International Journal of Modern Physics A

We discuss the Casimir effect in heterotic string theory. This is done by considering a ${\mathbb{Z}}_2$ twist acting on one external compact direction and three internal coordinates. The hyperplanes fixed by the orbifold generator $G$ realize the two infinite parallel plates. For the latter to behave as “conducting material,” we implement in a modular invariant way the projection $(1-G)/2$ on the spectrum running in the vacuum-to-vacuum amplitude at one-loop. Hence, the relevant projector to account for the Casimir effect is orthogonal to that commonly used in string orbifold models which is $(1+G)/2$. We find that this setup yields the same net force acting on the plates in the context of quantum field theory and string theory. However, when supersymmetry is not present from the onset, finiteness of the resultant force in field theory is reached by adding formally infinite forces acting on either side of each plate, while in string theory, both contributions are finite. On the contrary, when supersymmetry is spontaneously broken à la Scherk–Schwarz, finiteness of each contribution is fulfilled in field and string theory.

We have considered the effects of space and momentum noncommutativity separately on the zitterbewegung (ZBW) phenomenon. In the space noncommutativity scenario, it has been expressed that, due to the conservation of momentum, the Fourier decomposition of the expectation value of position does not change. However, the noncommutative (NC) space corrections to the magnetic dipole moment of electron, that was traditionally perceived to come into play only in the first-order of perturbation theory, appear in the leading-order calculations with the similar structure and numerically the same order, but with an opposite sign. This result may explain why for large lumps of masses, the Zeeman effect due to the noncommutativity remains undetectable. Moreover, we have shown that the x- and y-components of the electron magnetic dipole moment, contrary to the commutative (usual) version, are nonzero and with the same structure as the z-component. In the momentum noncommutativity case, we have indicated that, due to the relevant external uniform magnetic field, the energy spectrum and also the solutions of the Dirac equation are changed in 3+1 dimensions. In addition, our analysis shows that in 2+1 dimensions, the resulted NC field makes electrons in the zero Landau level rotate not only via a cyclotron motion, but also through the ZBW motion with a frequency proportional to the field which doubles the amplitude of the rotation. In fact, this is a hallmark of the ZBW in graphene that provides a promising way to be tested experimentally.

We investigate $B_s^0\to {\ell }^{+}{\ell }^{-}\gamma$ decays in a nonuniversal $Z^{\prime }$ model derived from the extension of the Standard Model (SM). Considering the $Z^{\prime }$-mediated flavor-changing neutral current (FCNC) effects, we calculate the branching ratio and forward–backward asymmetry $(A_{\mathrm{\text{FB}}})$ for $B_s^0\to {\ell }^{+}{\ell }^{-}\gamma$ decay processes. We compare the obtained results with predictions of the SM and discuss the sensitivity of the observables to $Z^{\prime }$ boson coupling parameters. We find that the branching ratios are enhanced by one order from SM predictions in $Z^{\prime }$ model scenario. We also observe that the variation of forward–backward asymmetry with the $Z^{\prime }$ boson coupling parameters portrays discrimination between NP effects and SM results.

Starting from the classical nonrelativistic electrodynamics in 1+1 dimensions, a higher-derivative version is proposed. This is made by adding a suitable higher-derivative term for the electromagnetic field to the Lagrangian of the original electrodynamics, preserving its gauge invariance. By following the usual Hamiltonian method for singular higher-derivative systems, the canonical quantization for the higher-derivative model is developed. By extending the Faddeev–Senjanovic algorithm, the path integral quantization is carried out. Hence, the Feynman rules are established and the diagrammatic structure is analyzed. The use of the higher-derivative term eliminates in the Landau gauge the ultraviolet divergence of the primitively divergent Feynman diagrams of the original model, where the electromagnetic field propagator is present. A generalization of the BRST quantization is also considered.

The color confinement in Quantum Chromodynamics (QCD) remains an interesting and intriguing phenomenon. It is considered as a very important nonperturbative effect to be taken into account in all models intended to describe the QCD many-parton system. During the deconfinement phase transition, the non-Abelian character of the partonic plasma manifests itself in an important manner. A direct consequence of color confinement is that all states of any partonic system must be colorless and the requirement of the colorlessness condition is more than necessary. Indeed, the colorless state is a result of the multiparton interactions, from which collective phenomena can emerge, inducing strong correlations and giving rise to a long-range order of liquid-like phase, a behavior fundamentally different from that of a conformal ideal gas. Within our Colorless QCD MIT-Bag Model and using the ${\mathcal{ℒ}}_{m,n}$-method, three Thermal Response Functions, related to the Equation of State, like pressure $\mathcal{𝒫}(T,V)$, sound velocity ${\mathcal{𝒞}}_s^2(T,V)$ and energy density $𝜖(T,V)$ are calculated and studied as functions of temperature $(T)$ and volume $(V)$. Also and in the same context, two relevant correlation forms $\frac{\mathcal{𝒫}}{𝜖}(𝜖)$ and ${\mathcal{𝒞}}_s^2(𝜖)$ are calculated and studied intensively as functions of $(𝜖)$ at different volumes. A detailed comparative study between our results and those obtained from lattice QCD simulation, hot QCD and other phenomenological models is carried out. We find that the Liquid Partonic Plasma Model is the model which fits our Equation of State very well, in which the Bag constant term is revealed very important. Our Colorless Partonic Plasma, just beyond the finite volume transition point, is found in a state where the different partons interact strongly showing a liquid behavior in agreement with the estimate of the plasma parameter $7.92\le {\mathrm{\Gamma }}_{\mathrm{\text{CPP}}}\le 10.10$ and supporting the result obtained from the fitting work. This allows us to understand experimental observations in Ultra-Relativistic Heavy-Ion Collisions and to interpret lattice QCD results.

The color structure of the gluon field magnetic mass is investigated in the lattice SU(2) gluodynamics. To realize that the interaction between a monopole–antimonopole string and external neutral Abelian chromomagnetic field flux is considered. The string is introduced in the way proposed by Srednicki and Susskind. The neutral Abelian field flux is introduced through the twisted boundary conditions. Monte Carlo simulations are performed on 4D lattices at finite temperature. It is shown that the presence of the Abelian field flux weakens the screening of the string field. That means decreasing the gluon magnetic mass for this environment. The contribution of the neutral Abelian field has the form of “enhancing” factor in the fitting functions. This behavior independently confirms the long-range nature of the neutral Abelian field reported already in the literature. The comparison with analytic calculations is given.

We are considering a possibility for detecting nonperturbative effect in process of top pair production in association with a high $p_T$ photon. Starting from previous results on two solutions for a spontaneous generation of an effective interaction of a top pair with a pair of electroweak bosons, we show that a solution with effective cutoff $\mathrm{\Lambda }\simeq 10^2\mathrm{\text{TeV}}$ is already contradicting to the existing data, while the other one with $\mathrm{\Lambda }\simeq 10^{16}\mathrm{\text{TeV}}$ (just the Planck scale) could be reconciled with data and give predictions for process $p+p\to \bar{t}t\gamma +X$, which could be effectively checked at the LHC with $\sqrt{s}=13\mathrm{\text{TeV}}$. The confirmation of the predictions would mean a strong support for the existence of nonperturbative effects in the electroweak interaction.