Modern Physics Letters A

We show in general that for a relativistic theory with curved momentum space, i.e. a theory with deformed relativistic symmetries, the physical velocity of particles coincides with their group velocity. This clarifies a long-standing question about the discrepancy between coordinate and group velocity for this kind of theories. The first evidence that this was the case had been obtained at linear order in the deformation parameter in Ref. 1 for the specific case of $\kappa$-momentum space. The proof was based on the recent understanding of how relative locality affects these scenarios. Here we rely again on a careful implementation of relative locality effects, and obtain our result for a generic (relativistic) curved momentum space framework at all orders in the deformation/curvature parameter. We also discuss the validity of this result when the deformation depends on the coordinates as well as on the momenta.

We extend the recent one-loop analysis of the ultraviolet completion of the $ℂ\mathbb{P}(N)$ nonlinear $\sigma$ model in six dimensions to two-loop order in the $\overline{\mathrm{\text{MS}}}$ scheme for an arbitrary covariant gauge. In particular we compute the anomalous dimensions of the fields and $\beta$-functions of the four coupling constants. We note that like Quantum Electrodynamics (QED) in four dimensions the matter field anomalous dimension only depends on the gauge parameter at one loop. As a nontrivial check we verify that the critical exponents derived from these renormalization group functions at the Wilson–Fisher fixed point are consistent with the $𝜖$ expansion of the respective large $N$ exponents of the underlying universal theory. Using the Ward–Takahashi identity we deduce the three-loop $\overline{\mathrm{\text{MS}}}$ renormalization group functions for the six-dimensional ultraviolet completeness of scalar QED.

We calculate ${\bar{B}}_s^0\to \varphi$ translation form factors $V$, $A_0$, $A_1$, $A_2$ based on QCD sum rule and study the nonleptonic two-body decay of ${\bar{B}}_s^0\to J/\psi \varphi$ with the form factors obtained. We calculate the time-integrated branching ratio of ${\bar{B}}_s^0\to J/\psi \varphi$ decay. The results for both the total branching ratio and the cases for the final vectors in longitudinal and transverse polarizations are consistent with experimental data.

We make a number of comments about the way the Plücker embedding, which can be derived via the Grassmann-Plücker relations, can be associated to totally antisymmetric gauge fields. As a first step we discuss the case of the electromagnetic field strength, showing that the Plücker map implies both the true degrees of freedom of the electromagnetic field and the 1-brane (string) structure. The procedure is generalized in order to prove that the true degrees of freedom of a totally antisymmetric field and the p-brane structure are, in part, consequence of the Plücker coordinates.

We investigate analyticity properties of correlation functions in conformal field theories (CFTs) in the Wightman formulation. The goal is to determine domain of holomorphy of permuted Wightman functions. We focus on crossing property of three-point functions. The domain of holomorphy of a pair of three-point functions is determined by appealing to Jost’s theorem and by adopting the technique of analytic completion. This program paves the way to address the issue of crossing for the four-point functions on a rigorous footing.

It is found explicitly 5 Liouville integrals in addition to total angular momentum which Poisson commute with Hamiltonian of 3-body Newtonian Gravity in ${ℝ}^3$ along the remarkable figure-8-shape trajectory discovered by Moore-Chenciner-Montgomery. It is verified that they become constants of motion along this trajectory. Hence, 3-body choreographic motion on figure-8-shape trajectory in ${ℝ}^3$ Newtonian gravity (Moore, 1993), as well as in ${ℝ}^2$ modified Newtonian gravity by Fujiwara et al., is maximally superintegrable. It is conjectured that any 3-body potential theory that admits Figure-8-shape choreographic motion is superintegrable along the trajectory.

We propose a $B-L$ Standard Model (SM) extension based on $\mathrm{\Delta }(27)$ symmetry in which neutrino mass orderings and the tiny neutrino masses are produced by the type-I seesaw mechanism. The obtained physical parameters are well consistent with the global fit of neutrino oscillation.¹ The model is predictive in the sense that it reproduces the experimental values of neutrino parameters. Two of the predicted parameters have little deviations from the best-fit values given in Ref. 1, however they are consistent with the other experimental results.${}^{2,3}$

One usually defines the Brown–York energy for a 2-surface embedded in a space-like 3-slice as an integration of the mean curvature of the 2-surface isometrically embedded into the 3-slice, with a proper reference 3-space. We demonstrate that this naive definition is ill for stationary spacetimes. As an example, we investigate the Kerr–Newman spacetime in detail. We show that the naive definition of the Brown–York energy is not a component of the Brown–York boundary stress tensor, and thus deviates from the original idea of Brown and York. Furthermore, we present the exact form of the Brown–York energy for the Kerr–Newman spacetime with proper reference.

In this paper we study the interaction between two qutrits ($\mathrm{\Lambda }$-type three-level atoms) with a two-mode field in a high quality cavity, considering the field-field (F-F) correlation and dipole-dipole (D-D) interaction. By defining a Hamiltonian corresponds to D-D interaction related to the two three-level atoms, we introduce a generalized Hamiltonian of Jaynes-Cummings model for the desired system and then the associated Schrödinger equation is solved. Finally, by achieving the reduced density matrix and then the linear entropy as a criterion for the entanglement, we investigate the influence of the F-F and D-D coupling on the degree of entanglement of the system. Our results show that there exists specific initial superposition of atomic states wherein the stable value of linear entropy is accessible. In addition, in such cases the F-F correlation and D-D interaction have not considerable effect on the entropy. Moreover, in general, as we have shown, the entanglement can be tuned appropriately by choosing the parameters involve in the model.