Neutral top-pion and $t\gamma(z)$ production at the HERA and THERA colliders

In the context of top-color assisted technicolor ($TC2$) models, we calculate the contributions of the neutral top-pion $ \pi_{t}^{0}$ to $t\gamma$ and $tz$ production via the processes $ ep\to \gamma c \to t\gamma $ and $ ep\to \gamma c \to tz$ at the $HERA$ and $THERA$ colliders. Our results show that the cross sections $\sigma_{t\gamma}(s)$ and $\sigma_{tz}(s)$ are very small at the $HERA$ collider with $\sqrt{s}=320GeV $. However, in most of the parameter space, $\sigma_{t\gamma}(s)$ or $\sigma_{tz}(s)$ is in the range of about $0.1pb \sim 1 pb$ at the $THERA$ collider with $\sqrt{s}=1000GeV$.

Single top quark production is very sensitive to the anomalous top quark couplings tqv, in which q represents the up quark or charm quark and v represents the gauge bosons z, γ, or g [1]. This type of couplings can be generated in supersymmetry, top-color scenario, and other specific models beyond the standard model (SM). Thus, studying the contributions of the tqv couplings to single top production is of interest. This fact has led to many studies involving single top production via the tqv couplings in lepton colliders [2,3] and hadron colliders [4,5].
The HERA collider and the T HERA collider [6] with the center-of-mass energy √ s = 320GeV and 1000GeV , respectively, are the experimental facilities where high energy electron-proton and positron-proton interactions can be studied. It is well known that, in the SM, single top quark can not be produced at an observable rate in these high energy colliders. However, it has been shown that the HERA collider and the T HERA collider can provide a very good sensitivity on the tqv couplings via single top production [7]. This type of single top production may be detected in these colliders [5,8]. The HERA and T HERA colliders are powerful tools for searching for the anomalous top quark couplings tqv.
The presence of the top-pions π 0,± t in low-energy spectrum is an inevitable feature of top-color scenario [9]. These new particles have large Yukawa couplings to the third family quarks and can induce the tree-level flavor changing(F C) couplings, which have significant contributions to the anomalous top quark couplings tqv [10]. In Ref. [5] we study the contributions of the tqv couplings generated by π 0 t exchange to single top production via the t-channel process eq → et at the HERA and T HERA colliders. We have shown that it can generate significant effects on the process ec → et, which may be observable in the T HERA collider. The aim of this Letter is to consider the contributions of the tcv couplings given by π 0 t exchange to the processes ep → γc → tγ and ep → γc → tz in the context of topcolor-assisted technicolor (T C2) models [11], and see whether the effects of the neutral top-pion π 0 t on tγ and tz production can be detected in the HERA collider or the T HERA collider.
For T C2 models [9,11], the underlying interactions, topcolor interactions, are assumed to be chiral critically strong at the scale about 1 T eV and coupled preferentially to the third generation, and therefore do not posses GIM mechanism. The non-universal gauge interactions result in the tree-level F C coupling vertices when one writes the interactions in the mass eigen-basis, which can induce the anomalous top quark couplings tuv and tcv. However, the tuv couplings can be neglected because the F C scalar coupling π 0 t tu is very small [12]. The effective forms of the tcγ and tcz coupling vertices Λ tcγ , Λ tcz have been given in Eq. [4] and Eq. [5] of Ref. [10]. From the above discussion, we can see that the neutral top-pion π 0 t can generate contributions to the subprocesses γc → tγ and γc → tz via the anomalous top quark couplings tcγ and tcz generated by the π 0 tt c coupling. The relevant Feynman diagrams are shown in Fig.1.
The renormalized amplitudes for these processes can be written as: Where µ is a real parameter, which is introduced to make the integral convergent. Γ t is the total decay width of the top quark.
After calculating the cross sectionσ i (ŝ) of the subprocesses γc → tγ or γc → tz, the total cross section σ i (s) of tγ production or tz production can be obtained by foldingσ i (ŝ) with the charm quark distribution f c/p (x) in proton and the backscattered high energy photon spectrum f γ/e ( τ x ): can be written as [13]: )]] (x 0 = 4.83).
The parton distribution function f c/p (x) of the charm quark runs with the energy scale.
In our calculation, we will take the CTEQ5 parton distribution function for f c/p (x) [14]. To obtain numerical results, we take the fine structure constant α e = 1 128.8 , m t = 175GeV , m c = 1.2GeV , m z = 91.2GeV , and assume that the total decay width Γ t of the top quark is dominated by the decay channel t → wb, which has been taken Γ(t → wb) = 1.56GeV [15]. The limits on the mass m πt of the top-pion π 0 t may be obtained via studying it's effects on observables [9]. It has been shown that m πt is allowed to be in the range of a few hundred GeV depending on the models. For T C2 models, top-color interactions make small contributions to electroweak symmetry breaking and give rise to the main part of the top quark mass, (1-ε)m t , with the parameter ε ≪ 1. As numerical estimation, we will take m πt and ε as free parameters. Our numerical results are summarized in Fig.2-Fig.5. From these figures, we can see that the cross sections σ tγ (s) and σ tz (s) of tγ and tz production at the HERA and T HERA colliders increase as the parameter ε increases and m πt decreases. In all of the parameter space, we have that the cross section σ tγ (s) of the process ep → γc → tγ is larger than the cross section σ tz (s) of the process ep → γc → tz. For ε ≤ 0.08 and m πt ≥ 200GeV , σ tγ (s) and σ tz (s) at the HERA collider are smaller than 0.14pb and 0.066pb, respectively. However, at the T HERA collider with √ s = 1000GeV , σ tγ (s) and σ tz (s) are in the ranges of 0.14pb ∼ 1.37pb and 0.13pb ∼ 1.35pb, respectively, for 0.02 ≤ ε ≤ 0.08 and 200GeV ≤ m πt ≤ 400GeV .
If we assume that the HERA collider with √ s = 320GeV has a yearly integrated luminosity of £ = 160pb −1 and the T HERA collider with √ s = 1000GeV has a yearly integrated luminosity of £ = 470pb −1 [6], then the yearly production events of tγ and tz can be easily estimated. In most of the parameter space of T C2 models, there may be only about 10 or less of tγ events or tz events generated a year in the HERA collider, which is very difficult to detect. However, there may be hundreds of tγ events or tz events to be generated a year in the T HERA collider. For example, for m πt = 300GeV and ε = 0.05, the T HERA collider can generate 252 tγ events and 240 tz events. Thus, the effects of the neutral top-pion π 0 t on tγ production and tz production may be detected at the T HERA collider. In conclusion, T C2 models predict the existence of the neutral top-pion π 0 t , which can induce the anomalous top quark couplings tcγ and tcz and further contribute to single top quark production. In this letter, we calculated the contributions of π 0 t to tγ production and tz production via the processes ep → γc → tγ and ep → γc → tz at the HERA and T HERA colliders. We find that the cross sections of tγ and tz production are very small at the HERA collider. The effects of the neutral top-pion π 0 t on tγ and tz production can not be observed at the HERA collider. However, π 0 t exchange can generate several hundred tγ or tz events at the T HERA collider.