Higgs-Meson and Higgs-Gluon Interaction and Mass Acquiring Mechanism By Wan-Chung Hu Higgs-meson interaction First, I will discuss the interaction of Higgs boson and mesons. I suggest that meson, especially pion, is also a force mediating boson which regulates the atrtractive nuclear force between nucleons. This is in the spectrum of quantum hrardon dynamics. Because the pion mediated force is also belonging to SU(2), the Yang-Mills theory: Here, i is imaginary number, g is QHD coupling constant, T is isospin, and P(X) is meson field. And, I will prove that meson acquired mass from Higgs mechanism. The isospins of pions are: Because pions include three particles:π+,π-, and π0, we should use a real scalar field to interact with Higgs field. The Langranian is according to Nanbu-Glodstone theorem: 1 2 퐿(휑) = (휕 휑)(휕푣휑) − 휇2(휑(푥)) 2 푣 The Higgs fields: (0,0, 푉⁄ ) √2 Then, we include QHD covariant and isospin matrix into the Langranian: 1 + |[(igTP(x)) ∗ φ(x)] [(igTP(x)) ∗ φ(x)]| = 2 1 1 1 (0, v(gPx − igPy), −gvPz) × (0, v(gPx + igPy), −gvPz) 4 √2 √2 The above equation becomes: 1 푔2푣2 푔2푣2 (0, 푔푣푃−, −푔푣푃 ) × (0, 푔푣푃+, −푔푣푃 ) = 푃+푃− + 푃2 4 푧 푧 4 4 푧 If π+ = P+，π- =P- and π0 = Pz, then all three pions can get the mass of gv/2. The mass term is M2v2. That is the reason why the three pions have the same mass via Higgs mechanism. Thus, π+ =UD, π- =DU, and π0=UU or DD. The neutral pion is midly slighter than the charged pions due to the charges on the charged pions. The mass of pion is about 135 MeV/c2. Up quark mass is about 1.7-3.1MeV / c2, and down quark mass is about 4.1-5.7MeV / c2. Thus, meson should acquire their mass via Higgs mechanism. In the later chapter, we will see the mass is equal to neutral gluon.。 Strong-Light Unification In previous research, Professor Weinberg proposed an electroweak interaction to predict the masses of W and Z particles. His theory is very successful. However, it is actually the interaction of photon and W/Z bosons. So, it is Weak-Light Interaction. It is the interaction between weak force and light. Here, I propose an interaction between strong force and light. Thus, it can solve the problem of gluon mass. Based on Yang-Mills theory of standard model, we know the Yang-Mills equation is: Fuv = ∂uAv − ∂vAu − [Au, Av] In addition, the QHD formula is: 8 U(SU(2)) = exp⁡[ig ∑ Fj Gj(x)] j=1 Thus, the covariant derivative is: ∂μ = ∂μ + igF ∗ G(x) Besides, F=1/2λ, and λ is Gell-Mann matrix: 0 1 0 λ1 = [1 0 0] 0 0 0 0 −i 0 λ2 = [ i 0 0] 0 0 0 1 0 0 λ3 = [0 −1 0] 0 0 0 0 0 1 λ4 = [0 0 0] 1 0 0 0 0 −i λ5 = [0 0 0 ] i 0 0 0 0 0 λ6 = [0 0 1] 0 1 0 0 0 0 λ7 = [0 0 −i] 0 i 0 1 1 0 0 λ8 = [0 1 0 ] √3 0 0 −2 For photon, there is another matrix: 1 0 0 λ9 = [0 1 0] 0 0 1 We let r or |r>=(1,0,0), b or |b>=(0,1,0), and g or |g>=(0,0,1). Then, the whole matrix is: rr̅ br̅ gr̅ [rb̅ bb̅ gb̅] rg̅ bg̅ gg̅ In addition, each matrix has its corresponding gluons and photon: 1 ̅ G1 = (rb + br̅) √2 i ̅ G2 = (rb − br̅) √2 1 ̅ G3 = (rr̅ − bb) √2 1 G4 = (rg̅ + gr̅) √2 i G5 = (rg̅ − gr̅) √2 1 ̅ G6 = (gb + bg̅) √2 i ̅ G7 = (bg̅ − gb) √2 1 ̅ G8 = (rr̅ + bb − 2gg̅) √6 Besides, the photon boson is: 1 ̅ B = G9 = (rr̅ + bb + gg̅) √3 Thus, there are totally 9 bosons(8 gluons plus 1 photon) for the whole 3X3 matrix, and they are acquiring masses due to the interaction with Higgs bosons. In order to maximize the total gluons, we need to use complex scalar field here to include 6 Higgs bosons. We predict that six of the bosons will interact with Higgs field, and three gluons will have no mass. The Higgs field is: φ1 + iφ2 1 φ(x) ≡ (φ3 + iφ4) √2 φ5 + iφ6 And, we letφ1 = φ2 = φ3 = φ4 = φ6 = 0⁡and⁡φ5 = v. Thus, the Higgs field should be (0,0,V/√2) The lagrangian for the complexl scalar field is: v 2 2 4 L(φ) = (∂vφ)(∂ φ) − μ (φ(x)) − λ(φ(x)) Then, we introduce the covariant derivative of QCD and Gell-Mann matrixinto the lagrangian. It becomes: 1 + |[(igλG(x)) ∗ φ(x)] [(igλG(x)) ∗ φ(x)]| = 4 1 (gv(G − iG ), gv(G − iG ), v(푔′B − g′′G )) × (gv(G + iG ), gv(G + 8 4 5 6 7 8 4 5 6 iG7), v(g′B − g′′G8)) 4 5 6 7 We let G =1/√2(G4+iG5), G =1/√2(G4-iG5) and so for G and G . And we let √2/√3g =g’’ and 1/√3k =g’. g=k for equal strong-electric coupling constant. Then, 8u u u 2 2 We let G =(g′B − g′′G8)/√(g′ + g′′ ) and u u u 2 2 A =(g′′G8 + g′B )/√(g′ + g′′ ) Similar to electroweak theory, we get the mass of G8 1 m⁡G8 = v√g′2 + g′′2 2 And the mass of photon Au is still zero. Similar to electroweak theory, we get G8 field and photon field: ′ 8 g′ g G = B − G8 = B sin θ − G8 cos θ √g′′2 + g′2 √g′′2 + g′2 g′ g′′ A = G8 + B = G8 sin θ + B cos θ √g′′2 + g′2 √g′′2 + g′2 In addition, the mass of the new gluons G1, G2, and G3 is still zero after the Higgs mechanism. Besides, the mass of gluons G4, G5, G6, and G7 is 1/2vg. The G8 gluon becomes gg after the Higgs mechanism. Besides, we know 1 1 (G − iG ) = rb̅ , and (G + iG ) = br̅ etc √2 1 2 √2 1 2 G8 and photon Higgs interaction is in the right and bottom most position of the matrix, and we get a final gg gluon. Thus, we can get the new sets of the eight gluons G1-8: rb,br, rr/bb, bg,gb,gr,rg, and gg. The mass term for colored gluon is M2V, so mass 8 2 8u of bg,gb,gr,rg is 1/2vg, respectively. G mass term is 1/2M G G8u, so gg mass is 1/2푣푔.⁡The form of rr/bb is (which is similar to neutral pion): 1 (rr̅ − bb̅) √2 I don’t know the exact coupling constant ratio between photon and strong force. However, if the alpha ratio is 1/2 which is similar to the color force, we can get: 1 sin θ = √3 √2 cos θ = √3 Thus, we will get the results of G8-A interaction (mixing). G8 = gg̅ 1 A = (rr̅ + bb̅) √2 Green-related gluons have masses, and non-green gluons have no mass. This solves Yang-Mills mass gap problem for gluons. That’s why neutron/proton has more mass than its quarks. From above, we know alpha decay is related to meson and beta decay is related to W boson. Both are SU(2). According to stronglight unification, we can get five green gluons with mass: bg, gb, gr, rg, and gg. Besides, we have four massless bosons: λ1, λ2, λ3,& A. The later four can again interact with Higgs boson (0,V/√2) to get rb and br with mass vg/2 and bb with mass vg/2,⁡and massless rr. Thus, there are total eight same mass gluons to mediate short range strong force. The above A boson is the B0 boson in the electroweak theory. The four bosons can also interact with Higgs boson in the electroweak interaction with different coupling constant and generate massive W+, W-, Z, and massless . Thus, we can unite strong force, weak force, and light (electromagnetism). Besides, I will discuss the origin of mesons. I propose here that meson such as pion is produced from nucleon-antineucleon annihilation such as proton-proton annihilation or neutron-neutron annihilation. The proton is composed of UUD, and the anti- proton is composed of UUD. Because the Yukawa potential for strong interaction V(r)=e-kmr/r. The gluon between quarks inside neucleon should have mass for the short range strong force. Based on my above deduction, a neucleon should have eight gluons to make its white color. The mass of proton or neutron is seven times of each gluon or pion. The pion gets mass 135Mev/c2 from the proton/neutron mass 940Mev/c2. The ratio is about 1/7 after subtracting quark masses. We can view pion as a boson with a neutral gluon. And, neutron or proton is a composite of neucleon with pion. If pion has negative mass due to time reversal asymmetry as an anti- matter, we can let eight gluons to subtract one pion to get total seven gluons to form neutron or proton. This is the origin of mass of neucleon. Then, we state why quarks and leptons have three generations. The electroweak interaction is the main source of the three generations of leptons such as electron and neutrino.