13 August 2019 AD; St Hippolytus and St Cassian; St Radegund

 

The sum of the pairs of elements will form either a triangle (sum of the internal angles equal to 180 deg) - this is a pair of Quark and Graviton.

Or another sum of the angles of the pair will form a quadrangle - probably a rectangle, with the sum of internal angles 360 deg this is the sum of Neutrino and Boson. If you add all four elements the sum of internal angles will be 540 deg forming a pentagon (the sum of Quark angles, Graviton angles, Neutrino angles, and Boson angles). Other sums will have values of the angles between 180 deg and 360 deg.

To get the spherical angles correctly, I have to introduce an idea of a unit angle, which is about 90 deg.

For quark and graviton pair the calculation is as follows:

The sum of the quark angles equals to 90.4706 deg + sum of the graviton angles equals to 90.5494 deg = 181.0200 deg. 

The arithmetic mean of this sum equals to 181.0200 deg / 2 = 90.5100 deg.

This is the unit angle for quark and graviton pair.

In a similar way unit angle of neutrino and boson, the sum equals to 257.8801 deg + 102.8371 deg = 360.7172 deg

Dividing this value by 4 we get 

360.7172 deg / 4 = 90.1793 deg

This is the unit angle for neutrino and boson pair.

Unit angles are necessary to calculate exactly value s of pairs, triplets, and singles as well as quadruplet of the sum of the angles.

 

PAIRS:

 

The First Pair - Quark and Neutrino:

δ CP Q/N = 90.4706 deg + 257.8801 deg = 348.3507 deg * ( 2 / 3 ) = 232.2338 deg

 

The second pair - Neutrino, and Graviton:

δ CP N/G = 257.8801 deg + 90.5494 deg = 348.4295 deg * ( 2 / 3 ) = 232.2863 deg

 

The third pair - Quark, and Boson: 

δ CP Q/B = 90.4706 deg + 102.8371 deg = 193.3077 deg * ( 6 / 5 ) = 231.9692 deg

 

The fourth pair - Boson, and Graviton:

δ CP B/G = 102.8371 deg + 90.5494 deg = 193.3865 deg * ( 6 / 5 ) = 232.0638 deg

 

The fifth pair - Quark, and Graviton:

δ CP Q/G = 90.4706 deg + 90.5494 deg + 4 X 90.5100 deg (spherical unit angle) = 181.0200 deg + 362.0400 deg = 543.0600 deg * ( 3 / 7 ) = 232.7400 deg

 

The sixth pair - Boson, and Neutrino:

δ CP B/N = 102.8371 deg + 257.8801 deg + 2 X 90.1793 deg (spherical unit angle) = 360.7172 deg + 180.3586 deg = 541.0758 deg * ( 3 / 7 ) = 231.8896 deg

 

The arithmetic mean of pairs:

δ CP Pairs Arithmetic Mean = 1393.18272 deg / 6 = 232.19712 deg

 

Now, a quadruplet (sum of all four elements). The value of the sum of the internal angles equals 540 deg, forming a Pentagon.

Quark + Neutrino + Boson + Graviton:

δ CP Q/N/B/G = 90.4706 deg + 257.8801 deg + 102.8371 deg + 90.5494 deg = 541.73716 deg * ( 3 / 7 ) = 232.1707 deg

 

SINGLES:

 

Quark:

δ CP Q = 90.4706 deg + 5 X 90.4706 deg = 542.82336 deg * ( 3 / 7 ) = 232.63858 deg

 

Graviton:

δ CP G = 90.5494 deg + 5 X 90.5494 deg = 543.29640 deg * ( 3 / 7 ) = 232.84131 deg 

 

Boson:

δ CP B = 102.8371 deg + 90.1793 deg = 193.01640 deg * ( 6 / 5 ) = 231.61968 deg

 

Neutrino:

δ CP N = 257.8801 deg + 90.1793 deg = 348.05940 deg * ( 2 / 3 ) = 232.03960 deg

 

The arithmetic mean of singles:

δ CP Singles Mean = 929.13917 deg  / 4 = 232.28479 deg

 

TRIPLETS:

I will skip the boring part which is the calculation of the spherical unit angle correction.

 

Quark, and Neutrino and Graviton:

δ CP Q/N/G = 438.9001 deg - 90.3998 deg = 348.5003 * ( 2 / 3 ) = 232.3335 deg

 

Quark, and Boson and Graviton:

δ CP Q/B/G = 283.8571 deg - 90.3998 deg = 193.4573 deg * ( 6 / 5 ) = 232.1488 deg 

 

Neutrino, and Boson and Graviton:

δ CP N/B/G = 451.2666 deg + 90.2895 deg = 541.5561 deg * ( 3 / 7 ) = 232.0955 deg

 

Quark, and Neutrino and Boson:

δ CP Q/N/B = 451.1878 deg + 90.2895 deg = 541.4773 deg * ( 3 / 7 ) = 232.0617 deg 

 

The Arithmetic Mean of the Triplets:

δ CP Arithmetic Mean Triplets = 928.6395 deg / 4 = 232.15988 deg

 

Total Arithmetic Mean For CP Violation Phase for neutrino:

δ CP Total Mean Neutrino = 232.19712 deg X 6 (pairs) + 232.1707 deg X 1 ( pentagon) + 232.15988 deg X 4 (triplets) + 232.28479 deg X 4 (singles) = 3483.13211 deg / 15 = 232.20881 deg

In radians:

δ CP Total Mean Neutrino = 60.792124 rad / 15 = 4.05281 rad

 

The next articles - CP Violation Phase for Graviton and Boson.