At the inception of the universe, countless yY particles emerged from the source

Figure 1. New Particle Model (NPM). Additional particles are proposed beyond the Standard Model: yY (Ying & Yang particle that forms the communication field), Ex (expandon, the dark energy particle that forms the expansion field), G (graviton that forms the gravitation field), EM (the electromagnetic particle that forms EM field), Ax (Axion, the cold dark matter particle), gluons (with three flavours and their heavy-states: g e , g μ , g τ , g μ * , g τ * ), heavy-state leptons ( e * , μ * , τ * ), heavy-state quarks ( s * , c * , b * , t * ). Strictly speaking, only the yY particle is a fundamental particle.

field exhibiting zero-dimensional movement (point vibration). Subsequently, the universe evolved into symmetrical multiverses with varying densities of yY particles within each distinct universe. The universe we stay is part of a broader multiverse formation. The periodic multiverse model adheres to symmetry principles, the law of energy conservation, the fine structure constant, and Lorentz transformation, among other rules, which will be elaborated upon in a separate paper.

yY particles are extremely short-lived but can instantly revive, enabling them to create a communication field across the multiverse. Some longer living yY particles form Ex particles or expandons, which move in one dimension and develop a dynamic expansion field known as dark energy.

A single expandon is a very short-lived particle. Some expandons that lasted longer attracted each other to form gravitons, which rotate in two dimensions and collectively created a stable gravitational field.

Like yY particles and expandons, gravitons are fleeting. Some, however, interact in a spiral path, forming new electromagnetic particles (EMs) with chirality and charge. Right-handed motion creates positive E M + with a +1/2e charge, while left-handed motion forms negative E M − with a –1/2e charge.

EM particles are transient and can quickly reappear. There are two types: ground-state and excited-state EMs. Ground-state EMs form a dynamic, isotropic EM field. Pairs of ground-state E M + and E M − create ground-state photons, which make up the EMfield in a quadrupole structure (see Figure 2).

All fundamental particles exhibit particle-wave duality, and their wave properties can be effectively described using Euler’s formula variations:

The functions of fundamental forces through wave interaction and resonance can also be described using various forms of Euler’s formula, which will be covered in another work. This paper focuses on the internal structures and interactions of particles.

Figure 2. EM field: A dynamic grid composed of numerous pairs of fleeting ground-state E M + and E M − , arranged in an electromagnetic quadrupole structure.

Numerous excited-state EMs were released from the EM field and interacted with each other to form four different particles: W + ( E M + + E M + , + 1 e ) , W − ( E M − + E M − , − 1 e ) , γ ( E M − + E M + , stable neutral ) and Z ( E M − + E M + , unstable neutral ) .

Inside photons (γ), gravitational attraction and centrifugal force balance at a distance possibly less than the Planck length. The coupling chirality of interior EMs determines the γ’s polarization: the left-handed γ L , the right-handed γ R , and the linear γ | . Within γ L and γ R , EMs have orbital planes perpendicular to the axial direction; in linear γ | , their orbits and the axial are coplanar, which is different from the linear polarization of light (photon beam).

Within W bosons, gravitational attraction and electromagnetic repulsion balance at a tiny scale, possibly smaller than the Planck length. W bosons exhibit only left- or right-handed chirality, lacking linear polarization likely due to internal EM repulsion. Contrary to the Standard Model, W bosons do not decay; their short lifespan is due to interactions with gluons (see details in Sec. 9.1).

The Z boson is an unstable state of the photon (γ) caused by a high-energy event like a particle collision that disrupts the equilibrium of internal electromagnetic forces.

In the Standard Model (SM), W,Z, and γ bosons act as virtual particles delivering fundamental forces. In the New Particle Model (NPM), they behave as real particles, forming new particles through coupling or resonating in extreme conditions like the universe’s early stage. As components of fermions and gluons, they influence strong and weak interactions (see Sections 6-9).

When two photons (γ) interact, they can form particles such as axions(Ax) and gluons(g).

Inside axions, two photons (or four EMs) interact dynamically, resulting in an almost isotropic electric distribution. Therefore, axions are chargeless, have negligible mass [4] and possess an electric dipole moment (EDM). As hypothetical dark matter candidates in the SM, axions only respond to gravity and have very low interaction cross-sections for electromagnetic, weak, and strong forces.

Gluons, composed of two identical photons rotating around each other with regular frequency, thus have a spin number of 1(See Sec. 3 for more on spin). In NPM, there are three flavours of gluons: g e , g μ and g τ . Electron gluons ( g e ) consist of two γs with different chirality, muon gluons ( g e ) have two γs with the same chirality, and tau gluons ( g τ ) are formed by one left- or right-handed γ rotating with one linear γ, which can be expressed accordingly as follows:

The two internal photons of a gluon orbit each other, exhibiting either left-handed or right-handed orbital chirality. If one of the two photons possesses chirality that matches the orbital chirality, the gluon is classified as a light state gluon (g). Conversely, if the chirality differs, it is referred to as a heavy state gluon ( g * ). The electron gluon g e lacks a heavy state.

Therefore, considering both spin chirality and orbiting chirality, gluons are classified as follows:

When aγ combines with a W − , they form three types (flavors) of charged leptons: an electron e ( W L − + γ R ) or e ( W R − + γ L ) , a muon μ ( W L − + γ L ) or μ ( W R − + γ R ) ; a tau τ ( W L − + γ | ) or τ ( W R − + γ | ) .

Similarly, when considering orbiting chirality, charged leptons also exhibit two energy states that are influenced by the chirality of the W boson. If the orbiting chirality matches the W boson’s chirality, the lepton is in a light state; otherwise, it is in a heavy state. Therefore, charged leptons and their anti-particles can be classified and described accordingly:

Although the heavy state leptons are not currently recognized by the physics community, they are essential for understanding the compositions of quarks and mesons (see details in Section 7).

In NPM, a Higgs boson (H) is an unstable combination of two Z bosons, which can be produced in high-energy events such as particle and antiparticle collisions. As 3rd generation excited particles, Higgs bosons are not involved in the mass origination of particles (see details in Sec. 4.1).

In the early stages of particle formation, particles like W bosons, electrons, muons, taus, and their antiparticles collided, releasing immense energy. The remaining particles formed a dense, hot plasma. As the universe expanded and cooled, gluons began combining leptons and their antiparticles to form quarks.

Quarks are charged leptons bound by gluons. Light state gluons bind e,μ,τ leptons to form d,s,b quarks and their anti-particles:

Note: a quark can be bound by different gluons (see details in Section 7).

Similarly, light state gluons bind heavy leptons e * + , μ * + , τ * + and their anti-particles to form u,c,t quarks and their anti-particles:

When light state leptons bind with a heavy state gluon g * , they form down heavy state quarks and their antiquarks, which can be classified and expressed as follows:

Similarly, when heavy state leptons bind with a heavy state gluon g * , they form up heavy state quarks and their antiquarks, which can be expressed as follows:

Many of the heavy state quarks mentioned above are mistreated to be intermediate mesons in the Standard Model, as will be discussed in Section 7.

As the universe continued to cool and expand, gluons and leptons combined to form quarks and hadrons, such as mesons, protons, neutrons, and other baryons in a plasma soup filled with charged leptons and bosons. During this period, numerous collisions and annihilations occurred between charged particles and their respective anti-particles. Additionally, during this phase, an unexplained minor symmetry breaking event resulted in that more positrons and heavy positrons than electrons and heavy electrons were captured by gluons to form the uud core structure of protons, thus there were more protons than anti-protons while more electrons and heavy electrons than positrons and heavy positrons were left free and moving around protons or captured by protons to form neutrons (uud+d). This explains why protons and electrons are nearly equal in number and marks the earliest examples of C violation in the universe.

After numerous annihilations of particles and anti-particles, most remaining hadrons and leptons include particles like protons, neutrons, electrons, and mesons. The apparent predominance of matter over antimatter is misleading; missing antimatter like positrons and heavy positrons exist as the excess up quarks within protons. When counting the number of positive and negative fermions (leptons and bound leptons) of any atoms there is no matter and antimatter asymmetry. Current technology cannot distinguish between electrons and heavy electrons (or between positrons and heavy positrons) due to the tiny difference of their masses (see Sec. 4.3 for details).

In NPM, protons have a uud core structure like the SM. However, neutrons differ with a core structure of uud+d, having an extra down quark (electron or heavy electron bound by a gluon, see Figure 3). The binding force between this extra down quark and the uud is weaker than the binding forces within the uud structure (see details on strong force in Sec. 6 and nuclear force in Sec.11). This difference explains the varying behaviors of protons and neutrons in beta decay (see Sec. 9 for more information).

Figure 3. Main components of proton and neutron: uud core and uud+d core. ucan be d̅ (a gluon bound positron or heavy positron), and dcan be u̅ (a gluon bound electron or heavy electron). The “sea” consists of quantum fluctuations of (anti)quarks and gluons.

The proposed uud+d structure of the neutron aligns with the structures and compositions of tetraquarks recently observed in various experiments [5]-[7]. On the other hand, recent nEDM experiments have indicated a discrepancy of 13 orders of magnitude between the precision of measurement of the neutron EDM and the expected quantum uncertainty for this quantity [8][9], which suggests that the current model of the internal structure and composition of the neutron requires considerable modification.

The recent high-energy collisions between argon and scandium atomic nuclei at CERN SPS implicate isospin asymmetry with proton and neutron. The isotope ⁴⁰Ar has 18 protons and 22 neutrons, and the isotope ⁴⁵Sc has 21 protons and 24 neutrons. As mentioned, in the Standard Model (SM), protons are composed of two up quarks and one down quark, while neutrons have one up quark and two down quarks. Therefore, more down quarks are expected in the systems before and after collision. However, the experiment result suggests more up quarks post-collision [10]. According to NPM, this result corresponds to the anticipated uud core structure of protons and the uud-d core structure of neutrons, which clearly shows the isospin asymmetry between proton and neutron because neutron has one more up quark in the core than the udd core suggested by the current theory. Further analysis is in Sec. 7.3.

We predict that similar outcome will occur in other neutron-rich isotope collisions, and the more neutrons in the system, the more charged Kmesons (thus more up quarks) will be produced than the SM suggests. For example, colliding ⁴¹Ar with ⁴⁷Sc will yield even more charged K mesons than the current experiments, deviating further from the current theorical prediction.

As the universe continued to expand and cool, it formed primary elements, molecule gas, black holes, stars, and galaxies through processes such as nucleosynthesis, radioactive decay, photodisintegration, cosmic ray spallation, gravitational accumulation, and stellar merging.

In addition to particle and antiparticle annihilation, numerous processes during the evolution of the universe may result in the release of photons from particles like gluons, quarks and charged leptons. In certain scenarios, these internal photons may be emitted as a specific type of photons that retains the coupling characteristics of its previous combination. These are neutrinos, which exist in three flavors: v e , v μ , v τ . These correspond to the three flavors of gluons, quarks, and charged leptons, respectively. For example, the v μ could represent the internal “γ” released from μ , μ * , g μ , g μ * , s , s * , c , c * .

In equations of this paper involving neutrino interactions, replacing the particle’s internal “γ” with “ν” does not affect validity. Details on neutrinos are covered in Section 8.

In the Standard Model, elementary particles are indivisible point-like entities that oddly exhibit different spin and spin numbers, as well as varying masses and charges.

Physicists often use Dirac’s equation [11] to describe charged fermions with spin, viewing the four-dimensional spinors as the mathematical form of charged (anti) fermion with left-handed and right-handed spin, or up-state spin and down-state spin in an abstract state space. However, Roger Penrose suggested that these four-dimensional spinors can be interpreted as pairs of two-dimensional spinors, each representing a massless particle with left-handed (Zig) or right-handed (Zag) spin. These particles move at the speed of light in a zigzag pattern, alternating between forward and backward motions [12], suggesting they are composite with internal physical spinors.

A recent study suggested that an electron’s spin is due to angular momentum from energy circulation in its wave field, and its magnetic moment arises from a circulating charge, though the author thought this is not a description about the internal structure of electrons [13].

In NPM, elementary particles are composed of pair of more fundamental particles. The spin state of a particle is determined by the coupling state of the two interior particles, including factors such as their shape, whether they are spinning regularly, whether they are orbiting each other, and their distance from one another, etc.

If the two interior particles only vibrate without spinning, the particle’s spin state depends on the relative position and velocity of the interior particles. When the two interior particles are identical and their spins are synchronized, the particle’s overall spin matches theirs. If they differ and have unsynchronized spins, the faster-spinning interior particle dominates the spin state. If a particle returns to its original spin state after the interior particles complete n rotations (n2π), its spin number is 1/n, reflecting the coupling of interior particles; thus, this spin number is a discrete quantum value.

In the Standard Model (SM), the spin state of a particle is a superposition state; while the magnitude of the spin remains constant, the spin direction can change and switch between up direction and down direction. In contrast, in the New Particle Model (NPM), both the spin magnitude and spin direction of a particle remain unchanged because they are intrinsic properties of the particle, similar to its charge and mass. As a result, the spin number of a particle does not change. This principle applies to all elementary particles and their internal particles.

The Stern-Gerlach experiment first demonstrated quantization of magnetic moment and angular momentum [14][15], though its interpretation was flawed. It is the direction of silver atoms’ spin axes, not their chirality that is indeterminate until exposed to a magnetic field. In a vertical magnetic field, they deflect up or down without changing chirality; in a horizontal field, they move left or right, again retaining chirality. As discussed in Sec.3.3, the silver atom’s spin is a layer-associated property, rather than just the sum of its quark and electron spins.

A recent SPDC experiment demonstrated that orbital angular momentum (OAM) is conserved when a single photon splits into entangled pairs [16], indicating OAM and spin cannot exist as a superposition value.

The Pauli exclusion principle states that an atomic orbital can contain a maximum of two electrons, each with opposite spins. This means electron spin states within an orbital cannot be combined or superposed—they must remain distinct and stable.

Spin-2 particles

In NPM, gravitons are the first generation of excited particles with interior particles orbiting each other. Gravitons consist of two identical, non-spinning expandons, resuming their original spin state after half a rotation (n = 1/2). Thus, gravitons have a spin number of 2, or more precisely, |2|, as they lack polarization or chirality, meaning no spin direction (left or right-handed).

The EMs can be viewed as special gravitons with polarization or chirality, thus having a spin number of ±2. Negative EMs are left-handed with a spin of –2, while positive EMs are right-handed with a spin of +2.

Spin-1 particles

In the context of NPM, photons, W bosons, and Z bosons exhibit a spin number of ±1 due to their composition of two identical particles (EMs) with intrinsic spin. When these internal EMs complete a rotation around each other, the bosons return to their original spin state. Left-handed photons, W bosons, or Z bosons possess a spin number of –1, whereas right-handed bosons have a spin number of +1.

As mentioned in Sec. 2.5, neutrinos are a type of photon with the same spin number: –1 for left-handed and +1 for right-handed. Thus, in NPM, neutrinos are not fermions (spin-1/2 particles). Neutrinos were observed to exhibit only left-handed helicity. This conclusion was drawn from indirect analysis, for example, the Goldhaber Experiment (1958) [17], which examined gamma ray polarization after electron capture by Europium-152—rather than direct measurement. These analyses did not account for layer-associated spin (see Sec. 3.3 for details) or consider incident neutrinos involved in beta decay and electron capture (see Sec.9 for details).

Gluons ( g e , g μ , g τ , g μ * , g τ * ) consist of two identical particles, either photons or neutrinos, which possess spin. Consequently, their spin number is also ±1.

Spin-0particles

Axions (Ax), which are considered cold dark matter particles, consist of two photons analogous to gluons. However, the internal photons within Ax exhibit a closer and more intense coupling, resulting in highly dynamic relative motions. These interactions can be interpreted as four intertwined electromagnetic fields. Regardless of how many times the two photons rotate around each other, the overall spin state never returns to its original configuration (n→∞), leading to a spin number of 0.

The Higgs particle (H) consists of two Z bosons, with an interior situation like Ax, resulting in a spin number of 0. However, the Z boson is highly unstable, which causes the H particle to be extremely unstable as well.

Spin-1/2 particles

Charged leptons ( e , μ , τ , e * , μ * , τ * ) and their antiparticles are composed of two distinct spinning particles: a photon (or neutrino) and a Wboson. The spins of the photon and the W boson are asynchronous, requiring the internal particles to complete at least two rotations for the charged lepton to restore its spin state. Consequently, the spin number of charged leptons can be ±1/2 or ±1/n (where n ≥ 2). For left-handed charged leptons, the spin number is negative, while it is positive for right-handed charged leptons. Further research is necessary to definitively determine the exact spin number for charged leptons. For instance, the electron’s spin number could be precisely ±1/2 as its charge rotates twice as fast as its mass [18]. The charge rotation comes from the movement of the W boson, and the mass rotation depends on interactions between the W boson and the photon. This also provides an explanation for why the electron’s gyromagnetic factor is close to 2 (see details in Sec. 5.1).

As detailed in Section 2.4, a quark is a charged lepton bound by a gluon, resulting in a spin number of ±1/2 or ±1/n (where n ≥ 2).

Protons and neutrons each consist of two distinct internal components: the core structure and the virtual particle sea. The relative motion between the core and the sea can be compared to the movement between the Earth and its cloud atmosphere or the interaction between interior photons and W bosons within leptons. Consequently, the spin numbers of protons and neutrons are ±1/2 or ±1/n (where n ≥ 2).

The spin number of gluons is the same (spin-1) as that of photons, W bosons, and Z bosons, but they present a spin state at different layers. Similarly, the spin number of protons and neutrons is identical to that of quarks (spin-1/2), yet they also display spin states at different layers. The spin number is a discontinuous quantum number that reflects the state of relative motion or orbital state between the interior components rather than the sum of the spin numbers of its interior particles. For example, a photon consists of an E M − with spin number –2 and an E M + with spin number +2, but its spin number is either +1, or –1, never 0. Similarly, the spin number of a proton or neutron is not the sum of all interior particles’ spin.

The spin angular momentum of particles mainly depends on the orbital angular momentum of their primary sublayers, such as the uud core and virtual particle sea in protons. Deeper sublayer contributions to spin and angular momentum are negligible. Therefore, the proton’s spin is mainly influenced by the orbital angular momentum of the uud core and surrounding sea, not by the valence quarks’ spins at deeper sublayer. This suggests that the EMC experiment findings [19][20] which showed nearly equal numbers of valence quarks spinning in both directions, should not be considered a “proton spin crisis.” [21]-[23].

In NPM, three valence quarks and three gluons form a stable uud core in the proton, with both contributing only to the core’s collective angular momentum. Sea (anti)quarks and non-massless sea gluons exist as quantum fluctuations and contribute solely to the sea’s angular momentum. Both the core and the sea together determine the proton’s overall angular momentum at an upper layer, an aspect often neglected in theoretical and experimental analyses [24]-[28]. The conservation of angular momentum and quantum spin number applies only within the same system layer.

In the Standard Model (SM), elementary particles are point-like entities that do not exhibit true spinning. This concept is based on two key assumptions: the theory of relativity, which states that nothing can travel faster than the speed of light (C), and the Heisenberg uncertainty principle, a fundamental principle of quantum theory.

For a particle as small as an electron or even smaller, it would need to rotate at speeds faster than light to achieve the observed angular momentum and magnetic moment. The uncertainty principle indicates that when examining objects or structures smaller than photons and electrons, the momentum of these internal particles becomes too large for precise measurement. Additionally, the general theory of relativity suggests that a significant amount of energy concentrated in a very small space could result in sharp space-time curvature, potentially leading to the formation of a black hole.

A recent study on electrons indicates that the superluminal velocity of both mass flow and charge flow of electrons can be avoided due to the distribution of the electron’s mass and charge over sufficiently large spaces [18]. In the NPM framework, electrons and other fundamental particles are not considered rigid point-like objects. Rather, the internal W and photon (or neutrino) components that constitute the electron progress in a spiral manner. The angular momentum of the electron is thus an average value produced by this spin-precession effect, ensuring that it does not exceed the speed of light.

Scientists acknowledge that every theory has its limits, including the uncertainty principle. The Planck size, based on the speed of light, is not necessary the finalized boundary. In NPM, yY particles and expandons existed before the electromagnetic field, possibly moving faster than light, which accounts for the superluminal phenomena observed in quantum entanglement, to be discussed further elsewhere.

Essential mass

As delineated in Section 1, it is established that all known elementary particles contain electromagnetic particles (EMs), which can be considered as gravitons with polarization. Consequently, the mass of elementary particles originates from their internal gravitons and EMs through interactions with the gravitational field and the electromagnetic field.

A particle’s mass is its resistance to movement in the gravitational field and electromagnetic field. More mass means more resistance, causing slower movement. Particles have two types of mass: gravitational mass, determined by the number of gravitons they contain, and electromagnetic mass, defined by the structure and state of their internal EMs.

Elementary particles generally show a spiral precession within the electromagnetic field. In addition to their longitudinal motion, these particles also exhibit transverse movement, leading to both longitudinal and transverse electromagnetic mass.

Mass is a concept associated with observation and measurement. Gravitons and gravitational field, electromagnetic particles (EMs) and EM field could be the current technological boundary for measurement. Thus, particles such as yY particles and expandons that formed before the formation of gravitational field and electromagnetic field are outside the scope of the concept of mass. In Sec. 4.2, we will discuss that the energy is more fundamental than mass.

It is more accurate to refer to a particle’s mass as intrinsic mass or net mass, rather than rest mass or static mass, because all elementary particles are perpetually in motion. Motion is an innate characteristic of these particles. Although gravitons and photons in a gravitational field and electromagnetic field may remain in a ground state, they do not remain at rest but instead undergo dynamic changes.

Many scientists, including Newton and Einstein, refer to the net mass of an object as its inertial mass. Newton defined inertia as the capacity or tendency of a substance to resist changes in its state, which is proportional to its mass [29].

Gravity is transmitted at the speed of light through the state transitions of adjacent gravitons in the gravitational field. Gravitons are fleeting, with zero gravitational mass.

Electromagnetic force travels at the speed of light via virtual photons in the EM field. These ground-state grid pairs of positive and negative EMs are also fleeting and massless.

The movement speed C of virtual gravitons and virtual photons is based on state transitions, determined by the transit frequency and the distance between adjacent particles (the Planck length). This allows for the calculation of the maximum energy and frequency of a gamma ray.

Some EMs with longer lifespans were excited by the EM field and combined to form other particles, such as photons (γ), Z particles, and W particles, as described in Sec. 2.2. The excited photons in NPM have mass, so they are not the γ bosons in quantum theory, which are the same as the virtual photons discussed above.

Excited photons live longer than virtual photons but remain fleeting. They reappear quickly and consistently, creating an impression of stability. Their motion through the electromagnetic field is comparable to that of virtual photons and nearly instantaneous, a topic discussed further elsewhere.

Masses of Composite Particles

Excited free photons contain only two electromagnetic particles (EMs), resulting in an extremely small gravitational mass. These photons share the same composition as virtual photons that lack transverse electromagnetic mass; thus, their EM mass is also minimal. Consequently, free photons have a very small mass (< 1 × 10⁻¹⁸ eV) [30], measurable by experiments like the Eddington experiment [31].

In the Standard Model, elementary particles gain mass through electroweak symmetry breaking via the Higgs mechanism, a virtual process in which particles move in the Higgs field and couple with the Higgs particle to obtain mass through repeated conversion of positive and negative spin states [32]. However, this does not explain how the Higgs particle itself acquires mass. In the NPM, mass forms similarly, but involves interactions between particles, including the Higgs, and EM pairs in the electromagnetic field.

In the electroweak theory, W + , W − , Z and γ are composed of a pair of four massless bosons ( W 1 , W 2 , W 3 and B ). These bosons exist within weak isospin fields and weak supercharge fields. The particles W + , W − and Z acquire mass through the Higgs mechanism by interacting with the Goldstone boson, whereas γ remains massless as it does not interact with the Goldstone boson [33][34].

While direct evidence for weak isospin and supercharge fields is lacking, electroweak theory implies that W, Z, and γ are composite particles [35], indirectly supporting the New Particle Model (NPM). NPM also treats the Higgs boson as an ordinary composite particle, which addresses the Standard Model’s hierarchy problem [36]-[38].

Free photons have a structure like virtual photons, resulting in a large magnetic moment, small mass, and near-light speed movement. In contrast, W bosons have a different structure with a large mass and small magnetic moment, preventing fast movement.

In NPM, when paired with a W boson, a photon can increase the magnetic moment and reduce the mass of the composite particle. The spin and orbiting chirality of the W boson and photon inside a charged lepton primarily determine its properties such as flavour, mass, and magnetic moment. Leptons with different spin chirality between their interior W boson and photon have a larger magnetic moment and smaller mass compared to those with identical spin chirality.

Similarly, leptons with a linear interior photon have a much weaker magnetic moment and a larger mass. Thus,

They are also applied to the three generations of quarks, hence

The analysis indicates that the net mass of elementary particles is derived from underlying particles and interactions, influenced directly by the gravitational field and the electromagnetic field. Consequently, hidden energy and fields play a crucial role in determining the particle’s mass.

Einstein’s renowned mass-energy equivalence formula, E = m c 2 , posits that mass and energy are interchangeable.

Since energy is more fundamental, energy is always conserved, but mass is not. For instance, the low-energy positron and electron could annihilate each other and produce two or more photons and high-energy positron and electron annihilation could produce 10 mesons and a pair of proton and anti-proton [39]. The extra particles and mass here are converted by the kinetic energy of the positron and electron, and their interior particles and binding energy.

Gravitons become EMs by attracting and approaching each other. EMs retain the graviton’s gravitational mass and convert their internal angular kinetic energy or circular energy into EM mass. Excited elementary particles gain both gravitational and electromagnetic mass from their internal EMs, coupling with the grid gravitons of the gravitational field and the grid EMs of the electromagnetic field.

The mass and internal energy of a particle are primarily determined by its internal components, yet these properties are typically observed or measured externally. Consequently, the mass and energy of a particle’s internal components may not be observable. For instance, the significant mass of internal W particles and the binding energy of internal photons within an electron are entirely concealed from observation and measurement. Likewise, numerous masses and energies exist within fundamental particles and hidden fields in the universe, which is essential for understanding and addressing the cosmological constant problem [40][41].

The contributions of gravitational field and electromagnetic field to an object’s total mass vary across different levels. Elemental particles are significantly influenced by both fields, while hadrons are mainly affected by the EM field. Atoms primarily derive their mass from nucleons, with minimal impact from EM interactions between electrons and nucleons.

Spin-orbit coupling causes particles in the same generation of charged leptons and quarks to have different masses. When the orbiting chirality is opposite to the W’s spin chirality, the particle has a higher mass (heavy state) than when they are aligned. Therefore, the following equations apply:

As stated in Sec. 4.2, the binding energy of gluons increases the mass of quarks compared to their corresponding leptons. Therefore, the following predictions are made:

Since both m u and m d are increased by the same factors from m e * + and m e , the difference between them is likely to be proportionally magnified. Therefore, we deduce:

About the Mass of Down Quark and Up Quark

Equation (4.12) suggests m u > m d , which contradicts the Particle Data Group data: m u = 2.16 ± 0.07   MeV and m d = 4.70 ± 0.07   MeV , with m d − m u ≈ 2.54   MeV [42]. These PDG values are inconsistent with the mass of the neutral pion π 0 also provided by PDG, m π 0 = 134.9768 ± 0.0005   MeV [42]. Considering the composition of π 0 ( u u ¯ or d d ¯ ), the uncertainty indicates that | m u u ¯ − m d d ¯ | < 0.0005   MeV , suggesting | m u − m d | is most likely less than 0.0005 MeV.

In NPM, the value of | m u − m d | has been found to be up to 5 orders of magnitude less than 0.0005 MeV. The core composition of a proton is the uudstructure or similar combinations that include u ¯ and d ¯ , such as u u u ¯ , u d ¯ d , u d ¯   u ¯ , d ¯   d ¯   u ¯ , and d ¯   d ¯ d . Since m u = m u ¯ and m d = m d ¯ , the largest mass difference among these combinations is between u u u ¯ and d ¯   d ¯ d , which is 3 n | m u − m d | , where n > 1 represents the mass enlarging factor due to gluons and the “sea” of virtual particles in the proton. According to CODATA 2022 [43], the mass of a proton is 938.27208943 (29) MeV. The precision level suggests that

3 n | m u − m d | < 0.00000001   MeV , implying | m u − m d | < 0.000000003   MeV , and, together with Equation (4.23), suggest that m e * + − m e < 0.000000003   MeV . This makes distinguishing e * from e quite challenging.

We also found that the core structure of proton and neutron in NPM could explain the mass difference between the proton and neutron better than that in the SM. According to the value of CODATA 2022 [44], the mass of neutron is 939.56542194 (48) MeV, resulting in m N − m P = 1.29333251 ( 19 ) MeV . This difference primarily arises from the mass of the additional down quark in the uud+d core structure of the neutron. This is consistent with considering Equation (4.18) m d > m e and the electron mass m e = 0.51099895069 ( 16 ) [45].

About the Mass of Strange Quark

According to 2024 PDG data [42], m s = 93.5 ± 0.8   MeV , m μ = 105.6583755 ± 0.0000023   MeV , indicating m s < m μ , contrary to NPM’s prediction of Equation(4.20) m s > m μ . Since m μ is experimentally well-established, any issue likely arises from the value of m s , which combines measurement data and model calculations. Recent research shows that it could get m s = 120   MeV by setting m c = 1.35   GeV and m b = 4.0   GeV under certain conditions, implying m s > m μ [46].

Adjusting the masses of d, u, and s quarks using NPM predictions reveals a consistent pattern in the masses of quarks and charged leptons within each generation of elemental particles in the Standard Model.

Theoretical Contradiction

In NPM, only E M + and E M − particles have fractional charges of +1/2e and –1/2e, respectively. These particles can bind to form ±1e or neutral particles. Therefore, NPM does not allow for particles with fractional charges of ±1/3e or ±2/3e, like quarks in the SM. Quarks are considered charged leptons bound by gluons and will be detected as such when escaping gluon bond, like electrons and positrons in beta decay.If particles with charges of –1/3e and +1/3e are allowed, as assumed with down and bottom quarks and their antiparticles, then particles carrying charges of integer multiples of 1/3e—such as the up, charm, and top quarks, as well as leptons and their antiparticles—would have to be composite. This argument suggests an inconsistency within the Standard Model theory.

Observational Quandary

The fractional charges of quarks were determined during the development of Quantum Chromodynamics (QCD) theory and were initially attributed to integer charges [47][48]. However, scientists have not observed fractionally charged quarks directly. Consequently, the theory of quark confinement (or gluon confinement) was developed to explain this phenomenon.

Studies suggest that quarks can move freely and bind to form hadrons in the early universe [49][50], and a free up quark combining with a free down quark would form a meson with charge +1/3e and a different mass than the (anti)down quark. As a result, scientists theorized that fractionally charged particles (FCP) might be found in remnants of the Big Bang or other cosmic events. However, despite numerous experiments over decades, including oil drop, high atmosphere experiments like BESS [51], space missions like AMS-01 and DAMPE [52], and underground experiments like CUORE [53], no FCPs were detected.

Current MS theories predict similar numbers of anti-up and anti-down quarks in the proton, but a recent study found about 50% more anti-down than anti-up quarks [54]. Existing proton models cannot yet explain this asymmetry. NPM suggests that the anomaly likely results from the fact that higher fractional charge (2/3e) is assigned to (anti) up quarks in comparison to the (anti) down quarks’ charge (1/3e), thus measurements are presented as more sensitive to u ¯ quarks in the equations. As a result, calculations yield about 50% less u ¯ than d ¯ .

Anomalous Magnetic Moment (AMM)

In the SM, the relationship between the charge, mass and the magnetic moment of a charged lepton with spin-1/2 can be expressed as [55]:

where g ℓ = 2 ( 1 + a ℓ ) , which is the gyromagnetic factor of ℓ ( e , μ ) , a ℓ is the anomalous magnetic moment (AMM). As noted in Sec. 3.2, the AMM may result from interactions between a lepton’s internal W boson and photon.

The Dirac Equation (11) predicts g = 2 , Schwinger increased the g value with a radiative correction and predicted the electron AMM a e = α / 2 π [56]. In 2020 the international g-2 community predicted the muon AMM a μ ( S M ) = 116591810 ( 43 ) × 10 − 1 (0.37ppm) based on a data-driven approach [57], which is 4.2 standard deviations with measurement of experiments. While the magnetic moment is considered an intrinsic property of particles in the framework of NPM, current theories predict and calculate the muon’s anomalous magnetic moment by incorporating several external factors such as hadronic vacuum polarization [58][59], hadronic light-by-light scattering [60][61], and electroweak interactions [62][63].

The international g-2 community recently updated the Standard Model prediction for α μ using new data-driven and lattice-QCD results, which raised the SM value and reduced its discrepancy with experiments [64]. However, it is premature to say the muon AMM puzzle is resolved, given ongoing misconceptions regarding the SM in the lepton and hadron sectors discussed earlier and in upcoming sections. For example, the muon interaction with the invisible free gluon g_e (see the Equation (9.2)) may have contribution to the g-2 experimentally, though current theories do not account for them. Additionally, the measurement of the π + π − channel in the g-2 community is affected by significant statistical uncertainty, systematic uncertainty, and inconsistencies between different data sets [65]. The issue is likely caused by misunderstandings about π ± compositions (see details in Sec. 7.1).

The anomalous magnetic moment (AMM) of quarks in the presence of an external magnetic field has been a subject of study for over two decades [66]-[68]. Similar to the research on muon AMM, most studies on quark AMM have concentrated on external contributions such as magnetic catalysis [69] and chirality magnetic effect [70].

NPM suggests that the quark AMM may be directly affected by the problematic fractional charges and masses of quarks. A recent study shows that it mainly influences the electric ∼iE3σ3 component under strong magnetic fields, and up and down quarks have proportionally different AMMs [66].

The properties of up quarks and down quarks, including their fractional charges, were mainly inferred from MIT-SLAC deep inelastic scattering experiments and nucleon composition models using probability analysis and scattering cross-sections [71]. Fractional charges are only supported by quark-parton model data—which is half what a simple three-quark model predicted—and are consistent with models featuring neutral gluons only if gluons carry about half the proton’s momentum, though recent research indicates gluons account for only about 40% [28].

In 2014, D0 collaborations reported measuring the electric charge of top quarks in t t ¯ events from p p ¯ collisions at the Tevatron. This measurement is also model-dependent and involves complex calculations. It assumes the Standard Model process t → W + b , and determines thebjets’ charge using a jet charge algorithm developed by Feynman [72].

When reporting the discovery of the top quark, the authors noted that energetic scattering at wide angles, like Rutherford scattering, offers insights into the structure of colliding objects. One interpretation is that excess jets are caused by collisions of smaller objects within quarks, which no other experiment has observed [73]. Fractionally charged particles like tand b quarks should contain smaller charges due to charge conservation, but the suspicious result shows they split into excess jets with larger, integer charges. This observation prompts an important question: what mechanism inhibits fractionally charged particles from appearing in the final state of jets?

In the Standard Model (SM), mesons are either neutral or possess integer charges, such as π + ( + 1 e ) ≡ u ( + 2 / 3 e ) d ¯ ( + 1 / 3 e ) and K − ( − 1 e ) ≡ s ( − 1 / 3 e ) u ¯ ( − 2 / 3 e ) . When considering electric charge coupling without the constraints of the meson definition and the “color” hypothesis of Quantum Chromodynamics (QCD) (see details in Sec.6.2), a question arises: why is there no meson with fractional charge combinations such as d ¯ ( + 1 / 3 e ) d ¯ ( + 1 / 3 e ) , u ( + 2 / 3 e ) u ( + 2 / 3 e ) , u ¯ ( − 2 / 3 e ) d ¯ ( + 1 / 3 e ) and u ( + 2 / 3 e ) d ( − 1 / 3 e ) ? What mechanism prevents these from existing in nature? Additionally, in certain meson decays such as J / φ ( 1 s ) , an intermediate γ can produce hadrons or leptons but never fractionally charged quarks—why is this the case? This phenomenon is clearly explained within the New Particle Model (NPM), where all quarks have integer charges (+1e or –1e) because they are bound leptons.

Similarly, why is there no baryon with fractional charge combinations like u ( + 2 / 3 e ) u ¯ ( − 2 / 3 e ) d ¯ ( + 1 / 3 e ) and d ¯ ( + 1 / 3 e ) u ( + 2 / 3 e ) d ( − 1 / 3 e ) ? In NPM, the answer is straightforward as discussed. Furthermore, in contrast to mesons, what fundamental factors preclude the existence of particles composed of electron-positron pairs, muon-antimuon pairs, or tau-antitau pairs, held together by gluons? What mechanisms are responsible for inhibiting the formation of such composite particles? Section 7 will explain that these lepton pairs are actual compositions of common mesons.

In NPM, quarks with identical charge rarely combine to form a meson due to the strong repulsive force of the same charge, which prevents the gluon from holding them together. Therefore, combinations such as u u , d ¯   d ¯ , u d ¯ , u ¯ d , u s ¯ and u ¯ s is not allowed in NPM. This makes the compositions of mesons like π + , π − , K + , K − , ρ + and ρ − significant for further study. For example, both π + and ρ + have the same composition of u d ¯ in the SM, yet they have different masses and decay modes. The cause of mass difference between π meson and ρ meson is explained by different G-parity and different J P C [74] or different number of massive gluons involved [75]. However, NPM reveals that π meson and ρ meson have totally different components that can easily explain their mass difference. More detailed analysis of these phenomena will be provided in Section 7.

Similarly, we anticipate that baryon compositions such as Δ + + ( u u u ) , Δ − ( d d d ) , Ω − ( s s s ) , Σ * − ( d d s ) , Ω c c c + + ( c c c ) , Ω b b * − ( s b b ) and Ω b b b − ( b b b ) in the Standard Model is incorrect. This is attributable to the inability of gluons to bind three quarks carrying identical charges (total +3e or –3e), as the substantial repulsive force prevents these formations.

The strong force, classified as one of the four fundamental forces in the Standard Model, is responsible for binding quarks into hadrons through gluon exchange. The residual strong force maintains the cohesion of nucleons by means of virtual mesons. In the Standard Model, descriptions of gluons vary: they are sometimes likened to rubber bands in relation to quark confinement, occasionally referenced as possessing mass [75], yet also described as massless particles traveling at the speed of light when defined as gauge bosons.

In NPM, gluons consist of two photons or neutrinos and possess mass, so they don’t travel at light speed. The strong force operates through the coupling of gluon’s internal photons with bound particles.

At a nucleon or sub-nucleon scale, gluons act like rubber bands between particles. Their binding force weakens as particles get closer and strengthens as they move apart, but not enough to achieve confinement as described by the Standard Model [76]. With enough energy, bound particles like quarks can escape their binding force and become independent, as seen in pion decay and free quarks in Quark-Gluon Plasma [77]. We can better understand it when we know that quarks are charged leptons bound by gluons.

The magnitude of the strong force is predominantly influenced by electromagnetic interactions between the two bound particles, as well as the electromagnetic effects from external factors or the environment. For example, in the proton’s uud core structure, the binding forces between the three valence quarks are significantly strong due to the mediating gluons counteracting the repulsive Coulomb effects generated by the two up quarks (even influencing the interaction between up quark and down quark), thereby ensuring the stability of the uud core. Conversely, in the neutron’s duu-d core structure, the binding force between the duu structure and the additional down quark is weak because the connecting gluon becomes less taut owing to the reduction of repulsive Coulomb force. Consequently, the extra down quark is more susceptible to being displaced by neutrino impacts (as detailed in Section 9).

Similarly, in a neutral meson, the binding force is also weak because the channeling gluon is less constrained due to the presence of only attractive Coulomb force between the quark and anti-quark pair, rendering most mesons unstable (as detailed in Section 7).

In BCS theory [78], a Cooper pair is a bound electron pair formed in metals at very low temperatures, enabling superconductivity when attraction of phonons (lattice vibrations) overcomes electron repulsion. From the NPM view, it is gluons that bind the electrons into Cooper pairs—similar to their role in mesons—and lower temperatures facilitate this process.

In quantum chromodynamics (QCD), color charges describe and calculate the strong force, but their physical meaning is not well understood.

In NPM, “colors” in QCD represent different coupling modes between quarks and gluons: ν mode (gluon couples with the interior ν of the quark), W mode (gluon couples with the interior W of the quark), and νW mode (gluon couples with the entire quark). A quark’s state, considering both coupling and electric charge, is termed colour charge.

According to the Pauli Exclusion Principle, a gluon’s two neutrinos cannot couple quarks with the same mode or colour. Therefore, in baryons like protons and neutrons, there are 6 types of colour charges based on three coupling modes and two electric charges.

Inside mesons, quarks often change coupling modes due to the loose binding of gluons, creating a superposition like state that appears “colorless.” Despite this undifferentiated state, there are still two sequences of transitions between positive and negative quarks, resulting in 2 colour charges. Adding these with the 6 colour charges in baryons, there are a total of 8 colour charges with NPM interpretation, matching the QCD theory.

In Quantum Chromodynamics (QCD), “colors” for quarks or antiquarks denote their energy states, which can be described by wave functions. For gluons, “color” is an intrinsic attribute, with each type of gluon facilitating the conversion between specific pairs of “colors”. Consequently, there are 8 distinct types of gluons. In the uud structure at the proton core, theoretically, 3 × 6 gluons are involved in strong interactions, as it necessitates 6 different gluons between each pair of valence quarks.

With NPM interpretation, a single gluon can handle all “color” conversions with quarks by adjusting its coupling modes. Thus, only three gluons are needed in the proton’s uud core structure. Simplifying the calculation of strong forces is possible if we can constrain the coupling constant for each mode.

In QCD, gluons act as virtual bosons that move between quarks and antiquarks and change their “colors”. In NPM, gluons are considered real particles that respond to mode changes between quarks or antiquarks and can be classified into three different flavours with varying masses and binding strengths.

In Section 11, we will explain that nuclear forces are better described by the electromagnetic interactions and coupling between nucleon quarks via real gluons or mesons, rather than the exchange of virtual mesons as in QCD.

The strong CP problem[79] concerns why quantum chromodynamics (QCD) seems to preserve CP-symmetry, and it’s commonly referred to as “the most underrated puzzle in all of physics.”

CP combines charge conjugation (C) and parity (P) symmetries. While QCD theory permits CP violation in strong interactions, experiments have not detected it, leading to a “fine tuning” problem in particle physics.

The NPM does not have a strong CP problem. As described in Sec. 6.1, the strong interaction is based on electromagnetic processes that involve gluon internal photons coupling with bound particles. The strong interaction keeps CP symmetry intact by allowing changes in color charge (coupling mode) without affecting charge conjugation or parity.

The Yang-Mills mass gap problem[80] refers to the apparent paradox wherein classical Yang-Mills equations suggest that strong force carriers, such as gluons (the gauge fields), are massless. However, experimental evidence indicates that these combine through confinement into massive particles (hadrons), which requires the existence of massive bound gluons.

NPM does not encounter this issue. In NPM theory, strong interactions involve massless photons within gluons coupling with bound particles, while gluons themselves are always massive. The mass gap between photons and gluons is not problematic. Unlike the Standard Model, NPM does not exhibit confinement: if binding forces are disrupted, quarks transition into charged leptons.

In most mesons composed of eand e + (or e * and e * + ), only the

gluon acts as a bond. The g μ ( g μ * ) and g τ ( g τ * ) gluons are excluded due to their incompatible size and coupling properties.

Wheneande⁺have opposite chirality

In the SM, the neutral pion π 0 is a superposition of u u ¯ and d d ¯ ; in NPM, π 0 consists of a pair of e and e + (or e * and e * + ) with opposite chirality, which can be expressed as:

Note: for present purposes ( e L ) ( g e ) ( e R * + ) , ( e R * ) ( g e ) ( e L + ) and d L ( g e ) u R , u L ( g e ) u ¯ R , u R ( g e ) u ¯ L are not listed.

When π 0 decays, e and e + annihilate due to the close coupling within the meson, releasing 2γ with a (98.823 ± 0.034)% probability [42].

Wheneande⁺have same chirality

In theory, π meson may also consist of a pair of eand e + (or e * and e * + ) with same chirality. This meson is called π ′ and can be expressed as:

When π ′ decays, the electron (e) and positron ( e + ) separate due to a bit loose coupling within the meson, while the gluon may either merge with the background field or convert into a photon. Thus:

In the SM, π ′ is π 0 that has decay mode with a (1.174 ± 0.035)% fraction [42]; in NMP, π ′ and π 0 should be treated as different mesons due to their different components.

The π 0 can also decay into an electron and a positron when interacting with a neutrino, like the process observed in β + decay (refer to Sec. 9.4 for more information).

Theoretically, when π ′ decays, the gluon may also split into two neutrinos that briefly bind with e and e + . This creates intermediate states like eν and e + v , which eventually decay into e, e + and 2ν. Thus,

About π + and π −

As mentioned in Sec. 5.3, couplings like u d ¯ and d u ¯ are not allowed in NPM. A charged pion acts as an intermediate state of a broken meson, such as ρ 0 ( 770 ) and ω ( 782 ) , when the binding gluon splits into two neutrinos, each temporarily pairing with μ and μ + . Thus,

This is why π ± decays to μ ± + v with a fraction of (99.98770 ± 0.00004)% [42], suggesting a clear lepton flavour universality violation (LFUV).

If a meson is defined as a particle consisting of a lepton and anti-lepton pair (or quark and anti-quark), then π ± particles would not be classified as mesons. Their designated names may not be appropriate, as they do not share characteristics with π 0 particles. In addition to the different decay modes, the mean lifetime of π ± particles and π 0 particles differs by approximately 9 orders of magnitude, and their masses vary significantly more than the mass difference between protons and neutrons [42]. The measurement of the π + π − channel in the g-2 community is affected by substantial statistical uncertainty, systematic uncertainty, and inconsistencies between different data sets [65]. This issue is most likely due to misconceptions regarding the compositions of π ± .

Similarly, the K ± , ρ ± , D ± and B ± should also not be classified as mesons due to their actual compositions (see more introductions in Sec. 7.3 and 7.4).

Whenµandµ⁺have opposite spin chirality

Just like π 0 , when the constituent µ and μ + have opposite chirality in a meson, they tend to annihilate each other. However, the meson is more complex than π 0 due to the involvement of two types of gluons ( g e and g μ ). By analyzing decay modes, we find that they correspond well to the eta meson η ( 548 ) and the eta prime meson η ′ ( 958 ) , which can be expressed as:

Since the g e can bind effectively with the interior neutrinos of µ and μ + with opposite chirality, the η ( 548 ) possesses a relatively small mass and primarily decays into 2γ (from μ μ + annihilation) or pions (possibly inspired from the 2γ) [42]. Conversely, due to the same chirality of interior neutrinos, the gµ cannot bind µ and μ + as effectively and closely as the g e , resulting in the η ′ ( 958 ) having a significantly larger mass than the η ( 548 ) , which provides a straightforward explanation for the “ η − η ′ puzzle” [81] without requiring a complex hypothesis. The majority of η ′ ( 958 ) decay modes produce charged particles, including π + and π − (or μ + v and µν) [42].

We predict that µ and μ + with opposite chirality might couple with g μ * to form heavy η′ mesons in rare situations.

Whenµandµ⁺have same spin chirality

1) Bound with g e

It may be uncommon and challenging for a g e to bind μ L and μ L + (or μ R and μ R + ) together. However, we propose that the observed f 0 ( 500 ) could serve as an appropriate candidate for this combination, expressed as:

2) Bound with g μ

The g μ binds µ and μ + in a meson due to their same flavour, forming two coupling states. One state has the same chirality for g μ and bound µand μ + , making it more stable and lighter. The other state has different chirality, resulting in higher mass. This can be represented by ρ 0 ( 770 ) and ω ( 782 ) accordingly as:

The ρ 0 ( 770 ) decays to π − + π + with a 100% fraction [42]. during which the g μ splits into 2ν that bind with µ and μ + separately and temporarily. According to the Equation (7.4), the decay can be expressed as (for present purposes, in the rest of work, we will present process using only right-handed gluon or only left-handed gluon because both have the same patten):

ω ( 782 ) may decay with more intense, thus g μ breaks into 2νand excites an additional π 0 with a fraction of (89.2 ± 0.7)% [42]:

There is an intermediate state before the final decay of ω ( 782 ) , where π 0 is bound with either π − or π + . The former combination forms ρ − , and the latter forms ρ + . Both combinations will decay into two π with a 100% fraction [42], which can be expressed as:

Equations (7.10) and (7.11b) indicate that ρ ± differs from ρ 0 , and their mass difference should be at least as large as that between π ± and π 0 .

The second common decay of ω(782) occurs via μ μ + annihilation into a γ and the bound g μ exciting a π 0 with a (8.33 ± 0.25)% fraction [42].

3) Bound with g *

In rare instances, a g μ * may bind the µ and μ + (or s * and s * + ) with same spin chirality to form heavy states of ρ meson and ω meson.

μ ∗ decay modes

We predict that μ * has a shorter lifetime than µ and may decay to µ,e or e * through interactions with various gluons. Here are some examples of μ * decay modes:

Note: the marks ′, ′′ and ′′′ in this paper are for tracking locations and improving readability.

Gluons may further decay into π 0 or ( π − + π + ) depending on the cause of the decay. Thus, the μ * decay modes above can be simply expressed as:

The exchange of neutrinos can alter the chirality of newly produced leptons and gluons, for instance:

or simply expressed as: