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Advances in High Energy Physics
Volume 2012 (2012), Article ID 571874, 8 pages
The Impact of Excited Neutrinos on Process
Department of Physics, Cumhuriyet University, 58140 Sivas, Turkey
Received 24 August 2012; Revised 24 October 2012; Accepted 25 October 2012
Academic Editor: Joseph Formaggio
Copyright © 2012 S. C. İnan and M. Köksal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We examine the effect of excited neutrinos on the annihilation of relic neutrinos with ultrahigh energy cosmic neutrinos for the process. The contributions of the excited neutrinos to the neutrino-photon decoupling temperature are calculated. We see that photon-neutrino decoupling temperature can be significantly reduced below the obtained value of the Standard Model with the impact of excited neutrinos.
According to standard cosmology, neutrinos are probably one of the most abundant particles of the universe. The universe is filled with a sea of relic neutrinos that decoupled from the rest of the matter within the first few seconds after the Big Bang. It is excessively difficult to measure relic neutrinos since the interactions of their cross-sections with matter are tremendously suppressed. Besides, it is crucial to detect relic neutrinos in order to test the neutrino aspects of the Big Bang model of cosmology, but it would seem impossible with present methods. However, some indirect evidences of the relic sea may be observed. For example, Weiler  have shown that the UHE cosmic neutrinos may interact with relic neutrinos via the following reactions occurring on the resonance: In such an event, a UHE cosmic neutrino has energy eV. Therefore, the interaction of relic neutrinos and UHE cosmic neutrinos would have significant cross-section.
The high energy photon-neutrino interactions are very important in astrophysics, high energy cosmic ray physics, and cosmology. From Yang's theorem [2, 3], the leading term of the cross-section for the process is very small due to the vector-axial vector nature of the weak coupling when the neutrinos are massless. It is shown that , where is the electron mass and is the photon energy in the center of the mass frame, where the cross-section for the process is in the order of , and is the boson mass [4–6]. The dimension-8 effective Lagrangian for the photon-neutrino interaction in Standard Model (SM) is as follows : where is the neutrino field, is the electroweak gauge coupling, is the photon field tensor, is the fine structure constant, and is the following: Equation (1.2) can be rewritten as the following format : Here, and are the stress-energy tensors of the neutrinos and photons which are given as follows:
For the SM, the photons and neutrinos decouple, that is, process at a temperature GeV within one micro second after the Big Bang . When decoupling temperature is reduced to the QCD phase transition ( MeV), some remnants of the photons circular polarization can possibly be retained in the cosmic microwave background , which can be considered as an evidence for the relic neutrino background. For reducing the decoupling temperature, the cross-section for the process should be increased. This can be done via the models which are beyond the SM. For instance, contributions of large extra dimensions to these process have been calculated in . They have shown that the inclusion of the extra dimension effects did not provide large enough high energy neutrinos to scatter from relic neutrinos in this process but concluded that the photon decoupling temperature can be significantly reduced. Also, in , it has been remarked that unparticle physics can lower decouple temperature below the .
The SM has been successful in describing the physics of the electroweak interactions, and it is consistent with experiments. However, some questions are still left unanswered, such as, the number of fermion generation and fermion mass spectrum has not been exhibited by the SM. Attractive explanations are provided by models assuming composite quarks and leptons. The existence of excited states of the leptons and quarks is a natural consequence of these models, and their discovery would provide convincing evidence of a new scale of matter. In this model, charged and neutral leptons can be considered as a heavy lepton sharing leptonic quantum number with the corresponding SM lepton. They should be regarded as the composite structures which are made up of more fundamental constituents. Therefore, excited neutrinos can be considered to spin 1/2 bound states, including three spin 1/2 or spin 1/2 and spin substructures. All composite models have an underlying substructure which is characterized by a scale .
The interaction between spin 1/2 excited fermions, gauge bosons, and the SM fermions can be described by the invariant effective Lagrangian as follows [9–13]: In these expressions, with being the Dirac matrices, and are the field strength tensors of the and , and are the generators of the corresponding gauge group, and and are standard electroweak and strong gauge couplings. is the scale of the new physics responsible for the existence of excited neutrinos, and , scale the and couplings, respectively. The effective Lagrangian can be rewritten in the physical basis First term in the previous equation is a purely diagonal term with , and second term is a non-Abelien part which involves triple as well as quartic vertices with The chiral () interaction term can be found as follows: where is the momentum of the gauge boson, is the electroweak coupling parameter, and is defined for photon by , where we have assumed that .
Up to now, searches have not found any signal for excited neutrinos at the colliders. The current mass limits on excited neutrinos are GeV at the LEP  and GeV assuming at the HERA . Excited neutrinos have been also studied for hadron colliders [16–18] and next linear colliders [18, 19]. In these studies, it has been obtained that excited neutrinos masses up to TeV can be detected at the LHC.
In this paper, we examine the effect of the excited neutrinos on the interaction of the UHE cosmic and relic neutrinos for the process.
2. Process Including Excited Neutrinos
The SM contributions to process have been calculated in [4, 6] using (1.2). From this effective Lagrangian, the squared amplitude for the SM can be obtained in terms of Mandelstam invariants u and t as follows: where .
The new physics (NP) contribution comes from and channels of excited neutrino exchange. The analytical expressions for the polarization summed amplitudes square for NP, SM and NP interference terms are given as follows: where . Therefore, the whole squared amplitude can be calculated as follows: Because of low center of mass energy of the neutrinos, we have used an approximation, . In the limit , the amplitude turns into following formation: We have calculated the cross-section with/without approximation cross-section. We have seen that results are close for different and . Therefore, the differential cross-section for process can be obtained by using Then, the total cross-section can be found from (2.5) as follows: In Figure 1, we have plotted the total cross-sections as a function of the center of mass energy for both the and total cross-sections when GeV. These cross-sections are obtained for the two excited neutrinos, with masses of GeV and GeV. Also, in Figure 2, we have showed the cross-sections for GeV and three scales of the new physics GeV, GeV, and GeV. This figure shows similar behavior with Figure 1.
Extra contribution to the cross-section from excited neutrino exchange influences the decoupling temperature. The temperature at which this process ceases to take place can be found from the the reaction rate per unit volume, The terms in (2.7) are as the following: and are the momentum of the neutrino and antineutrino; and are their energies; is the temperature; is the flux. The can be given in terms of in the center of mass frame by use of invariance of , where and is the angle between and . Equation (2.7) can be found where and . Then, the reaction rate per unit volume has been obtained, where is the Riemann Zeta function. The interaction rate is obtained by dividing by the neutrino density at temperature . Thus, we have found that Multiplying (2.11) by the age of the universe, at least one interaction to occur is . The solution of the following equation gives the decoupling temperature: If and are replaced in the previous equation, then the following equation can be found: Figure 3 shows solution of this equation.
We have analyzed the contribution of excited neutrinos on the interaction of relic neutrinos with UHE cosmic neutrinos via the process. It is shown that excited neutrino contribution to total cross-section of the process is significant depending on the , . We have seen that for the appropriate values of these parameters, the SM and total cross-sections can be distinguished from each other in the specific center of mass energy regions.
For decreasing decoupling temperature, the total cross-section of the should be increased. If the or new physics parameter decrease, then the total cross-section increases. Therefore, can be decreased significantly. For different values of , have been shown in Figure 3 as a function of the new physics parameter . As seen from this figure, our obtained values of the decoupling temperature can decrease the value of the SM decoupling temperature (≈ 1.6 GeV).
As a result, excited neutrinos can allow lowering the decoupling temperature of the scattering. Therefore, they can provide significant contribution to search for relic neutrinos.
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