114 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) ISSN (Print) 2313-4410, ISSN (Online) 2313-4402 © Global Society of Scientific Research and Researchers http://asrjetsjournal.org/ The Proton Problem & Proton Spin Crisis: The Color Confinement Mathematical Mechanism for the Existence of the Hadrons Yazzed Al-Harbi* King Abdulaziz & his Companions Foundation for Giftedness & Creativity Nawariyah, Makkah 21514, Saudi Arabia Email: yazzed4444@gmail.com Abstract In this paper we will show the provement of the hadrons existence mechanism. Its duo to the physical consequences of the spinning quarks and the color charge. When we simulate the supposed situation by mathematics we find that it's achieves the perfect understanding of the all physical interactions and all the mysteries of the particle physics with its measurements which proved experimentally. Keywords: The Proton Problem; The Proton Spin Crisis; The Color Confinement; Proton Radius; The Hadrons Structure; The Quarks Spin Effect; Spherical Color Charged Energy As Higgs Bososns Waves. 1. Introduction There are lots of mysterious data about the hadrons. The recent determination of the proton radius using the measurement of the lamb shift in muonic hydrogen atom experiment startled the physics world. The obtained value of 0.84087(39) fm is 4% smaller than the value of the CODATA which is 0.8775(51) fm. And actually that’s called " the proton radius puzzle" [1,2]. In this paper, we will consider an idea that makes the obtained high-precision measured values as a dependent variables of the Planck length in a function. And we just modeling the idea by mathematics to reach the abstract proof step by step. ------------------------------------------------------------------------ * Corresponding author. http://asrjetsjournal.org/ http://asrjetsjournal.org/ American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 34, No 1, pp 114-122 115 2. Structure (Basic Idea) As we know that all the baryons [ a type of the hadrons] [3] are consist of an odd number of fundamental particles called quarks, like a proton consist of three quarks, or maybe more than three [4] , and all the quarks have a quantization spin state with 1/2ħ [5]. And now let's imagine the spacetime is a vacuum and the Higgs field is everywhere[6], Higgs bosons are attracting with the quarks ( 2 ups and 1 down ), since this attracting is the mechanism of the mass source, and the particle reaches its maximum mass by reaching the equilibrium state of the attracting, the quarks have an Intrinsic property (the spin) that's quantitative property consuming energy to establish a differentiation in the spacetime vacuum, and since we know that quarks have an "excited versions", or kinetic energy by its movement and the probability density, it's very hard to calculate [7]. furthermore, we don't know how effective this on the Higgs field with the intrinsic property (the spin) and according to the Higgs field energy, it's energy is unknown. this maybe causes a difference in the equilibrium state of the attracting with higgs field. And as we say, this difference can't be calculated. While imagining this case, we find that the quarks spin with its kinetic energy causes a difference in the Higgs field, the Higgs boson those around the sphere surface area of the quark, by giving them an amount of energy in all the directions (we will consider the kinetic energy and the spin energy as a vectors, and since the spin causes a case in all the direction it's resultants with KE vectors will be in all the directions). �∑ 𝑆𝑆𝐸𝐸2 +𝐾𝐾𝐾𝐾𝑞𝑞2− 2|𝑆𝑆𝐸𝐸2𝜋𝜋 0 ��𝐾𝐾𝐾𝐾𝑞𝑞�𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐� Eq[1] In order to understand this equation and the whole amount of energy by Eq(1), the spin KE is exactly in all the directions. we found that the energy resultant will be in all the directions with a difference in the magnitude ; because the angle of the direction . Furthermore, we know that in each circumstance of a circle that it's center has a vertical distance from the sphere center, there are two energy resultant vectors with the same magnitude. Now, we need to know how many circumstances are in the quark sphere. First we will calculate a ratio between the surface areas of two spheres, the sphere [S] with a radius (R) and the Sphere [D] with a radius of (R+n) , which are R,n∈ Z+. 4𝜋𝜋(𝑅𝑅+𝑛𝑛)2 4𝜋𝜋𝑅𝑅2 = 4𝜋𝜋𝑅𝑅2+8𝜋𝜋𝑅𝑅𝑛𝑛+4𝜋𝜋𝑛𝑛2 4𝜋𝜋𝑅𝑅2 = 1 + 2𝑛𝑛 𝑅𝑅 + 𝑛𝑛2 𝑅𝑅2 Eq[2] So, we can calculate the surface area of any sphere according to another sphere. Lets suppose that a sphere with a radius of a Planck length ℓP and it’s the origin sphere. American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 34, No 1, pp 114-122 116 𝐴𝐴𝑛𝑛 = 𝐴𝐴ℓP �1 + 2𝑛𝑛 ℓP + 𝑛𝑛2 (ℓP)2� Eq[3] Now we can find the radius (n) to find the number of the circumferences in the sphere (n) by the same radius (n) of 𝑡𝑡ℎ𝑒𝑒 𝑐𝑐𝑠𝑠ℎ𝑒𝑒𝑒𝑒𝑒𝑒 (𝑛𝑛) ∶ 𝑅𝑅𝑛𝑛 = �𝐴𝐴ℓP�1+ 2𝑛𝑛 ℓP+ 𝑛𝑛2 (ℓP)2 � 4𝜋𝜋 Eq[4] 𝐶𝐶𝑛𝑛 = π� 𝐴𝐴ℓP�1+ 2𝑛𝑛 ℓP+ 𝑛𝑛2 (ℓP)2 � 𝜋𝜋 Eq[5] ∑ 𝐶𝐶𝑛𝑛 𝑛𝑛∞,𝑘𝑘∞ 𝑛𝑛=1,𝑘𝑘=0 = ∑ π� 𝐴𝐴ℓP�1+ 2(𝑛𝑛+𝑘𝑘𝑛𝑛) ℓP +(𝑛𝑛+𝑘𝑘𝑛𝑛)2 (ℓP)2 � 𝜋𝜋 𝑛𝑛∞,𝑘𝑘∞ 𝑛𝑛=1,𝑘𝑘=0 Eq[6] Since the term (n+kn) is identical to (ℓP + 𝑘𝑘ℓP): (n + kn) ≡ (ℓP + 𝑘𝑘ℓP) We can rewrite the above equation to: ∑ 𝐶𝐶𝑘𝑘 𝑘𝑘∞ 𝑘𝑘=0 = ∑ π� 𝐴𝐴ℓP�1+ 2(ℓP+𝑘𝑘ℓP) ℓP +(ℓP+𝑘𝑘ℓP)2 (ℓP)2 � 𝜋𝜋 𝑘𝑘∞ 𝑘𝑘=0 Eq(7) And now lets suppose and imagine that the difference that happens from the spin kinetic energy and the KE of the quark result vector [that "push" the higgs bosons on the surface area of the quark to collision with the others higgs bosons and lose their energy to return in the ground state of energy on the surface of the quark] in other words, as we suppose and imagine that the higgs bosons are like bouncing around the quark, they pushed away and return again to the surface of the quark, and these are the only bosons on the surface of the quark, or like I would to call this " the Ground state of higgs bosons energy" . The higgs bosons and the higgs field are everywhere in the universe [3]. In order to determine the ground state approximately density we need to suppose that at every point of the Planck Length there is a higgs boson, If it's incorrect its will be relative; because as we said we can't calculate the resultant vector and the higgs bosons are everywhere. And we just modeling the idea by mathematics to reach the abstract proof step by step. Now if we American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 34, No 1, pp 114-122 117 consider the Planck length as length unit, the higgs field as an energy unit, then the ground state higgs bosons density will be as we said : 𝜑𝜑𝑘𝑘° = 𝑉𝑉𝑞𝑞 ( 𝑍𝑍𝐻𝐻 ℓP )3 4𝜋𝜋𝑅𝑅𝑞𝑞 𝐻𝐻𝑚𝑚 Eq(8) And ZH is higgs field energy, Vq is the volume of the quark, Hm is the higgs boson mass. Where k note here indicates to the ground energy density state. If we continue imagining we will find that the energy which transfer from the bouncing ground state higgs bosons- will reach the next energy density state, and then transfer with a lower magnitude; because its collision with next energy density state higgs bosons { in a spherical coordinate system}- in the same directions. And we figure out in Eq(2) that the surface area of a sphere with a radius (n) formula, now we need an equation to the whole action: �𝐾𝐾𝐾𝐾°→(𝐾𝐾+1)�= �∑ 𝑆𝑆𝐸𝐸2 +𝐾𝐾𝐾𝐾𝑞𝑞2− 2|𝑆𝑆𝐸𝐸2𝜋𝜋 0 ��𝐾𝐾𝐾𝐾𝑞𝑞�𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐� �∑ π� 𝐴𝐴ℓP�1+ 2(ℓP+𝑘𝑘ℓP) ℓP +(ℓP+𝑘𝑘ℓP)2 (ℓP)2 � 𝜋𝜋 𝑘𝑘2 𝑘𝑘=0 ��𝜑𝜑𝑘𝑘° � Eq(9) −𝑉𝑉𝑞𝑞 (𝑍𝑍𝐻𝐻ℓP)3 𝐴𝐴ℓP �1 + 2(ℓP + 𝑘𝑘ℓP) ℓP + (ℓP + 𝑘𝑘ℓP)2 (ℓP)2 � − 𝑍𝑍𝐸𝐸𝐻𝐻 The above equation is for the transformation from 𝐾𝐾° → (𝐾𝐾 + 1) To write the equations for the whole action : {�𝐾𝐾𝐾𝐾°→(𝐾𝐾𝑛𝑛)�= �∑ 𝑆𝑆𝐸𝐸2 +𝐾𝐾𝐾𝐾𝑞𝑞2− 2|𝑆𝑆𝐸𝐸2𝜋𝜋 0 ��𝐾𝐾𝐾𝐾𝑞𝑞�𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐� �∑ π� 𝐴𝐴ℓP�1+ 2(ℓP+𝑘𝑘ℓP) ℓP +(ℓP+𝑘𝑘ℓP)2 (ℓP)2 � 𝜋𝜋 𝑘𝑘2 𝑘𝑘=0 ��𝜑𝜑𝑘𝑘° � Eq[10] − � 𝑉𝑉𝑞𝑞 (𝑍𝑍𝐻𝐻ℓP)3 𝐴𝐴ℓP �1 + 2(ℓP + 𝑘𝑘ℓP) ℓP + (ℓP + 𝑘𝑘ℓP)2 (ℓP)2 � 𝑘𝑘𝑛𝑛 (𝑘𝑘=0) −𝑍𝑍𝐸𝐸𝐻𝐻 We know that the bouncing higgs bosons will reach the maximum energy state and lost all their kinetic energy. And that takes a sphere shape. Also we know that all the quarks have the same spin magnitude, and its not really necessary to determine the direction of the spin; because the bouncing higgs boson are moving in all the directions. The direction of the spin actually doesn’t make any difference. Z is the higgs field energy, American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 34, No 1, pp 114-122 118 Now that’s leaves us with two cases; because the quarks properties are the same and the difference of them doesn't matter: Case 1: The kinetic energy of the quarks are the same. Case 2: The kinetic energy of the quarks are not the same. Now lets take the first case, we know that the bouncing takes a spherical shape: because its movement is in the all the directions and all the quarks properties that makes a difference in this case is the same. That’s mean that all the bouncing higgs bosons reach the same energy density state in the same time. And furthermore, their spherical bouncing is in a hadron, let's take an example, the proton is made of three quarks; two up quarks and one down quark. If we want to put three identical spheres in one sphere and simulate it by the geometry we find that the radiuses of the three spheres are equal to half the radius of the proton. Now after all the hypothesizes, here is the abstract proof of all the above, by returning to the eq[3] we find that : 𝑅𝑅𝑘𝑘 = �𝐴𝐴ℓP�1+ 2(ℓP+𝑘𝑘ℓP) ℓP +(ℓP+𝑘𝑘ℓP)2 (ℓP)2 � 4𝜋𝜋 Eq[11] 𝑅𝑅𝑘𝑘 = ℓP��1 + 2(ℓP+𝑘𝑘ℓP) ℓP + (ℓP+𝑘𝑘ℓP)2 (ℓP)2 � Eq[12] And actually Rk is the distance between the original sphere center𝐴𝐴ℓP to any sphere with the radius of Rk. (n + kn) ≡ (ℓP + 𝑘𝑘ℓP)≡ 𝑅𝑅𝑘𝑘 Eq[13 And we can actually rearrange the equations from eq[2] to eq[5] by the formula : 𝐴𝐴𝐾𝐾 = 𝐴𝐴ℓP[1 + 2ℓP��1+2(ℓP+𝑘𝑘ℓP) ℓP +(ℓP+𝑘𝑘ℓP)2 (ℓP)2 � ℓP + ℓP��1+2(ℓP+𝑘𝑘ℓP) ℓP +(ℓP+𝑘𝑘ℓP)2 (ℓP)2 � 2 (ℓP)2 ] Eq[14] And now, the most exciting part; finding the value of the proton's radius by using the functions above about the circumferences or the surface areas of the spheres sequences [ the bouncing transform the energy between the supposed states in a spherical shape] . As we said the bouncing bosons reaches the highest energy density states when its spherical shape got a radius that is half the radius of the proton, so : American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 34, No 1, pp 114-122 119 Rp = ℓP� ⎣ ⎢ ⎢ ⎡ 1 + 2ℓP��1+2(ℓP+𝑘𝑘ℓP) ℓP +(ℓP+𝑘𝑘ℓP)2 (ℓP)2 � ℓP + ℓP2�1+2(ℓP+𝑘𝑘ℓP) ℓP +(ℓP+𝑘𝑘ℓP)2 (ℓP)2 � (ℓP)2 ⎦ ⎥ ⎥ ⎤ Eq [15] Rp = ℓP��2 + 2��1 + 2(ℓP + 𝑘𝑘ℓP) ℓP + (ℓP + 𝑘𝑘ℓP)2 (ℓP)2 �+ 2(ℓP + 𝑘𝑘ℓP) ℓP + (ℓP + 𝑘𝑘ℓP)2 (ℓP)2 � When we graph this function we find that when k = 5.430458*10^19 Rp = 8.77562*10^-16 And 8.77562*10^-16/1.616*10^-35 = 5.43007*10^19 That’s mean the equation above is a function describes the distance that the bouncing higgs bosons moving in the spacetime and attracting with the others higgs boson, this function prove that the proton is just a continuous higgs field spherical waves that emitted by the spinning of its structure particles; which are the quarks. Since the gluons doesn’t attract with the higgs field. And this idea is also explain the proton's mass and spin because these spherical waves duo to the spinning of the quarks so its got a rotation, furthermore, it might be crazy idea but its also describes the radius of the proton and its not invariant but change according the function above. I think this is the best physical explanation for the function which matching the reality. Now, we should continue to model the whole idea by the mathematics. As we say, the spherical shape of the bouncing is identical of all the three quarks when its radius reach half the radius of the proton, we don’t actually know the position of the three quarks exactly, we just sure about their bouncing higgs bosons spherical shapes. The three identical spheres are actually doesn’t full the protons volume. Approximately the three empty volumes in the proton faces the quarter of the surface areas of two spheres. . Since the bosons are keep bouncing, two bosons will confluence and they will push by their resultant energy in all the directions to the empty volume of the proton 𝑐𝑐𝑠𝑠ℎ𝑒𝑒𝑒𝑒𝑒𝑒 𝑎𝑎𝑛𝑛𝑎𝑎 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑓𝑓𝑡𝑡. The black vector is equals to the total energy resultant and it’s the sum of all the energy resultants of the bouncing higgs bosons in the empty volume space in the proton. All the three vectors can be described mathematically as: ∑ ∏ ∆𝐾𝐾° ∆𝐸𝐸° ∆𝐸𝐸𝑚𝑚𝑚𝑚𝑚𝑚 𝑘𝑘2=𝜋𝜋−𝜃𝜃 𝑘𝑘2=0 |E|𝑛𝑛 𝑛𝑛° cos [𝜃𝜃+𝑘𝑘2] 𝑐𝑐𝑐𝑐𝑐𝑐𝜃𝜃 ∑ 6π� 𝐴𝐴ℓP�1+ 2(ℓP+𝑘𝑘ℓP) ℓP +(ℓP+𝑘𝑘ℓP)2 (ℓP)2 � 𝜋𝜋 𝑘𝑘∞ 𝑘𝑘=0 Eq[16] The term ∏ ∆𝐾𝐾° ∆𝐸𝐸° ∆𝐸𝐸𝑚𝑚𝑚𝑚𝑚𝑚 |E|𝑛𝑛 𝑛𝑛° is actually sequence of the different transformer energies between the energy American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 34, No 1, pp 114-122 120 density state using a ratio between every two continuous states until the last one. Figure 1 Now, we are finally got the formula of the proton total energy (mass) using the equations [9] and [15]: 𝑃𝑃𝑚𝑚 = �∑ 𝑆𝑆𝐸𝐸2 +𝐾𝐾𝐾𝐾𝑞𝑞2 − 2|𝑆𝑆𝐸𝐸2𝜋𝜋 0 ��𝐾𝐾𝐾𝐾𝑞𝑞�𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐� �∑ π� 𝐴𝐴ℓP�1+ 2(ℓP+𝑘𝑘ℓP) ℓP +(ℓP+𝑘𝑘ℓP)2 (ℓP)2 � 𝜋𝜋 𝑘𝑘2 𝑘𝑘=0 ��𝜑𝜑𝑘𝑘° � Eq[17] − � 𝑉𝑉𝑞𝑞 (𝑍𝑍𝐻𝐻ℓP)3 𝐴𝐴ℓP �1 + 2(ℓP + 𝑘𝑘ℓP) ℓP + (ℓP + 𝑘𝑘ℓP)2 (ℓP)2 � 𝑘𝑘𝑛𝑛 (𝑘𝑘=0) −𝑍𝑍𝐸𝐸𝐻𝐻 + � � ∆𝐾𝐾° ∆𝐸𝐸° ∆𝐸𝐸𝑚𝑚𝑚𝑚𝑚𝑚 𝑘𝑘2=𝜋𝜋−𝜃𝜃 𝑘𝑘2=0 |E|𝑛𝑛 𝑛𝑛° cos [𝑐𝑐+ 𝑘𝑘2] 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 �6π� 𝐴𝐴ℓP �1 + 2(ℓP + 𝑘𝑘ℓP) ℓP + (ℓP + 𝑘𝑘ℓP)2 (ℓP)2 � 𝜋𝜋 𝑘𝑘∞ 𝑘𝑘=0 We can write the rest energy of the three spheres of the spherical waves no matter what the distance between any two spheres at any time even when its identical and mathematically the formula of the volume by using a ratio between the spherical waves distance : 𝑉𝑉𝑝𝑝 = 3 �2[∑ 2𝑅𝑅𝑞𝑞 3−2𝑅𝑅𝑞𝑞3 cos(𝜋𝜋−2𝜃𝜃) 𝑑𝑑 + 𝑅𝑅𝑅𝑅] 𝜋𝜋 2 0 � �1 + 3(𝑅𝑅𝑞𝑞+𝑘𝑘𝑅𝑅𝑞𝑞) 𝑅𝑅𝑞𝑞 + 3(𝑅𝑅𝑞𝑞+𝑘𝑘𝑅𝑅𝑞𝑞)2 𝑅𝑅𝑞𝑞2 + (𝑅𝑅𝑞𝑞+𝑘𝑘𝑅𝑅𝑞𝑞)3 𝑅𝑅𝑞𝑞3 � Eq(18) 1. QCD: In quantum chromodynamics, when a quark emits a colorless gluon, in this case the colorless gluon can convert to another colorless gluon according the super-position property. and separate into two gluons which absorbed by the quarks, and we can write the probabilities of this action as[8]. 𝑆𝑆𝑎𝑎𝑐𝑐𝑎𝑎𝑎𝑎𝑐𝑐𝑛𝑛 = 1 √22 �𝜙𝜙𝑔𝑔ǧ2° +𝜙𝜙𝑔𝑔ǧ3°�+ 1 √22 ��𝜙𝜙𝑔𝑔ǧ2� 1 √62 [𝑔𝑔𝑔𝑔2 + ǧǧ2] + �𝜙𝜙𝑔𝑔ǧ3� 1 √62 [𝑔𝑔𝑔𝑔3 + ǧǧ3]� Eq(19) American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 34, No 1, pp 114-122 121 Lately we considered that the energy (mass) of the proton is just an energy spherical waves fluctuations duo to the quarks spinning . Now, let's consider something which show us the subject associated and better for understanding. Let's imagine and consider that the color charge as a quantity, the gluons field is a spherical wave that collision with other gluon spherical wave by the color charged spinning quark. for imaging the action that we already talked about, the colorless gluon by the spherical waves concept we find that the model is actually explains the emiting of the pion (meson) to keep the nucleons valence and that because the model consider the the gluon field is actually carried by the bouncing Higgs bosons (making spherical waves) as we show mathematically. the quark-antiquark in the meson are emoted by the bouncing carring charge Higgs boson after the action in rest of hadron mass when the bouncing spherical waves of the spinnnig quarks reaches its maximum limit by the case of the colorless gluon eq () : 𝑀𝑀𝑞𝑞 = � � ∆𝐾𝐾° ∆𝐸𝐸° ∆𝐸𝐸𝑚𝑚𝑚𝑚𝑚𝑚 𝑘𝑘2=𝜋𝜋−𝜃𝜃 𝑘𝑘2=0 |E|𝑛𝑛 𝑛𝑛° cos [𝑐𝑐+ 𝑘𝑘2] 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 �4π� 𝐴𝐴ℓP �1 + 2(ℓP + 𝑘𝑘ℓP) ℓP + (ℓP + 𝑘𝑘ℓP)2 (ℓP)2 � 𝜋𝜋 𝑘𝑘∞ 𝑘𝑘=0 1 √22 �𝜙𝜙𝑔𝑔ǧ2° +𝜙𝜙𝑔𝑔ǧ3°� + 1 √22 [�𝜙𝜙𝑔𝑔ǧ2� 1 √62 [𝑔𝑔𝑔𝑔2 + ǧǧ2] + �𝜙𝜙𝑔𝑔ǧ3� 1 √62 [𝑔𝑔𝑔𝑔3 + ǧǧ3]] And since the Higgs bosons carried the charge while bouncing in SW (spherical waves) we found 𝑆𝑆𝑎𝑎𝑐𝑐𝑎𝑎𝑎𝑎𝑐𝑐𝑛𝑛 ≡ ∑ ∏ ∆𝐾𝐾° ∆𝐸𝐸° ∆𝐸𝐸𝑚𝑚𝑚𝑚𝑚𝑚 𝑘𝑘2=𝜋𝜋−𝜃𝜃 𝑘𝑘2=0 |E|𝑛𝑛 𝑛𝑛° cos [𝜃𝜃+𝑘𝑘2] 𝑐𝑐𝑐𝑐𝑐𝑐𝜃𝜃 ∑ 4π� 𝐴𝐴ℓP�1+ 2(ℓP+𝑘𝑘ℓP) ℓP +(ℓP+𝑘𝑘ℓP)2 (ℓP)2 � 𝜋𝜋 𝑘𝑘𝑚𝑚𝑚𝑚𝑚𝑚 𝑘𝑘=0.5 𝑘𝑘𝑅𝑅𝑅𝑅 Eq(21) ∑ ∏ ∆𝐾𝐾° ∆𝐸𝐸° ∆𝐸𝐸𝑚𝑚𝑚𝑚𝑚𝑚 𝑘𝑘2=𝜋𝜋−𝜃𝜃 𝑘𝑘2=0 |E|𝑛𝑛 𝑛𝑛° cos [𝜃𝜃+𝑘𝑘2] 𝑐𝑐𝑐𝑐𝑐𝑐𝜃𝜃 [𝑆𝑆𝑎𝑎𝑐𝑐𝑎𝑎𝑎𝑎𝑐𝑐𝑛𝑛]∑ 4π� 𝐴𝐴ℓP�1+ 2(ℓP+𝑘𝑘ℓP) ℓP +(ℓP+𝑘𝑘ℓP)2 (ℓP)2 � 𝜋𝜋 𝑘𝑘𝑚𝑚𝑚𝑚𝑚𝑚 𝑘𝑘=0.5 𝑘𝑘𝑅𝑅𝑅𝑅 Eq(22) = 4.8−0.3 +0.5𝑀𝑀𝑒𝑒𝑉𝑉 And that’s actually the down quark mass. 3. Conclusion In this paper we achieved mathematically that the excistence of the hadrons duo to the physical consequences of quarks spin in the higgs field for creating spherical color charged energy as higgs bosons waves. This real model explains and predict all the physical interactions between particles, the proton radius and the proton spin. It's able to change the world vision of the renewable energy and the all the energy industries in the world; because its simulate the process of creating an energy in our universe that we can obviously use. And show us the process of creating the hadrons which are the most familiar family of particles that particles physics deal with. A new concept will help us improving the standard model of particle physics; because it's solve one of the most theoretical physics problems of all the time: The Proton Problem , The Proton Spin Crisis and the behavior of a valence quarks. American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 34, No 1, pp 114-122 122 4. Recommendation This is a brand new discovery in the world of the renewable energy; it's show us the process of creating energy that the particles are made of. It can change our understanding about the energy in the future by controlling the process of creating the existence itself. And also help us to solve most of the mysterious problem in theoretical physics. Using this research as a brand new gate to a new theoretical & industrial physics will help the world. Its open a new gates in physics, engineering and a lot of applied sciences. And also this module which give us a lots of facts about the behavior of the quarks give us the opportunity to simulate the whole existence by the basics of mathematics starting from this model and that obviously help us to explain, predict and control chemical reactions in the nature & human body and the shapes of the existence in the universe. References [1] J. J. Krauth,1,2 K. Schuhmann,3,4,5 M. Abdou Ahmed,6 F. D. Amaro,7 P. Amaro,8 F. Biraben,9 J. M. R. Cardoso,7 M. L. Carvalho,8 D. S. Covita,10 A. Dax,11,4 S. Dhawan,11 M. Diepold,1 L. M. P. Fernandes,7 B. Franke,1 S. Galtier,9 A. Giesen,6,5 A. L. Gouvea,7 J. Go ̈tzfried,1 T. Graf,6 M. Guerra,8 J. Haack,2 T. W. Ha ̈nsch,1 M. Hildebrandt,4 P. Indelicato,9. "The Proton Radius Puzzle" Internet: https://arxiv.org/pdf/1706.00696.pdf Jun. 2,2017 [Jun. 8, 2017] [2] L. Julien,9 K. Kirch,3,4 A. Knecht,4 P. Knowles,12 F. Kottmann,3 E.-O. Le Bigot,9 Y.-W. Liu,13 J. A. M. Lopes,7 L. Ludhova,12 J. Machado,8 C. M. B. Monteiro,7 F. 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