Lorentz Conserving Noncommutative Standard Model

We consider Lorentz conserving noncommutative field theory to construct the Lorentz conserving noncommutative standard model based on the gauge group $SU(3)\times SU(2)\times U(1)$. We obtain the enveloping algebra-valued of Higgs field up to the second order of the noncommutativity parameter $\th_{\mu\nu}$. We derive the action at the leading order and find new vertices which are absent in the ordinary Standard Model as well as the minimal noncommutative standard model. We briefly study the phenomenological aspects of the model.Comment: 18 pages, 1 figure, to appear in Phys. Rev.

Massive Neutrino in Non-commutative Space-time

We consider the noncommutative standard model based on $SU(3)\times SU(2)\times U(1)$. We study the gauge transformation of right handed neutrino and its direct interaction with photon in the noncommutative space-time. We show that the massive Dirac neutrinos, through the Higgs mechanism, can not accommodate this extension of the standard model; while the massive Majorana neutrinos are consistent with the gauge symmetry of the model. The electromagnetic properties and the dispersion relations for the neutrino in the noncommutative standard model is examined. We also compare the results with the noncommutative standard model based on $U(3)\times U(2)\times U(1)$.Comment: 14 pages, 1 figure, to appear in Phys. Rev.

The decay of singlet scalar dark matter to unparticle and photon

We consider the unparticle physics introduced by Georgi and show that if the standard model is extended to include a singlet scalar as a dark matter candidate, there is a channel which leads to its decay to photon and unparticle. We calculate the decay rate for this new channel and find a lower bound on unparticle physics scale by demanding the stability of this candidate of the dark matter.Comment: 5 page

Photon Neutrino Scattering in Non-Commutative Space

We extend the non-commutative standard model based on the minimal $SU(3)\times SU(2)\times U(1)$ gauge group to include the interaction of photon with neutrino. We show that, in the gauge invariant manner, only the right handed neutrino can directly couple to the photon. Consequently, we obtain the Feynman rule for the $\gamma\nu\bar\nu$-vertex which does not exist in the minimal extension of non-commutative standard model (mNCSM). We calculate the amplitude for $\gamma\nu\to\gamma\nu$ in both the nonminimal non-commutative standard model (nmNCSM) and the extended version of mNCSM. The obtained cross section grows in the center of mass frame, respectively, as $(\theta_{NC})^2{M}_Z^{-4}E^6$ and $(\theta_{NC})^4E^6$ which can exceed the cross section for $\gamma\nu\to\gamma\gamma\nu$ and $\gamma\nu\to\gamma\nu$ in the high energy limit in the commutative space.Comment: 12 pages, 3 figures, to appear in Phys. Rev.

Noncommutative QED+QCD and β\beta-function for QED

QED based on $\theta$-unexpanded noncomutative space-time in contrast with the noncommutative QED based on $\theta$-expanded U(1) gauge theory via the Seiberg-Witten map, is one-loop renormalizable. Meanwhile it suffers from asymptotic freedom that is not in agreement with the experiment. We show that QED part of $U_\star(3)\times U_\star(1)$ gauge group as an appropriate gauge group for the noncommutative QED+QCD, is not only one-loop renormalizable but also has a $\beta$ function that can be positive, negative and even zero. In fact the $\beta$ function depends on the mixing parameter $\delta_{13}$ as a free parameter and it will be equal to its counterpart in the ordinary QED for $\delta_{13}=0.367\pi$.Comment: 33 pages, 30 figures, to appear in PR

Neutral current neutrino oscillation via quantum field theory approach

Neutrino and anti-neutrino states coming from the neutral current or $Z_0$ decay are blind with respect to the flavor. The neutrino oscillation is observed and formulated when its flavor is known. However, it has been shown that we can see neutrino oscillation pattern for $Z_0$ decay neutrinos provided that both neutrino and anti-neutrino are detected. In this paper, we restudy this oscillation via quantum field theory approach. Through this approach, we find that the oscillation pattern ceases if the distance between the detectors is larger than the coherence length, while both neutrino and antineutrino states may be coherent. Also the uncertainty of source (region of $Z_0$ decay) does not have any role in the coherency of neutrino and antineutrino.Comment: to appear in PL

Singlet particles as cold dark matter in noncommutative space-time

We extend the noncommutative (NC) standard model to incorporate singlet particles as cold dark matter. In the NC space-time, the singlet particles can be coupled to the U(1) gauge field in the adjoint representation. We Study the relic density of the singlet particles due to the NC induced interaction. Demanding either the singlet fermion or the singlet scalar to serve as cold dark matter and the NC induced interactions to be relevant to the dark matter production, we obtain the corresponding relations between the NC scale and the dark matter masses, which are consistent with some existing bounds.Comment: 14 pages, to appear in Phys. Rev.