7.59E-4 | |

0 | (b) | 2.00E-3 | 2.17E-3 | 1.27 E-3 |

(c) | 1.80E-3 | 2.20E-3 | 1.01 E-3 | |

(d) | 1.95E-3 | 2.15E-3 | 9.93 E-3 | |

0.0251 | 0.0245 | 5.93E-3 | ||

0.0249 | 0.0259 | 5.48E-3 | ||

1 | 0.0191 | 0.0240 | 7.89E-3 | |

0.0231 | 0.0256 | 6.45E-3 | ||

0.0229 | 0.0253 | 6.45E-3 | ||

0.115 | 0.0825 | 9.00E-3 | ||

0.121 | 0.0810 | 8.53E-3 | ||

2 | 0.0874 | 0.0786 | 0.0124 | |

0.107 | 0.0819 | 9.92E-3 | ||

0.106 | 0.0823 | 0.0104 | ||

0.236 | 0.0897 | |||

0.240 | 0.0847 | |||

3 | 0.188 | 0.106 | ||

0.225 | 0.0938 | |||

0.220 | 0.0942 | |||

0.239 | 0.0298 | |||

0.239 | 0.0270 | |||

4 | 0.230 | 0.0473 | ||

0.238 | 0.0334 | |||

0.239 | 0.0361 | |||

0.117 | ||||

0.110 | ||||

5 | 0.152 | :4.810 0.009 pb SM | ||

0.126 | :13.93 0.03 pb (a) | |||

0.128 | :13.49 0.04 pb (b) | |||

:13.52 0.02 pb (c) | ||||

0.0209 | :13.89 0.03 pb (d) | |||

0.0177 | ||||

6 | 0.0388 | |||

0.0241 | ||||

0.0263 |

jets leptons | 0 | 1 | 2 | |
---|---|---|---|---|

(SM) | 0.0155 | 6.81E-3 | 1.36E-4 | |

(a) | 0.0188 | 7.30E-3 | 1.31E-4 | |

0 | (b) | 0.0107 | 5.70E-3 | 1.84 E-3 |

(c) | 0.0148 | 6.66E-3 | 1.53 E-3 | |

(d) | 0.0137 | 6.85E-3 | 1.57 E-3 | |

0.105 | 0.0430 | 3.48E-3 | ||

0.109 | 0.0455 | 3.04E-3 | ||

1 | 0.0602 | 0.0395 | 6.04E-3 | |

0.0927 | 0.0428 | 3.98E-3 | ||

0.0876 | 0.0437 | 4.32E-3 | ||

0.270 | 0.0670 | 2.50E-3 | ||

0.295 | 0.0631 | 1.87E-3 | ||

2 | 0.177 | 0.0795 | 5.73E-3 | |

0.257 | 0.0696 | 2.85E-3 | ||

0.250 | 0.0720 | 3.12E-3 | ||

0.280 | 0.0370 | |||

0.290 | 0.0304 | |||

3 | 0.258 | 0.0684 | ||

0.283 | 0.0409 | |||

0.278 | 0.0447 | |||

0.130 | 4.58E-3 | |||

0.121 | 2.48E-3 | |||

4 | 0.197 | 0.0161 | ||

0.141 | 5.97E-3 | |||

0.150 | 6.70E-3 | |||

0.0262 | ||||

0.0176 | ||||

5 | 0.0722 | |||

0.0320 | ||||

0.0355 | ||||

2.29E-3 | ||||

7.31E-4 | ||||

6 | 9.62E-3 | |||

3.14E-3 | ||||

3.49E-3 |

jets leptons | 0 | 1 | 2 | 3 | 4 |
---|---|---|---|---|---|

0 | 1.18E-5 | 1.80E-6 | |||

1 | 1.76E-4 | 3.55E-5 | |||

2 | 1.15E-3 | 1.67E-4 | |||

3 | 3.30E-3 | 3.50E-4 | |||

4 | 5.05E-3 | 2.43E-4 | |||

5 | 0.0326 | 3.86E-3 | |||

6 | 0.0258 | 1.04E-3 | |||

7 | 0.0770 | 0.0103 | |||

8 | 0.0391 | 1.69E-3 | |||

9 | 0.0589 | 0.0106 | |||

10 | 0.0192 | 1.11E-3 | = 758 2pb | ||

11 | 4.01E-3 | ||||

12 | 3.51E-4 |

jets leptons | 0 | 1 | 2 | 3 | 4 |
---|---|---|---|---|---|

0 | 4.75E-6 | 1.37E-6 | |||

1 | 9.65E-5 | 2.45E-5 | |||

2 | 7.94E-4 | 1.66E-4 | |||

3 | 3.13E-3 | 4.29E-4 | |||

4 | 6.03E-3 | 3.65E-4 | |||

5 | 0.0347 | 5.40E-3 | |||

6 | 0.0335 | 1.86E-3 | |||

7 | 0.0942 | 0.0173 | |||

8 | 0.0607 | 3.73E-3 | |||

9 | 0.0792 | 0.0207 | |||

10 | 0.0350 | 3.22E-3 | =67.32 0.16pb | ||

11 | 9.75E-3 | ||||

12 | 1.09E-3 |

jets leptons | 0 | 1 | 2 | 3 | 4 |
---|---|---|---|---|---|

0 | 1.71E-6 | 7.62E-7 | |||

1 | 6.02E-5 | 1.70E-5 | |||

2 | 5.92E-4 | 1.29E-4 | |||

3 | 2.76E-3 | 3.61E-4 | |||

4 | 5.51E-3 | 3.23E-4 | |||

5 | 0.0334 | 4.76E-3 | |||

6 | 0.0302 | 1.55E-3 | |||

7 | 0.0879 | 0.0142 | |||

8 | 0.0607 | 3.73E-3 | |||

9 | 0.0687 | 0.016 | |||

10 | 0.0287 | 2.29E-3 | =9.448 0.024pb | ||

11 | 6.71E-3 | ||||

12 | 8.79E-4 |