arXiv:2602.00308

Wave-like amplification of near-threshold two-particle reactions: from muon-catalyzed fusion to $Λ\barΛ$ production at $e^-e^+$ annihilation

Vladimir S. Melezhik

hep-phquant-phSubmitted Jan 30, 2026• Announced Feb 3, 2026

Abstract

A simple model is proposed to explain the recently found wave-like enhancement of the $Λ\barΛ$ pair production near the threshold at the $e^-e^+$ annihilation, which allows extracting parameters of the $Λ\barΛ$ interaction and the $Λ$-hyperon rms-radius from the oscillatory nature of the measured cross section. In particular, it predicts a single bound state of $Λ\barΛ$ with a binding energy of $\varepsilon_{Λ\barΛ}=(36\pm5)$MeV. The model is a generalization of the formulas obtained in our earlier work [1] to explain the effect of wave-like amplification found in it near the threshold of fusion reactions screened by a muon or electron. The analysis allows us to conclude that the effect of wave-like amplification is an integral feature of any two-particle near-threshold reaction. In this regard, it seems promising to investigate, within the framework of our model, the oscillatory nature of the electromagnetic form factors of hyperons and nucleons extracted in experiments on $e^- e^+$ annihilation. A natural further development of the model could be its generalization to processes of producing various hadron pairs in $e^-e^+$ annihilation.

Comments: 7 pages, 5 figures

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QUANTIZATION OF RADIATION FIELD

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Chapman & Hall/CRC eBooksDec 12, 20080 citations

First quantized pair interactions

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Jun 8, 20142 citations

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H. J. Spencer

Dec 1, 20160 citations

Three level Lambda system, Feynman amplitudes and relativistic invariance

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Formation of metastable dtμ molecules in tμ(2s)−D2 collisions

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Physical Review AAug 1, 199621 citations

What If the Electron Is a Spinning Filament of Spacetime? A Conceptual Model Explaining 14 Quantum Puzzles

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Aug 12, 20260 citations

arXiv:2602.00308

Wave-like amplification of near-threshold two-particle reactions: from muon-catalyzed fusion to $Λ\barΛ$ production at $e^-e^+$ annihilationWave-like amplification of near-threshold two-particle reactions: from muon-catalyzed fusion to $Λ\barΛ$ production at $e^-e^+$ annihilation

Vladimir S. Melezhik

hep-phquant-phSubmitted Jan 30, 2026• Announced Feb 3, 2026

arXiv HTML PDF

Abstract

A simple model is proposed to explain the recently found wave-like enhancement of the

Λ\barΛ

pair production near the threshold at the

e^-e^+

annihilation, which allows extracting parameters of the

Λ\barΛ

interaction and the

Λ

-hyperon rms-radius from the oscillatory nature of the measured cross section. In particular, it predicts a single bound state of

Λ\barΛ

with a binding energy of

\varepsilon_{Λ\barΛ}=(36\pm5)

MeV. The model is a generalization of the formulas obtained in our earlier work [1] to explain the effect of wave-like amplification found in it near the threshold of fusion reactions screened by a muon or electron. The analysis allows us to conclude that the effect of wave-like amplification is an integral feature of any two-particle near-threshold reaction. In this regard, it seems promising to investigate, within the framework of our model, the oscillatory nature of the electromagnetic form factors of hyperons and nucleons extracted in experiments on

e^- e^+

annihilation. A natural further development of the model could be its generalization to processes of producing various hadron pairs in

e^-e^+

annihilation.

Comments: 7 pages, 5 figures

Related papers

QUANTIZATION OF RADIATION FIELD

Vishnu S. Mathur, Surendra Singh

In atomic, nuclear and particle physics we come across several situations where particles or radiation quanta (photons) are created or destroyed. For example in the beta decay of the neutron, a neutron is annihilated and a proton, electron and antineutrino are created. In some situations the interaction of radiation with matter can result in creation or annihilation of a pair of electron and positron. Such processes cannot be understood on the basis of (non-relativistic or relativistic) single particle wave equations because in such theories the probability ψ∗ψdτ (of finding the particle in the region of space dτ) when integrated over the whole space, results in unity at all times and so the existence of the particle is always guaranteed. Hence in the framework of single particle wave equation it is not possible to understand the creation or annihilation of particles. Even a simple process in which an atom undergoes a transition from an excited to the ground state by spontaneous emission of a photon in the absence of a perturbing electromagnetic field cannot be explained within this framework.In atomic, nuclear and particle physics we come across several situations where particles or radiation quanta (photons) are created or destroyed. For example in the beta decay of the neutron, a neutron is annihilated and a proton, electron and antineutrino are created. In some situations the interaction of radiation with matter can result in creation or annihilation of a pair of electron and positron. Such processes cannot be understood on the basis of (non-relativistic or relativistic) single particle wave equations because in such theories the probability ψ∗ψdτ (of finding the particle in the region of space dτ) when integrated over the whole space, results in unity at all times and so the existence of the particle is always guaranteed. Hence in the framework of single particle wave equation it is not possible to understand the creation or annihilation of particles. Even a simple process in which an atom undergoes a transition from an excited to the ground state by spontaneous emission of a photon in the absence of a perturbing electromagnetic field cannot be explained within this framework.

Chapman & Hall/CRC eBooksDec 12, 20080 citations

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Aaron Bennett

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Jun 8, 20142 citations

Quantum Optical Mechanics

H. J. Spencer

This is the sixth report on a new research programme investigating the electromagnetic (EM) interaction. This paper analyzes the effects of interactions arising from multiple, remote electrons on one or several, local ‘target’ electrons. These interactions are the result of the new quantized form of the EM impulse introduced in the previous paper. This model is used to re-interpret various optical effects that have previously required the existence of a fundamental object known as ‘LIGHT’: a basic entity, considered to be either a particle or a wave (or even both? - the ‘photon’) that travels across space. In contrast, this new EM model is constructed upon the key role of the ‘light’ emission processes, categorized as either oscillatory (as in antenna) or transitory (as within atoms). These real emission processes are now integrated into the asynchronous action-at-a-distance model of the EM interaction that is the basis of this new theory. 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The emphasis is on the electrons and on the relationship between electrons and not on some hypothetical ‘carrier’ that travels between them – this is the Newtonian action-at-a-distance particulate model extended to multiple times. The idea of selection leads to the introduction of information waves that identify the location and velocities of all other electrons that might participate in a ray-like exchange of momentum between pairs of electrons (saturation) that always act like particles (real trajectories across space). These supra-luminal waves do not carry momentum but ensure that the interaction minimizes the exchange of action across a non-local region of space. This new model resolves the long-time paradox of electrons as waves or particles: electrons are seen here as real point particles that interact periodically (rather than continuously) together; the focus is on the relationship between them that can be described by the discrete mathematics of particles or the periodic mathematics usually associated with waves. This paper includes the first analytical solution to the 3D scattering of two electrons – in the center-of-mass frame of reference both electrons are shown to go in quantized spiraling, conical motions: towards each other and then away from each other. The present theory provides an alternative to Feynman’s mathematical approach to “the mysterious properties of light” while providing a physical explanation for some of the calculational diagrams introduced by Feynman in his approach to quantum electrodynamics (QED). This now replaces all field theories of ‘light’ without introducing the concept of the photon or virtual particles and so eliminates all QED infinities in the physical properties associated with the interactions of electrons arising from the false idea of vacuum polarization, returning the vacuum to its Newtonian role as the passive, empty space between real particles. This new EM theory establishes a firm foundation for a new quantum theory that covers all scales of nature from the macroscopic to the heart of the atomic nucleus, while covering the complete range of interaction sets from a pair of electrons to the myriads of electrons existing in macroscopic objects. The next (companion) paper will explain the wave-like properties of electrons while providing a new, comprehensive theory of quantum measurement. This next paper will finally establish the critical link between the realistic model of the micro-world introduced so far and the macroscopic world of scientific measurements. * Surrey B.C. Canada (604) 542-2299spsi99@telus.net © H. J. Spencer Version 1.340 23-06-201Begun 23-06-2010 (pp. 133; 97Kw, 1900KB)This is the sixth report on a new research programme investigating the electromagnetic (EM) interaction. This paper analyzes the effects of interactions arising from multiple, remote electrons on one or several, local ‘target’ electrons. These interactions are the result of the new quantized form of the EM impulse introduced in the previous paper. This model is used to re-interpret various optical effects that have previously required the existence of a fundamental object known as ‘LIGHT’: a basic entity, considered to be either a particle or a wave (or even both? - the ‘photon’) that travels across space. 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This now replaces all field theories of ‘light’ without introducing the concept of the photon or virtual particles and so eliminates all QED infinities in the physical properties associated with the interactions of electrons arising from the false idea of vacuum polarization, returning the vacuum to its Newtonian role as the passive, empty space between real particles. This new EM theory establishes a firm foundation for a new quantum theory that covers all scales of nature from the macroscopic to the heart of the atomic nucleus, while covering the complete range of interaction sets from a pair of electrons to the myriads of electrons existing in macroscopic objects. The next (companion) paper will explain the wave-like properties of electrons while providing a new, comprehensive theory of quantum measurement. This next paper will finally establish the critical link between the realistic model of the micro-world introduced so far and the macroscopic world of scientific measurements. * Surrey B.C. Canada (604) 542-2299spsi99@telus.net © H. J. Spencer Version 1.340 23-06-201Begun 23-06-2010 (pp. 133; 97Kw, 1900KB)

Dec 1, 20160 citations

Three level Lambda system, Feynman amplitudes and relativistic invariance

Navin Khaneja

In this paper, we develop an analogy between the three level atomic system so called Lambda system and scattering processes in quantum electrodynamics (QED). In a Lambda system we have two ground state levels $|1 \rangle$ and $|3 \rangle$ at energy $E_1$ and excited level $|2 \rangle$ at energy $E_2$ . The transition from $|1 \rangle$ to $|2 \rangle$ has strength $\Omega_1$ and transition from $|2 \rangle$ to $|3 \rangle$ has strength $\Omega_2$ . When we adiabatically eliminate the excited state, i.e. go in the interaction frame of natural Hamiltonian of the system, we get a second order term connecting level $|1 \rangle$ to $|3 \rangle$ with strength $\frac{\Omega_1\Omega_2}{2(E_1-E_2)}$ . This term creates an effective coupling between ground state levels and drives transition from $|1 \rangle$ to $| 3\rangle$ . Scattering processes in QED can be modelled like this. Feynman amplitudes are calculation of second order term ${\cal M} = \frac{\Omega_1\Omega_2}{2(E_1-E_2)}$ . In the rest frame $O'$ ({\bf CM} frame) where sum of momentum of incoming particles is $0$ , if the Feynman amplitude is ${\cal M'}$ , then in a frame $O$ in which $O'$ moves with velocity $v$ , the time gets dilated to $t = \frac{t'}{\sqrt{1-\frac{v^2}{c^2}}}$ and hence it must be true that ${\cal M} = {\cal M'} \sqrt{1-\frac{v^2}{c^2}}$ . We show that to make this relativistic invariance of $\mathcal{M}$ to work, we have to modify the QED interaction Hamiltonian. Using this modification, we calculate the scattering amplitude for QED processes, Compton scattering and M{\o}ller Scattering.In this paper, we develop an analogy between the three level atomic system so called Lambda system and scattering processes in quantum electrodynamics (QED). In a Lambda system we have two ground state levels $|1 \rangle$ and $|3 \rangle$ at energy $E_1$ and excited level $|2 \rangle$ at energy $E_2$. The transition from $|1 \rangle$ to $|2 \rangle$ has strength $\Omega_1$ and transition from $|2 \rangle$ to $|3 \rangle$ has strength $\Omega_2$. When we adiabatically eliminate the excited state, i.e. go in the interaction frame of natural Hamiltonian of the system, we get a second order term connecting level $|1 \rangle$ to $|3 \rangle$ with strength $\frac{\Omega_1\Omega_2}{2(E_1-E_2)}$. This term creates an effective coupling between ground state levels and drives transition from $|1 \rangle$ to $| 3\rangle$. Scattering processes in QED can be modelled like this. Feynman amplitudes are calculation of second order term ${\cal M} = \frac{\Omega_1\Omega_2}{2(E_1-E_2)}$. In the rest frame $O'$ ({\bf CM} frame) where sum of momentum of incoming particles is $0$, if the Feynman amplitude is ${\cal M'}$, then in a frame $O$ in which $O'$ moves with velocity $v$ , the time gets dilated to $t = \frac{t'}{\sqrt{1-\frac{v^2}{c^2}}}$ and hence it must be true that ${\cal M} = {\cal M'} \sqrt{1-\frac{v^2}{c^2}}$. We show that to make this relativistic invariance of $\mathcal{M}$ to work, we have to modify the QED interaction Hamiltonian. Using this modification, we calculate the scattering amplitude for QED processes, Compton scattering and M{\o}ller Scattering.

arXiv:1801.08393Jan 25, 20180 citations

Formation of metastable dtμ molecules in tμ(2s)−D2 collisions

Janne Wallenius, P. Froelich

The formation process of metastable $\mathrm{dt}\ensuremath{\mu}$ molecules in ${D}_{2}\ensuremath{-}{T}_{2}$ mixtures in investigated. The $\mathrm{dt}\ensuremath{\mu}$ molecule exhibits a series of three-body resonances embedded in the $t\ensuremath{\mu}+d$ scattering continuum just below the $t\ensuremath{\mu}(2s)+d$ threshold. These states can be formed in collisions of excited $t\ensuremath{\mu}(2s)$ atoms with ${D}_{2}$ molecules, whereby the excess of binding energy is absorbed by the rovibrational degrees of freedom of ${D}_{2}$ . We present a scattering-theoretic model for this process, and perform a numerical calculation of its cross section. The essential transition amplitudes are obtained from three-body wave functions for the $\mathrm{dt}\ensuremath{\mu}$ subcluster, and adiabatic wave functions for the entire hybrid system in the final channel. It is found that the effective formation rate is limited by the Auger-transition rates of the molecular complex formed. The calculated cross sections exhibit broad "peaks," with magnitudes large enough for the formation process to favorably compete with deexcitation of $t\ensuremath{\mu}(n=2)$ atoms via radiative and collisional processes. The formation of metastable $\mathrm{dt}\ensuremath{\mu}$ can therefore be one of the fastest processes depleting the $n=2$ levels of the $t\ensuremath{\mu}$ atom in hydrogen mixtures, of importance for low-energy muon science, electroweak physics, and muon catalyzed fusion.The formation process of metastable $\mathrm{dt}\ensuremath{\mu}$ molecules in ${D}_{2}\ensuremath{-}{T}_{2}$ mixtures in investigated. The $\mathrm{dt}\ensuremath{\mu}$ molecule exhibits a series of three-body resonances embedded in the $t\ensuremath{\mu}+d$ scattering continuum just below the $t\ensuremath{\mu}(2s)+d$ threshold. These states can be formed in collisions of excited $t\ensuremath{\mu}(2s)$ atoms with ${D}_{2}$ molecules, whereby the excess of binding energy is absorbed by the rovibrational degrees of freedom of ${D}_{2}$. We present a scattering-theoretic model for this process, and perform a numerical calculation of its cross section. The essential transition amplitudes are obtained from three-body wave functions for the $\mathrm{dt}\ensuremath{\mu}$ subcluster, and adiabatic wave functions for the entire hybrid system in the final channel. It is found that the effective formation rate is limited by the Auger-transition rates of the molecular complex formed. The calculated cross sections exhibit broad "peaks," with magnitudes large enough for the formation process to favorably compete with deexcitation of $t\ensuremath{\mu}(n=2)$ atoms via radiative and collisional processes. The formation of metastable $\mathrm{dt}\ensuremath{\mu}$ can therefore be one of the fastest processes depleting the $n=2$ levels of the $t\ensuremath{\mu}$ atom in hydrogen mixtures, of importance for low-energy muon science, electroweak physics, and muon catalyzed fusion.

Physical Review AAug 1, 199621 citations

What If the Electron Is a Spinning Filament of Spacetime? A Conceptual Model Explaining 14 Quantum Puzzles

Sna samii

This preprint presents a conceptual model—not a mathematical theory—of the electron as a rotating filament of spacetime: a "spacetime spaghetti" that spins, stretches, and tangles. The model offers a single, unified mechanism to explain fourteen long-standing puzzles in quantum mechanics, including wave-particle duality, wavefunction collapse, electron spin and g-factor, the double-slit experiment, the delayed-choice experiment, the Pauli exclusion principle, pair production and annihilation, photon emission, and the quantization of atomic energy levels. Core idea: The electron is not a point particle. It is a thin, rapidly rotating filament of spacetime. Its rotation—defined as spacetime torsion relative to the background fabric—creates an extended curvature well (the "cloud"). When energy is injected past a critical threshold, the filament contracts to its ground state, releasing a ripple in spacetime (the photon). This single mechanism naturally explains both wave-like and particle-like behavior. Important note: This is a conceptual framework under active development. The rigorous mathematical formulation and quantitative experimental predictions are not yet complete. The purpose of this preprint is to share the core ideas openly, establish intellectual priority, and invite collaboration from mathematicians and theoretical physicists. Testable predictions include: · A critical detector energy threshold in the double-slit experiment · A nonlinear deviation in electron interference patterns compared to photons · A critical time delay in delayed-choice experiments (temporal depth of the electron cloud) · Possible deviations from QED in strong-field regimesThis preprint presents a conceptual model—not a mathematical theory—of the electron as a rotating filament of spacetime: a "spacetime spaghetti" that spins, stretches, and tangles. The model offers a single, unified mechanism to explain fourteen long-standing puzzles in quantum mechanics, including wave-particle duality, wavefunction collapse, electron spin and g-factor, the double-slit experiment, the delayed-choice experiment, the Pauli exclusion principle, pair production and annihilation, photon emission, and the quantization of atomic energy levels. Core idea: The electron is not a point particle. It is a thin, rapidly rotating filament of spacetime. Its rotation—defined as spacetime torsion relative to the background fabric—creates an extended curvature well (the "cloud"). When energy is injected past a critical threshold, the filament contracts to its ground state, releasing a ripple in spacetime (the photon). This single mechanism naturally explains both wave-like and particle-like behavior. Important note: This is a conceptual framework under active development. The rigorous mathematical formulation and quantitative experimental predictions are not yet complete. The purpose of this preprint is to share the core ideas openly, establish intellectual priority, and invite collaboration from mathematicians and theoretical physicists. Testable predictions include: · A critical detector energy threshold in the double-slit experiment · A nonlinear deviation in electron interference patterns compared to photons · A critical time delay in delayed-choice experiments (temporal depth of the electron cloud) · Possible deviations from QED in strong-field regimes

Aug 12, 20260 citations

Wave-like amplification of near-threshold two-particle reactions: from muon-catalyzed fusion to

Λ\barΛ

production at

e^-e^+

annihilation

A simple model is proposed to explain the recently found wave-like enhancement of the

Λ\barΛ

pair production near the threshold at the

e^-e^+

annihilation, which allows extracting parameters of the

Λ\barΛ

interaction and the

Λ

-hyperon rms-radius from the oscillatory nature of the measured cross section. In particular, it predicts a single bound state of

Λ\barΛ

with a binding energy of

\varepsilon_{Λ\barΛ}=(36\pm5)

e^- e^+

annihilation. A natural further development of the model could be its generalization to processes of producing various hadron pairs in

e^-e^+

annihilation.

\mathcal{TPC}

conjugation is another elementary property of the parametrized formalism.

|1 \rangle

and

|3 \rangle

at energy

E_1

and excited level

|2 \rangle

at energy

E_2

. The transition from

|1 \rangle

|2 \rangle

has strength

\Omega_1

and transition from

|2 \rangle

|3 \rangle

has strength

\Omega_2

. When we adiabatically eliminate the excited state, i.e. go in the interaction frame of natural Hamiltonian of the system, we get a second order term connecting level

|1 \rangle

|3 \rangle

with strength

\frac{\Omega_1\Omega_2}{2(E_1-E_2)}

. This term creates an effective coupling between ground state levels and drives transition from

|1 \rangle

| 3\rangle

. Scattering processes in QED can be modelled like this. Feynman amplitudes are calculation of second order term

{\cal M} = \frac{\Omega_1\Omega_2}{2(E_1-E_2)}

. In the rest frame

O'

({\bf CM} frame) where sum of momentum of incoming particles is

0

, if the Feynman amplitude is

{\cal M'}

, then in a frame

O

in which

O'

moves with velocity

v

, the time gets dilated to

t = \frac{t'}{\sqrt{1-\frac{v^2}{c^2}}}

and hence it must be true that

{\cal M} = {\cal M'} \sqrt{1-\frac{v^2}{c^2}}

. We show that to make this relativistic invariance of

\mathcal{M}

to work, we have to modify the QED interaction Hamiltonian. Using this modification, we calculate the scattering amplitude for QED processes, Compton scattering and M{\o}ller Scattering.

{D}_{2}

molecules, whereby the excess of binding energy is absorbed by the rovibrational degrees of freedom of

{D}_{2}

. We present a scattering-theoretic model for this process, and perform a numerical calculation of its cross section. The essential transition amplitudes are obtained from three-body wave functions for the $\mathrm{dt}\ensuremath{\mu}$ subcluster, and adiabatic wave functions for the entire hybrid system in the final channel. It is found that the effective formation rate is limited by the Auger-transition rates of the molecular complex formed. The calculated cross sections exhibit broad "peaks," with magnitudes large enough for the formation process to favorably compete with deexcitation of $t\ensuremath{\mu}(n=2)$ atoms via radiative and collisional processes. The formation of metastable $\mathrm{dt}\ensuremath{\mu}$ can therefore be one of the fastest processes depleting the

n=2

levels of the $t\ensuremath{\mu}$ atom in hydrogen mixtures, of importance for low-energy muon science, electroweak physics, and muon catalyzed fusion.