arXiv subjects

Abouzeid M. Shalaby

Publications and source records attributed to Abouzeid M. Shalaby.

22 records · Page 2Linked to original sources

arXiv2009

Possible treatment of the Ghost states in the Lee-Wick Standard Model

Very recently, the Lee-Wick standard model has been introduced as a non-SUSY extension of the Standard model which solves the Hierarchy problem. In this model, each field kinetic term attains a higher derivative term. Like any Lee-Wick theory, this model suffers from existence of Ghost states. In this work, we consider a prototype scalar field theory with its kinetic term has a higher derivative term, which mimics the scalar sector in the Lee-Wick Standard model. We introduced an imaginary auxiliary field to have an equivalent non-Hermitian two-field scalar field theory. We were able to calculate the positive definite metric operator $η$ in quantum mechanical and quantum field versions of the theory in a closed form. While the Hamiltonian is non-Hermitian in a Hilbert space with the Dirac sense inner product, it is Hermitian in a Hilbert space endowed by the inner product $ $ as well as having a correct-sign propagator (no Lee-Wick fields). Besides, the obtained metric operator also diagonalizes the Hamiltonian in the two fields (no mixing). Moreover, the Hermiticity of $η$ constrained the two Higgs masses to be related as $M>2m$, which has been obtained in another work using a very different regime and thus supports our calculation. Also, an equivalent Hermitian (in the Dirac sense) Hamiltonian is obtained which has no Ghost states at all, which is a forward step to make the Lee-Wick theories more popular among the Physicists.

hep-th↗

arXiv2008

Will the $PT$ Symmetric and Non-Hermitian $ϕ^4$ Theory Solve the Hierarchy and Triviality Problems in the Standard Model?

Very recently, the Large Hadron Collider was turned on. There, the experiments are aiming to test different scenarios for elementary particles interactions from SUSY, Extra dimensions to others. In fact, SUSY was invented to kill the conceptual problems existing in the conventional Standard model \textit{i.e.} the Hierarchy problem. However, in recent years, certain theories which was rejected in the past like the wrong sign $ϕ^{4}$ theory is now well known to be a truly physically acceptable theory. Here, we analyze the renormalization group flow of the different parameters in the theory. We find that, rather than the conventional $ϕ^{4}$ theory and because the theory is asymptotically free, it does not sufferer from the catastrophic blow up of the mass parameter for UV scales. This feature greatly recommend that this theory is a plausible candidate to play the role of the $SU(2)\times U(1)$ symmetry breaking in the standard model. If this picture will agree with the experimental results from LHC, then the Higgs particle was massless in the far past. Moreover, the cosmological constant problem as a Hierarchy problem may be solved too. However, when trying to calculate the metric operator, we expected that the equivalent Hermitian theory may attain non-remormalizabe terms and thus the theory is incalculable. In fact, we show that there exists a Hermitian and renormalizable equivalent theory though of indefinite metric. We reformulated the Klein-Gordon equation in such a way that the wrong sign in the propagator attains a new physical meaning that the Higgs particle is made from exotic matter.

hep-th↗

arXiv2007

A Novel phase in the phase structure of the $(gϕ^4 + hϕ^6)_{1+1}$ field theoretic model

In view of the newly discovered and physically acceptable $PT$ symmetric and non-Hermitian models, we reinvestigated the phase structure of the ($gϕ^{4}+hϕ^{6}$)$_{1+1}$ Hermitian model. The reinvestigation concerns the possibility of a phase transition from the original Hermitian and $PT$ symmetric phase to a non-Hermitian and $PT$ symmetric one. This kind of phase transition, if verified experimentally, will lead to the first proof that non-Hermitian and $PT$ symmetric models are not just a mathematical research framework but are a nature desire. To do the investigation, we calculated the effective potential up to second order in the couplings and found a Hermitian to Non-Hermitian phase transition. This leads us to introduce, for the first time, hermiticity as a symmetry which can be broken due to quantum corrections, \textit{i.e.}, when starting with a model which is Hermitian in the classical level, quantum corrections can break hermiticity while the theory stays physically acceptable. In fact, ignoring this phase will lead to violation of universality when comparing this model predictions with other models in the same class of universality. For instance, in a previous work we obtained a second order phase transition for the $PT$ symmetric and non-Hermitian $(-gϕ^{4})$ and according to universality, this phase should exist in the phase structure of the ($gϕ^{4}+hϕ^{6}$) model for negative $g$. Finally, among the novelties in this letter, in our calculation for the effective potential, we introduced a new renormalization group equation which describes the invariance of the bare vacuum energy under the change of the scale. We showed that without this invariance, the original theory and the effective one are inequivalent.

hep-th↗

arXiv2006

Non-perturbative calculations for the effective potential of the $PT$ symmetric and non-Hermitian $(-gϕ^{4})$ field theoretic model

We investigate the effective potential of the $PT$ symmetric $(-gϕ^{4}) $ field theory, perturbatively as well as non-perturbatively. For the perturbative calculations, we first use normal ordering to obtain the first order effective potential from which the predicted vacuum condensate vanishes exponentially as $G\to G^+$ in agreement with previous calculations. For the higher orders, we employed the invariance of the bare parameters under the change of the mass scale $t$ to fix the transformed form totally equivalent to the original theory. The form so obtained up to $G^3$ is new and shows that all the 1PI amplitudes are perurbative for both $G\ll 1$ and $G\gg 1$ regions. For the intermediate region, we modified the fractal self-similar resummation method to have a unique resummation formula for all $G$ values. This unique formula is necessary because the effective potential is the generating functional for all the 1PI amplitudes which can be obtained via $\partial^n E/\partial b^n$ and thus we can obtain an analytic calculation for the 1PI amplitudes. Again, the resummed from of the effective potential is new and interpolates the effective potential between the perturbative regions. Moreover, the resummed effective potential agrees in spirit of previous calculation concerning bound states.

hep-th↗