arXiv subjects

M. Haghighat

Publications and source records attributed to M. Haghighat.

30 records · Page 2Linked to original sources

arXiv2010

Noncommutative QED+QCD and $β$-function for QED

QED based on $θ$-unexpanded noncomutative space-time in contrast with the noncommutative QED based on $θ$-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 $β$ function that can be positive, negative and even zero. In fact the $β$ function depends on the mixing parameter $δ_{13}$ as a free parameter and it will be equal to its counterpart in the ordinary QED for $δ_{13}=0.367π$.

hep-ph↗

arXiv2010

Generation of circular polarization of the CMB

According to the standard cosmology, near the last scattering surface, the photons scattered via Compton scattering are just linearly polarized and then the primordial circular polarization of the CMB photons is zero. In this work we show that CMB polarization acquires a small degree of circular polarization when a background magnetic field is considered or the quantum electrodynamic sector of standard model is extended by Lorentz-noninvariant operators as well as noncommutativity. The existence of circular polarization for the CMB radiation may be verified during future observation programs and it represents a possible new channel for investigating new physics effects.

hep-th↗

arXiv2008

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) $.

hep-ph↗

arXiv2007

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 $þ_{μν}$. 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.

hep-ph↗

arXiv2006

Bound State of an Electron on a $^4$He Superfluid Droplet as a Test for Quantum Gravity

We address the problem of finding a system in which there would be measurable quantum gravitational effects. Following standard quantum-field methods, we have calculated the first-order radiative correction of graviton exchange on the binding energy of an electron with an ultra cold superfluid droplet of $^4$He with mass about the Planck mass. For two $^4$He droplets with a mass difference of about one microgram, we show that the relative difference in the binding energies is about one percent.

gr-qc↗

arXiv2006

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 $γν\barν$-vertex which does not exist in the minimal extension of non-commutative standard model (mNCSM). We calculate the amplitude for $γν\toγν$ 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 $(θ_{NC})^2{M}_Z^{-4}E^6$ and $(θ_{NC})^4E^6$ which can exceed the cross section for $γν\toγγν$ and $γν\toγν$ in the high energy limit in the commutative space.

hep-ph↗

arXiv2004

Parton Model in Lorentz Invariant Non-Commutative Space

We consider the Lorentz invariant non-commutative QED and complete the Feynman rules for the theory up to the order $θ^2$. In the Lorentz invariant version of the non-commutative QED the particles with fractional charges can be also considered. We show that in the parton model, even at the lowest order, the Bjorken scaling violates as $\simθ^2Q^4$.

hep-ph↗

arXiv2004

Relativistic Kinetic Vertex in Positronium

We derive Spinless Salpeter equation for the positronium using the NRQED Lagrangian. Consequently, we consider the Spinless Salpeter wavefunction instead of the Schrodinger wavefunction to show that the NRQED calculation can be done easier. We also discuss that the singularity of the Spinless Salpeter wavefunction at the origin is necessary to cancel the ultraviolet divergence in the NRQED calculations.

hep-ph↗

arXiv2003

Coherent State for a Relativistic Spinless Particle

The Klein-Gordon equation with scalar potential is considered. In the Feshbach-Villars representation the annihilation operator for a linear potential is defined and its eigenstates are obtained. Although the energy levels in this case are not equally-spaced, depending on the eigenvalues of the annihilation operator, the states are nearly coherent and squeezed. The relativistic Poschl-Teller potential is introduced. It is shown that its energy levels are equally-spaced. The coherence of time evolution of the eigenstates of the annihilation operator for this potential is evaluated.

quant-ph↗

arXiv2003

Three Body Bound State in Non-Commutative Space

The Bethe-Salpeter equation in non-commutative QED (NCQED) is considered for three-body bound state. We study the non-relativistic limit of this equation in the instantaneous approximation and derive the corresponding Schrödinger equation in non-commutative space. It is shown that the experimental data for Helium atom puts an upper bound on the magnitude of the parameter of non-commutativity, $θ\sim10^{-9}λ_e^2$.

hep-th↗

arXiv2002

Positronium Hyperfine Splitting in Non-commutative Space at the Order $α^6$

We obtain positronium Hyperfine Splitting owing to the non-commutativity of space and show that, in the leading order, it is proportional to $θα^6$ where, $θ$ is the parameter of non-commutativity. It is also shown that spatial non-commutativity splits the spacing between $n=2$ triplet excited levels $E(2^3S_1)\to E(2^3P_2)$ which provides an experimental test on the non-commutativity of space.

hep-ph↗

arXiv2001

Scalar-Scalar Bound State in Non-commutative Space

Bethe-Salpeter equation in the non-commutative space for a scalar-scalar bound state is considered. It is shown that in the non-relativistic limit, the effect of spatial non-commutativity appears as if there exist a magnetic dipole moment coupled to each particle.

hep-th↗