Precise photoproduction of the charged top-pions at the LHC with forward detector acceptances

We study the photoproduction of the charged top-pion predicted by the top triangle moose ($TTM$) model (a deconstructed version of the topcolor-assisted technicolor $TC2$ model) via the processes $pp\rightarrow p \gamma p \rightarrow \pi^\pm_t t +X$ at the 14 $TeV$ Large Hadron Collider ($LHC$) including next-to-leading order ($NLO$) $QCD$ corrections. Our results show that the production cross sections and distributions are sensitive to the free parameters $\sin\omega$ and $M_{\pi_t}$. Typical $QCD$ correction value is $7\% \sim 11\%$ and does not depend much on $\sin\omega$ as well as the forward detector acceptances.


Introduction
The top quark is the heaviest known elementary particle which makes it an excellent candidate for new physics searches. Origin of its mass might be different from that of other quarks and leptons, a top quark condensate (< tt >), for example, could be responsible for at least part of the mechanism of electroweak symmetry breaking (EW SB). An interesting model involving a role for the top quark in dynamical EW SB is known as the topcolor-assisted technicolor (T C2) model [1]. Higgsless models [2] have emerged as a novel way of understanding the mechanism of EW SB without the presence of a scalar particle in the spectrum. Recently, combing Higgsless and topcolor mechanisms, a deconstructed Higgsless model was proposed, called the top triangle moose (T T M) model [3,4]. In this model, EW SB results largely from the Higgsless mechanism while the top quark mass is mainly generated by the topcolor mechanism. The T T M model alleviates the tension between obtaining the correct top quark mass and keeping ∆ρ small that exists in many Higgsless models, which can be seen as the deconstructed version of the T C2 model. The new physics models belonging to the topcolor scenario genetically have two sources of EW SB and there are two sets of Goldstone bosons. One set is eaten by the electroweak (EW ) gauge bosons W and Z to generate their masses, while the other set remains in the spectrum, which is called the top-pions (π 0 t and π ± t ). Topcolor scenario also predicts the existence of the top-Higgs h 0 t , which is the tt bound state. The possible signals of these new scalar particles have been extensively studied in the literature, however, most are done in the context of the T C2 model. Phenomenology analysis about the top-pions and top-Higgs predicted by the T T M model [3,4,5] is necessary.
The Large Hadron Collider (LHC) generates high energetic proton-proton (pp) collisions with a luminosity of L = 10 34 cm −2 s −1 . It provides high statistics data at high energies. On the other hand hadronic interactions generally involve serious backgrounds which should be concerned. A new phenomenon called exclusive production was observed in the measurements of CDF collaboration include the exclusive lepton pairs production [6], photon photon production [7], dijet production [8], the exclusive charmonium (J/ψ) meson photoproduction [9], etc. Complementary to pp interactions, studies of exclusive production of leptons, photon and heavy particles might be possible and opens new field of studying very high energy photon-photon (γγ) and photon-proton (γp) interactions.
Following the experience from HERA and the T evatron new detectors are proposed to be installed in the LHC tunnel as an additional upgrade of the AT LAS and CMS detectors. They have a program of forward physics with extra detectors located in a region nearly 100m-400m from the interaction point. These forward detector equipment allows one to detect intact scattered protons after the collision. Therefore the processes which spoil the proton structure, can be easily discerned from the exclusive photo-production processes. By use of forward detector equipment we can eliminate many serious backgrounds. This is one of the advantages of the exclusive photo-production processes.
Photoproduction of the charged top-pion at leading order (LO) has been studied in Ref. [26] which proceeds via the subprocess γc → π ± t b mediated by the flavor changing couplings and through γb → π ± t t at the large hadron-electron collider (LHeC) [27]. At the LHC, in general pp collision, the charged top-pion can be produced in association with a top quark through bottom-gluon fusion, gb → tπ − t , and through gluon-gluon fusion, gg →btπ − t , phenomenologically similar to a charged Higgs boson in a two-Higgsdoublet model with low tanβ. Related NLO study can be find in Ref. [28]. On the other hand, π ± t t associated production at the γp collision LHC will be very clean or at least with backgrounds easy going, thus leading a good chance to be detected. It can be a complementary process to be studied in addition of gb → tπ − t . In this paper, we present this production at the γp collision assuming a typical LHC multipurpose forward detector. Accurate theoretical predictions including higher order QCD corrections are included. Paper is organized as follows: in section 2 we present a brief introduction to the calculation framework including the T T M model description, EP A implementation and LO and NLO cross section calculations. Section 3 is arranged to present the numerical checks and results of our studies. Finally we summarize the conclusions in the last section.

The essential features of the T T M model
The detailed description of the T T M model can be found in Refs. [3,4], and here we just briefly review its essential features, which are related to our calculation. The Others remain as physical states in the spectrum, which are called the top-pions (π ± t and π 0 t ) and the top-Higgs h 0 t . In this paper, we will focus our attention on photoproduction of the charged top-pions via γp collisions at the LHC. The couplings of the charged top-pions π ± t to ordinary particles, which are related to our calculation, are given by Ref. [4] with Here we assume the CKM matrix to be identity and omit the light quark masses. M D is the mass scale of the heavy fermion and M W ′ is the mass of the new gauge boson W ′ .
Since the top quark mass depends very little on the right-handed delocalization parameter ε tR , we have set ε tR = 0 in Eq. (1). The parameter ε L describes the degree of delocalization of the left-handed fermions and is flavor universal, the parameter x presents the ratio of gauge couplings. The relationship between ε L and x, which is given in Eq. (2), is imposed by ideal delocalization.
Ref. [29] has shown that M W ′ should be larger than 380 GeV demanded by the LEP II data and smaller than 1.2 T eV by the need to maintain perturbative unitarity in W L W L scattering. It is obvious that the coupling π t tb is not very sensitive to the parameters with It is obvious that constant C is not sensitive to the value of sin ω and its value close to 1. The parameter sin ω indicates the fraction of EW SB provided by the top condensate.
The top-pion mass M πt depends on the amount of top-quark mass arising from the the extended technicolor (ET C) sector and on the effects of EW gauge interactions [30], and thus its value is model-dependent. In the context of the T T M model, Ref. [4] has obtained the constraints on the top-pion mass via studying its effects on the relevant experimental observables. Similarly with Refs. [4,31], we will assume it as a free parameter.

Equivalent Photon Approximation (EP A)
In γp collisions, the quasi-real photons are emitted from protons with very low virtuality so that it's a good approximation to assume that they are on-mass-shell. These quasi- with where α is the fine-structure constant, E is the energy of the incoming proton beam which is related to the quasi-real photon energy by E γ = ξE and M p is the mass of the proton. ξ = (|p| − |p ′ |)/|p|, where p and p ′ are momentums of incoming protons and intact scattered protons, respectively. µ 2 p = 7.78 is the magnetic moment of the proton. F E and F M are functions of the electric and magnetic form factors. In this case, if both incoming emitted protons remain intact provides the γγ collision and it can be cleaner than the γp collision, however, γp collisions have higher energy and effective luminosity with respect to γγ interactions.

The cross sections up to NLO
We denote the parton level process as γ( where p i are the particle four momentums. The hadronic cross section at the LHC can be converted by integrating γb → π ± t t over the photon(dN(x, Q 2 )) and quark(G b/p (x 2 , µ f )) spectra: where x 1 is the ratio between scattered quasi-real photons and incoming proton energy M inv is the total mass of the π ± t t final state. 2z x 1 is the Jacobian determinant when transform the differentials from dx 1 dx 2 into dx 1 dz. G b/p (x, µ f ) represent the bottom quark parton density functions, µ f is the factorization scale which can be chosen equal the renormalization scale µ r when the loop calculation is included. 1 avgfac is the times of spin-average factor, color-average factor and identical particle factor. |M n | 2 presents the squared n-particle matrix element and divided by the flux factor [2ŝ(2π) 3n−4 ]. dΦ n is the n-body phase space differential. Figure 1: Tree parton level Feynman diagrams for rb → π − t t in the T T M frame.
The parton Feynman diagrams at tree level are shown in Fig.1(a,b). We only consider the π − t t production while its charge-conjugate contribution is the same. At NLO QCD loop level, the Feynman diagrams are presented in Fig.2 and Fig.3, correspond to loop (σ loop ) and real (σ real ) contributions, respectively. There exist ultraviolet (UV ) and soft/collinear IR singularities in σ loop . To remove the UV divergences, we introduce the wave function renormalization constants δZ ψ q,L,R for massless bottom and mas- Figure 2: The QCD one-loop Feynman diagrams for the partonic process γb → π − t t(a-h). Counterterm diagrams correspond to Fig.1 are not shown here. Figure 3: The tree level Feynman diagrams for the real gluon/light-(anti)quark emission subprocess γb → π − t tg related to the first process in Eq.7(a-f) and γg → π − t tb related to the second process in Eq.7(g,h).
correspond to real gluon emission and real light-(anti)quark emission partonic processes, respectively. After combining all these contributions above, the UV and IR singularities in σ total = σ born + σ loop + σ S + σ HC + σ HC are exactly canceled. Dependence on the arbitrary small cutoff parameters δ s and δ c are then vanished. These cancelations can be verified numerically in our numerical calculations.

Numerical Results and Discussions
We use FeynArts, FormCalc and our modified LoopTools (FFL) [34,35,36] packages to perform the numerical calculation. We use CT10 [37] for the parton distributions for collider physics and BASES [38]

Cross sections and Distributions
In Fig.5  To see how the cross sections depend on the detector acceptances, in Fig.6 we fix ξ min = 0.0015 and take ξ max as a running parameter. One should note here that the detector acceptance is indeed a step function of ξ while here we show the dependence on  LO and NLO predictions, respectively. From these panels, we can see for ξ max < 0.5, the cross section enhance rapid when ξ acceptances become larger. Case is different for dσ dp

Signal Background Analysis and Parameter Sensitivity
Now let's turn to the signal and background analysis. From Ref. [4] we see that, for M ht ≥ 300GeV and M πt ≤ 600GeV , the charged top-pions π − t dominantly decay into tb and there is Br(π − t → tb) > 90%. As for the mass of M πt become heavier, the validity of this statement is no longer independent of the mass of, for example, top-Higgs mass M ht .
However, for each value of sin ω, a specific range of masses for the top-Higgs is excluded by the Tevatron data. For example, the illustrative value sin ω = 0.5, the data implies that the mass range 140GeV < M Ht < 195GeV is excluded. Here we concentrate on the case where M ht ≥ 350GeV . Even though, as the mass M πt become heavier than 600 GeV , the decay mode π ± → W ± H t becomes more and more competitive, where the assumption of a branching ratio Br(π − t → tb) < 90% should be considered. We concentrate on the π ± t → tb(tb) decay modes. In this case, photoproduction of the charged top-pion associated with a top quark can easily transfer to the ttb final state through In addition, another tagging method based on the same physics properties of photoproduction events is to place an exclusivity condition on reconstructed particle tracks on the gap side which can obviously reduce patronic backgrounds [43]. Even if both conditions are used and partronic background is reduced to a level that not allows proper signal extraction, elastic photon emission can be tagged using very forward detector (V F D) [44] placed hundreds of meters away from the interaction point. For instance, the case for which V F D stations would be put at 220m and 420m from the interaction point and is mandatory in order to retain partonic backgrounds low [45]. Indeed, when an intact proton is scattered with a large pseudorapidity it escapes detection from the central detectors. But since its energy is lower than the beam energy, its trajectory decouples from the beam path into the very forward region. Forward detectors can detect particles with a large pseudorapidity. The detection of final state intact protons by the forward detectors provides a characteristic signature. Backgrounds from usual DIS processes can also be rejected by use of this characteristic signature provided by the forward detectors.
Therefore in our paper, the only considered backgrounds come from protoproduction. From this point we can see that the backgrounds would come from tt plus jet (ttj) photoproduction. Different from normal pp collision, in γp collisions where photoproduction of top quark pairs has similar cross sections like, for example, W − t productions, only ∼1.4 pb [10], while for ttj, roughly ∼ 16fb after considering the fake b-tagging efficiency, leading such related background processes easier going than in case of the pp collision. Here we assume that the π ± t fully decay to tb(tb) if M πt < 600GeV while Br(π ± t → tb(tb) < 90%) [4] should be considered if M πt ≥ 600GeV . For the SM gauge bosons W ± decay leptonically, W ± → lν, the signal is 2 and the corresponding background Our results show that, for low M πt , the sin ω discovery range is larger than the case of high M πt . As the top-pion mass becomes larger, the sin ω discovery range is suppressed.
When M πt > 900GeV , heavy final state strongly suppress the phase space. The signal becomes much small and makes it more challenge to be detected. In this case, higher luminosity is needed to make the detection possible and push the discovery boundary larger. Two ways can be used in order to constraint the parameters or the excluding sin ω boundary more strictly: one is, as we see, to enhance the luminosity which can expand the related parameter space, see in Table.1, while the other one is to take more kinematical cuts to improve the ratio S/ √ B. In our case for example, if a p jet T cut taken to be larger than 200 GeV can strongly suppress the ttj backgrounds and thus lead better S/ √ B in parts of the T T M parameter space.

Summary
In this work, we present the precise photoproduced charged top-pion π ± t production associated with a top through pp → pγp → π ± t t + X at the 14 T eV LHC at NLO QCD loop level. We find the cross sections are sensitive to T T M parameters, and the smaller the sin ω is or the lighter the top-pion π − t is, the larger the cross sections will be. The typical QCD correction value is 7% ∼ 11% which does not depend much on the T T M parameter sin ω as well as the detector acceptances ξ. We also present the 5σ discovery and 3σ excluding boundaries as functions of the T T M parameters for three values of the luminosity at the future LHC.