Related papers: The solution to the `$1/2$ vs $3/2$' puzzle
The Bethe-Salpeter equation (BSE) can provide an accurate description of low-energy optical spectra of insulating crystals - even when excitonic effects are important. However, due to high computational costs it is only possible to include…
This study presents a systematic estimation of the relativistic correction to the binding energies of two-body hadronic molecular states by comparing the numerical solutions of the three-dimensional (3D) Schr{\"o}dinger, 3D Salpeter, and…
Determining absolute neutrino masses remains a central challenge in particle physics. Relations among the neutrino mass-squared differences could facilitate this determination and shed additional light on the underlying mass-generation…
The hyperfine splittings $\Delta_D=(m_{D^*_s}-m_{D_s})-(m_{D^{*+}}-m_{D^+})$ and $\Delta_B=(m_{B^*_s}-m_{B_s})-(m_{B^{*0}}-m_{B^0})$ are analyzed in the framework of an effective lagrangian possessing chiral, heavy flavour and spin…
We obtain an essentially optimal estimate for the moment of order 32/3 of the exponential sum having argument $\alpha x^3+\beta x^2$. Subject to modest local solubility hypotheses, we thereby establish that pairs of diagonal Diophantine…
In this proceeding we present predictions of the effective Majorana mass $|m_{\beta\beta}|$ in neutrinoless double-$\beta$ decay for the standard $3\nu$ mixing case and for the 3+1 neutrino mixing case indicated by the short-baseline…
Exclusive semileptonic B decays into $D_1$ and $D_2^*$ mesons are investigated including order $\Lambda_{QCD}/m_{c,b}$ corrections using the heavy quark effective theory. At zero recoil, the $\Lambda_{QCD}/m_{c,b}$ corrections can be…
In this study, we calculate the mixing angles between the axial-vector mesons $D_{1(s1)} - D_{1(s1)}^\prime$ and $B_{1(s1)} - B_{1(s1)}^\prime$ using the QCD sum rules approach. Our results are $\theta_1 = 28.2 \pm 0.6^\circ$, $\theta_2 =…
In this paper we consider a semi-linear, energy sub-critical, defocusing wave equation $\partial_t^2 u - \Delta u = - |u|^{p -1} u$ in the 3-dimensional space with $p \in [3,5)$. We prove that if initial data $(u_0, u_1)$ are radial so that…
Many results in mass partitions are proved by lifting $\mathbb{R}^d$ to a higher-dimensional space and dividing the higher-dimensional space into pieces. We extend such methods to use lifting arguments to polyhedral surfaces. Among other…
The Bethe-Salpeter equation for two massive scalar particles interacting by scalar massless exchange has solutions of two types, which differ from each other by their behavior in the non-relativistic limit: the normal solutions which turn…
In the presence of mixing between massive neutrino states, the distortion of the electron spectrum in beta decay is, in general, a function of several masses and mixing angles. For $3\nu$-schemes which describe the solar and atmospheric…
A general form of multi-channel Bethe-Salpeter equation is considered. In contradistinction to the hitherto applied approaches, our coupled system of equations leads to the simultaneous solutions for all relativistic four-point Green…
A particle with spin 1/2 is investigated both in expanding and oscillating cosmological de Sitter models. It is shown that these space-time geometries admit existence of the non-relativistic limit in the covariant Dirac equation. Procedure…
The number of lattice points in $d$-dimensional hyperbolic or elliptic shells $\{m : a<Q[m]<b\}$, which are restricted to rescaled and growing domains $r\;\Omega$, is approximated by the volume. An effective error bound of order…
Observing the list of compatible second order equations of Absolute Parallelism (AP) found by Einstein and Mayer (they used D=4), we choose the one-parameter class of equations which take on a 3-linear form (when contra-frame density of…
After formulating the pressure wave equation in half-space minus a crack with a zero Neumann condition on the top plane, we introduce a related inverse problem. That inverse problem consists of identifying the crack and the unknown forcing…
A Hamiltonian that approaches the study of the three-body problem in general relativity is obtained. We use it to study the relativistic version of the circular restricted three-body problem in which the first body is the heaviest and the…
Starting from the two-particle Bethe-Salpeter equation in the ladder approximation and integrating over the time component of momentum, we rederive three dimensional scattering integral equations satisfying constraints of relativistic…
In this paper we derive a fully relativistic kinetic theory for spin-1/2 particles and its coupling to Maxwell's equations, valid in the long scale-length limit, where the fields vary on a scale much longer than the localization of the…