Unparticle As Possible Source

One interesting feature of unparticle is that it has no definite mass and instead has a continuous spectral density as a consequence of scale invariance

where P is the 4-momentum, Adu is the normalization factor and du is the scaling dimension. The theoretical bounds of the scaling dimension du are 1 ≤ du ≤ 2 (for boson unparticle) or 3/2 ≤ du ≤ 5/2 (for fermion unparticle). The pressure and energy density of the thermal boson unparticle are given by

where C(du) = B(3/2, du)Γ(2du + 2)_(2du + 2), while B, Γ, ζ are the Beta, Gamma and Zeta functions, Thus, the EoS of boson unparticle reads

For the fermion unparticle, we find the EoS has the same form as that of boson one. Obviously, the EoS of unparticle !u is positive which is different from that of DE and DM. Since the unparticle interacts weakly with standard model particles, it can be regarded as a new form of dark component. Since the fermion unparticle has charge it could be another possible origin of local brane lensing. In the Einstein theory, the a flat FRW universe is described by the standard Friedmann equation and Raychaudhuri field equation

H is the Hubble parameter and k is the constant 8πG. The total energy density

, where

correspond to the energy densities of DM, DE and unparticle, respectively. The interaction among DE, DM and unparticle can be described in the background by the balance equations

The terms describe the coupling among DE, DM and unparticles. The total conservation equation demands that

The effective total EOS !tot is given by One can also have the coupling terms

which are

You now have not only DE transfers to DM, and the coupling terms also denotes that DM can be convert to unparticle. The dynamical equations of the system have the forms

and the critical points are

indicates that A2 is an unstable point. And one can get a saddle function out of this..

However when we find that all of eigenvalues are negative, which indicates that C2 is a stable point. This can translate to a case where a system will be dominated by unparticle if the coupling constant b is large enough. This idea of the unparticle has been offered in outside articles as a solution to the observational coincidence problem when the coupling constant is weak. However, the case of charged fermion unparticles could offer a solution to local brane lensing when the coupling constant is large enough to at least produce a local lensing out to around the orbit of Jupter with drop off after that point. For the sake of our field generator idea we would need around a 1AU field in the forward region at least to encompass the ability to take advantage of the faster light velocity for navigation. This would require us to be able to alter the coupling constant to fit our needs. This still requires us to craft wise limit usage of such a field outside of the confines of the solar system. But for lab testing and usage on a small probe to test the field we could shorten the field and run the craft in an area already known to have no objects in our path. To arrive at a better understanding of the unparticle we introduce couplings between new physics operator OUV with mass dimension dUV, which is singlet under the SM gauge group, and the SM operator OSM with mass dimension dSM at a mass scale M

where cn is a dimensionless constant. It is assumed that new physics sector has an infrared fixed point at a scale Auv, below which the operator OUV matches onto a new (composite) operator OU. With dimension dU through the dimensional transmutation. As a result, the effective interaction term arises of the form

where λn is a coupling constant and Δ is an effective cutoff scale of low energy physics. Depending on the nature of new physics operator OUV, the resulting unparticle may have different Lorentz structure. One can use scale invariance can be used to fix the two-point function of unparticle operators

where

With as the normalization factor. This factor is fixed by identifying with dU-body phase space of massless particle to be

The Feynman propagator is

and similarly for the vector unparticle (with only the transverse mode)

By requiring conformal invariance, the scalar unparticle propagator remains the same form while the vector unparticle propagator is modified to

It is also possible as mentioned to have no Lorentz invariance with the resulting propagator changes to the above. But, the fact that our local brane lensing remains invariant suggests one of the above to be the case here if unparticles are involved. The scaling dimension for the scalar unparticle is constrained as dU ≥ 1 while for the vector unparticle the bound is dU ≥ 3. For fermions effective interactions of the scalar unparticle with the SM fields are given by, for gluon the fermion part is

The interactions with fermions can be simplified by utilizing the equation of motion for a fermion

But here again, as one can notice the charge element would actually come from coupling to regular SM matter which leads to an indirect effect somewhat used to rule out the axion case before. This again seems to be a dead end leading back to the Neutrino solution.