Pseudoscalar Top-Bottom Quark-Antiquark Composite as the Resonance with 28 GeV at the LHC: Hadron Masses and Higgs Boson Masses Based on the Periodic Table of Elementary Particles

This paper posits that the observed resonance with 28 GeV at the LHC is the pseudoscalar top-bottom quark-antiquark composite which has the calculated mass of 27.9 GeV derived from the periodic table of elementary particles. The calculated mass is for the mass of bb ̅ + (bb ̅ + tt ̅ )/2. In the periodic table of elementary particles, t quark (13.2 GeV) in the pseudoscalar top-bottom quark-antiquark composite is only a part of full t quark (175.4 GeV), so pseudoscalar tt ̅ (26.4 GeV) cannot exist independently, and can exist only in the top-bottom quark-antiquark composite. As shown in the observation at the LHC, the resonance with 28 GeV weakens significantly at the higher energy collision (13 TeV), because at the higher collision energy, low-mass pseudoscalar tt ̅ in the composite likely becomes independent full high-mass vector tt ̅ moving out of the composite. The periodic table of elementary particles is based on the seven mass dimensional orbitals derived from the seven extra dimensions of 11 spacetime dimensional membrane. The calculated masses of hadrons are in excellent agreement with the observed masses of hadrons by using only five known constants. For examples, the calculated masses of proton, neutron, pion (π ± ), and pion (π 0 ) are 938.261, 939.425, 139.540, and 134.982 MeV in excellent agreement with the observed 938.272, 939.565, 139.570, and 134.977MeV, respectively with 0.0006%, 0.01%, 0.02%, and 0.004%, respectively for the composite (27.9 GeV), hadrons, and the Higgs bosons by the periodic table of elementary particles are in excellent agreement with the observed masses of resonance with 28 GeV at the LHC, hadrons, and the Higgs bosons, respectively.


Introduction
In the search for resonances in the mass range 12 -70 GeV produced in association with a b quark jet and a second jet, and decaying to a muon pair, the CMS Collaboration at the LHC recently reported an excess of events above the background near a dimuon mass of 28 GeV [1]. The search is carried out in two mutually exclusive event categories from proton-proton collisions at center-of-mass energies of 8 and 13 TeV. The first category involves a b quark jet in the central region and at least one jet in the forward region, while the second category involves two jets in the central region, at least one of which is identified as a b quark jet, no jets in the forward region. At the 8 TeV collision, the first category has 4.2 standard deviations, while the second category has 2.9 standard deviations. At the 13 TeV collision, the first category has 2.0 standard deviations, while the second category results in a 1.4 standard deviation deficit.
This potential new particle at 28 GeV does not match the properties of any of particles in the standard model. It is also puzzling that the resonance at 28 GeV weakens, disappears, or gets inverted at 13 TeV. This paper posits that the resonance with 28 GeV observed recently at the LHC is the pseudoscalar top-bottom quark-antiquark composite which has the calculated mass of 27.9 GeV derived from the periodic table of elementary particles in good agreement with the observed 28 GeV. The calculated mass is the mass of three pseudoscalar b quarks and one pseudoscalar t quark which represent the composite of b p b̅ p + (b p b̅ p + t p t̅ p )/2 where p = pseudoscalar. (The quark in pseudoscalar meson is denoted as "pseudoscalar quark", while the quark in vector mesons is denoted as "vector quarks" which has higher mass than pseudoscalar quark.) As described in the periodic table of elementary particles, pseudoscalar t quark (13.2 GeV) is only a part of full t quark (175.4 GeV), so pseudoscalar t p t̅ p (26.4 GeV) cannot exist independently, and can exist only in the top-bottom quark-antiquark composite. As shown in the observation at the LHC, the resonance with 28 GeV weakens significantly at the higher energy collision (13 TeV), because at the higher collision energy, low-mass pseudoscalar tt̅ in the composite likely becomes independent full high-mass vector tt̅ moving out of the composite. To account for the observed two jets, the composite has two jets consisting of a bb̅ jet and a b + t jet, where bb̅ jet for (b p b̅ p + t p t̅ p )/2 is more stable than b + t jet which decays faster into the jet in the forward region to constitute the first category of the search by the CMS Collaboration at the LHC.
The periodic table of elementary particles is based on the seven mass dimensional orbitals derived from the seven extra dimensions of 11 spacetime dimensional membrane particles [2] [3] [4]. The seven mass dimensional orbitals include the seven principal mass dimensional orbitals for stable baryonic matter leptons (electron and neutrinos), gauge bosons, gravity, and dark matter and the seven auxiliary mass dimensional orbitals for unstable leptons (muon and tau) and quarks, and calculate accurately the masses of all elementary particles and the cosmic rays by using only five known constants [5] [6]. Hadron

The Periodic Table of Elementary Particles and the Mass Formulas
The periodic  ), gravity, and dark matter (five sterile dark matter neutrinos) and the seven auxiliary mass dimensional orbitals for unstable leptons (muon and tau) and quarks (d, u, s, c, b, and t) as in Figure 1 and Table 1.
where d is the mass dimensional orbital number, F is fermion, and B is boson.
Each dimension has its own α d , and all α d 's except α 7 (α w ) of the seventh dimension (weak interaction) are equal to α, the fine structure constant of electromagnetism. The given observed masses are the mass of electron for F 6 Table 2.
The lowest energy gauge boson (B 5 ) at d = 5 is the Coulomb field for electromagnetism. The second gauge lowest boson (B 6 ) at d = 6 is basic gluon (g* = 70 MeV ≈ one half of pion) is the strong force as the nuclear force in the pion theory [7] where pions mediate the strong interaction at long enough distances (longer than the nucleon radius) or low enough energies. At short enough distances (shorter than the nucleon radius) or high enough energies, gluons emerge DOI: 10.4236/jmp.2018.914164 GeV) derived from observed gravity as (ћc/G) 1/2 where c is the speed of light, G is the gravitational constant, and ħ is the reduced Planck constant.
which is in excellent agreement with observed 1776.82 MeV, and means that during this dipole-interaction in a circular orbit for τ, an electron with total mass of 17M e is lost. 17M e is shown as the observed 17 MeV for 34M e in the light boson (17 ee̅ ) [12] [13].
Quark has fractional charge (±1/3 or ±2/3), 3-color gluons (red, green, and blue) for 3g*, and both the principal mass dimensional orbitals and axillary mass dimensional orbitals, so similar to Equation (4), d and u in the principal mass dimensional orbital involves e/3 or 2e/3 and 3g* as follows.
The quark mass formula at d = 7 is the combination of Equations (7) and (9) as follows. where a = 1, 2, 3, 4, and 5 for u 7 /d 7 , s 7 , c 7 , b 7 , and t 7 , respectively. The quark mass at a = 5 for the auxiliary mass dimensional orbital at d = 7 is the maximum mass below the mass of B 7 , so the next auxiliary mass dimensional orbital has to start from B 7 .There are b and t at d = 8, so it is necessary to have µ 8 for the masses of b and t. Like µ 7 in Equation (4), the mass of µ 8 is as follows.
Since at d = 7, there are 3-color basic gluons, at d = 8, 3-color basic gluons are not needed, and only one basic gluon ( 7 g * ) at d = 7 is used. Similar to Equations (7) and (9). The quark mass formulas for the principal and auxiliary mass dimensional orbitals are as follows.
The quark mass formula at d = 8 is the combination of Equations (12) and (13) as follows.
where a' = 1 and 2 for b 8 and t 8 , respectively.

Quarks and Hadrons
The calculated masses and the observed masses [10] of baryons are listed in Table 4. The binding energy for each d or u quark involves the auxiliary mass dimensional orbital at d = 7 from Equation (9). The primary binding energy E Q1 for d or u quark from Equation (9) is as follows.   The secondary binding energy E Q2 for d or u quark is as follows.
The tertiary binding energy E Q3 for d or u quark bond is as follows.
3 for quark 2 The binding energy E QQ for each dd, uu, and du bond is 2E Q .
The calculated mass of neutron is in excellent agreement with the observed value 939.565 MeV with the % mass difference between the calculated and the observed masses = −0.01%.
Proton (duu) is more stable than neutron, so it involves the additional binding energy from the tertiary binding energy E QQ3 . For the mass of proton, the baryon number conservation involves the loss of the mass of positron to prevent the decay into positron. Proton becomes permanently stable. The proton mass formula is as follows.
The calculated mass of proton is in excellent agreement with the observed value 938.272 MeV with the % mass difference between the calculated and the observed masses = −0.0006%.
Being less stable than du bond, the primary binding energy for us bond is one-third of the primary binding energy for du as follows.
The secondary binding energy E Q2 for u and s is as follows.
Only one bond (with binding energy) or less per baryon is allowed for the baryons with s, c, and b. The mass of Sigma (Σ + ) as uus is as follows. In the two baryons with the same quark composition, the difference in the masses between the two baryons is equal to the multiple of g*, and one baryon has morebond (with binding energy) than the other baryon, so a bond is added or subtracted in one of the two baryons. For example, the two baryons, Lambda (Λ 0 ) and Sigma (Σ 0 ), are uds. Lambda (Λ 0 ) has the mass of u + d + s -g* − E QQus1 + E QQus2 which is 1117.7 MeV in excellent agreement with the observed 1115.7 MeV. One bond is subtracted in Sigma (Σ 0 ) which has the mass of u + d + s which is 1196.1 MeV in excellent agreement with 1192.6 MeV.
The binding energies of dd, uu, du, uc, and ub are the same. The binding energies of ds, dc, and db are zero. The calculated masses and the observed masses [10] of mesons are in Table 5. For lower-mass pseudoscalar mesons (antiparallel spins), pseudoscalar t is a part of vector t, pseudoscalar b and c are vector quarks minus g*, and pseudoscalar d, u, and s are derived from g*.
The mass of π ± is the mass of 2g* minus the mass of e ± as proposed by Peter Cameron [17]. The calculated mass of π ± is 139.5395 MeV which is in excellent agreement with the observed 139.5702 MeV. π ± has much longer mean lifetime than other mesons to indicate that the composite of π ± is not normal composite The secondary binding energy is as follows.
The binding energy E QQ for each dd, uu, and du bond is 2E Q . π 0 is (u p u̅ p + d p d̅ p )/2, so similar to Equation (20), the mass of π 0 is as follows.
The secondary binding energy is as follows.  The mass of η as (u p u̅ p + d p d̅ p + s p s̅ p )/2 is as follows. The mass of η' as (u p u̅ p + d p d̅ p )/2 + s p s̅ p is as follows. The binding energy for vector dd, uu, and du bonds involves the same binding energy as baryonic d/u quark bond as Equations (16) and (17), so vector ρ + as u v d̅ v with the binding energy derived from Equations (16) and (17) is as follows.
which is in excellent agreement with the observed value 775.11 MeV. As in the baryons with the same quark composition, charged rho meson (ρ + ) and omegameson (ω) have the same composition as u v d̅ v , so 1/2 bond is subtracted in omegameson (ω) which has the mass as follows.
which is in excellent agreement with the observed value 782.65 MeV. The binding energy for vector ds bond and us bond is twice of the binding energy for d/u quarks. The mass for kaon (K *+ ) with u v s̅ v is as follows.  [18] to match the masses of mesons derived from the quark mass formula as Equation (15). The MacGregor's meson mass formula derived from the muon mass formula as Equation (4)  Pseudoscalar and partial t quark is t 7 , while vector and full t quark is t 7 + t 8 .
Vector and full t quark with enormous mass is extremely short-lived, so top quark-antiquark does not have time before they decay to form hadrons, resulting in "bare" t quark and antiquark. The calculated mass of t is 175.4 GeV in good agreement with the observed 172.4 GeV.

The Top-Bottom Quark-Antiquark Composite
In the search for resonances produced in association with a b quark jet and a second jet, and decaying to a muon pair, the CMS Collaboration at the LHC recently reported an excess of events above the background near a dimuon mass of As shown in Figure 1, Table 1, Table 3, and Table 5, pseudoscalar t quark is To account for the observed two jets, the composite has two jets consisting of a bb̅ jet and a b + t jet for (b p b̅ p + t p t̅ p )/2, where bb̅ jet is more stable than b + t jet which decays faster into the jet in the forward region to constitute the first category of the search by the CMS Collaboration at the LHC. Since t p t̅ p is less stable than b p b̅ p , so the decay of the b + t jet is faster to allow the greater standard deviations for the first category than for the second category. The sum of the standard deviations from both categories is greater than 5.

The Higgs Boson Doublet
One important open theoretical issue about the Higgs boson is the triviality problem [19]. Within the perturbation theory, the Higgs boson mass squared is proportional to the self-coupling. However, the scalar self-coupling for the scalar