Assignments of the X 4140 , X 4500 , X 4630 , and X 4685 Based on the QCD Sum Rules

In this article, we take into account our previous calculations based on the QCD sum rules, and tentatively assign the X 4630 as the D s ∗ D ¯ s 1 − D s 1 D ¯ s ∗ tetraquark molecular state or c s P c ¯ s ¯ A + c s A c ¯ s ¯ P tetraquark state with the J P C = 1 − + , and assign the X 3915 and X 4500 as the 1S and 2S c s A c ¯ s ¯ A tetraquark states, respectively, with the J P C = 0 + + . Then, we extend our previous works to investigate the LHCb’s new tetraquark candidate X 4685 as the first radial excited state of the X 4140 with the QCD sum rules and obtain the mass M X = 4.70 ± 0.12 GeV , which is in very good agreement with the experimental value 4684 ± 7 − 16 + 13 MeV . Furthermore, we investigate the two-meson scattering state contributions in details and observe that the two-meson scattering states alone cannot saturate the QCD sum rules, the contributions of the tetraquark states play an unsubstitutable role, and we can saturate the QCD sum rules with or without the two-meson scattering states.

Irradiation-induced Kondo resonance in two-dimensional electron systems

We demonstrated theoretically that formation of the resonant scattering states in the two-dimensional (2D) electron system irradiated by a circularly polarized electromagnetic field leads to the emergence of localized magnetic moments. As a consequence, the corresponding Kondo resonances appear. For GaAs-based quantum wells and microwave fields, we estimate the Kondo temperature around 2.5 K, which can be detected in state-of-the-art measurements.

Bound and scattering states solutions of the Klein–Gordon equation with the attractive radial potential in higher dimensions

In this study, the Klein–Gordon equation (KGE) is solved with the attractive radial potential using the Nikiforov–Uvarov-functional-analysis (NUFA) method in higher dimensions. By employing the Greene–Aldrich approximation scheme, the approximate bound state energy equations as well as the corresponding radial wave function are obtained in closed form. Also, the expression for the scattering phase shift is obtained in D-dimensions. The effects of the screening parameter and the total angular momentum quantum number on the bound state energy and the scattering states’ phase shift are also studied numerically and graphically at different dimensions. An interesting result of this study is the inter-dimensional degeneracy symmetry for scattering phase shift. Hence, this concept is applicable in the areas of nuclear and particle physics.

Strichartz Estimates for Wave Equations with Charge Transfer Hamiltonians

We prove Strichartz estimates (both regular and reversed) for a scattering state to the wave equation with a charge transfer Hamiltonian in R 3 \mathbb {R}^{3} : \[ ∂ t t u − Δ u + ∑ j = 1 m V j ( x − v → j t ) u = 0. \partial _{tt}u-\Delta u+\sum _{j=1}^{m}V_{j}\left (x-\vec {v}_{j}t\right )u=0. \] The energy estimate and the local energy decay of a scattering state are also established. In order to study nonlinear multisoltion systems, we will present the inhomogeneous generalizations of Strichartz estimates and local decay estimates. As an application of our results, we show that scattering states indeed scatter to solutions to the free wave equation. These estimates for this linear models are also of crucial importance for problems related to interactions of potentials and solitons, for example, in [Comm. Math. Phys. 364 (2018), no. 1, pp. 45–82].

(2, 2) Scattering and the celestial torus

Analytic continuation from Minkowski space to (2, 2) split signature spacetime has proven to be a powerful tool for the study of scattering amplitudes. Here we show that, under this continuation, null infinity becomes the product of a null interval with a celestial torus (replacing the celestial sphere) and has only one connected component. Spacelike and timelike infinity are time-periodic quotients of AdS3. These three components of infinity combine to an S3 represented as a toric fibration over the interval. Privileged scattering states of scalars organize into SL(2, ℝ)L×SL(2, ℝ)R conformal primary wave functions and their descendants with real integral or half-integral conformal weights, giving the normally continuous scattering problem a discrete character.

Consistent Theory of Alpha-Decay

In the framework of the Goldberger–Watson decay theory, we consider the a-decay of nuclei as a transition between the initial bound state of the nucleus and scattering states of the continuum spectrum with a-particle. The scattering wave functions for the a-decay with arbitrary orbital angular momentum are derived in the quasiclassical approximation. The a-particle is described by the square-integrable wave packet formed by these functions, whose amplitude exponentially grows outside the nucleus up to the wave front. The Moshinsky’s distortions of the a-wave front are analyzed. The derived general expression for the decay rate is approximated by the quasiclassical formula.