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.

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.

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