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Andrzej Czarnecki

Publications and source records attributed to Andrzej Czarnecki.

At least 19 recordsLinked to original sources
arXiv2026

Bound-state decay of a charged scalar particle in an external Coulomb field

We determine the decay rate $Γ$ of a scalar particle bound to a light nucleus, numerically and analytically. As a model system, we consider a negatively charged kaon in the ground state of a hydrogen-like ion decaying into charged and neutral scalar pions, $K^-\to π^-π^0$. All particles are assumed point-like; the nucleus is infinitely heavy. The partial wave expansion converges slowly, as in a recent analysis of the bound-muon decay. To overcome this difficulty, we introduce a subtraction method: the free $π^-$ contribution is evaluated separately, while the partial-wave sum is used only for the Coulomb distortion. The ratio of bound-to-free decay rates, $Γ/Γ_0$, is found for light nuclei, $1\leq Z\leq 10$. The numerical calculation is complemented by a diagrammatic small-$αZ$ expansion. We find $ Γ/Γ_0 = 1-(αZ)^2/2 + 17(αZ)^4/24 +\mathcal{O}((αZ)^5)$, in agreement with the all-orders numerical calculation at low $Z$.

hep-ph↗
arXiv2026

A Simple Pendulum in Schwarzschild Spacetime

We determine the small-oscillation period of a simple pendulum in Schwarzschild spacetime. After transients decay, the displaced rope coincides with a geodesic of the induced spatial metric. This determines the radial lift of the bob to quadratic order in the angular amplitude and leads to the period measured by an observer at the bob's equilibrium position, $r=r_2$, with the fulcrum at $r_1$, \[ T_{(2)}=4π\frac{r_2^2}{c r_s}\sqrt{N_2(N_1-N_2)}, \] where $N_i=N(r_i)$ and $N(r)=\sqrt{1-r_s/r}$ is the Schwarzschild lapse. The result is therefore expressed in terms of the same function that determines clock rates and gravitational redshifts. In the Newtonian limit, we reproduce the classical result $T=2π\sqrt{L_0/g}$. We interpret the period close to the horizon in terms of an effective pendulum length. We compare our treatment with the coordinate-length constraint adopted in an earlier study and argue that the two problems are inequivalent away from the classical, weak-field limit.

gr-qc↗
arXiv2026

Radiative Corrections in Bound States: Recent Results

Two recent studies of radiative corrections to bound state properties are discussed. The change of the decay rate of a muon bound to a light nucleus has been calculated for several light nuclei $4\leq Z \leq 9$ with high precision, resolving a long-standing discrepancy between analytical and numerical results for oxygen ($Z=8$). The decay of parapositronium into three photons has been calculated including effects of the $Z$ boson. The resulting rate is many orders of magnitude smaller than previously estimated.

hep-ph↗
arXiv2026

Shock Wave in the Beirut Explosion: Theory and Video Analysis

Videos of the 2020 Beirut explosion offer a rare opportunity to see a shock wave. We summarize the non-linear theory of a weak shock, derive the Landau-Whitham formula for the thickness of the overpressure layer and, using frame-by-frame video analysis, we demonstrate agreement of data and theory.

nlin.CD↗
arXiv2026

Parapositronium decay into three photons and implications for the neutral pion

We complete the determination of the parapositronium decay into three photons by evaluating amplitudes mediated by the $Z$ boson. We show that, contrary to the expectation that the extra mass scale $m_e$ may bring an enhancement to the overall scaling, the amplitude turns out to start at $1/m_Z^6$ order, similarly to the $W$ boson mediated amplitude. The decay rate with both $W$ and $Z$ boson contributions is found to be $1.1\cdot 10^{-80}$ eV, about 47 orders of magnitude smaller than previously estimated. We also discuss its implication for the $π^0\to3γ$ amplitude.

hep-ph↗
arXiv2025

False-vacuum decay and flaws in Frampton's model of the origin of life

We briefly review false-vacuum decay and examine a recent proposal by Frampton to model the origin of the first single-celled organism (SCO) as a phase transition between no-life and life vacua. In his calculation the exponent $n$ entering the probability $P_{\rm SCO}\sim 10^{-n}$ has dimensions of inverse time: it is an energy barrier divided by the Planck constant, rather than a dimensionless tunnelling action. The resulting probability is mathematically ill-defined and does not determine a tunnelling rate. Apart from this dimensional issue, the assumed initial configuration, a toroidal structure made of long molecules, and its treatment in empty space are inconsistent with soft-matter physics and with the hot, collisional environment expected for prebiotic chemistry. Consequently, the claimed exponential suppression of biogenesis, and the inference that extraterrestrial life is likely absent, are not supported.

hep-ph↗
arXiv2025

Total decay rate of a muon bound to a light nucleus

We revisit the total decay rate of a muon being in the ground state of a Coulomb potential with atomic charge numbers $4\leq Z \leq 9$. The discrepancy between the perturbative $(αZ)^2$ result of [Phys. Rev. \textbf{119}, 365 (1960)] and the fully relativistic partial-wave calculation of [At. Data Nucl. Data Tables \textbf{54}, 165 (1993)] for oxygen ($Z=8$) is shown to originate from insufficient convergence of the partial-wave series in the latter work. Our accurate relativistic calculations restore agreement with the perturbative $αZ$~expansion and indicate a negative sign for the next-order $(αZ)^3$ correction.

hep-ph↗
arXiv2025

Hidden Momentum and the Absence of the Gravitational Spin Hall Effect in a Uniform Field

We re-examine the recent claim that a Dirac particle freely falling in a uniform gravitational field exhibits a spin-dependent transverse deflection (gravitational spin Hall effect). Using a circulating mass model, we show that hidden momentum arises in uniform fields when an object carries angular momentum. On the quantum side, we analyze the Dirac Hamiltonian in a uniform potential, construct its Foldy--Wouthuysen form, and evaluate the Heisenberg evolution of spin-polarized Gaussian packets. The state used previously, with $\langle p\rangle =0$, is not at rest: because canonical and kinetic momenta differ, the packet carries a spin-dependent hidden momentum from $t=0$. Imposing $\langle x(0)\rangle =\langle v(0)\rangle=0$ requires a compensating spin-dependent $\langle p(0)\rangle$; with this preparation $\langle x(t)\rangle =0$ to leading order in the gravitational acceleration $g$. Generalizing, an exact Foldy--Wouthuysen transformation (linear in $g$ but to all orders in $1/c$) shows that spin-dependent transverse motion begins no earlier than at $O(g^2)$ for a broad class of wave packets. We conclude that a uniform field does not produce a gravitational spin Hall effect at linear order; the previously reported drift stems from inconsistent initial states and misinterpreting canonical momentum.

gr-qc↗
arXiv2024

Thomas precession, relativistic torque, and non-planar orbits

We analyze the angular momentum balance for a particle undergoing Thomas precession. The relationships among relativistic torque, the center of mass, and the center of inertia for a spinning particle are clarified. We show that spin precession is accompanied by orbital angular momentum precession, and present examples of the resulting out-of-plane motion.

hep-ph↗
arXiv2023

Energy-momentum tensor of a hydrogen atom: stability, D-term, and the Lamb shift

We clarify two issues related to the so-called $D$-term in matrix elements of the energy-momentum tensor. First, we show that in a stable system, the $D$-term can have either sign, contrary to claims that it must be negative. Second, we demonstrate a logarithmic enhancement of the $\mathcalα$ correction to the $D$-term in any state of the hydrogen atom. We contrast this enhancement with the Lamb shift where it is present only in S-states.

hep-ph↗
arXiv2023

Acceleration due to buoyancy and mass renormalization

The acceleration of a light buoyant object in a fluid is analyzed. Misconceptions about the magnitude of that acceleration are briefly described and refuted. The notion of the added mass is explained and the added mass is computed for an ellipsoid of revolution. A simple approximation scheme is employed to derive the added mass of a slender body. The slender-body limit is non-analytic, indicating a singular character of the perturbation due to the thickness of the body. An experimental determination of the acceleration is presented and found to agree well with the theoretical prediction. The added mass illustrates the concept of mass renormalization in an accessible manner.

physics.flu-dyn↗
arXiv2022

Gravitational time dilation, free fall, and matter waves

We demonstrate that a de Broglie wave of a particle in a gravitational field turns towards the region of a smaller gravitational potential, causing the particle to fall. This turning is caused by clocks running slower in the smaller potential. We use the analogy of ocean waves that are slower in shallower water and turn towards beaches. This approach explains the free fall qualitatively and quantitatively without postulating motion along geodesics and with only elementary algebra.

gr-qc↗
arXiv2022

Positronium hydride decay into proton, electron, and one or zero photons

Decay rates of the positronium hydride PsH, a bound state of a proton, a positron, and two electrons, are determined for two rare channels, PsH $\to p^+ e^- γ$ and PsH $\to p^+ e^-$. Previous studies overestimated these rates by factors of about 2 and 700, respectively. We explain the physics underlying these wrong predictions. We confirm a range of static PsH properties, including the non-relativistic ground state energy, expectation values of inter-particle distances and their powers, and the three and four particle coalescence probabilities, using a variational method in the Gaussian basis.

hep-ph↗
arXiv2022

Negative energy states in pionic hydrogen

Probabilities of finding an antiparticle in an atom or ion containing a particle of spin 1/2 or spin 0 are determined. The spin 1/2 case was previously solved by Hans Bethe and his work is summarized. The spin 0 case is treated numerically for an arbitrary atomic number and analytically for small atomic numbers. The main tool for the spin 0 case is the Feshbach-Villars representation of the Klein-Gordon equation.

hep-ph↗
arXiv2022

Basis for time crystal phenomena in ultra-cold atoms bouncing on an oscillating mirror

We consider classical dynamics of a 1D system of $N$ particles bouncing on an oscillating mirror in the presence of gravitational field. The particles behave like hard balls and they are resonantly driven by the mirror. We identify the manifolds the particles move on and derive the effective secular Hamiltonian for resonant motion of the particles. Proper choice of time periodic oscillations of the mirror allows for engineering of the effective behaviour of the particles. In particular, the system can behave like a $N$-dimensional fictitious particle moving in an $N$-dimensional crystalline structure. Our classical analysis constitutes a basis for quantum research of novel time crystal phenomena in ultra-cold atoms bouncing on an oscillating atom mirror.

cond-mat.quant-gas↗