On new gauge boson signals according to the littlest higgs model in future e+ e- colliders

Abstract

There is a recent proposal of identifying the Higgs particle of the Standard Model as a pseudo Nambu-Goldstone boson. This new broken symmetry introduces new particles and new interactions. Among these new interactions a central role to get an experimental signal of a new physics is played by the new neutral gauge bosons, A H and Z H. We study the associated production of general new neutral gauge boson Z¢ and a hard photon in the process e+ + e- <FONT FACE=Symbol>® m</FONT> + + µ- + gamma. For M AH < <FONT FACE=Symbol>Ö</FONT>S we show that the hard photon energy distribution in e+ + e- <FONT FACE=Symbol>® g</FONT> + f + f can present a model dependence and establish the theoretical origin of a new possible heavy neutral gauge boson.

Littlest Higgs; New Gauge Bosons

POSTERS

On new gauge boson signals according to the littlest higgs model in future e⁺e^- colliders

F. M. L. de Almeida Jr.^I; Y. A. Coutinho^I; J. A. Martins Simões^I; A. J. Ramalho^I; S. Wulck^I; M. A. B. do Vale^II

^IInstituto de Física, Universidade Federal do Rio de Janeiro, 21941-972, Rio de Janeiro, RJ, Brazil

^IIDepartamento de Ciências Naturais, Universidade Federal de São João Del Rei, 36301-160, São João del Rei, MG, Brazil

ABSTRACT

There is a recent proposal of identifying the Higgs particle of the Standard Model as a pseudo Nambu-Goldstone boson. This new broken symmetry introduces new particles and new interactions. Among these new interactions a central role to get an experimental signal of a new physics is played by the new neutral gauge bosons, A_H and Z_H. We study the associated production of general new neutral gauge boson Z^¢ and a hard photon in the process e⁺ + e^-® m ⁺ + µ^- + g. For M_AH < ÖS we show that the hard photon energy distribution in e⁺ + e^-® g + f + f can present a model dependence and establish the theoretical origin of a new possible heavy neutral gauge boson.

Keywords: Littlest Higgs; New Gauge Bosons

I. THE LITTLEST HIGGS MODEL

Recently, new models have been proposed as possible solutions to the hierarchy problem of the Standard Model (SM). The Little Higgs models [1] implement the idea that the Higgs boson is a pseudo-Goldstone boson. They are constructed by embedding the Standard Model inside a larger group with an enlarged symmetry. The minimal model was called the Littlest Higgs Model (LHM). The LHM consists of an SU(5) non-linear sigma model which is spontaneously broken to its subgroup SO(5) by vacuum expectation value (VEV) of order f. The gauged group (SU(2) Ä U(1))² is broken at the same time to its diagonal electroweak SM subgroup SU(2) Ä U(1). The new heavy states in this model consists of heavy gauge bosons (W_H, Z_H, A_H), a triplet Higgs F and a vector like top quark which cancels the quadratic divergences coming from the SM top quark. By construction, all of the new states acquire masses of order f and typically in the TeV range. The approximate mass relations for the heavy gauge bosons can be written as [2]:

where q_w is the Weinberg angle, v is the electroweak scale and the mass parameter M_W º gv/2 approaches the SM W-boson mass when f ® ¥. The neutral gauge boson A_H is typically light and should be the first signal of the LHM. A first property of this model is the presence of a second, heavier, new neutral gauge boson, named Z_H (M_ZH » 4 M_AH). The total decay width G_ZH is mainly dependent of the free parameters M_ZH and c (cosq), while the total decay width G_AH is sensitive to the free parameters M_AH and c' (cosq'). The parameter space for the two mixing angles, c and c', is 0 < c < 0.5 and 0.62 < c' < 0.73, consistent with the precision electroweak constraints.

II. THE HARD PHOTON

The most direct channel to study the A_H, Z_H properties is e⁺ + e^-® f + , at the ressonant energy = M_ZH,M_AH. As these masses are unknown, the new high-energy accelerators will have to vary . As this procedure is a very complex operation it is important to have physical alternatives at fixed .

In this work we explore the interesting properties of the fundamental interaction mechanism of the associated production of new neutral gauge bosons and a hard photon in the process e⁺ + e^-® m ⁺ + µ^- + g. (For more details see [3]). The Feynman diagrams for this channel are shown in Fig. 1.

A very simple consequence of the conservation of energy and momentum is that the final high energy photon has a fixed energy given by [4].

where D_g and D_Z' are the uncertainties in the photon energy and in M_Z'.

The study of the hard photon energy distribution will give most information as the direct new bosons decays, but in a simple and direct way. Since the new boson masses are not known, colliders are considered at the highest energy and so we are considering = 3 TeV. If indications of new bosons are found with masses lower than , a new run with a c.m. energy near the mass value is not necessary in order to study the new bosons properties in details.

III. RESULTS

In order to obtain the hard photon energy distribution, we imposed a set of realistic cuts: all final states particles were required to emerge with a polar cosq, measured with respect to the direction of the electron beam, in the range |cosq| < 0.995. The hard photon energy was required to be greater than 5 GeV. The resulting photon energy distributions are shown in Figs. 2 and 3 in the channel µ⁺ µ^-g for two different c' values (c' = 0.65 and c' = 0.71). For M_AH = 650 GeV, we can see two peaks, the first one associated to Z_H, and the second to A_H. For M_AH = 1300 GeV, only the peak associated to A_H appears. We remark the strong mixing angle dependence on the magnitude of the photon peak. We show in Fig. 4 the invariant mass Dalitz plot. The three horizontal lines correspond to the three different neutral gauge boson (Z, A_H, Z_H) masses. Depending on the heavy boson masses one can see two horizontal lines (Z and A_H) or even only the SM Z mass. In Fig. 5 we can see the hard-photon energy distribution associated with the A_H compared to the canonical h, c, y super-string inspired E₆ models. The h, c, y models have a much larger value for the total neutral gauge boson width and this fact makes the hard photon energy much broader.

IV. CONCLUSIONS

We have shown that the hard photon energy distribution can establish the theoretical origin of a new possible heavy neutral gauge boson independent of how all new boson decays. This alternative signature for Z^' production at the new electron-positron colliders could allow us to study its properties, at a fixed collider energy > M_Z'. Moreover, if the neutral gauge boson is identified, due to the width of the hard photon energy distribution, as the A_H of the LHM, this would imply the existence of another neutral gauge boson, the Z_H, with mass approximately four times the A_H mass.

Acknowledgments: CNPq, FAPERJ and FAPEMIG.

[3] F. M. L. Almeida Jr., Y. A. Coutinho, J. A. Martins Simões, A. J. Ramalho, S. Wulck, and M. A. B. do Vale, [arXiv:hep-ph/0601102].

Received on 19 January, 2007

• [1] N. Arkani-Hamed, A. G. Cohen, and H. Georgi, Phys. Lett. B 513, 232 (2001) [arXiv:hep-ph/0105239].
• [2] T. Han, H. E. Logan, B. McElrath, and L. T. Wang, Phys. Rev. D 67, 095004 (2003) [ar-Xiv:hep-ph/0301040].
• [4] F. M. L. Almeida Jr., Y. A. Coutinho, J. A. Martins Simőes, A. J. Ramalho, S. Wulck, and M. A. B. do Vale, Eur. Phys. J. C 44, 127 (2005).

Publication Dates

• Publication in this collection
  13 Aug 2007
• Date of issue
  July 2007

History

• Received
  19 Jan 2007