Using recent DØ data on the dijet mass spectrum, we present a limit on flavor-universal colorons. At 95% CL we find GeV. We discuss the implications of this limit for models of quark compositeness, non-standard gluon interactions, and dynamical electroweak symmetry breaking. In addition, we place a lower bound TeV on the scale of color-octet axial-vector contact interactions among quarks which could arise in models of quark compositeness.

## 1 Introduction

The flavor-universal coloron model [1] was originally proposed to explain the apparent excess of high- jets in the inclusive jet spectrum measured at the Fermilab Tevatron by the CDF Collaboration [2]. This model is a flavor-universal variant of the coloron model of Hill and Parke [3] which involves a minimal extension of the standard description of the strong interactions, including the addition of one gauge interaction and a scalar multiplet, but no new fermions. The flavor-universal coloron model of the strong interactions can be grafted onto the standard one-Higgs-doublet model of electroweak physics, yielding a simple, complete, and renormalizable theory. Alternatively, it can provide the basis for dynamical generation of electroweak symmetry breaking and the generation of the top quark’s mass in models [4, 5] akin to top-color-assisted technicolor [6].

Previous work on the phenomenology of the colorons has considered effects on the parameter [1, 4], the inclusive jet spectrum [1], the dijet spectrum and angular distributions [7, 8, 9], and b-tagged dijets [8]. The most recent of these analyses [9] put a limit GeV on the the coefficient of the four-fermion contact interaction to which heavy coloron exchange would give rise.

This letter explores the effects colorons would have on the dijet mass spectrum measured at the Tevatron by the DØ Collaboration [10] and establishes a still stronger limit on contact interactions arising from colorons: GeV at 95% CL. In Section 2, we briefly review the model. Section 3 explains how our limit was derived. Section 4 discusses our conclusions and the implications for models of quark compositeness, non-standard gluon interactions, and dynamical electroweak symmetry breaking. We also present a separate limit on the scale of color-octet axial-vector contact interactions among quarks.

## 2 The model

In the flavor-universal coloron model [1], the strong gauge group is extended to . The gauge couplings are, respectively, and with . Each quark transforms as a (1,3) under this extended strong gauge group.

The model also includes a scalar boson transforming as a under the two groups. For a range of couplings in the scalar potential, develops a vacuum expectation value which breaks the two strong groups to their diagonal subgroup [1]. We identify this unbroken subgroup with QCD.

When the extended color symmetry breaks, the original gauge bosons mix to form an octet of massless gluons and an octet of massive colorons. The gluons interact with quarks through a conventional QCD coupling with strength . The colorons interact with quarks through a new QCD-like coupling

(2.1) |

where is the color current

(2.2) |

and . The mass of the colorons may be written

(2.3) |

in terms of the parameters of the model.

Below the scale , coloron-exchange may be approximated by the effective four-fermion interaction

(2.4) |

This can be re-written in the form commonly used in studies of quark compositeness [11]

(2.5) |

where the scale is defined by . Contact interactions of this kind tend to increase quark-quark scattering at high invariant mass above the standard QCD prediction.

## 3 Effects on the Dijet Spectrum

The DØ Collaboration recently [10] measured the inclusive dijet mass spectrum at = 1.8 TeV for dijet masses above 200 GeV and jet pseudorapidity . The collaboration also measured the ratio of spectra at and and used this to place a limit on certain models of quark compositeness. We use this same ratio of spectra to place limits on the effects of flavor-universal colorons.

We calculated the leading-order (LO) dijet spectrum

in terms of the jets’ pseudorapidities (, ; ), combined invariant mass () and momentum fractions (); the parton distribution functions (); and the two-body parton scattering cross section

(3.2) |

The leading QCD contributions to may be found in
[12] and the contributions from heavy coloron exchange are
given^{1}^{1}1In ref. [1], the colorons’ contributions are
the terms in equations (4.2-4.5) in that paper which depend on
coefficient . in [1]. Note that we included only
production of gluons and light quarks in our calculations since produced
top quarks would not contribute appreciably to the DØ dijet
sample^{2}^{2}2The number of top quarks produced is relatively small
and a decaying top quark does not generally resemble a single
high-E jet.

Taking a series of different values for the coloron interaction strength
, we then determined the ratio
at values of corresponding to
the weighted center of each mass bin^{3}^{3}3As a check, we
re-calculated the ratio for the very wide highest mass bin by
integrating over for 800 GeV 1400 GeV; this yielded the
same ratio as keeping fixed at the weighted center value of 873.2
GeV. measured by DØ in ref.[10]. We evaluated the
fractional difference between the dijet spectra for pure QCD and for the
various values of . To simulate a next-to-leading order
(NLO) prediction of the effects of colorons, we multiplied a NLO QCD
prediction obtained using the jetrad program [14] by the LO
fractional differences. The results are illustrated in Figure 1.

We extract a limit on the coloron interaction strength from the DØ data [10] using Bayesian techniques with a Gaussian likelihood function

(3.3) |

where is the vector of data points for the different mass bins, is the vector of theory points for the different masses at different values of , and is the covariance matrix. Motivated by the form of (eqn. (2.5)), the prior probability is assumed to be flat when . Since the ratio of spectra at NLO is sensitive to the choice of and parton distribution function, each possible choice is treated as a different theory. The 95% confidence limit (CL) on is calculated by requiring that

(3.4) |

The limit in is then transformed back into a limit on and thence into a limit on .

The most conservative lower bound we obtain at the 95% CL is GeV for the CTEQ3M pdf and (where is the maximum jet in the event) as illustrated in Figure 2. This limit is incompatible with the suggestion of a coloron interaction strength of order 700 GeV [1] in earlier measurements of the high jet inclusive cross-section [2].

## 4 Discussion

Our limit places a new exclusion bound in the vs. parameter space of the flavor-universal coloron model. As shown in Figure 3, this improves on the recent DØ limit based on the dijet angular distribution [9]. Note that the region at where our limit appears to provide a direct lower bound on has already been excluded by CDF’s search for new particles decaying to dijets [16]. This is fortunate, because our limit actually becomes less reliable here: the condition , under which (2.4) is a reasonable approximation to coloron exchange, would no longer hold for the highest-energy data point. An updated search for new resonances decaying to dijets would be a useful complement to the bounds we report here.

In the context of the dynamical electroweak symmetry breaking model of [4] in which flavor-universal colorons help produce the mass of the top quark, the value of is approximately 4. In other words, the interaction strength is near its upper limit for the Higgs phase of the model [1, 8]. Our bound implies that TeV in such models, placing them at the upper right of the allowed region in Figure 3.

Our findings also set a limit on a broader array of new strong interaction physics. Writing eqn.(2.4) in the more conventional form for compositeness studies (2.5) shows that our limit is equivalent to a lower bound TeV on the scale of new color-octet vectorial current-current interactions. Such interactions could arise from quark compositeness or from non-standard gluon interactions (e.g. gluon compositeness) [17].

Finally, we have used the same methods to set a limit on a color-octet axial-vector current-current interaction among quarks. This has the form

(4.1) |

where . The contributions of this contact interaction
to parton scattering are given^{4}^{4}4The relevant terms are those
in equations (4.2-4.5) in that paper which depend on coefficient . in
[1]. The most conservative bound we find is TeV at 95 CL. Note that we cannot self-consistently
interpret this as providing a lower bound on the mass of an
axigluon [18, 19] whose exchange underlies the contact
interaction (4.1). The relation (since for axigluons) shows that the
mass of the supposed axigluon would not satisfy the condition
. Instead, our limit should be interpreted as bounding
the scale of contact interactions arising in models of quark compositeness.

Acknowledgments

We thank the DØ collaboration for making the measurements that made this work possible. We also thank R.S. Chivukula for comments on the manuscript. E.H.S. acknowledges the support of the NSF Faculty Early Career Development (CAREER) program and the DOE Outstanding Junior Investigator program. I.B. thanks the DØ Collaboration for their support and contributions to this work and, W.T. Giele, E.W.N. Glover, and D.A. Kosower for help with jetrad. This work was supported in part by the National Science Foundation under grant PHY-95-1249 and by the Department of Energy under grant DE-FG02-91ER40676 with Boston University and grant DE-FG02-91ER40684 at Northwestern University.

## References

- [1] “New Strong Interactions at the Tevatron?”, R.S. Chivukula, A.G. Cohen, and E.H. Simmons, hep-ph/9603311, to appear in Physics Letters B (1996).
- [2] “Inclusive Jet Cross Section in Collisions at TeV”, CDF Collaboration, F. Abe et al., FERMILAB-PUB-96/020-E, hep-ex/9601008.
- [3] C.T. Hill Phys. Lett. B266 (1991) 419; C.T. Hill and S.J. Parke, Phys. Rev. D49 (1994) 4454.
- [4] M.B. Popovic and E.H. Simmons, ‘A Heavy Top Quark from Flavor-Universal Colorons’. To appear in Physical Review D. hep-ph/9806287.
- [5] K.D. Lane, Phys. Lett. B433 (1998) 96. hep-ph/9805254
- [6] C.T. Hill, Phys. Lett. B 345 (1995) 483. hep-ph/9411426.
- [7] R.M. Harris, private communication. See preliminary CDF results on the World Wide Web at http://www-cdf.fnal.gov/physics/new/qcd/qcd_plots /twojet/public/dijet_new_physics.html .
- [8] E.H. Simmons, Phys. Rev. D55 (1997) 1678. hep-ph/9608269; E.H. Simmons, hep-ph/9701282 and hep-ph/9608349.
- [9] B. Abbott et al. (D0 Collaboration), Presented at the XXIX International Conference on High Energy Physics - ICHEP98, July 23-29, 1998, Vancouver, B.C., Canada. FERMILAB-Conf-98/279-E. hep-ex/9809009.
- [10] B. Abbott et al. (D0 Collaboration), Fermilab-Pub-98/220-E, hep-ex/9807014.
- [11] E. Eichten, K. Lane, and M. E. Peskin, Phys. Rev. Lett. 50 (1983) 811.
- [12] B.L. Combridge, J. Kripfganz and J. Ranft, Phys. Lett. B70 (1977) 234; J.F. Owens and E. Reya, Phys. Rev. D18 (1978) 1501.
- [13] H.L. Lai et al. (CTEQ Collaboration), Phys. Rev. D51 (1995) 4763.
- [14] W.T. Giele, E.W.N. Glover and D.A. Kosower, Nucl. Phys. B403 (1993) 633. hep-ph/9302225.
- [15] H. Jeffreys, Theory of Probability (Clarendon Press, Oxford, 1939, revised 1988), p 94.
- [16] CDF Collaboration (F. Abe et al.) Phys. Rev. Lett. 74 (1995) 3538. hep-ex/9501001.
- [17] E. H. Simmons, Phys. Lett. B226 (1989) 132 and Phys. Lett. B246 (1990) 471; P. Cho and E. H. Simmons Phys. Lett. B323 (1994) 401 and Phys. Rev. D51 (1995) 2360.
- [18] J. Pati and A. Salam, Phys. Lett. 58B (1975) 333; J. Preskill, Nucl. Phys. B177 (1981) 21; L. Hall and A. Nelson, Phys. Lett. 153B (1985) 430; P.H. Frampton and S.L. Glashow, Phys. Lett. B190 (1987) 157 and Phys. Rev. Lett. 58 (1987) 2168.
- [19] J. Bagger, C. Schmidt, and S. King, Phys. Rev. D37 (1988) 1188.
- [20] “Search for New Particles Decaying to dijets, and at CDF” The CDF Collaboration (R.M. Harris for the collaboration), Fermilab-Conf-95/152-E, June 1995. Published in Proceedings of the 10th Topical Workshop on Proton-Antiproton Collider Physics, Fermilab, May 9-13, 1995. hep-ex/9506008.