International Journal of Modern Physics A

NUMEN proposes an innovative technique to access the nuclear matrix elements entering the expression of the lifetime of the double beta decay by cross-section measurements of heavy-ion induced Double Charge Exchange (DCE) reactions. Despite the fact that the two processes, namely neutrinoless double beta decay and DCE reactions, are triggered by the weak and strong interaction respectively, important analogies are suggested. The basic point is the coincidence of the initial and final state many-body wave functions in the two types of processes and the formal similarity of the transition operators. The main experimental tools for this project are the K800 Superconducting Cyclotron and MAGNEX spectrometer at the INFN-LNS laboratory. However, the tiny values of DCE cross-sections and the resolution requirements demand beam intensities much higher than those manageable with the present facility. The on-going upgrade of the INFN-LNS facilities promoted by the POTLNS project in this perspective is intimately connected to the NUMEN project. This paper describes the solutions proposed as a result of the R&D activity performed during the recent years. The goal is to develop suitable technologies allowing for the measurements of DCE cross-section under extremely high beam intensities.

Recent work [S. R. Beane, D. B. Kaplan, N. Klco and M. J. Savage, Phys. Rev. Lett. 122, 102001 (2019), arXiv:1812.03138.] conjectured that entanglement is minimized in low-energy hadronic scattering processes. It was shown that the minimization of the entanglement power (EP) of the low-energy baryon–baryon $S$-matrix implies novel spin–flavor symmetries that are distinct from large-$N_c$ QCD predictions and are confirmed by high-precision lattice QCD simulations. Here, the conjecture of minimal entanglement is investigated for scattering processes involving pions and nucleons. The EP of the $S$-matrix is constructed for the $\pi \pi$ and $\pi N$ systems, and the consequences of minimization of entanglement are discussed and compared with large-$N_c$ QCD expectations.

In this paper, we give an update on divergent problems concerning the radiative corrections of quantum electrodynamics in $(3+1)$ dimensions. In doing so, we introduce a geometric adaptation for the covariant photon propagator by including a higher derivative field. This derivation, so-called generalized quantum electrodynamics, is motivated by the stability and unitarity features. This theory provides a natural and self-consistent extension of the quantum electrodynamics by enlarging the space parameter of spinor-gauge interactions. In particular, Haag’s theorem undermines the perturbative characterization of the interaction picture due to its inconsistency on quantum field theory foundations. To circumvent this problem, we develop our perturbative approach in the Heisenberg picture and use it to investigate the behavior of the operator current at one-loop. We find the two- and three-point correlation functions are ultraviolet finite, electron self-energy and vertex corrections, respectively. On the other hand, we also explain how the vacuum polarization remains ultraviolet divergent only at $e^2$ order. Finally, we evaluate the anomalous magnetic moment, which allows us to specify a lower bound value for the Podolsky parameter.

Relativistic quantum mechanics of free fermions in the presence of the spiral dislocation of space–time with a distortion of a radial line into a spiral is studied within the Katanaev–Volovich geometric approach. The generalized Dirac equation in this background is constructed. Exact closed-form solutions are found by reducing the problem to that of a nonrelativistic two-dimensional $1/r$-problem with a complex coupling constant. The influence of the defect parameter related to the spiral dislocation on these solutions is investigated. We also study the charge density of free fermions in the presence of such a spiral dislocation in space–time. Based on the Bender–Boettcher approach for non-Hermitian Hamiltonians we study, in addition, bound-state solutions of the system.

In this paper, we estimate the net information exchange between adjacent quantum subsystems holographically living on the boundary of $\mathrm{\text{AdS}}$ space–time. The information exchange is a real-time phenomenon and only after long-time interval it may get saturated. Normally, we prepare systems for small time intervals and measure the information exchange over finite interval only. We find that the information flow between entangled subsystems gets reduced if systems are in excited state whereas the ground state allows maximum information flow at any given time. Especially for ${\mathrm{\text{CFT}}}_2$ we exactly show that a rise in the entropy is detrimental to the information exchange by a quantum dot and vice-versa. We next observe that there is a reduction in circuit (CV) complexity too in the presence of excitations for small times.

It is well known that the Klein–Gordon equation in curved spacetime is conformally noninvariant, both with and without a mass term. We show that such a noninvariance provides nontrivial physical insights at different levels, first within the fully relativistic regime, then in the nonrelativistic regime leading to the Schrödinger equation, and then within the de Broglie–Bohm causal interpretation of quantum mechanics. The conformal noninvariance of the Klein–Gordon equation coupled to a vector potential is confronted with the conformal invariance of Maxwell’s equations in the presence of a charged current. The conformal invariance of the nonminimally coupled Klein–Gordon equation to gravity is then examined in light of the conformal invariance of Maxwell’s equations. Finally, the consequence of the noninvariance of the equation on the Aharonov–Bohm effect in curved space–time is discussed.

Exchange $\mu -\tau$ symmetry in the effective Majorana neutrino mass matrix does predict a maximal mixing for atmospheric neutrino oscillations asides to a null mixing that cannot be straightforwardly identified with reactor neutrino oscillation mixing, ${𝜃}_{13}$, unless a specific ordering is assumed for the mass eigenstates. Otherwise, a nonzero value for ${𝜃}_{13}$ is predicted already at the level of an exact symmetry. In this case, solar neutrino mixing and scale, as well as the correct atmospheric mixing arise from the breaking of the symmetry. I present a mass matrix proposal for normal hierarchy that realizes this scenario, where the smallness of $tan{𝜃}_{13}$ is naturally given by the parameter $𝜖\sim \sqrt{\mathrm{\Delta }{m}_{\mathrm{\text{sol}}}^2/\mathrm{\Delta }{m}_{\mathrm{\text{ATM}}}^2}$ and the solar mixing is linked to the smallness of $\mathrm{\Delta }{m}_{\mathrm{\text{sol}}}^2$. The proposed matrix remains stable under renormalization effects and it also allows to account for CP violation within the expected region without further constrains.

We apply the “systematic” first-order cosmological perturbation theory method to re-derive the formulation of an inflationary model generated by variation of constants, then to study the case where it is nonminimally coupled to gravity within both the “Metric” and “Palatini” formulations. Accommodating Planck 2018 data with a length scale $\ell$ larger than Planck length $L_{\mathrm{\text{pl}}}$ requires amending the model. First, we assume $f(R)$ gravity where we show that an $R^2$-term within Palatini formulation is able to make the model viable. All along the discussions, we elucidate the origin of the difference between the “Metric” and “Palatini” formalisms, and also highlight the terms dropped when applying the shortcut “potential formulae method,” unlike the “systematic method,” for the observable parameters. Second, another variant of the model, represented by a two-exponentials potential, fits also the data with $\ell >L_{\mathrm{\text{pl}}}$.

The lowest critical point of one unitary matrix model with cosine plus logarithmic potential is known to correspond with the $(A_1,A_3)$ Argyres–Douglas (AD) theory and its double scaling limit derives the Painlevé II equation with parameter. Here, we consider the critical points associated with all cosine potentials and determine the scaling operators, their vacuum expectation values (vevs) and their scaling dimensions from perturbed string equations at planar level. These dimensions agree with those of $(A_1,A_{4k-1})$ AD theory.

In this paper, we explore the theoretical constraints on the observable parameters of neutrino mixing on predictions for the leptonic Dirac CP-violating phase within a well-studied class of simple theoretical models that includes a single source of CP violation due to charged lepton corrections. The approach guarantees that a physically meaningful prediction for the most likely values for the leptonic Dirac CP-violating phase is obtained.

An alternative scenario about the phenomenology of primordial universe is $k$-inflation. According to this concept, inflation can be achieved by nonstandard kinetic term of scalar field, namely, the inflaton. In this paper, we focus on $k$-essence models in the presence of a higher order and a linear kinetic term. Furthermore, the inflationary phenomenology with a Dirac–Born–Infeld scalar field is briefly examined, which arises from quantum theories of gravity such as superstring theory. Our approach about the inflationary era is that it can be described in the context of Einstein’s gravity involving quantum corrections such as the Chern–Simons string inspired parity violating gravitational term. The equations of motion namely, the Friedmann equation, the Raychadhuri equation and the Klein–Gordon equation for an expanding background are extracted from the gravitational action utilizing the variational principle. The consequential system of differential equations with respect to Hubble’s parameter and the inflaton field was quite perplexed in order to be solved with an analytic way. Therefore, the slow-roll conditions during inflationary era were imposed and terms with minor numerically contribution were neglected. From the overall phenomenological analysis, it is proved that models with exotic kinetic terms can generate viable results in consistency with the latest Planck data. Finally, the presence of Chern–Simons quantum corrections shifts the primordial spectral tensor index to blue. Even though blue gravitational waves are yet to be observed, if detected, compatibility with the aforementioned theory can be achieved.

In this paper, structural features of quark mass matrices have been analyzed in the flavor basis which is allowed by weak basis transformations in the Standard Model. Using the latest precised data pertaining to quark mixing matrix and small quark masses, we find that the texture structure of these cannot be simplified further. However, we find enormous amount of simplification is possible wherein we have found that a single phase in the mass matrix is adequate to accommodate the CP violating phase of CKM matrix.

Recently, H. Benzair et al. [Mod. Phys. Lett. A 35, 2050246 (2020).] formulated in one dimension the nonrelativistic propagator for position-dependent mass (PDM) from the generalized displacement operator approach. According to the path integral formulation, we generalize this process in $D$-dimensional space. As a result, the wave functions are obtained analytically for the pseudo-harmonic oscillator and the inverse square plus Coulomb potentials, and the corresponding energy spectrum are studied. In addition, the effects of PDM on the canonical partition function and other thermodynamic functions have been extracted. The limit cases are then deduced for a small parameter.

In this paper, some possible Lagrangians for the quadratically damped systems are investigated. The corresponding classical Hamiltonians are investigated with Hamilton equations. The quantum Hamiltonians are also constructed so that they may be Hermitian. As an example, the quantum mechanics for the harmonic oscillator with a small quadratic damping is discussed.

In this paper, we derive a general formulation for thermal Lie superalgebras motivated by thermofield dynamics formalism (TFD). Particularly, we construct the thermal Poincaré superalgebras. The operators in TFD are defined through the doubling of the degrees of freedom of the system and it can be related to Hopf algebras. In this way, we explore the notion of quantum group associated with these superalgebras and we show the noncommutativity in this thermal scenario. Furthermore, the thermal M-superalgebra is also derived from TFD prescription.