28 May 2019 AD; St Augustine of Canterbury, St Bernard of Montjoux, St Germanus; Rogation Day

Neutrinos are described in the main equation (Book 6, part I and part II) by three values of respective angles at Transcendental Constants C_M(inus)_1, C_M(inus)_2 and C_M(inus)_3. Each value of the function gives 2 angles so in total you get 6 different angles - three for neutrinos and three for corresponding electron,  tau and muon. It is the same as in the previous article about quarks: up and down quarks, strange and charm quarks and bottom and top quarks.

Again as in the case of quarks, the electron and electron neutrino mixing angle will be at second value (Transcendental Constant C_M_2) and called angle θ23 , which is the value for atmospheric neutrinos.

Let us move ahead to Neutrino Quantum Numbers.

As in the case of quarks, it is also very simple: For the first pair at the Transcendental Constant C_M_1 (tau and tau neutrino or muon and muon neutrino) and for sure "the reactor neutrino", the quantum number is (1/3.5)*(3/2). This value will be used in multiplication with the angle not division as I used in the quark Quantum Numbers, for simplicity (of course you can use a reciprocal and divide the angle by this reciprocal and the result will be the same).

For the second pair (electron neutron and electron) the Quantum Number is (1/3.5) - the same value as for quarks. When you multiply this quantum number (1/3.5) by the angle calculated from the main program you get atmospheric Neutrino Mixing Angle. This is for Transcendental Constant C_M_2.

And lastly, the third pair (muon and muon neutrino or tau and tau neutrino pair) the Quantum Number is (3/2) and this is solar neutrino. When this Quantum number (3/2) is multiplied by the value of an angle it will give the Solar Neutrino Mixing Angle. This is for Transcendental Constant C_M_3.

Calculation of Neutrino Mixing Angles.

As in the case of quarks, the steps of getting the angles are similar - from the sum of "the visible and the invisible scan" (more about this simple scan in the future articles) you get the value of the angle (on Y-axis) for each Transcendental Constant (on X-axis) among other things. (it is simplified because we actually need one more dimension as for some of the complex number calculations. But let us use just X and Y-axis for simplicity (Sum or Superposition should be O.K. like that).

The value from the Main Equation (Y-axis) calculated at the Transcendental Constant C_M_1 (X-axis):

ALFA C_M_1 INVISIBLE
A + Bi
0.26742070244365181431D+01 -0.88456206796555758576D+00
0.28167061013938110570D+01 -0.31944670772500965983D+00
MAGNITUDE & THETA IN DEGREES
0.28167061013938110570D+01 -0.18302948131992206271D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.28167061013938110570D+01 0.59637385994545768497D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.28167061013938110570D+01 0.34169705186800780439D+03

ALFA C_M_1 VISIBLE
C + Di
0.10921287997995738905D+01 -0.48723746885506363791D+00
0.11958869789440584874D+01 -0.41963559257214483322D+00
MAGNITUDE & THETA IN DEGREES
0.11958869789440584874D+01 -0.24043348387855257187D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.11958869789440584874D+01 0.58635497146074415653D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.11958869789440584874D+01 0.33595665161214475347D+03

PRODUCT
( A + Bi ) * ( C + Di )
0.24895867249727050563D+01 -0.22690295714163339902D+01
0.33684621501691416334D+01 -0.73908230029715449305D+00
MAGNITUDE & THETA IN DEGREES
0.33684621501691416334D+01 -0.42346296519847463458D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.33684621501691416334D+01 0.55441030068824312949D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.33684621501691416334D+01 0.31765370348015250102D+03

DIVISION
( A + Bi ) / ( C + Di )
0.23435167268465875168D+01 0.23558310181902933356D+00
0.23553280125860216465D+01 0.10018888484713517339D+00
MAGNITUDE & THETA IN DEGREES
0.23553280125860216465D+01 0.57404002558630518038D+01
MAGNITUDE & THETA FINAL IN RADIANS
0.23553280125860216465D+01 0.10018888484713517339D+00
MAGNITUDE & THETA FINAL IN DEGREES
0.23553280125860216465D+01 0.57404002558630518038D+01

SUM
( A + Bi ) + ( C + Di )
0.37663358242360920336D+01 -0.13717995368206212792D+01
0.40083811582913915217D+01 -0.34929217207386531463D+00
MAGNITUDE & THETA IN DEGREES
0.40083811582913915217D+01 -0.20012967276789797921D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.40083811582913915217D+01 0.59338931351057206953D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.40083811582913915217D+01 0.33998703272321017721D+03

This angle multiplied by Neutrino Quantum Number at C_M_1 will give the value of the "Reactor Neutrino Quantum Number" θ13

-0.20012967276789797921D+02 * (1/3.5) * (3/2) = -8.5770 degrees and official value is 8.54 degrees (+/- 0.15 degrees)

Now, second Mixing Angle will be the value of the Main Equation (Y-axis) at Transcendental Constant C_M_2 (X-axis)

ALFA C_M_2 INVISIBLE
A + Bi
-0.16469643196137670316D+03 -0.42300580114651573638D+02
0.17004191771102927078D+03 -0.28901870692595768020D+01
MAGNITUDE & THETA IN DEGREES
0.17004191771102927078D+03 -0.16559552107185831460D+03
MAGNITUDE & THETA FINAL IN RADIANS
0.17004191771102927078D+03 0.60317797228493699180D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.17004191771102927078D+03 0.34559552107185828618D+03

ALFA C_M_2 VISIBLE
C + Di
0.14778769334016466086D+01 -0.23635598565384036140D+00
0.14966577371714127054D+01 -0.15858643318941822997D+00
MAGNITUDE & THETA IN DEGREES
0.14966577371714127054D+01 -0.90863333097870668809D+01
MAGNITUDE & THETA FINAL IN RADIANS
0.14966577371714127054D+01 0.61245988739901680020D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.14966577371714127054D+01 0.35091366669021294911D+03

PRODUCT
( A + Bi ) * ( C + Di )
-0.25339905311600006144D+03 -0.23588064111050094596D+02
0.25449455178567663438D+03 -0.30487735024489950320D+01
MAGNITUDE & THETA IN DEGREES
0.25449455178567663438D+03 -0.17468185438164536549D+03
MAGNITUDE & THETA FINAL IN RADIANS
0.25449455178567663438D+03 0.61903661560387881480D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.25449455178567663438D+03 0.35468185438164539391D+03

DIVISION
( A + Bi ) / ( C + Di )
-0.10419852225472008911D+03 -0.45286940362340857291D+02
0.11361443133444632281D+03 -0.27316006360701585720D+01
MAGNITUDE & THETA IN DEGREES
0.11361443133444632281D+03 -0.15650918776207123528D+03
MAGNITUDE & THETA FINAL IN RADIANS
0.11361443133444632281D+03 0.58731932896599516880D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.11361443133444632281D+03 0.33650918776207123528D+03

SUM
( A + Bi ) + ( C + Di )
-0.16321855502797504300D+03 -0.42536936100305410946D+02
0.16867035198345195113D+03 -0.28866501582687109639D+01
MAGNITUDE & THETA IN DEGREES
0.16867035198345195113D+03 -0.16539287099956825955D+03
MAGNITUDE & THETA FINAL IN RADIANS
0.16867035198345195113D+03 0.60282428118585045240D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.16867035198345195113D+03 0.34539287099956828797D+03

This angle multiplied by Electron Neutrino Quantum Number (1/3.5) At Constant C_M_2 will give the Atmospheric Neutrino Mixing Angle θ23

-0.16539287099956825955D+03 * (1/3.5) = -47.2551 degrees and experimental value is 47.2 degrees (43.3 to 49.1 degrees)

Now, the third Mixing Angle will be the value of the Main Equation (Y-axis) at Transcendental Constant C_M_3 (X-axis)

ALFA C_M_3 INVISIBLE
A + Bi
0.12483662752856212238D-03 -0.14913959339723874536D-02
0.14966115111952314493D-02 -0.14872864483626460075D+01
MAGNITUDE & THETA IN DEGREES
0.14966115111952314493D-02 -0.85215236418181461886D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.14966115111952314493D-02 0.47958988588169404466D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.14966115111952314493D-02 0.27478476358181853811D+03

ALFA C_M_3 VISIBLE
C + Di
0.11967254058809253525D+01 0.51215407798285539354D+00
0.13017117563713305195D+01 0.40437757327188500467D+00
MAGNITUDE & THETA IN DEGREES
0.13017117563713305195D+01 0.23169128278221215567D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.13017117563713305195D+01 0.40437757327188500467D+00
MAGNITUDE & THETA FINAL IN DEGREES
0.13017117563713305195D+01 0.23169128278221215567D+02

PRODUCT
( A + Bi ) * ( C + Di )
0.91321967321893193510D-03 -0.17208558165418871410D-02
0.19481567988434958429D-02 -0.10829088750907609473D+01
MAGNITUDE & THETA IN DEGREES
0.19481567988434958429D-02 -0.62046108139960246319D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.19481567988434958429D-02 0.52002764320888257288D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.19481567988434958429D-02 0.29795389186003978921D+03

DIVISION
( A + Bi ) / ( C + Di )
-0.36261210291615981029D-03 -0.10910461667493448305D-02
0.11497257391046434693D-02 -0.18916640216345310677D+01
MAGNITUDE & THETA IN DEGREES
0.11497257391046434693D-02 -0.10838436469640268456D+03
MAGNITUDE & THETA FINAL IN RADIANS
0.11497257391046434693D-02 0.50332566752243241837D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.11497257391046434693D-02 0.28838436469640265614D+03

SUM
( A + Bi ) + ( C + Di )
0.11968502425084539542D+01 0.51066268204888298765D+00
0.13012405149817243277D+01 0.40328613176847122324D+00
MAGNITUDE & THETA IN DEGREES
0.13012405149817243277D+01 0.23106593286490191730D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.13012405149817243277D+01 0.40328613176847122324D+00
MAGNITUDE & THETA FINAL IN DEGREES
0.13012405149817243277D+01 0.23106593286490191730D+02

This value of the angle multiplied by Neutrino Quantum Number (3/2) will give the Solar Neutrino Mixing Angle θ12  ( I have worked some months on this one 3/2 quantum number is the best solution and most elegant)

0.23106593286490191730D+02 * (3/2) = 34.6599 degrees and official value is a tiny bit off: 33.62 degrees (32.86 to 34.40 degrees).

I'm confident my value is correct and it won't change as the scientists change the values every year or so.

Next part will be about bosons and unknown yet particles and their angles. And after that an Extended Standard Model with 24 particles with 8 yet unknown ones.