On Unparticle Searches through Photon-Photon Scattering

In this work, we study the effects of the spin-0 unparticle on γγ → γγ process. From the numerical results, we show that the cross section with unparticle effect should be about 1027 1030 times larger than the one that is confirmed by QED calculation. This could have important implications for unparticle searches and for the measurement of the photon-photon cross section.


Introduction
Photon-photon scattering is among the most important and carefully studied processes in particle physics [1]- [13].In ref. [12] Liang and Czarnecki have shown a simple way of correctly computing the low-energy γγ scattering.Noterworthy, in ref. [13], we have pointed out the cross section with radion effect should be about 10 20 times larger than the one without radion effects.It is well known that Georgi [14] made an interesting observation that a nontrivial scale invariance sector of scale dimension u d might manifest itself at low energy as a nonintegral number u d of invisible massless particles, dubbed unparticle u.If unparticles exist, their phenomenological implications should be discussed.In the literature, there have been many discussions which investigate various features of unparticle physics [15]- [24].In some of these reseaches several unparticle production processes have been studied.Possible evidence for this scale invariant sector might be the signature of a missing energy.It can be tested experimentally by examining missing energy distributions.Other evidence for unparticles can be explored by studying its virtual effects.In this letter, we consider the phenomenology of unparticle signals in γγ scattering.The unparticle analysis of γγ scattering has been done first by Cakir and Ozansoy [25] and later by Chang, Cheung and Yuan [26].This scattering is described by the Feynman diagrams presented in Figure 1.The γγ u vertex is given by ( ) The spin-0 unparticle propagator is [27] [28] ( ) ( ) ( ) where and ( ) if is negative and real e for positive with an infinitesimal.
The angular distribution is [26] ( ) ( ) From ( 4), the total cross section is found to be [26] ( ) We now turn to the numerical analysis of the total cross sections.The input parameters are 0 1; 1.5 TeV.The total cross section for the unparticle contributions for 1.1, 1.2, , 1.5 It is to be noticed that in refs.[10] [12] the authors have determined the differential and total cross section for the photon-photon scattering without radion and unparticle effects

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α ω σ = Next, in ref. [13] we have investigated the effect of the radion on photon-photon scattering.We obtained the total cross section as follows ( ) The form factors are given by ( ) ( ) ( ) The important property of ( )  From this, we have found that the effects of the radion can be strong.Interestingly, we have shown that the cross section with radion effect should be about 10 20 times larger than the one without radion and unparticle effects.Now, by the results just mentioned we give the numerical values of the ratio of the total cross section with unparticle effects u σ of ( 5) to the 0 σ of ( 7) at different energies in Table 2. So, direct computations have showed that the above cross section of ( 5) should be about 10 27 -10 30 times larger than the one in (7).
Finally, we have obtained the ratio of the cross section with unparticle effects u σ of (5) to the one with radion effects R σ of (8) at different energies in Table 3.We take 1.5 TeV as input parameters.
Table 1.The total cross section with radion effects of the process γγ γγ It has already been shown that the total cross section u σ is larger than the one R σ by 6 -8 order of magnitudes.
To conclude, in this letter we have studied the unparticle effects on gamma gamma scattering.From numerical results, we have found that the effects of the unparticle on the cross sections can be very strong.If the measurement is carried out at 300 GeV -3000 GeV S = , then the cross section for the photon scattering should be detectable.This could have important implications for unparticle searches at future colliders.Our work can be extended for other scatterings, for example, Bhabha scattering or e e γγ + − → process.

Figure 1 .
Figure 1.Feynman diagram for the gamma gamma scattering through a scalar unparticle.

Table 2 .
The ratio of the total cross section with unparticle effects to one without radion and unparticle effects at different energies.

Table 3 .
The ratio of the total cross section with unparticle effects to one with radion effects at different energies.