Related papers: Excellent approximate solution to the mysterious m…
Exponential lepton mass ratios are studied in a low energy phenomenology. In view of the known data, the mass patterns of the charged leptons and widely discussed quasi-degenerate neutrinos are related to one another by two different traits…
There are several ways to derive Einstein's celebrated formula for the energy of a massive particle at rest, $E=mc^2$. Noether's theorem applied to the relativistic Lagrange function provides an unambiguous and straightforward access to…
An overview of lattice results for the strange quark mass, $B_K$, $B_6$, $B_7$, and $B_8$ is presented. I give my assessment of the reliability of various estimates and prospects for future improvements.
The equation derived by F. Rohrlich (Phys. Rev. E 77, 046609 (2008)) has been known for 60 years (C. J. Eliezer, Proc. Royal Soc. London. Ser. A 194, 543 (1948)). For a long time this equation has been considered to be incorrect. If there…
We construct a class of renormalizable models for lepton mixing that generate predictions given in terms of the charged-lepton mass ratios. We show that one of those models leads, when one takes into account the known experimental values,…
We present a unified treatment of three cases of quasi-exactly solvable problems, namely, charged particle moving in Coulomb and magnetic fields, for both the Schr\"odinger and the Klein-Gordon case, and the relative motion of two charged…
Large-scale {\em ab initio} QED calculations are performed for the $2p_{3/2}$--$2p_{1/2}$ fine-structure interval of Li-like ions with nuclear charges $Z = 5\,$--$\,92$. Improved theoretical predictions are obtained by combining together…
We calculate the strong isospin breaking and QED corrections to meson masses and the hadronic vacuum polarization in an exploratory study on a $64\times24^3$ lattice with an inverse lattice spacing of $a^{-1}=1.78$ GeV and an isospin…
We propose $S_4$ symmetric four-generation models for charged leptons. Although an $S_4$ symmetric four-generation model has been already proposed, there are some additional symmetries in the model. We construct four-generation models for…
Wilson's formulation of lattice QCD is attractive for many reasons, but perhaps mainly because of its simplicity and conceptual clarity. Numerical simulations of the Wilson theory (and of its improved versions) tend to be extremely…
Using the QCD Sum Rule Method, we estimate the mass of the lowest strange hybrid baryon with $IJ^P=0(1/2)^-$. We find the mass is approximately that of the $\Lambda(1405)$, whose nature has been a puzzle for many decades. Possible tests of…
We give error estimates for a mixed finite element approximation of the two-dimensional elliptic Monge-Ampere equation with the unknowns approximated by Lagrange finite elements of degree two. The variables in the formulation are the scalar…
New sequences of orthogonal polynomials with ultra-exponential weight functions are discovered. In particular, it gives an explicit solution to the Ditkin-Prudnikov problem (1966). The 3-term recurrence relations, explicit representations,…
{The numerical approximation of the solution of the Fokker--Planck equation is a challenging problem that has been extensively investigated starting from the pioneering paper of Chang and Cooper in 1970. We revisit this problem at the light…
We consider a Fermi-Pasta-Ulam-Tsingou lattice with randomly varying coefficients. We discover a relatively simple condition which when placed on the nature of the randomness allows us to prove that small amplitude/long wavelength solutions…
The effective QCD-interaction as obtained from the front form Hamiltonian by DLCQ is Fourier transformed on the Retarded Schr\"odinger Equation for to describe the constituents of physical mesons. The crucial point is the use of a running…
The constant pairing Hamiltonian holds exact solutions worked out by Richardson in the early Sixties. This exact solution of the pairing Hamiltonian regained interest at the end of the Nineties. The discret complex-energy states had been…
It is shown that an idea proposed in 1996 that relates in a qualitatively correct way the inter-family mass hierarchies of the up quarks, down quarks, charged leptons, and neutrinos, can be combined with a predictive scheme recently…
We introduce the Shifted Legendre Symbol Problem and some variants along with efficient quantum algorithms to solve them. The problems and their algorithms are different from previous work on quantum computation in that they do not appear…
Within the frame of a novel treatment we make a complete mathematical analysis of exactly solvable one-dimensional quantum systems with non-constant mass, involving their ordering ambiguities. This work extends the results recently reported…