From the Dark Neutron to the Neutron Decay Anomaly and Lithium Cosmologic Problem ()

Abele Bianchi^{1}, Giovanni Guido^{2*}

^{1}External Contact Referent of the Extreme Energy Events (EEE) Project at the High Scholls, “Gandini”, Lodi, Milano, Italy.

^{2}External Contact Referent of the EEE Project at the High Scholl “C. Cavalleri”, Parabiago, Milano, Italy.

**DOI: **10.4236/jhepgc.2022.83036
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In the context of the geometric model of particles (PGM), we show two different forms of the structure of the quark positions making up the neutron: first, an ordinary form, while the second is a “dark” form (difficult to detect). By the “dark” form we attempt of explaining the anomaly of the neutron lifetime (*τ*) in its decay observed in two different experiments as that in “bottle” and “in beam” and expressed by discrepancy between the two lifetimes (*τ _{bottle}* ≠

Keywords

Anomaly, Dark Neutron, Structure Equation, Geometric Structure, Golden Number, Massive Coupling, Interpenetration, Lithium

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Bianchi, A. and Guido, G. (2022) From the Dark Neutron to the Neutron Decay Anomaly and Lithium Cosmologic Problem. *Journal of High Energy Physics, Gravitation and Cosmology*, **8**, 494-516. doi: 10.4236/jhepgc.2022.83036.

1. Introduction

In a series of studies [1] [2] [3] on the phenomenology of particles the possibility of representing massive particles as geometric structures of couplings between quantum oscillators of field emerges. The particle thus presents itself with a double aspect: a field of oscillations expressed by a wave equation and a structure at geometric shape of a set of the field oscillators of a field [4]. This obviously extends the descriptive horizon of particles and their interactions, deepening the understanding [5] [6] [7] of the Standard Model (SM). These new aspects suggest that we are facing a new descriptive paradigm of physics: the geometrization of the matter-form. Thanks to this new descriptive paradigm it is possible to formulate the hypothesis that matter occurs in two different forms: an ordinary form, which is easy to detect, and a “dark” form that has difficulty interacting and being detected [8]. Not only that, but the hypothesis of the “dark” form of matter implies a radical and innovative revision of some concepts related to decays or, in general, to interactions, and why not, to the particles themselves. From previous articles [1] [2] [3] [4], we recall the revisitation of the concept of mass, Section 2.1. We show that the mass property derives from the presence of an (additional) transverse coupling between the oscillator lines of a non-massive basic scalar field X. This justifies the hypothesis of structure and defines the new descriptive paradigm of interactions given by the geometric model [8] [9] of particles (PGM). In Section 2.2, it is then highlighted that the additional coupling expresses a generalized “Higgs” field that would give mass to the leptons in any type of interaction: *H *in the electromagnetic interactions (*H _{em}*) and

2. The Particles as Geometric Structures of Coupled Quantum Oscillators

2.1. The Massive Coupling

In previous studies [1] [2] [3] it was noted that the K-G equation describes a massive particle but also a system of pendulums connected by springs. If we put [*m = *(*hω*_{0}*/c*^{2})], then it is:

$\begin{array}{l}{\left\{\frac{{\partial}^{2}\Psi \left(x,t\right)}{\partial {t}^{2}}={c}^{2}\frac{{\partial}^{2}\Psi \left(x,t\right)}{\partial {x}^{2}}-{\omega}_{0}^{2}\Psi \left(x,t\right)\right\}}_{\text{pendolum}}\\ \Rightarrow {\left\{\frac{{\partial}^{2}\Psi \left(x,t\right)}{\partial {x}^{2}}-\frac{{\partial}^{2}\Psi \left(x,t\right)}{{c}^{2}\partial {t}^{2}}={\left(\frac{mc}{\hslash}\right)}^{2}\Psi \left(x,t\right)\right\}}_{\text{particle}}\end{array}$ (1)

then the “proper” frequency (*ω*_{0}) is called as massive frequency. The dispersion relationship of waves propagating in (*S _{lab}*), as described by the Klein-Gordon equation, is:

$\left\{{E}^{2}={m}^{2}{c}^{4}+{p}^{2}{c}^{2}\iff {\omega}^{2}={\omega}_{0}^{2}+{k}^{2}{c}^{2}\right\}$ (2)

We translate this system into a field seen in its representation at coupled oscillators, see Figure 1.

We conjectured that the massive particle-field (Y* _{KG}*) is originated by a “transversal coupling” (

Figure 1. Massive field as lattice of “pendulums” with springs.

produces the mass in (X), has been referred to as a “massive coupling”. All this can be depicted figuratively as shown in Figure 1. When we observe only the oscillation with frequency (*ω*_{0}) in all points (*x*) then we are at rest with the massive particle (
$m\iff {\omega}_{0}\iff {T}_{0}$ ) and X-field do not is involved. Instead when the X-field is involved the wave becomes progressive with frequency (*ω*) wave length (*λ*) and represent a massive particle with velocity (*v*), (see Equation (2)). In Figure 1 the *λ*º*λ*_{c} is the Compton wavelength and represents the space step of massive lattice. By Equation (2) and De Broglie relation one finds the Compton relation: [*λ _{c}*

$\pounds ={\left[{\partial}_{\mu}\Psi \left({x}_{i}\right)\right]}^{2}+{m}^{2}{\Psi}^{2}\left({x}_{i}\right)$ (3)

In the literature the Lagrange function, see (Equation (3)), has an additional term of mass (*m*Y^{2}), but one didn’t say anything about the origin of the mass idea. Now, instead, the additional term of mass (*m*Y^{2}), points out an additional coupling (*T*_{0}) to field (X) which makes pass from (X) to Y, see Figure 1. Note that the X-field is intrinsic to Y-field. This additional coupling determines into quantum field a “structure” coupled with quantum oscillators: this represents a massive particle. Some clarification is needed. If in field theory we consider a scalar field expressed by a wave function Y(*x*, *y*, *z*, *t*), we mean that in a point of the space of the laboratory SR it is observed that “something oscillates” and it propagates. The oscillation can be longitudinal or transverse: nobody knows what oscillates. The positives (fathers of QM, early 1900) have denied further investigations that go beyond the wave and corpuscular phenomena (energy quanta of the field). Thus, the whole theory of (quantum) fields can only be expressed in “phenomenological” terms. The Lagrangian function together with its Lagrange equation can only describe phenomena and their correlations (physical quantities). We know, in fact, what happens to particles with a mass, electric charge, color charge, spin, etc. when they interact but we do not know what oscillates in them and what intrinsically are their mass, electric charge, color charge, spin etc.. Now something is being added or rather it is deepening in the theory of quantum fields, see the SM. In the Lagrangian, the mass that appears as an additional term (*m*Y^{2}) to the one that describes the variations of the wave function (¶* _{m}*Y), is no longer a single parameter. Well, this additional coupling determines a coupling structure of the representative oscillators of the field: a particle thus becomes a structure that propagates together with its representative field. Even if we cannot investigate the additional elastic tension

2.2. The Fundamental Massive Bosons

Understanding the mass of a particle as the proper (*ω*_{0}) frequency of oscillation resulting from the additional transverse coupling in a basic scalar field, may seem to disagree with the idea of mass in the SM, where the Higgs field is the boson that gives the mass to the particles (exactly leptons, weak vector bosons and quarks). However, the same Higgs field has mass and, therefore, we ask us “what other field would give the mass to the Higgs field”. We, instead, assert that if the Higgs field has mass, then it is a lattice-field at additional coupling between the scalar field oscillators not massive (X* _{H}*) which is more fundamental of the same Higgs field. Thus, thanks to the Higgs field and its additional coupling, the particles that participate in the weak interaction acquire mass, see the Weinberg-Higgs mechanism [11]. This could also happen in the electromagnetic reactions of creating pairs
$\left(\gamma +\gamma \right)\to \left({e}^{-}+{e}^{+}\right)$. In the coupling between two photons, the massive lattice (

Due to its mass, see Figure 1, the “electromagnetic” Higgs field (*H** _{g}*) becomes an additional coupling “lattice” that allows electromagnetic energy (photons) to “transform” itself into massive quanta (lepton pair). It is immediately evident that with this new approach to the process of pair creating, a new descriptive paradigm is introduced into the physics of interactions: the interaction agent becomes a lattice-field capable of transforming the particles, from massless to massive or from massive to massive. We specify once again that this argumentation is purely formal and can be useful for didactic purposes. If we look at Figure 1, we can imagine for the

Here, an additional coupling of field oscillators with the spatial dimension of the wavelength *λ _{H}*and submultiples take origin in a massless scalar field X. If we

Figure 2. The H-lattice at Compton different wavelengths *λ _{H}*

look at Figure 1 and Figure 2, we can imagine for the *W** ^{±}*boson that it may be represented by Figure 3.

2.3. The PGM Model

We note that the (Y* _{H}*, Y

Figure 3. The *W*^{±}*-*lattice at Compton different wavelengths *λ _{w}*

in the reactions. Therefore, for the moment we can treat the structures in formal terms without further specifying the mathematical form of the matrix operators [((*a*_{0})), ((
${a}_{0}^{+}$ ))]. We indicate by the acronym (PGM) the Geometric Model of Particles: for the moment this model will be developed by a formal and representative approach didactically useful, but it is intuitive to understand that it can be developed and represented through an adequate mathematical language. The validity of this representative model of particles is based on the possibility of explaining the origin of the fundamental concepts, see mass [4] [7], electric charge [24] [25], color charge [26] and spin, and to deepen the experimental and theoretical aspects of the interaction processes and of particle generation.

3. The “Aureum” Geometric Model (AGM) of Quarks

3.1. Description of the Model

Since quarks also have mass then we need to assign structures of additional couplings of oscillators to them. There is a set of studies on quarks, see Guido [2] [4] [5] [7] and Guido-Bianchi [8], where we have mathematically demonstrated that quarks are triangular “golden” structures of coupled quantum oscillators. It is shown, in fact, that the d-quark will be associated with the basic golden triangle (*d*) with angles, base (72˚, 72˚), vertex 36˚), while the triangle also known as golden gnomon is associated to the u-quark with angles [base (36˚, 36˚), vertex 108˚)], see Figure 4.

(*A, B, C, D, E, F*) are vertex oscillators, while all others are junction oscillators (*AB, BC, CD, AD*) corresponding to gluons with charge of bi-colour [26]. The vector *s* represents the spin of the fermion quark. *X* is the propagation axis. To the translation (movement) along the *X* axis we could add a rotation (the different possible planes of oscillation) of the triangular structure of couplings around the propagation direction; the s-spin of the boson is of eigenvalues: *s* = ±1/2. Intuitively, it can be assumed that along the propagation axis *X*, the additional oscillations Y_{m}* *of the oscillators (*A, B, C*) and (*D, E, F*) with frequency *ω*_{0} overlap,

Figure 4. The d-quark and u-quark.

in phase, to combined oscillations of the two scalar fields (X* _{i}* Ä X

· the structures of quarks (*s, c, b, t*) are formed with the sub-triangles [2] [5].

· there exists a background lattice {(*d,u*)} of quarks and “sub-quarks” [4] [7].

In some publications [2] [4] [5] the geometric forms of “heavy” quarks have also been given, such as the quark (*s*, *c*, *b*, *t*). If we want to be more faithful to physical reality, we consider a background lattice containing “virtual” pairs of quark-antiquarks with the connected “sub-quarks”: {(*d, d*)Ä(*u, u*)}. All hadronic particles will propagate within this lattice and here they will interact with each other through quantum exchange. It is no coincidence that Yucawa found between two nucleons there are the pions as intermediary agents. Or even in recent times one speaks of quark “molecules” as lattice particles. By this new descriptive paradigm of hadronic phenomenology, we can explain the phenomenon of “hadronization” and the confinement of quarks. Therefore, the inseparability of quarks or hadronization so as confinement of quarks, would be a consequence of the geometric aspect of the background quark-lattice. The hadronic geometric field will thus be made up of golden quarks all set as in a puzzle. Any hadronic particle will thus be expressed by real “quanta” circulating within a quark-triangle structure, formed by couplings of quantum field oscillators, which in turn propagates along one or more coupled field lines. The potentials of QCD [27] [28] are none other than the diffusion of the quanta-gluons in the background lattice-field. Therefore, there are no “traditional” bond forces between two quarks that make up e.g. the pion. This is represented by a structure given by a coupling of a d quark with a u-quark, both belonging to the background hadron lattice of quarks, in which real quanta circulate (as if they were trapped in the structure) which identify the pion structure and describe its propagation. This structure then propagates along a propagation axis with or without its own rotations. Thus, we explain why the neutron [7] [9] is “embedded” in the pair (*d*, *d*) and the masses of the hadrons can be calculated by considering the pairs of bases (*d, d*). The same happens for all other quarks (*s, c, b, t*). The didactic value of AGM would be so remarkable: combining the various triangles-quarks it is possible to obtain all the “geometric” representations of hadrons, and possibly also those of the hypothesized “molecules” of quarks [8] [9] and the interactions.

3.2. The Nucleon Structure

The neutron can be built by composite structure of two golden triangles *d* and a golden triangle *u*;all three triangles-quarks have a common side lying on the same axis which coincides with the propagation axis of neutron [7] [9]. It is shown that the configurations of the ordinary nucleon, see Figure 5.

Where (*A, B, C, D, E*) are vertex quantum oscillators. Pay attention that the vertex *E* is not fixed in the side *BC* because *u*-quark rotates around *X*-axis. The junction oscillators (the sides of the two figures) are represented here by little circles with two colours. However, it should be noted that the junction oscillators can well represent the gluons that bind the vertex oscillators as well as the gluons binding the sides of different quarks. Again, in formal and “didactic” terms, it can be thought that the triangles-quarks rotate around the propagation *X*-axis, see the vectors *s*, determining an “orbital” spin that contributes to the total spin of the neutron, see ref. [7] [9]. We note that the description in terms of elasticity (junction oscillators and vertices) of the couplings between quarks is equivalent to that which QED makes of hadrons and their interactions through the potentials associated with the color action of the gluons. In precedents articles we gave the structural equation and calculated them masses [7] [9].

3.3. The Geometric Structure of the Deuteron and Tritium

The first structures in which the neutron binds to other nucleons are Deuteron and Tritium. We compose the Deuteron *D* (*n, p*) and the Tritium (*n, n, p*). Omitting for the moment to draw the pions, which would bind the nucleons, we obtain the configurations of Deuteron and Tritium, see Figure 6.

We note that the proton (in black) is *p *(*d*_{1}*, u*_{1}*, u*_{2}), while the neutron (in blue) is *n *(*d*_{2}*, u*_{3}*, d*_{3}). The vectors (*s** _{i}*) are the spins. Deuteron is a boson. In Tritium we

Figure 5. The geometric forms of two nucleons.

Figure 6. Deuteron configuration and tritium.

Figure 7. The system (*T *+ *D*).

note that *p *(*d*_{4}*, u*_{4}*, u*_{5}), *n *(*d*_{5}*, u*_{6}*, d*_{6}), *n *(*d*_{7}*, u*_{7}*, d*_{8}). Tritium, on the other hand, is a fermion. In Figure 6, note that along the *X*-axis of the tritium there are three aligned *d*-quarks in spin: this is possible thanks to the color charge, different in the three *d*-quarks. This aspect tells us that no more than three quarks of the same type can coexist along the propagation *X-*axis. Let’s now build the system (*D *+*T*), see Figure 7.

In Figure 7, note that along the X-axis of the (*D *+ *T*) there are five *d*-quark spin vectors (*s** _{d}*) on one side and four

We point out by the notation [(*d _{i}, d_{j}*)

${N}_{c}\left(d,u,d\right)={\displaystyle \underset{k=1}{\overset{7}{\sum}}{u}_{k}\left[{\displaystyle \underset{\begin{array}{l}i=1\\ i>j\end{array}}{\overset{8}{\sum}}{d}_{i}\left({\displaystyle \underset{j=i}{\overset{8}{\sum}}{d}_{j}}\right)}\right]}=196$ (4)

The numerical value of the summation gives us the number of combinations (*u _{k}*

The following array scheme may be useful:

The number of combinations *C* is

$\begin{array}{l}N{\left({\underset{\_}{C}}_{\left(2d,u\right)}\right)}_{\left(j=1,\cdots ,7\right)}\\ =\left[{\left(7\right)}_{\left({d}_{1},{d}_{2}\right),{u}_{j}}\times {\left(7\right)}_{\left({d}_{1},{d}_{i>2}\right),{u}_{j}}\right]+\left[{\left(7\right)}_{\left({d}_{2},{d}_{3}\right),{u}_{j}}\times {\left(6\right)}_{\left({d}_{2},{d}_{i>3}\right),{u}_{j}}\right]\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+\left[{\left(7\right)}_{\left({d}_{3},{d}_{4}\right),{u}_{j}}\times {\left(5\right)}_{\left({d}_{3},{d}_{i>4}\right),{u}_{j}}\right]+\left[{\left(7\right)}_{\left({d}_{4},{d}_{5}\right),{u}_{j}}\times {\left(4\right)}_{\left({d}_{4},{d}_{i>5}\right),{u}_{j}}\right]\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+\left[{\left(7\right)}_{\left({d}_{5},{d}_{6}\right),{u}_{j}}\times {\left(3\right)}_{\left({d}_{5},{d}_{i>6}\right),{u}_{j}}\right]+\left[{\left(7\right)}_{\left({d}_{6},{d}_{7}\right),{u}_{j}}\times {\left(2\right)}_{\left({d}_{6},{d}_{i>7}\right),{u}_{j}}\right]+\left[{\left(7\right)}_{\left({d}_{7},{d}_{8}\right),{u}_{j}}\times \left(1\right)\right]\\ =\left[\left(7\times 7\right)+\left(7\times 6\right)+\left(7\times 5\right)+\left(7\times 4\right)+\left(7\times 3\right)+\left(7\times 2\right)+\left(7\times 1\right)\right]=196\end{array}$

4. The Dark Neutron

4.1. The Structure Anomaly in the of the Neutron

Instead of forming the system (*D* + *T*) of Figure 7, it is possible that an anomalous system (*D* +*T*)** *takes origin*,* given by the coupling of the Tritium with a Deuteron along the *Y* axis passing through the AB side of *d*_{7} and *d*_{5}, see Figure 8.

Note that the (*X*, *X'*, *Y*) axes are coplanar. There is an interlocking of the quarks *d* which fixes the pair of quarks (*d*_{2}*, d*_{5}). The quark *d*_{5} will continue to rotate around the *X* axis, however dragging with it the *d*_{2}*-*quark and together with it the proton (*d*_{1}*, u*_{1}*, u*_{2}). This happens thanks to the present background lattice, {*q, q*} º {(*d, d*) Ä (*u, u*)} coplanar to the axes (*XX'*): the quanta of the Deuteron can penetrate into the lattice {*q*, *q*} and through the gluons of the sides fix the quarks (*d*_{2}*, d*_{5})*. *However, it could happen that the quark *d*_{3} couples with the quark *d*_{7}: the two quarks will detach from their rotation axes and begin to rotate around the *Y* axis. It could also happen that the *d*_{3} drags the quark *u*_{3}, with which it was bound in the Deuteron, along the Y-axis. In this way, a “strange” neutron is formed propagating and rotating around the Y axis: *n *(*u*_{3}*, d*_{3}*, d*_{7})***. Unlike the “ordinary” neutron, this neutron, see Figure 8, has only two quarks (*d*_{3}*, d*_{7}) along the propagation *Y*-axis: the other quark *u*_{3}, rotating around the *X*'-axis, is dragged by couple (*d*_{3}*, d*_{7})along *Y. *Note that *u*_{3}-quark cannot exchange quanta with any external quarks (belonging to other hadrons) which cross the strange neutron along the *Y*-axis. This makes the “strange” neutron difficult to interact with other hadrons. The vertex *D* is insufficient for external energy exchanges (quanta) which instead occur along the whole side *AB*. Furthermore, the strange neutron is neutral and therefore does not interact electromagnetically. If we highlight that all three quarks of a neutron are involved in its weak decay, it is immediately evident that even the weak decay is compromised because *u*_{3}-quark is not on the propagation axis. Later we will demonstrate that the strange neutron cannot decay like the ordinary neutron because it has a lower mass than the decay proton, see sec. 3.4. A neutron so made and with difficulty to interact can be a good candidate to become dark matter, see the hypothesis of the dark neutral pion in [8], therefore we will call it “dark” neutron (*n _{d}*). With

Figure 8. The anomaly reaction of fusion (*D *+ *T*)*** with a dark neutron.

with two parallel axes (*XX'*). The remaining quarks rotate around the *X*-axis and others around the X'-axis. The new neutron (*u*_{3}*, d*_{3}*, d*_{7}) will form the dark neutron *n _{d}*, see Figure 8. The reaction will be:
$D+T\to He*+\text{\hspace{0.17em}}{n}_{d}$. Due to its configuration, the

$P\left({n}_{d}\right)=2/196=0.0102$ (5)

A few clarifications must be made: the probability *P*((*D *+*T*)***) of an anomalous reaction forming could depend on the temperature of the neutron gas (*P* *µ*T*), but once the fusion reaction (*D *+*T*)*** has taken place the probability of having the emission of the dark neutron will be given by the report 2/196. The production of dark neutrons may have been so remarkable in the hot phases of the universe, the nucleosyntesis phase. Therefore, we can assert that in the nucleosyntesis phase most of that dark matter originated which today would be found in the galactic halos.

4.2. The Relative Discrepancy

Researchers try to explain the reason for the discrepancy in the values of the lifetime *τ* of the neutrons obtained in two different experimental situations: neutrons (*N _{b}*) confined in a container called “bottle” [13] [14] [15] and neutrons in a beam (

We can find the experimental value of relative discrepancy value:

${\left({d}_{r}\right)}_{exp}=\Delta \tau /\langle {\tau}_{f}\rangle =\left(887.7-878.68\right)/887.7=0.0102$ (6)

The result is that the experimental relative discrepancies (*d _{r}*)

4.3. Dark Neutron Detection Experiment

The first experiment that we could carry out to detect the presence of dark neutrons could be just that of fusion of Deuteron with Tritium, (*D *+*T*). If in the fusion process a dark neutron emerges, we should not detect any ordinary neutron:

$\left[D+T\to \left(He*+\text{\hspace{0.17em}}{n}_{d}\right)\equiv \left(He*+\text{\hspace{0.17em}}?\right)\right]$.

We would have the formation of a *He** which in some properties could differ from the “ordinary” *He*, without emission of a neutron. Therefore, in fusion processes (*D* + *T*) could miss some neutrons. The second experiment could be made in bottle. In the bottle, dark neutrons should remain which have not decayed and which are not subsequently counted in *n _{r}*. We can then think of detecting them in a way: directing a beam of pions on the bottle. Some dark neutrons can interact with a pion and determine a particular reaction that easily identifies the dark neutron (
${n}_{d}+{\pi}^{+}\to p+\gamma $ ). This reaction would be distinguishable from the ordinary reaction (
${n}_{o}+{\pi}^{+}\to p+\gamma $ ), because the mass of the dark neutron is different from that of the ordinary neutron

4.4. The Dark Neutron Mass

Using the “Aureum” Geometric Modell (AGM), see Section 2.1, we could take into account the structure equation [8] [9] of dark neutron, which is built on the geometric representation of particle, see Figure 8. We can represent the dark neutron also in the following way, Figure 9.

Note *u*-quark in rotation around to side *BC* and the pair (*d*_{3}*, d*_{3}). This pair represents the field of virtual quarks that “dresses” the mass of a hadron, as described in strong interactions, see Section 2.1. Note that the pairs (*d _{i},d_{i}*)

The AGM model is so physically equivalent to the field theory of SM. The structure equation allows you to calculate the mass of the dark neutron, using the same procedure by which we have calculated the mass of light mesons [6] [20] and nucleons [7] [8] [9] for the dark neutron we have:

$\left(n\right)=3{\kappa}_{n}\left(\left\{{\left(d\otimes \underset{\_}{d}\right)}_{A}\text{\hspace{0.17em}}\underset{\_}{\otimes}\text{\hspace{0.17em}}{\left[{d}_{1}\underset{\_}{\otimes}\text{\hspace{0.17em}}u\text{\hspace{0.17em}}\underset{\_}{\otimes}\text{\hspace{0.17em}}{d}_{2}\right]}_{B}\right\}\right)$ (7)

Here, the symbol Ä indicates the elastic coupling operation which can admit the interpenetration of quarks during their rotations, in the same way as happens in waves when they cross. The interpenetration is thus a purely quantum “wave” aspect: the quarks overlap as happens in the waves represented in QM by the Y states. The waves cross each other and at the points where they cross then they overlap (Y*= *Y_{1}+Y_{2}) or the oscillations are composed. The quarks, seen as geometric structures of coupled oscillators, are crossed along the sides (chains of junction gluons) by oscillations: the interpenetration of two quarks (*q*_{1}*,q*_{2}) implies that the oscillations (Y_{1},Y_{2}) in their respective sides when they cross then they overlap like waves and cross each other resuming their “path” along the joining sides. The symbol Ä indicates the combination of two operations: Ä º (Ä, Å), where Å indicates the dynamic coupling operation between quarks (exchange of energy quanta). To the structure equation we associate the spin structure equation (the spin distributions into internal quarks), which in the case of the dark neutron becomes:

Figure 9. The dark neutron configuration.

$\begin{array}{l}{s}_{n}=\left\{\begin{array}{c}{s}_{t}\left(q\right)=\left[{\left(\overline{)\downarrow}\overline{)\downarrow}\right)}_{\left({d}_{1},{d}_{2}\right)},{\left(\overline{)\uparrow}\right)}_{{u}_{1}}\right]\text{\hspace{0.17em}},\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left[{\left(\overline{)\uparrow}\overline{)\downarrow}\right)}_{{\left(d,\underset{\_}{d}\right)}_{\gamma}}\right]\equiv \left[{s}_{q}\left({u}_{1}\right)+{s}_{q}\left({d}_{1},{d}_{2}\right)\right]+{s}_{\gamma}\left(d,\underset{\_}{d}\right)=-\left(1/2\right)\\ {s}_{t}\left(l\right)=\left[{\left(\downarrow \downarrow \right)}_{\left({d}_{1},{d}_{2}\right)},{(\uparrow )}_{{u}_{1}}\right]\text{\hspace{0.17em}},\left[{\left(\uparrow \downarrow \right)}_{{\left(d,\underset{\_}{d}\right)}_{\gamma}}\right]\text{\hspace{0.17em}}\text{\hspace{0.17em}}\equiv {s}_{l}\left({u}_{1}\right)=\pm \left(1/2\right)\\ {s}_{t}\left(g\right)=\left[{\left(\uparrow \uparrow \right)}_{\left({d}_{1},{d}_{2}\right)},{(\downarrow )}_{{u}_{1}}\right]\text{\hspace{0.17em}},\text{\hspace{0.17em}}\left[{\left(\downarrow \uparrow \right)}_{{\left(d,\underset{\_}{d}\right)}_{\gamma}}\right]\text{\hspace{0.17em}}\equiv {s}_{g}\left({u}_{1}\right)=\mp \left(1/2\right)\end{array}\right\}\\ \text{}={s}_{q}\left({d}_{1}\right)=-\left(1/2\right)\end{array}$ (8)

In accordance with the procedure for calculating the mass of an ordinary nucleon in AGM, see ref. [7], we consider the “elastic” vertices of the geometric figure:

$\left\{{\left[A,B,C,D\right]}_{\left({d}_{1},{d}_{2}\right)},{\left[F,E\right]}_{\left({d}_{3},{\underset{\_}{d}}_{3}\right)},{\left[G\right]}_{\left(u\right)}\right\}$.

The number of “elastic” vertices is: *N*(*V _{el}*) º

The elastic tension does increase the oscillation frequency in an elastic system, see the harmonic oscillator: [*ω* = (*K _{el}*/

Instead, the inertial characteristic (*M _{in}*) of the structure is connected to the

$\begin{array}{l}\{[AC\left({d}_{1},{d}_{2}\right),AC\left({d}_{1},{\underset{\_}{d}}_{3}\right),AC\left({d}_{1},{d}_{3}\right);AC\left({d}_{2},{d}_{3}\right);\\ AC\left({d}_{2},{\underset{\_}{d}}_{3}\right);AC\left({d}_{3},{\underset{\_}{d}}_{3}\right)],\left[BC\left({d}_{1},u\right),BC\left({\underset{\_}{d}}_{3},u\right)\right]\}\end{array}$

It follows: *N'*(*M _{in}*) º

${\kappa}_{d}=\left(\frac{{N}_{el}}{{N}_{in}}\right)=\frac{7}{8}=0.875$ (9)

To elaborate the structure equation the following algebraic relationship is used [7]:

$\left[A\text{\hspace{0.17em}}\underset{\_}{\otimes}\text{\hspace{0.17em}}B\text{\hspace{0.17em}}\underset{\_}{\otimes}\text{\hspace{0.17em}}C\right]=\left\{\left[\left(A\right)\otimes \left(B\oplus C\right)\right]\oplus \left[\left(B\right)\otimes \left(C\oplus A\right)\right]\oplus \left[\left(C\right)\otimes \left(A\oplus B\right)\right]\right\}$

We obtain:

$\begin{array}{c}{n}_{d}=3{\kappa}_{d}\{{\left[\left(d\otimes \underset{\_}{d}\right)\right]}_{{B}_{0}}\text{\hspace{0.17em}}\underset{\_}{\otimes}\text{\hspace{0.17em}}\{{\left[u\otimes \left({d}_{1}\oplus {d}_{2}\right)\right]}_{{B}_{1}}\oplus {\left[{d}_{1}\otimes \left({d}_{2}\oplus u\right)\right]}_{{B}_{2}}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\oplus {\left[{d}_{2}\otimes \left(u\oplus {d}_{1}\right)\right]}_{{B}_{3}}\}\}\\ =3{\kappa}_{d}\{{\left[\left(d\otimes \underset{\_}{d}\right)\right]}_{{B}_{0}}\text{\hspace{0.17em}}\underset{\_}{\otimes}\text{\hspace{0.17em}}\{{\left[\left(u\otimes {d}_{1}\right)\oplus \left(u\otimes {d}_{2}\right)\right]}_{{B}_{1}}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\oplus {\left[\left({d}_{1}\otimes {d}_{2}\right)\oplus \left({d}_{1}\otimes u\right)\right]}_{{B}_{2}}\oplus {\left[\left({d}_{2}\otimes u\right)\oplus \left({d}_{2}\otimes {d}_{1}\right)\right]}_{{B}_{3}}\}\}\\ =3{\kappa}_{d}\left\{{\left[\left(d\otimes \underset{\_}{d}\right)\right]}_{{B}_{0}}\text{\hspace{0.17em}}\underset{\_}{\otimes}\left[{N}_{{B}_{1}}\oplus {N}_{{B}_{2}}\oplus {N}_{{B}_{3}}\right]\right\}\end{array}$ (10)

The mass calculation uses *F _{m}*-function applied to structure Equation (7), see [7] [9]. Then, it is:

$\begin{array}{c}m\left({n}_{d}\right)=3{\kappa}_{d}{F}_{m}\left({\left[\left(d\otimes \underset{\_}{d}\right)\right]}_{{B}_{0}}\text{\hspace{0.17em}}\underset{\_}{\otimes}\text{\hspace{0.17em}}{\left[{N}_{1}\oplus {N}_{2}\oplus {N}_{3}\right]}_{B}\right)\\ =3{\kappa}_{d}m\left({\left[\left(d\otimes \underset{\_}{d}\right)\right]}_{{B}_{0}}\oplus {\left[{N}_{1}\oplus {N}_{2}\oplus {N}_{3}\right]}_{B}\right)\\ =3{\kappa}_{d}{\left\{m{\left(d\otimes \underset{\_}{d}\right)}_{{B}_{0}}+m\left({\left[{N}_{1}\oplus {N}_{2}\oplus {N}_{3}\right]}_{B}\right)\right\}}_{\otimes}\\ ={\left[3{\kappa}_{d}m\left(d\right)\right]}_{{B}_{0}}+{\left\{3{\kappa}_{d}\left[m\left({N}_{1}\right)+m\left({N}_{2}\right)+m\left({N}_{3}\right)\right]\right\}}_{B}\end{array}$ (11)

where

${F}_{m}\left(A\underset{\_}{\otimes}B\right)=m\left(A\oplus B\right)=m\left(A\right)+m(\; B\; )$

$m\left(a\otimes b\right)=m\left(\langle a,b\rangle \right)=\left[\left(m\left(a\right)+m\left(b\right)\right)/2\right]$

with

$\begin{array}{l}m\left({N}_{1}\right)=m{\left[\left(u\otimes {d}_{1}\right)\oplus \left(u\otimes {d}_{2}\right)\right]}_{1}=m\left(\langle u,{d}_{1}\rangle \right)+m\left(\langle u,{d}_{2}\rangle \right)\\ m\left({N}_{2}\right)=m{\left[\left({d}_{1}\otimes {d}_{2}\right)\oplus \left({d}_{1}\otimes u\right)\right]}_{2}=m\left(\langle {d}_{1},{d}_{2}\rangle \right)+m\left(\langle {d}_{1},u\rangle \right)\\ m\left({N}_{3}\right)=m{\left[\left({d}_{2}\otimes u\right)\oplus \left({d}_{2}\otimes {d}_{1}\right)\right]}_{\text{3}}=m\left(\langle {d}_{2},u\rangle \right)+m\left(\langle {d}_{2},{d}_{1}\rangle \right)\end{array}$ (12)

In all two cases, the two quarks (*d*_{1}*, d*_{2}) cannot interpenetrate each other, because they have parallel spin, see the Equation (6): then, it is (*d*_{1}Ä*d*_{2}) = 0 and, thus, [*m*(*d*_{1}Ä*d*_{2}) = 0], see Table 2 in ref [9]. It follows, see Equation (12):

$\begin{array}{l}m\left({N}_{1}\right)=m{\left[\left(u\otimes {d}_{1}\right)\oplus \left(u\otimes {d}_{2}\right)\right]}_{1}=m\left(\langle u,{d}_{1}\rangle \right)+m\left(\langle u,{d}_{2}\rangle \right)\\ m\left({N}_{2}\right)=m{\left[\left({d}_{1}\otimes {d}_{2}\right)\oplus \left({d}_{1}\otimes u\right)\right]}_{2}=m\left(\langle {d}_{1},u\rangle \right)\\ m\left({N}_{3}\right)=m{\left[\left({d}_{2}\otimes u\right)\oplus \left({d}_{2}\otimes {d}_{1}\right)\right]}_{\text{3}}=m\left(\langle {d}_{2},u\rangle \right)\end{array}$ (13)

where the relative mass of two interpenetration quarks is given by:

$m\left(u\otimes d\right)=m\left(\langle u,d\rangle \right)=\left[\left({m}_{u}+{m}_{d}\right)/2\right]$

coupling while in dynamic interaction it is instead:
$m\left(u\oplus d\right)=\left({m}_{u}+{m}_{d}\right)$ *.*

Note that the *u*-quark is not interpenetrating with the *d*_{2}-quark. However, *u*-quark with the quark *d*_{2} it has a vertex C in common where it can exchange some bond “gluons”, so we can still associate a mass value to system (*u*Ä*d*_{2}) as if they are interpenetrating. Therefore, we have

$m\left({d}_{2}\otimes u\right)=m{\left(\langle {d}_{2},u\rangle \right)}_{C}=m{\left(\langle {d}_{1},u\rangle \right)}_{AC}$ *. *

Thus, it is:

$\begin{array}{l}m\left({N}_{1}\right)=m{\left[\left(u\otimes {d}_{1}\right)\oplus \left(u\otimes {d}_{2}\right)\right]}_{1}=m\left(\langle u,{d}_{1}\rangle \right)+m\left(\langle u,{d}_{2}\rangle \right)\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.05em}}\text{\hspace{0.05em}}=m\left(\langle u,{d}_{1}\rangle \right)+m\left(\langle u,{d}_{1}\rangle \right)\\ m\left({N}_{2}\right)=m{\left[\left({d}_{1}\otimes {d}_{2}\right)\oplus \left({d}_{1}\otimes u\right)\right]}_{2}=m\left(\langle {d}_{1},u\rangle \right)\\ m\left({N}_{3}\right)=m{\left[\left({d}_{2}\otimes u\right)\oplus \left({d}_{2}\otimes {d}_{1}\right)\right]}_{3}=m\left(\langle {d}_{2},u\rangle \right)=m\left(\langle u,{d}_{1}\rangle \right)\end{array}$ (14)

Then:

$m{\left({N}_{1,2,3}\right)}_{B}={\left[m\left({N}_{1}\right)+m\left({N}_{2}\right)+m\left({N}_{3}\right)\right]}_{B}={\left[4m\left(\langle {d}_{1},u\rangle \right)\right]}_{B}$ (15)

Having [*m _{u} *= (53.31) MeV

*
$m{\left({N}_{1,2,3}\right)}_{B}=\left[4m\left(\langle {d}_{1},u\rangle \right)\right]=\left(\text{279}\text{.16}\right)\text{MeV}$*

*It follows*

*
$\begin{array}{c}m\left({n}_{d}\right)=3{\kappa}_{d}\left[m{\left(d\right)}_{A}+m{\left({N}_{1,2,3}\right)}_{B}\right]=3{\kappa}_{d}\left[m\left(d\right)+m{\left({N}_{a,b,c}\right)}_{B}\right]\text{}\\ =3{\kappa}_{d}\left[\left(86.26\right)+\left(\text{279}\text{.16}\right)\right]\text{MeV}=3\left(\frac{7}{8}\right)\left(\text{365}\text{.42}\right)\text{MeV}\\ =\left(\text{959}\text{.23}\right)\text{MeV}\end{array}$ (16)*

*The matrix of mass defect also admits the elements A_{ii} ¹ 0. Then, see Table 1.*

*We calculate the value of table:*

*
$\begin{array}{l}\Delta {m}^{*}\left({n}_{d}\right)=\left[\Delta m{\left(4\left(u\otimes d\right)\right)}_{G1}+\Delta m{\left(2*\left(u\otimes d\right)\right)}_{G1}+\Delta m{\left(6\left(\underset{\_}{d}\otimes d\right)\right)}_{G2}\right]\\ \text{}+\left[\Delta m{\left(6\left({d}_{i}\otimes {d}_{j}\right)\right)}_{B1}+\Delta m{\left(2*\left(u\otimes \underset{\_}{d}\right)\right)}_{B2}\right]\\ \text{}+{\left[3\Delta m\left({\left({d}_{i}\otimes {d}_{i}\right)}_{1,2}\right)+\Delta m\left({\left({\underset{\_}{d}}_{i}\otimes {\underset{\_}{d}}_{i}\right)}_{\gamma}\right)+\Delta m\left(\left({u}_{i}\otimes {u}_{i}\right)\right)\right]}_{R}\end{array}$ (17)*

*Recall that:
$\Delta m\left(u\otimes u\right)=\Delta {m}_{u}=\left(3.51\right)\text{MeV}$ ,
$\Delta m\left(d\otimes d\right)=\Delta {m}_{d}=\left(5.68\right)\text{MeV}$ , *

*
$\Delta m\left(u\otimes d\right)=\Delta {m}_{ud}=\left(\Delta {m}_{u}+\Delta {m}_{u}/2\right)=4.59\text{\hspace{0.17em}}\text{MeV}$*

*For the spin ( s = 1/2), see the table of the neutron spin, we can have the term R':*

*
$\begin{array}{c}{R}^{\prime}\left(n\right)=[2\Delta m\left({\left({d}_{i}\otimes {d}_{i}\right)}_{1,2}\right)+\Delta m\left({\left({d}_{i}\otimes {d}_{i}\right)}_{\gamma}\right)\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+\Delta m\left({\left({\underset{\_}{d}}_{i}\otimes {\underset{\_}{d}}_{i}\right)}_{\gamma}\right)+{\Delta m\left(\left({u}_{i}\otimes {u}_{i}\right)\right)]}_{{R}^{\prime}}\\ =[{{r}^{\prime}}_{1}\Delta {m}^{\prime}{\left({d}_{(\downarrow )}\otimes {d}_{(\downarrow )}\right)}_{{d}_{1}}+{{r}^{\prime}}_{2}\Delta {m}^{\prime}{\left({d}_{(\downarrow )}\otimes {d}_{(\downarrow )}\right)}_{{d}_{2}}+{{r}^{\prime}}_{3}\Delta {m}^{\prime}{\left({d}_{(\uparrow )}\otimes {d}_{(\uparrow )}\right)}_{\gamma}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+{{r}^{\prime}}_{4}\Delta {m}^{\prime}{\left({\underset{\_}{d}}_{(\downarrow )}\otimes {\underset{\_}{d}}_{(\downarrow )}\right)}_{\gamma}+{{r}^{\prime}}_{5}\Delta {m}^{\prime}\left({u}_{(\uparrow )}\otimes {u}_{(\uparrow )}\right)]\\ =\left[\left(-{2}_{\left({d}_{1},{d}_{2}\right)}+{1}_{\gamma}-{1}_{\gamma}+{1}_{u}\right){\left(1.15\right)}_{R}\right]\text{MeV}=\left[(-){\left(1.15\right)}_{R}\right]\text{MeV}\end{array}$ (18)*

*Then, it is:*

*Table 1. The couplings with the interaction of quarks in a neutron.*

*
$\begin{array}{c}\Delta {m}^{*}\left(n\right)=\left[\Delta m{\left(4\left(u\otimes d\right)\right)}_{G1}+\Delta m{\left(2*\left(u\otimes d\right)\right)}_{G1}+\Delta m{\left(6\left(\underset{\_}{d}\otimes d\right)\right)}_{G2}\right]\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+\left[\Delta m{\left(6\left({d}_{i}\otimes {d}_{j}\right)\right)}_{B1}+\Delta m{\left(2*\left(u\otimes \underset{\_}{d}\right)\right)}_{B2}\right]+R\left(n\right)\\ =\left[\text{4}{\left(\text{4}\text{.59}\right)}_{G1}+\text{6}{\left(\text{5}\text{.68}\right)}_{G2}\right]\text{MeV}-\left[6{\left(5.68\right)}_{B1}\right]\text{MeV}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}+\left[-{\left(1.15\right)}_{R}\right]\text{MeV}\\ =\left(17.21\right)\text{MeV}\end{array}$ (19)*

*The pair ( d_{3}, d_{3}) in the structure of neutron shields the electromagnetic interactions between quarks, therefore it weakens the mass defect. The presence of the pair d-quark along diagonal, see Figure 9, splits all mass defects, see the ref. [7] [9], then it follows:*

*
$\Delta {m}^{**}\left({n}_{d}\right)={\left[\Delta {m}^{*}\left({n}_{d}\right)\right]}_{\left(d,\underset{\_}{d}\right)}=\left(\frac{1}{2}\right)\left[\Delta {m}^{*}\left({n}_{d}\right)\right]=\left(8.61\right)\text{MeV}$ (20)*

*Like the neutron being explicit the elasticity parameter k_{d}, it is, see the Equation (8):*

*
$\Delta m\left({n}_{d}\right)=3{\kappa}_{d}{\left[\Delta {m}^{**}\left({n}_{d}\right)\right]}_{\left(d,\underset{\_}{d}\right)}=3\left(\frac{7}{8}\right)\left(8.61\right)\text{MeV}=\left(22.60\right)\text{MeV}$ (21)*

*Thus, it is:*

*
${m}_{tot}\left({n}_{d}\right)=m\left({n}_{d}\right)-\Delta {m}_{\gamma}\left({n}_{d}\right)=\left\{\left(959.23\right)-\left(22.60\right)\right\}\text{MeV}=\left[\left(936.63\right)\right]\text{MeV}/{c}^{2}$ (22)*

*The difference between m(n_{d}) and m(n_{o}) is Δm_{od} = (939.57 - 936.63) MeV= (2.94) MeV. The mass of the dark neutron is even smaller than that of the proton.*

*5. The Consequences*

*5.1. The Origins of Matter-Antimatter Asymmetry*

*The idea of a dark nucleon, although paradoxical, opens the way to a decisive clarification on the nature of dark matter. The geometric structure of the dark neutron n_{d}, see Figure 9, makes it very low probability of interaction with ordinary matter. This is because the u-quark is not attached to the diagonal BD which lies on the propagation axis X', where the interacting particles exchange energy quanta. Therefore u-quark does not couple with any other quarks of other particles, except with quarks (d_{3}, d_{7}) which belong to the same dark neutron. This aspect will not allow the dark neutron to annihilate itself with ordinary and dark antineutrons. The dark neutron does not participate in electromagnetic interactions because it is electrically neutral. Finally, the mass value of the dark neutron (m(n_{d})< m(n_{o})) and the mass difference with the ordinary one (Δm_{od} = (2, 94) MeV) prevents it from decaying into a proton. The dark neutron is thus stable. The interaction difficulty and of annihilation could explain the asymmetry between matter and antimatter in the universe [21]. The first dark particle that originated (for example from a fusion reaction (D +T)) determined the matter-antimatter asymmetry because it has produced an excess of the antagonist ordinary particles: if instead of an ordinary antineutron there was a first dark antineutron (for example from a fusion reaction
$\left(\underset{\_}{D}+\underset{\_}{T}\right)\to \underset{\_}{He}*+\text{\hspace{0.17em}}{\underset{\_}{n}}_{d}$, which could not then annihilate a dark neutron or an ordinary neutron, then over time an excess of matter at the expense of antimatter it was formed:[(N)n, (N − 1)n + n_{d}].*

*5.2. The Asymmetry of Ordinary Matter and Dark*

*There may be a connection between matter-antimatter asymmetry and the production of excess dark hadronic matter. We have seen in the previous sec. that the dark neutrons formed can couple without annihilating themselves with the dark and ordinary antineutrons ( n_{d}, n_{d}), (n_{d}, n_{o}). On the other hand, the same geometric structure allows the aggregation of dark matter into “clusters” of dark neutrons interspersed with dark neutral pions. Thus, clusters of ordinary antimatter aggregated with dark antimatter and dark matter are so formed. These clusters do not annihilate with ordinary matter and do not participate in nuclear interactions; they can only aggregate into super-aggregates of clusters that are dynamically less mobile than neutrons. The ordinary and dark antimatter aggregated with dark matter will thus converge in slow and cold densities, which in the rotational dynamics of the proto-galaxies will be centrifuged outwards [22], determining the halos of dark matter and dark and ordinary antimatter.*

*5.3. The Lithium Cosmologic Problem*

*The fusion reaction between Tritium and Helium produces the isotope of Lithium ^{7}Li; we'll have:*

*
${T}_{\left(2n,p\right)}+H{e}_{\left(2p,2n\right)}\to {}^{7}L{i}_{\left(4n,3p\right)}$ (23)*

*If we did instead
$H{e}_{\left(2p,2n\right)}+{D}_{\left(n,p\right)}\to {}^{6}L{i}_{\left(3n,3p\right)}$ we would get a “regular” lithium ^{6}Li.*

*Instead, it turns out that ^{7}Li is much more abundant in the universe than ^{6}Li [23]; in fact it is found that ^{6}Li = (1%) ^{7}Li. *

*We point out that the first to be formed during the nucleosynthesis phase is Deuteron, then Tritium, followed by Helium and finally Lithium.*

*It is known that is:
${D}_{\left(n,p\right)}+{T}_{\left(2n,p\right)}\to H{e}_{\left(2p,2n\right)}+n.$ *

*In AGM we have demonstrated it “geometrically-mind”, see Section 3.3.*

*This neutron n can be made available to form another Deuteron D_{(n,p)} that is
$\left(n+p\right)\to {D}_{\left(n,p\right)}$ as well as other Tritium or He:*

*
$\left(n+p\right)\to {D}_{\left(n,p\right)}$,
$n+{D}_{\left(n,p\right)}\to {T}_{\left(2n,p\right)}$,*

*
${D}_{\left(n,p\right)}+{D}_{\left(n,p\right)}\to H{e}_{\left(2n,2p\right)}$*

*This D can then bind to the regular He and determine the ^{6}Li, see reaction R*: *

*
$\begin{array}{l}{D}_{\left(n,p\right)}+{T}_{\left(2n,p\right)}+p\to H{e}_{\left(2n,2p\right)}+n+p\to H{e}_{\left(2n,2p\right)}+\left(n+p\right)\\ \to He{*}_{\left(2n,2p\right)}+\text{}{D}_{\left(n,p\right)}\to {}^{6}L{i}_{\left(3n,3p\right)}\end{array}$ (24)*

*We refer to this reaction as R* and He* as Helium with a dark neutron inside it.*

*The ^{6}Li should be abundant in the nucleosynthesis phase. However, this is not the case: the ^{7}Li would be more abundant. In the innovative hypothesis that the dark neuter exists, we have seen that the following reaction can occur:*

*
${D}_{\left(n,p\right)}+{T}_{\left(2n,p\right)}\to H{e}_{\left(2p,2n\right)}+{n}_{d}$*

*In Section 4.1, see Equation (5), we have calculated that the probability of originating a dark neutron in the above fusion reaction is given by*

*
$P\left({n}_{d}\right)\approx 2/196=0.0102\approx 1\%$*

*In this case the n_{d} cannot be available to form a D. We will have 1% less Deuterons.*

*Therefore, the presence of n_{d} makes Deuteron less dense than Tritium T and therefore there would be more presence of Tritium and the most frequent reaction would be the one that gives us ^{7}Li and not ^{6}Li, see Equation (23). In fact, the reaction R*, Equation (24), is not activated because an initial Deuteron is missing.*

*6. Conclusion*

*The presence of the anomaly has made it possible to detect that dark matter and ordinary matter are two sides of the same coin: matter. This was possible because we moved from a perspective of point-like particles (quanta) quantum expression of fields to a perspective of particles structures of oscillators coupled with geometric shapes. This shift in perspective opens the way to a new descriptive paradigm in particle physics. We could also speak of a second attempt at the geometrization of physics: if the first concerned the geometrization of space-time, the second is that of the geometrization of particle-fields.*

*Conflicts of Interest*

*The authors declare no conflicts of interest regarding the publication of this paper.*

*References*

- 1. Weinberg, S. (1977) The Problem of Mass. Transactions of the New York Academy of Sciences, 38, 185-201. https://doi.org/10.1111/j.2164-0947.1977.tb02958.x
- 2. Guido, G. (2017) About Structure of the Quarks. Hadronic Journal, 40, 221-253. http://dx.doi.org/10.29083/HJ.40.03.2017
- 3. Crawford Jr., F.S. (1965) Waves. McGraw-Hill, New York.
- 4. Guido, G. (2019) The Bare and Dressed Masses of Quarks in Pions via the of Quarks’ Geometric Model. Journal of High Energy Physics, Gravitation and Cosmology, 5, 1123-1149. https://doi.org/10.4236/jhepgc.2019.54065
- 5. Guido, G. (2017) Regarding the Structure of Quarks and Hadrons. Hadronic Journal, 40, 187-219. http://dx.doi.org/10.29083/HJ.40.02.2017
- 6. Guido, G. (2020) The Theoretical Value of Mass of the Light ŋ-Meson via the of Quarks’ Geometric Model. Journal of High Energy Physics, Gravitation and Cosmology, 6, 368-387. https://doi.org/10.4236/jhepgc.2020.63030
- 7. Guido, G. (2021) Theoretical Spectrum of Mass of the Nucleons: New Aspects of the QM. Journal of High Energy Physics, Gravitation and Cosmology, 7, 123-143. https://doi.org/10.4236/jhepgc.2021.71006
- 8. Bianchi, A. and Guido, G. (2021) A New Hypothesis on the Dark Matter. Journal of High Energy Physics, Gravitation and Cosmology, 7, 572-594. https://doi.org/10.4236/jhepgc.2021.72033
- 9. Guido, G. (2020) A New Descriptive Paradigm in the Physics of Hadrons, and Their Interactions. Global Journal of Science Frontier Research (A): Physics and Space Science, 20, 41-50. https://doi.org/10.34257/GJSFRAVOL20IS13PG41
- 10. Morpurgo, G. (1992) Introduzione alla fisica delle particelle. Zanichelli, Milan.
- 11. Quigg, C. (1997) Gauge Theories of the Strong, Weak, and Electromagnetic Interactions. Perseus Westview Press, Boulder.
- 12. Ito, T.M., et al. (2018) Performance of the Upgraded Ultracold Neutron Source at Los Alamos National Laboratory and Its Implication for a Possible Neutron Electric Dipole Moment Experiment. Physical Review C, 97, Article ID: 012501. https://doi.org/10.1103/PhysRevC.97.012501
- 13. Arzumanov, S., Bondarenko, L., Chernyavsky, S., et al. (2015) A Measurement of the Neutron Lifetime Using the Method of Storage of Ultracold Neutrons and Detection of Inelastically Up-Scattered Neutrons. Physics Letters B, 745, 79-89. https://doi.org/10.1016/j.physletb.2015.04.021
- 14. Morris, C.L., Adamek, E.R., Broussard, L.J., et al. (2017) A New Method for Measuring the Neutron Lifetime Using an in Situ Neutron Detector. Review of Scientific Instruments, 88, Article ID: 222501. https://doi.org/10.1063/1.4983578
- 15. Serebrov, A.P., Kolomensky, E.A., Fomin, A.K., et al. (2018) Neutron Lifetime Measurements with the Big Gravitational Trap for Ultracold Neutrons. Physical Review C, 97, Article ID: 055503.
- 16. Yue, A.T., Dewey, M.S., Gilliam, D.M., et al. (2013) Improved Determination of the Neutron Lifetime. Physical Review Letters, 111, Article ID: 222501. https://doi.org/10.1103/PhysRevLett.111.222501
- 17. Hoogerheide, S.F. (2019) Progress on the BL2 Beam Measurement of the Neutron Lifetime. EPJ Web of Conferences, 219, Article ID: 03002.https://doi.org/10.1051/epjconf/201921903002
- 18. Fornal, B. and Grinstein, B. (2018) Dark Matter Interpretation of the Neutron Decay Anomaly. Physical Review Letters, 120, Article ID: 191801. https://doi.org/10.1103/PhysRevLett.120.191801
- 19. Gonzalez, F.M., Fries, E.M., Cude-Woods, C., et al. (2021) Improved Neutron Lifetime Measurement with UCNτ. Physical Review Letters, 127, Article ID: 162501. https://doi.org/10.1103/PhysRevLett.127.162501
- 20. Guido, G. (2020) The Theoretical Value of Mass of the Light ŋ-Meson via the of Quarks’ Geometric Model. Journal of High Energy Physics, Gravitation and Cosmology, 6, 368-387. https://doi.org/10.4236/jhepgc.2020.63030
- 21. Casaus, J. (2009) The AMS-02 Experiment on the ISS. Journal of Physics: Conference Series, 171, Article ID: 012045. https://doi.org/10.1088/1742-6596/171/1/012045
- 22. Trimble, V. (1994) Proceedings of the 1st International Symposium on Sources of Dark Matter in the Universe, Los Angeles, California. World Scientific, Singapore.
- 23. Mathews, G.J., Kedia, A., Sasankan, N., et al. (2020) Cosmological Solutions to the Lithium Problem. JPS Conference Proceedings, 31, Article ID: 011033. https://doi.org/10.7566/JPSCP.31.011033
- 24. Guido, G. (2014) The Substructure of a Quantum Field-Oscillator. Hadronic Journal, 37, 83.
- 25. Guido, G. (2012) The Substructure of a Quantum Oscillator Field. arXiv:1208.0948.
- 26. Guido, G. (2019) The Origin of the Color Charge into Quarks. Journal of High Energy Physics, Gravitation and Cosmology, 5, 1-34. https://doi.org/10.4236/jhepgc.2019.51001
- 27. Bazavov, A., Toussaint, D., Bernard, C., et al. (2010) Nonperturbative QCD Simulations with 2+1 Flavors of Improved Staggered Quarks. Reviews of Modern Physics, 82, 1349-1417. https://doi.org/10.1103/RevModPhys.82.1349
- 28. Ishikawa, T., Aoki, S., Fukugita, M., et al. (2008) Light Quark Masses from Unquenched Lattice QCD CP-PACS and JLQCD Collaborations. Physical Review D, 78, Article ID: 011502. https://doi.org/10.1103/PhysRevD.78.011502

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

[1] |
Weinberg, S. (1977) The Problem of Mass. Transactions of the New York Academy of Sciences, 38, 185-201. https://doi.org/10.1111/j.2164-0947.1977.tb02958.x |

[2] |
Guido, G. (2017) About Structure of the Quarks. Hadronic Journal, 40, 221-253. http://dx.doi.org/10.29083/HJ.40.03.2017 |

[3] | Crawford Jr., F.S. (1965) Waves. McGraw-Hill, New York. |

[4] |
Guido, G. (2019) The Bare and Dressed Masses of Quarks in Pions via the of Quarks’ Geometric Model. Journal of High Energy Physics, Gravitation and Cosmology, 5, 1123-1149. https://doi.org/10.4236/jhepgc.2019.54065 |

[5] |
Guido, G. (2017) Regarding the Structure of Quarks and Hadrons. Hadronic Journal, 40, 187-219. http://dx.doi.org/10.29083/HJ.40.02.2017 |

[6] |
Guido, G. (2020) The Theoretical Value of Mass of the Light ŋ-Meson via the of Quarks’ Geometric Model. Journal of High Energy Physics, Gravitation and Cosmology, 6, 368-387. https://doi.org/10.4236/jhepgc.2020.63030 |

[7] |
Guido, G. (2021) Theoretical Spectrum of Mass of the Nucleons: New Aspects of the QM. Journal of High Energy Physics, Gravitation and Cosmology, 7, 123-143. https://doi.org/10.4236/jhepgc.2021.71006 |

[8] |
Bianchi, A. and Guido, G. (2021) A New Hypothesis on the Dark Matter. Journal of High Energy Physics, Gravitation and Cosmology, 7, 572-594. https://doi.org/10.4236/jhepgc.2021.72033 |

[9] |
Guido, G. (2020) A New Descriptive Paradigm in the Physics of Hadrons, and Their Interactions. Global Journal of Science Frontier Research (A): Physics and Space Science, 20, 41-50. https://doi.org/10.34257/GJSFRAVOL20IS13PG41 |

[10] | Morpurgo, G. (1992) Introduzione alla fisica delle particelle. Zanichelli, Milan. |

[11] | Quigg, C. (1997) Gauge Theories of the Strong, Weak, and Electromagnetic Interactions. Perseus Westview Press, Boulder. |

[12] |
Ito, T.M., et al. (2018) Performance of the Upgraded Ultracold Neutron Source at Los Alamos National Laboratory and Its Implication for a Possible Neutron Electric Dipole Moment Experiment. Physical Review C, 97, Article ID: 012501. https://doi.org/10.1103/PhysRevC.97.012501 |

[13] |
Arzumanov, S., Bondarenko, L., Chernyavsky, S., et al. (2015) A Measurement of the Neutron Lifetime Using the Method of Storage of Ultracold Neutrons and Detection of Inelastically Up-Scattered Neutrons. Physics Letters B, 745, 79-89. https://doi.org/10.1016/j.physletb.2015.04.021 |

[14] |
Morris, C.L., Adamek, E.R., Broussard, L.J., et al. (2017) A New Method for Measuring the Neutron Lifetime Using an in Situ Neutron Detector. Review of Scientific Instruments, 88, Article ID: 222501. https://doi.org/10.1063/1.4983578 |

[15] | Serebrov, A.P., Kolomensky, E.A., Fomin, A.K., et al. (2018) Neutron Lifetime Measurements with the Big Gravitational Trap for Ultracold Neutrons. Physical Review C, 97, Article ID: 055503. |

[16] |
Yue, A.T., Dewey, M.S., Gilliam, D.M., et al. (2013) Improved Determination of the Neutron Lifetime. Physical Review Letters, 111, Article ID: 222501. https://doi.org/10.1103/PhysRevLett.111.222501 |

[17] |
Hoogerheide, S.F. (2019) Progress on the BL2 Beam Measurement of the Neutron Lifetime. EPJ Web of Conferences, 219, Article ID: 03002. https://doi.org/10.1051/epjconf/201921903002 |

[18] |
Fornal, B. and Grinstein, B. (2018) Dark Matter Interpretation of the Neutron Decay Anomaly. Physical Review Letters, 120, Article ID: 191801. https://doi.org/10.1103/PhysRevLett.120.191801 |

[19] |
Gonzalez, F.M., Fries, E.M., Cude-Woods, C., et al. (2021) Improved Neutron Lifetime Measurement with UCNτ. Physical Review Letters, 127, Article ID: 162501. https://doi.org/10.1103/PhysRevLett.127.162501 |

[20] |
Guido, G. (2020) The Theoretical Value of Mass of the Light ŋ-Meson via the of Quarks’ Geometric Model. Journal of High Energy Physics, Gravitation and Cosmology, 6, 368-387. https://doi.org/10.4236/jhepgc.2020.63030 |

[21] |
Casaus, J. (2009) The AMS-02 Experiment on the ISS. Journal of Physics: Conference Series, 171, Article ID: 012045. https://doi.org/10.1088/1742-6596/171/1/012045 |

[22] | Trimble, V. (1994) Proceedings of the 1st International Symposium on Sources of Dark Matter in the Universe, Los Angeles, California. World Scientific, Singapore. |

[23] |
Mathews, G.J., Kedia, A., Sasankan, N., et al. (2020) Cosmological Solutions to the Lithium Problem. JPS Conference Proceedings, 31, Article ID: 011033. https://doi.org/10.7566/JPSCP.31.011033 |

[24] | Guido, G. (2014) The Substructure of a Quantum Field-Oscillator. Hadronic Journal, 37, 83. |

[25] | Guido, G. (2012) The Substructure of a Quantum Oscillator Field. arXiv:1208.0948. |

[26] |
Guido, G. (2019) The Origin of the Color Charge into Quarks. Journal of High Energy Physics, Gravitation and Cosmology, 5, 1-34. https://doi.org/10.4236/jhepgc.2019.51001 |

[27] |
Bazavov, A., Toussaint, D., Bernard, C., et al. (2010) Nonperturbative QCD Simulations with 2+1 Flavors of Improved Staggered Quarks. Reviews of Modern Physics, 82, 1349-1417. https://doi.org/10.1103/RevModPhys.82.1349 |

[28] |
Ishikawa, T., Aoki, S., Fukugita, M., et al. (2008) Light Quark Masses from Unquenched Lattice QCD CP-PACS and JLQCD Collaborations. Physical Review D, 78, Article ID: 011502. https://doi.org/10.1103/PhysRevD.78.011502 |

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