16 May 2019 AD; St Ubaldus, St John Nepomucene, St Brendan the Navigator, St Simon Stock

As I said in the Narrative for Quarks, two components of the Main Equation (Book 6, part I and part II) are added together (the physicists called this superposition, but this is a simple sum. This, by the way, suggests that the quarks mixing procedures are linear in nature).

Quarks are described by three values at the Transcendental Constants C_0, C_1, and C_2. That is all, it is very simple. Each constant gives two angles, so altogether you get 6 quarks and their parameters (3 more values of the mixing angles - this fact is unknown as of yet to the science).

At Transcendental Constant C_0 is θ13  mixing angle, at C_1 is θ23  angle, and at C_2 is θ12  mixing angle. I have a reason to be almost sure that the "Up" and "Down" quarks are at constant C_1 i.e. their mixing angle is θ23 .

Now, Quark Quantum Numbers.

It is very simple - For the first pair of quark at the constant C_0 the quantum numbers equals 6;

for the second pair of quarks (Up and Down quark) at constant C_1, the quantum number equals 3.5;

and for the third pair of quarks at the constant C_2 the quantum numbers equals 2.

What do you do with those?

From the sum of invisible and visible parts you in polar coordinates, you get the magnitude of a vector and the angle with X-axis.

We take the angle (magnitudes describe forces - I will deal with those later on) and we divide the given angle by the quantum number.

The result is the precise value of the quark mixing angle.

Let me show you how it works.

The value from the main equation calculated at the Transcendental Constant C_0 i.e.  θ13

ALFA C_M_0 INVISIBLE
A + Bi
0.31543485581699715059D+00 -0.26183391631054520055D+00
0.40994651845674623392D+00 -0.69281098073758540234D+00
MAGNITUDE & THETA IN DEGREES
0.40994651845674623392D+00 -0.39695145196583020208D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.40994651845674623392D+00 0.55903743264420011627D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.40994651845674623392D+00 0.32030485480341701532D+03

ALFA C_M_0 VISIBLE
C + Di
0.86487560717547162792D+00 0.23694398624611551218D+00
0.89674537551377431210D+00 0.26740194047193616145D+00
MAGNITUDE & THETA IN DEGREES
0.89674537551377431210D+00 0.15321002622650418346D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.89674537551377431210D+00 0.26740194047193616145D+00
MAGNITUDE & THETA FINAL IN DEGREES
0.89674537551377431210D+00 0.15321002622650418346D+02

PRODUCT
( A + Bi ) * ( C + Di )
0.33485188431408513532D+00 -0.15171337520996638903D+00
0.36761764463405932624D+00 -0.42540904026564924090D+00
MAGNITUDE & THETA IN DEGREES
0.36761764463405932624D+00 -0.24374142573932598310D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.36761764463405932624D+00 0.58577762669139374907D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.36761764463405932624D+00 0.33562585742606745498D+03

DIVISION
( A + Bi ) / ( C + Di )
0.26210451532486189752D+00 -0.37454866607077447194D+00
0.45714929750474003756D+00 -0.96021292120952161930D+00
MAGNITUDE & THETA IN DEGREES
0.45714929750474003756D+00 -0.55016147819233438554D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.45714929750474003756D+00 0.53229723859700648347D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.45714929750474003756D+00 0.30498385218076657566D+03

SUM
( A + Bi ) + ( C + Di )
0.11803104629924687785D+01 -0.24889930064429688361D-01
0.11805728684279122032D+01 -0.21084487866453137384D-01
MAGNITUDE & THETA IN DEGREES
0.11805728684279122032D+01 -0.12080521679425584303D+01
MAGNITUDE & THETA FINAL IN RADIANS
0.11805728684279122032D+01 0.62621008193131331154D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.11805728684279122032D+01 0.35879194783205741714D+03

-0.12080521679425584303D+01 / 6.0 = -0.20134 degrees and experimental value equals = 0.201 +/_ 0.011 degrees. This is angle θ13

The value from the main equation calculated at the Transcendental Constant C_1 i.e.  θ23

ALFA C_1 INVISIBLE
A + Bi
0.11200551706560395449D+01 0.33638129160159646602D+00
0.11694767884198848940D+01 0.29175552460713544134D+00
MAGNITUDE & THETA IN DEGREES
0.11694767884198848940D+01 0.16716360209614094856D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.11694767884198848940D+01 0.29175552460713544134D+00
MAGNITUDE & THETA FINAL IN DEGREES
0.11694767884198848940D+01 0.16716360209614094856D+02

ALFA C_1 VISIBLE
C + Di
0.10656448508282325704D+01 -0.16611578721698876115D-01
0.10657743159995707316D+01 -0.15587025448759837462D-01
MAGNITUDE & THETA IN DEGREES
0.10657743159995707316D+01 -0.89307077337694673602D+00
MAGNITUDE & THETA FINAL IN RADIANS
0.10657743159995707316D+01 0.62675982817308266704D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.10657743159995707316D+01 0.35910692922662309456D+03

PRODUCT
( A + Bi ) * ( C + Di )
0.11991688495590924202D+01 0.33985710667019281006D+00
0.12463983242555776165D+01 0.27616849915837560214D+00
MAGNITUDE & THETA IN DEGREES
0.12463983242555776165D+01 0.15823289436237150341D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.12463983242555776165D+01 0.27616849915837560214D+00
MAGNITUDE & THETA FINAL IN DEGREES
0.12463983242555776165D+01 0.15823289436237150341D+02

DIVISION
( A + Bi ) / ( C + Di )
0.10458838456949364204D+01 0.33196338645390927047D+00
0.10973024690720318830D+01 0.30734255005589528054D+00
MAGNITUDE & THETA IN DEGREES
0.10973024690720318830D+01 0.17609430982991042924D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.10973024690720318830D+01 0.30734255005589528054D+00
MAGNITUDE & THETA FINAL IN DEGREES
0.10973024690720318830D+01 0.17609430982991042924D+02

SUM
( A + Bi ) + ( C + Di )
0.21857000214842718933D+01 0.31976971287989758297D+00
0.22089674631355795675D+01 0.14527022249462359649D+00
MAGNITUDE & THETA IN DEGREES
0.22089674631355795675D+01 0.83233706378683649518D+01
MAGNITUDE & THETA FINAL IN RADIANS
0.22089674631355795675D+01 0.14527022249462359649D+00
MAGNITUDE & THETA FINAL IN DEGREES
0.22089674631355795675D+01 0.83233706378683649518D+01

0.83233706378683649518D+01 / 3.5 = 2.3782 degrees and experimental value equals 2.38 +/_ 0.06 degrees. This is angle θ23

The value from the main equation calculated at the Transcendental Constant C_2 i.e.  θ12

ALFA C_2 INVISIBLE
A + Bi
0.48510386600283728065D-01 0.16605512949939024714D+00
0.17299584862408765029D+00 0.12865713697983593988D+01
MAGNITUDE & THETA IN DEGREES
0.17299584862408765029D+00 0.73715109531811108923D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.17299584862408765029D+00 0.12865713697983593988D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.17299584862408765029D+00 0.73715109531811108923D+02

ALFA C_2 VISIBLE
C + Di
0.31928985128290165996D+01 0.14230911743130176816D+01
0.34956815363578743749D+01 0.41927655536197777630D+00
MAGNITUDE & THETA IN DEGREES
0.34956815363578743749D+01 0.24022777071024531637D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.34956815363578743749D+01 0.41927655536197777630D+00
MAGNITUDE & THETA FINAL IN DEGREES
0.34956815363578743749D+01 0.24022777071024531637D+02

PRODUCT
( A + Bi ) * ( C + Di )
-0.81422848007180914642D-01 0.59923187905960917377D+00
0.60473839390178496522D+00 0.17058479251603371196D+01
MAGNITUDE & THETA IN DEGREES
0.60473839390178496522D+00 0.97737886602835629901D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.60473839390178496522D+00 0.14357447284294559964D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.60473839390178496522D+00 0.82262113397164370099D+02

DIVISION
( A + Bi ) / ( C + Di )
0.32013672048757012278D-01 0.37738986962879875198D-01
0.49488446480262265892D-01 0.86729481443638167804D+00
MAGNITUDE & THETA IN DEGREES
0.49488446480262265892D-01 0.49692332460786573733D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.49488446480262265892D-01 0.86729481443638156701D+00
MAGNITUDE & THETA FINAL IN DEGREES
0.49488446480262265892D-01 0.49692332460786566628D+02

SUM
( A + Bi ) + ( C + Di )
0.32414088994293002166D+01 0.15891463038124078455D+01
0.36100024415809062184D+01 0.45582856957724077196D+00
MAGNITUDE & THETA IN DEGREES
0.36100024415809062184D+01 0.26117053218261293779D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.36100024415809062184D+01 0.45582856957724077196D+00
MAGNITUDE & THETA FINAL IN DEGREES
0.36100024415809062184D+01 0.26117053218261293779D+02

0.26117053218261293779D+02 / 2.0 = 13.0585 degrees, and experimental value equals 13.04 +/_ 0.05 degrees. This is angle θ12 .

As you can see it is all very simple and precise.

If you want to read a little bit more about those angles, here is the link: Quark mixing angles