Modern Physics Letters A

Rare charm decays offer the unique possibility to explore flavor-changing neutral-currents in the up-sector within the Standard Model and beyond. Due to the lack of effective methods to reliably describe its low energy dynamics, rare charm decays have been considered as less promising for long. However, this lack does not exclude the possibility to perform promising searches for New Physics per se, but a different philosophy of work is required. Exact or approximate symmetries of the Standard Model allow to construct clean null-test observables, yielding an excellent road to the discovery of New Physics, complementing the existing studies in the down-sector. In this review, we summarize the theoretical and experimental status of rare charm $\left|\mathrm{\Delta }c\right|=\left|\mathrm{\Delta }u\right|=1$ transitions, as well as opportunities for current and future experiments such as LHCb, Belle II, BES III, the FCC-ee and proposed tau-charm factories. We also use the most recent experimental results to report updated limits on lepton-flavor conserving and lepton-flavor violating Wilson coefficients.

The contributions of the chiral gauge leptoquarks $V^{L,R}$ induced by the chiral four-color quark–lepton symmetry to the branching ratios of $K_L^0,B^0,B_s\to l_1{l}_2$ decays are calculated and analyzed using the general parametrizations of the fermion mixing matrices in the leptoquark currents. From the current experimental data on these decays under assumption $m_{V^L}\ll m_{V^R}$, the lower mass limit $m_{V^L}cos{\gamma }_L>5.68\mathrm{\text{TeV}}$ is found, which in particular case of equal gauge coupling constants gives $m_{V^L}>8.03\mathrm{\text{TeV}}$. The branching ratios of the decays under consideration predicted by the chiral gauge leptoquarks are calculated and analyzed in dependence on the leptoquark masses and the mixing parameters. It has shown that in consistency with the current experimental data, these branching ratios for $B_s,B^0\to \mu e$ decays can be close to their experimental limits and those for $B_s,B^0\to \tau e,\tau \mu$ decays can be of order of $10^{-7}$. The calculated branching ratios will be useful in the further experimental searches for these decays.

We consider collision of two particles 1 and 2 near the horizon of the extremal Reissner–Nordström (RN) black hole that produces two other particles 3 and 4. There exists such a scenario that both new particles fall into a black hole. One of them emerges from the white hole horizon in the asymptotically flat region, and the other one oscillates between turning points. However, the unbounded energies $E$ at infinity (super-Penrose process (SPP)) turn out to be impossible for any finite angular momenta $L_{3,4}$. In this sense, the situation for such a white hole scenarios is opposite to the black hole ones, where the SPP is found earlier to be possible for the RN metric even for all $L_i=0$. However, if $L_{3,4}$ themselves are unbounded, the SPP does exist for white holes.

A new redshift formula is obtained considering the longitudinal Doppler effect in the de Sitter expanding universe where the relative geodesic motion is governed by the Lorentzian isometries of our new de Sitter relativity [I. I. Cotăescu, Eur. Phys. J. C 77, 485 (2017)]. This formula combines in a nontrivial manner the well-known cosmological contribution given by Lamaître’s law with that of the relative motion of the source with respect to a fixed observer as in de Sitter relativity instead of special relativity. Other related quantities as the dispersion relation, the propagation time of the photon and the real distance between the source and observer at the moment of observation are discussed pointing out their specific features in the de Sitter relativity.

We conjecture that the random walk and the corresponding diffusion in the relativistic velocity space is an adequate method for describing the acceleration process in relativistic jets. Considering a simple toy model, the main features of diffusion in the velocity space are demonstrated in both non-relativistic and relativistic regimes.

We have recently proposed a Lagrangian in trace dynamics to describe a possible unification of gravity, Yang–Mills fields, and fermions, at the Planck scale. This Lagrangian for the unified entity — called the aikyon — is invariant under global unitary transformations, and as a result possesses a novel conserved charge, known as the Adler–Millard charge. In this paper, we derive an eigenvalue equation, analogous to the time-independent Schrödinger equation, for the Hamiltonian of the theory. We show that in the emergent quantum theory, the energy eigenvalues of the aikyon are characterized in terms of a fundamental frequency times Planck’s constant. The eigenvalues of this equation can, in principle, determine the values of the parameters of the standard model. We also report a ground state, in this theory of spontaneous quantum gravity, which could characterize a non-singular initial epoch in quantum cosmology.

In this work, we consider the relativistic Duffin–Kemmer–Petiau equation for spin-one particles with a nonminimal vector interaction in the presence of minimal uncertainty in momentum. By using the position space representation, we exactly determine the bound-states spectrum and the corresponding eigenfunctions. We discuss the effects of the deformation and nonminimal vector coupling parameters on the energy spectrum analytically and numerically.

In this paper, we investigate the exact bound state solution of the Klein–Gordon equation for an energy-dependent Coulomb-like vector plus scalar potential energies. To the best of our knowledge, this problem is examined in literature with a constant and position dependent mass functions. As a novelty, we assume a mass-function that depends on energy and position and revisit the problem with the following cases: First, we examine the case where the mixed vector and scalar potential energy possess equal magnitude and equal sign as well as an opposite sign. Then, we study pure scalar and pure vector cases. In each case, we derive an analytic expression of the energy spectrum by employing the asymptotic iteration method. We obtain a nontrivial relation among the tuning parameters which lead the examined problem to a constant mass one. Finally, we calculate the energy spectrum by the Secant method and show that the corresponding unnormalized wave functions satisfy the boundary conditions. We conclude the paper with a comparison of the calculated energy spectra versus tuning parameters.

Nearest private query (NPQ) allows user to query which element in the database is the nearest to his private data without revealing any private information and this query is typically used for location query services. However, the previous NPQ protocol only involved the implementation of its functions and ignored the user’s private experience. In addition, the average number of key bits obtained by the user is only determined by the size of the database. In order to improve the flexibility and practicality of the protocol, we proposed a flexible protocol for nearest private query based on quantum oblivious key distribution (QOKD). The parameter $𝜃$ was added to the prepared quantum state. The average number of the key bits Alice obtained can locate on any fixed value by adjusting the parameter $𝜃$ whatever the database size was. In addition, our protocol is flexible and fault-tolerant.