Triple Photon Production at the Tevatron in Technicolor Models

We study the process p bar{p} -->gamma gamma gamma as a signal for associated photon-technipion production at the Tevatron. This is a clean signature with relatively low background. Resonant and non-resonant contributions are included and we show that technicolor models can be effectively probed in this mode.


Introduction
The origin of fermion masses and mixings is one of most important issues in particle physics. Unfortunately, these parameters are inputs in the well-tested Standard Model (SM). Fermion masses are possibly related to the electroweak symmetry breaking mechanism, which is not known at the moment and is the top priority of present and future experiments. In the SM, a scalar electroweak doublet with self-interactions described by an ad hoc quartic potential is responsible for the symmetry breaking, leaving a scalar physical boson, the Higgs boson (J PC = 0 ++ ), as a remnant. Favorite extensions of the SM, like the minimal supersymmetric standard model (MSSM) [1], also predict the existence of a heavy pseudoscalar boson (J PC = 0 −+ ), in addition to a light scalar boson.
Another interesting possibility is that the electroweak symmetry breaking is triggered by some new strong interaction, generally called technicolor, and in this case the lightest boson could be a pseudoscalar, like a pion, named technipion. In fact, in these models of dynamical symmetry breaking a whole new set of resonances related to the technicolor sector is predicted [2].
It is important to find experimental signatures that can distinguish these different models of symmetry breaking. A compilation of experimental signatures for different technicolor models, like multiscale and top-color assisted walking technicolor, can be found in [3].
In this letter we focus on the signature arising from associated photon-technipion production. This is analogous to the associated gauge-higgs boson production. The T is a isospin triplet (singlet) technipion, can be enhanced by low-lying technicolor resonances like the techni-rho and the techni-omega.
These processes have been studied in [4] and the importance of the process involving the final state photon has been stressed in [5].
The process e + e − → γΠ (′) T was analysed for LEP and future linear colliders in [6]. Recently, Lane et al. [7] re-studied this process taking into account both continuum and resonance contributions, but concentrating on the dominant bb decay mode.
In this letter we study the possibility of using the process pp → γΠ (′) T → γγγ, which is a clean signature with relatively low background even in a hadronic environment, to put some constraints in some technicolor models. We also include both resonant and non-resonant contributions in our analysis and perform a simulation of the significance level of this signature.

The Model
The coupling of the technipion to two gauge bosons is mediated by the Adler-Bell-Jackiw anomaly [8] arising from a techniquark triangle. The Π (′) T B 1 B 2 coupling can be parametrized as: where ε 1,2 and k 1,2 are the polarization vectors and momenta of the gauge bosons B 1,2 respectively. F Π T is the technipion decay constant, which is related to the technipion coupling to the axial current. The group-theoretical factor S Π T B 1 B 2 is given by [9]: where g 1 and g 2 are the corresponding gauge coupling constants and Q 1 , Q 2 and Q Π T are the charges under the gauge groups and isospin respectively of the technifermions circulating in the loop. For our purposes we will be concerned only with the Π T γZ couplings, since they provide the only contributions to the process pp → γΠ (′) T , shown in Figure 1, and the corresponding group-theoretical factors, for a one-family technicolor model with gauge group SU(N T C ), are given by : Consequently, the decay of neutral techni-pions into two photons is induced entirely by the anomaly. In contrast, the associated production of a photon with a neutral technipion is mediated by both Π contributions, as these are due to very different energy scales, the former being a lowenergy effect and therefore is not important at the resonance mass scale.
In the absence of isospin violation, the techni-omega mixes with the isoscalar part of the electroweak current, the B µ field, whereas the techni-rho mixes with the isotriplet part, the W 3 µ field. In terms of the physical fields of the photon and the Z-boson, the mixing strengths are given by: and where α is the fine structure constant and α T is related to the technicolor coupling constant g T and can be estimated by a naïve scaling from QCD: Finally, the relevant amplitudes for the decays ρ T , ω T → γΠ T are given by, in the notation of [5]: where M V is a mass parameter usually taken to be 200 GeV and In the equation above χ and χ ′ are mixing angles between the isospin eigentates and the mass eigenstates. In our computations we use a value of sin χ = sin χ ′ = 1/3 and Q U + Q D = 5/3 [5]. In order to compute the fermionic widths of the techni-pions we use

Simulation of the process
The inputs to our codes are the relevant masses of Π (′) T , ω T , ρ T , the technipion decay constant F Π T and the resonance widths Γ ρ T and Γ ω T . In order to reduce the number of parameters, we will use in our calculations the reference set of values m Π (′) T = 110 GeV and m ω T = m ρ T . We also adopt N T C = 4 and F Π T = 82 GeV, as appropriate in multiscale walking technicolor, but the results are relatively insensitive to this choice since the couplings of the vector resonances and the branching ratio BR(Π (′) T → γγ) are independent of F Π T . The vector resonance widths were obtained from Pythia version 6.125 [10].
We used the parton distribution function CTEQ6 [11] with both momentum and factorization scales set at √ŝ and a total center-of-mass energy of √ s = 2000 GeV. We convoluted the relevant parton distribution functions with the amplitudes described above.
The irreducible background was generated using the program CalcHEP 2.1 [12]. The main irreducible contribution comes from uū, dd → γγγ.
A gaussian smearing for the final state photon energy with σ E /E = 0.20/ √ E [13] was applied to both signal and background.

Results
In Figures 3 and 4 Fig. 4 shows a peak centered around the techni-vector meson mass. In this case, the width in the histogram reflects the resonance width together with the photon energy resolution that we use in the simulation. In addition, the distribution away from the peak is dominated by the anomaly contribution. As it is comparable to the background, the non-resonant contribution cannot be detected.
In order to further suppress the background, the following cuts were used: In Table I we present our results for the total number of 3-photon events for a given techni-resonance mass and for 2 different integrated luminosities, namely L = 2 fb −1 and 30 fb −1 .
We can see that resonances up to 350 GeV can be found at the 5σ level even with  GeV can be detected at the 3σ level. In Figure 5 we show the statistical significance of the signal as a function of the techni-resonances for the two luminosities.

Conclusions
In this paper we have examined the triple photon production at the Tevatron as a signature