**1. Strong interaction**

**Generality**

We want know what is a mass ? Mass is given by energy. Energy is given by a derivation of the action in function of the time. Therefore the mass is given by an event. This event is necessarily an event which use entities ; and for these entities mass is absurdity when they are isolated. Therefore we take two entities. The first is the graviton, and the second is named entity two. We have about one graviton in 10 ^{-45} m^{3}. These gravitons run through the second entity with a mean speed equal to the speed of light. This event is the action. Its unit is h (Planck constant), and it gives to the particle a property named mass. For an isolated graviton the notions of mass ,charge , spin , time , Relativity and many other things are nonsense .

**Calculation of the mass**

For many events we have Schödinger’s equation and other equation of the "Mecanique Quantique". But for one event with one good particle it is necessary to use Hamilton-Jacobi’s equation which gives action S.

We have :

v is the speed of the graviton.

To resolve this equation we take spherical geometry and v^{2} = a + br^{2} , a and b are constants.

We have

We take : with

We have :

with and g = F/B

K, F et B are constants. F and B are whole numbers with

S_{1} = exp j (n Arctan (x/n) - B Arctan (x/B) ) with bn^{2} = B^{2}b - K^{2}

We have also and n is a whole number .

Energy is given by :

with Y = S_{1} . S_{2} . S_{3} . S_{4}

But we have also , , and these equations give

Y = 1

The interaction is periodic. Therefore KT = 2kπ where T is the period and k a whole number.

We see that we have = whole number. It is necessary to find T.

We use the electron and the relation hN = mc² with N = 1/T. This equation is not a law of the physics. But an interpretation of the reality (hN) in our mathematical and abstract concepts (mu). Where u is a potential. Einstein explains u = c².

Therefore we have : m_{e} = 2h/137,036 T c^{2 }where c is the speed of light and T = 11,8.10^{-23} s and m = 35,013 Mev .

But a complete particle have 2B + 1 states, with n, B and whole numbers.

**Examples**

n = 5 B = 4 with one state, we have m = 105,039 Mev. This mass is near the mass of meson μ

n = 5 B = 3 with one state, we have m = 140,052 Mev. This mass is near the mass of meson π

n = 5 B = 4 with nine states, we have m = 945,35 Mev. This mass is near the mass of the

nucleon.

n = 5 B = 3 with seven states, we have m = 980,36 Mev. We have a resonance with this mass. But the half give the mass of meson K

And so on …

**Observations**

- The mass are not exactly the mass of the particles. It is necessary to make electric corrections..

b) We have much solutions. But we have especially n - B = 1.

n = 5 B = 4 m = 945 Mev n = 113 B = 112 m = 118 Gev

n = 13 B = 12 m = 4,4 Gev n = 145 B = 144 m = 172 Gev

n = 25 B = 24 m = 12 Gev n = 181 B = 180 m = 240 Gev

n = 41 B = 40 m = 25,5 Gev n = 221 B = 220 m = 324 Gev

n = 61 B = 60 m = 46,6 Gev n = 265 B = 264 m = 426 Gev

n = 85 B = 84 m = 77 Gev

n = 5 et B = 4 give the nucleon.

n = 13 et B = 12 give the charmonium system and the mass of the quark bottom .

We have :

4375 ® 4200 ® 4025 ® 3850 ® 3675 ® 3500 ® 3325 ® 3150 ® 2975 ®

and some states mix to give states p.

n = 25 and B = 24 give the bottomonium system.

We see we have especially multiple of 5 for n or ( n^{2}-B^{2})^{1/2 } and 4 for B.

n = 85 gives 77 Gev and 77 + 1 = 78 et 78 + 12 = 90. We have nearly the mass of W and Z. We have a triplet .

n = 145 gives 172 Gev and 172 + 1 = 173. This mass is the mass of the quark top. In fact we have a resonance.

Therefore . It is possible to have 118 Gev, which is able to give a particle at 123Gev .

and to have 426 + 1 = 427 Gev. But it is a big particle with a small probability .

The classification of all resonances is possible. But for that it is necessary to debate.

Notice

In fact the electric adjustments are quantified . For n=265 it is possible to have 420 or 426 or 432 or 438 or444 or 450 or 457 Gev . The last value is given for 6 quanta and it seems it is a maximum .For 118Gev it is possible to have 123,5 or 125 or 126,5 Gev for 4,5,or 6 quanta .This is classic .For W and Z we have 4 quanta

It is possible to have in Gev:

547,1500,3200 for the first series.

And 426,690 1258,1770,1947 for the second series.

The electric perturbations can go to 5%.

The probability is very weak ,and it is very difficult to have 5 sigmas ,

and they are very big .