Related papers: Irrational constants in positronium decays
The positronium, as the lightest purely leptonic bound state, provides an ideal testing ground for a quantum field--theoretical (QFT) description of composite systems. While its electromagnetic annihilation is well understood as the…
A well known theorem of Lagrange states that the simple continued fraction of a real number $\alpha$ is periodic if and only if $\alpha$ is a quadratic irrational. We examine non-periodic and non-simple continued fractions formed by two…
Neutron-antineutron oscillations are considered in the light of recently proposed particle models, which claim to resolve the neutron lifetime anomaly, indicating the existence of baryon violating $\Delta B=1$ interactions. Possible…
The heavy and superheavy elements of the periodic table predominately disintegrate by {\alpha}-decay, facilitating transitions mainly between ground states and occasionally involving isomeric states. This study focuses on estimating the…
Two-loop QED corrections to the decay rate of parapositronium (p-Ps) into two photons are presented. We find Gamma(p-Ps --> 2 photons) = 7989.64(2)/microsec. The non-logarithmic O(alpha^2) corrections turn out to be small, contrary to some…
We study how the decay properties of particles are changed by acceleration. It is shown that under the influence of acceleration (1) the lifetime of particles is modified and (2) new processes (like the decay of the proton) become possible.…
One possible probe to physics beyond the standard model is to look for scalar bilinears, which couple to two fermions of the standard model. We point out that the scalar bilinears allow new diagrams contributing to the neutrinoless double…
Realistic calculations of nuclear disappearance lifetimes induced by neutron-antineutron oscillations are reported for oxygen and iron, using antineutron nuclear potentials derived from a recent comprehensive analysis of antiproton atomic…
We present a precise theoretical prediction for the decay width of the bound state of two electrons and a positron (a negative positronium ion), Gamma(Ps^-) = 2.087 085(12)/ns. We include O(alpha^2) effects of hard virtual photons as well…
We consider the semi-linear beam equation on the d dimensional irrational torus with smooth nonlinearity of order n -- 1 with n $\ge$ 3 and d $\ge$ 2. If $\epsilon$ $\ll$ 1 is the size of the initial datum, we prove that the lifespan…
Current laboratory bounds imply that protons are extremely long-lived. However, this conclusion may not hold for all time and in all of space. We find that the proton lifetime can be $\sim 15$ orders of magnitude shorter in the relatively…
Following earlier results of Sondow, we propose another criterion of irrationality for Euler's constant $\gamma$. It involves similar linear combinations of logarithm numbers $L\_{n,m}$. To prove that $\gamma$ is irrational, it suffices to…
In this note, we prove the irrationality of $\zeta(5)$ and generalize the method to prove the irrationality of all higher odd zeta values. Our proof relies on the method of contradiction, existence of solution of a system of Linear…
For any prime $p$ and $\varepsilon>0$ we prove that for any sufficiently large positive odd integer $s$ at least $(c_p-\varepsilon) \sqrt{\frac{s}{\log s}}$ of the $p$-adic zeta values $\zeta_p(3),\zeta_p(5),\dots,\zeta_p(s)$ are…
The logarithmically enhanced alpha^7 ln(1/alpha) contribution to the hyperfine splitting of the positronium ground-state energy levels is calculated in the framework of dimensionally regularized nonrelativistic quantum electrodynamics. The…
An unexplained $>4\,\sigma$ discrepancy persists between "beam" and "bottle" measurements of the neutron lifetime. A new model proposed that conversions of neutrons $n$ into mirror neutrons $n'$, part of a dark mirror sector, can increase…
Let $k\geq 1$ be a small fixed integer. The rational approximations $\left |p/q-\pi^{k} \right |>1/q^{\mu(\pi^k)}$ of the irrational number $\pi^{k}$ are bounded away from zero. A general result for the irrationality exponent $\mu(\pi^k)$…
We study particle decay in de Sitter space-time as given by first order perturbation theory in a Lagrangian interacting quantum field theory. We study in detail the adiabatic limit of the perturbative amplitude and compute the "phase space"…
The basic properties of oscillons -- localized, long-lived, time-dependent scalar field configurations -- are briefly reviewed, including recent results demonstrating how their existence depends on the dimensionality of spacetime. Their…
This talk gives an elementary introduction to the basic properties of positronium. Recent progress in theoretical studies of the hyperfine splitting and lifetime of the ground state is reviewed. Sensitivity of these precisely measured…