25 July 2019 AD; St James the Greater; St Christopher

"Give me an experimental angle from Quantum Mechanics and I will calculate its value exactly."

All the spherical sums of the angles for quarks, neutrinos, bosons, and gravitons, when multiplied by a unique fraction (more in next article), should give CP Violation Phase angle, which is **for quarks calculated at δ = 68.755 deg +/- 4.5837deg, **and they do indeed give this result.

*It is quite possible that the CP Violation Phase for Graviton is different than for Quark, even if the sum of all the angles are almost the same.

**The calculation for quark.**

First, in spherical geometry - the sum of all six quark mixing angles (three mixing angles and three final mixing angles) is: **90.4706 deg**

The fraction to multiply the above value to get a result close to CP Violation Phase = **δ = 68.755 deg is ( 4 / 21 )**

Here is the "procedure":

[ 90.4706 deg + 3 * ( 90.4706 deg ) ] * ( 4 / 21 ) = 361. 8824 deg * ( 4 / 21 ) = **68. 9230 deg (spherical)**

Now, we have to transform this spherical value into regular "flat" geometry:

**The correction coefficient , ε is:**

ε = ( 0.4706 deg ) / ( 90.4706 deg ) = **5.2017 X 10 ^{-3} **

In degrees, the correction is:

68.9230 deg * ε = 0.3585 deg

Now, "flat" angle equals to

68.9230 deg - 0.3585 deg = **68.5644 deg**** ("flat")**

The angle inbetween spherical and regular geometry is average of those two terms:

( 68.9230 deg + 68.5644 deg ) / 2 = **68.7437 deg (ave)**

The same fraction ) 4 / 21 ) is applied to the graviton to get the spherical angle, regular angle, and the angle in between, a mix of spherical and flat geometry.

The calculation of a spherical value of **CP Violation Phase Angle for Graviton **:

(This result for Graviton will be tested later on, I can tell you now, that CP Violation Phase Angle of Graviton is different than that of Quark).

[ 90.5494 deg + 3 * ( 90.5494 deg ) ] 8 ( 4 / 21 ) = 362.1976 deg * ( 4 / 21 ) = **68.9900 deg (spherical)**

Correction factor, epsilon, to get back to flat geometry:

ε = ( 0.5494 deg / 90.5494 deg ) = **6.0674X10 ^{-3} deg**

Flat value of the CP Angle is:

68.9900 deg - 6.0674X10^{-3} * 68.9900 deg = **68.5714 deg (flat)**

Average between those two values is:

[ 68.9900 deg + 68.5714 deg ] / 2 = **68.7807 deg (ave)**

**The quark and graviton together:**

Spherical value of CP Angle:

(90.4706 deg + 90.5494 deg = 181.0200 deg

[ 181.0200 deg + 181.0200 deg ] * ( 4 / 21 ) = **68.9600 deg (spherical)**

The transformation to flat geometry:

The correction factor, epsilon

ε = 1.0200 deg / 181.0200 deg = 5.6347 X 10^{-3}

68.9600 deg - ( ε ) * (68.9600 deg ) = **68.5714 deg (flat)**

Average between spherical and flat geometries :

**ave = 68.7657 deg (ave)**

So, the final results are:

**Quark δ = 68.7437 deg (ave)**

**Graviton δ = 68.7807 deg (ave)**

**Quark and Graviton together δ = 68.7657 deg (ave)**

If we take the average of Quark and (Quark and graviton together) then the average is**δ = 68.7547 deg**

**Official value is 68.755 deg** but with only one decimal place of accuracy, i.e. **δ = 68.7 deg**

Before proceeding to other properties of CP Violation phase for quark and neutrino, in the next article I post some rules for those "Quantum Fractions".

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