17 July 2019 AD; St Alexis the Beggar; Bl Martyrs of Compiegne

To get final angles for bosons I use the same transformation as for quarks:

The transformation is as follows:

first quadrant: theta final = theta

second quadrant: theta final = 180 degrees - absolute value |theta|

third quadrant: theta final = 180 degrees + absolute value |theta|

fourth quadrant: theta final = 360 degrees - absolute value |theta|

This is a boring part - just calculations but it has to be done so you know where the Final Angles come from.

There will be three different angles, with the same quantum numbers as before - for "regular"  boson mixing angles.

First final angle:

These printouts are the results of substituting for Real value X constant C_3, C_4 and C_5 in the main program (more about it later):

First Boson Mixing Angle Final is as follows:

These printouts are the results of substituting for Real value X constant C_3 in the main program (more about it later):

ALFA C_3 INVISIBLE
A + Bi
0.64759436369930378774D+00 0.32519895096782575061D+00
0.72466048436883923056D+00 0.46537777239092886772D+00
MAGNITUDE & THETA IN DEGREES
0.72466048436883923056D+00 0.26664182237200069636D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.72466048436883923056D+00 0.46537777239092886772D+00
MAGNITUDE & THETA FINAL IN DEGREES
0.72466048436883923056D+00 0.26664182237200069636D+02

ALFA C_3 VISIBLE
C + Di
-0.15649776905358818269D+02 -0.65463764592633753026D+01
0.16963801517758334114D+02 -0.27454065586322395909D+01
MAGNITUDE & THETA IN DEGREES
0.16963801517758334114D+02 -0.15730020885716291446D+03
MAGNITUDE & THETA FINAL IN RADIANS
0.16963801517758334114D+02 0.58869992122220331510D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.16963801517758334114D+02 0.33730020885716294288D+03

PRODUCT
( A + Bi ) * ( C + Di )
-0.80058325598689847880D+01 -0.93286875301759604184D+01
0.12292996624595604160D+02 -0.22800287862413108897D+01
MAGNITUDE & THETA IN DEGREES
0.12292996624595604160D+02 -0.13063602661996284837D+03
MAGNITUDE & THETA FINAL IN RADIANS
0.12292996624595604160D+02 0.54216214398311040057D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.12292996624595604160D+02 0.31063602661996287679D+03

DIVISION
( A + Bi ) / ( C + Di )
-0.42615832529359735925D-01 -0.29533755263877396573D-02
0.42718047815534614109D-01 0.32107843310231682921D+01
MAGNITUDE & THETA IN DEGREES
0.42718047815534614109D-01 0.18396439109436298054D+03
MAGNITUDE & THETA FINAL IN RADIANS
0.42718047815534614109D-01 0.62139936297462110559D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.42718047815534614109D-01 0.35603560890563704788D+03

SUM
( A + Bi ) + ( C + Di )
-0.15002182541659514925D+02 -0.62211775082955496075D+01
0.16240952268971049932D+02 -0.27484913873336704881D+01
MAGNITUDE & THETA IN DEGREES
0.16240952268971049932D+02 -0.15747695652227574215D+03 This is angle θ13  from before the transformation
MAGNITUDE & THETA FINAL IN RADIANS
0.16240952268971049932D+02 0.58900840409234636041D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.16240952268971049932D+02 0.33747695652227571372D+03 This is angle θ13 after the transformation

θ13 = ( - 0.15747695652227574215D+03 ) * [(1/(3.5)) * (5/8)] = -28.1209 degrees

θ13 Final = (0.33747695652227571372D+03) * [(1/(3.5)) * (5/8)] = 60.2637 degrees

i.e ("ordinary" angle) * (quantum number) = final angle

Second Final Angle is:

These printouts are the results of substituting for Real value X constant C_4 in the main program (more about it later):

ALFA C_4 INVISIBLE
A + Bi
-0.80889091531721078354D+02 0.14782012859895979773D+03
0.16850470482404983841D+03 0.20714972651757492805D+01
MAGNITUDE & THETA IN DEGREES
0.16850470482404983841D+03 0.11868805056746275284D+03
MAGNITUDE & THETA FINAL IN RADIANS
0.16850470482404983841D+03 0.10700953884140438355D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.16850470482404983841D+03 0.61311949432537247162D+02

ALFA C_4 VISIBLE
C + Di
-0.14782012859896008194D+03 -0.80889091531720850980D+02
0.16850470482404998052D+03 -0.26408917152089426139D+01
MAGNITUDE & THETA IN DEGREES
0.16850470482404998052D+03 -0.15131194943253737506D+03
MAGNITUDE & THETA FINAL IN RADIANS
0.16850470482404998052D+03 0.57824843687987357299D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.16850470482404998052D+03 0.33131194943253734664D+03

PRODUCT
( A + Bi ) * ( C + Di )
0.23914071824944068794D+05 -0.15307745290185921476D+05
0.28393835547840189975D+05 -0.56939445003319333338D+00
MAGNITUDE & THETA IN DEGREES
0.28393835547840189975D+05 -0.32623898865074615117D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.28393835547840189975D+05 0.57137908571463933427D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.28393835547840189975D+05 0.32737610113492542041D+03

DIVISION
( A + Bi ) / ( C + Di )
0.19934125913220434222D-14 -0.99999999999999922284D+00
0.99999999999999911182D+00 0.47123889803846914504D+01
MAGNITUDE & THETA IN DEGREES
0.99999999999999911182D+00 0.27000000000000011369D+03
MAGNITUDE & THETA FINAL IN RADIANS
0.99999999999999911182D+00 0.47123889803846914504D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.99999999999999911182D+00 0.27000000000000011369D+03

SUM
( A + Bi ) + ( C + Di )
-0.22870922013068116030D+03 0.66931037067238946747D+02
0.23830163888584669962D+03 0.28568954285731971154D+01
MAGNITUDE & THETA IN DEGREES
0.23830163888584669962D+03 0.16368805056746273863D+03 This is angle θ2 from before the transformation
MAGNITUDE & THETA FINAL IN RADIANS
0.23830163888584669962D+03 0.28469722501659600056D+00
MAGNITUDE & THETA FINAL IN DEGREES
0.23830163888584669962D+03 0.16311949432537268478D+02 This is angle θ23 after the transformation

θ23 = ( 0.16368805056746273863D+03 ) * [(1 / (3.5)2)] = 13.3623 degrees

θ23 Final = (0.16311949432537268478D+02) * [(1 / (3.5)2)] = 1.3316 degrees

i.e ("ordinary" angle) * (quantum number) = final angle

The third final boson angle is:

These printouts are the results of substituting for Real value X constant C_5 in the main program (more about it later):

ALFA C_5 INVISIBLE
A + Bi
-0.87397052630973103078D+04 -0.18283336316201144655D+05
0.20264817663554993487D+05 -0.20167015898078664016D+01
MAGNITUDE & THETA IN DEGREES
0.20264817663554993487D+05 -0.11554848963331410516D+03
MAGNITUDE & THETA FINAL IN RADIANS
0.20264817663554993487D+05 0.51582942433976590735D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.20264817663554993487D+05 0.29554848963331409095D+03

ALFA C_5 VISIBLE
C + Di
0.10089908633354231715D+07 0.10115879306024222169D+07
0.14287661472875305917D+07 0.78668347127292348464D+00
MAGNITUDE & THETA IN DEGREES
0.14287661472875305917D+07 0.45073642716639653827D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.14287661472875305917D+07 0.78668347127292348464D+00
MAGNITUDE & THETA FINAL IN DEGREES
0.14287661472875305917D+07 0.45073642716639653827D+02

PRODUCT
( A + Bi ) * ( C + Di )
0.96769195899043331146D+10 -0.27288699655507392883D+11
0.28953685458641765594D+11 -0.12300181185349430280D+01
MAGNITUDE & THETA IN DEGREES
0.28953685458641765594D+11 -0.70474846916674451336D+02
MAGNITUDE & THETA FINAL IN RADIANS
0.28953685458641765594D+11 0.50531671886446432040D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.28953685458641765594D+11 0.28952515308332556287D+03

DIVISION
( A + Bi ) / ( C + Di )
-0.13379959993924446515D-01 -0.47060190998235119572D-02
0.14183439117750051839D-01 -0.28033850610807897752D+01
MAGNITUDE & THETA IN DEGREES
0.14183439117750051839D-01 -0.16062213234995374478D+03
MAGNITUDE & THETA FINAL IN RADIANS
0.14183439117750051839D-01 0.59449777146705828912D+01
MAGNITUDE & THETA FINAL IN DEGREES
0.14183439117750051839D-01 0.34062213234995374478D+03

SUM
( A + Bi ) + ( C + Di )
0.10002511580723258667D+07 0.99330459428622107953D+06
0.14096653490297417156D+07 0.78191366808625295537D+00
MAGNITUDE & THETA IN DEGREES
0.14096653490297417156D+07 0.44800353124935384130D+02 This is angle θ12 before the transformation
MAGNITUDE & THETA FINAL IN RADIANS
0.14096653490297417156D+07 0.78191366808625295537D+00
MAGNITUDE & THETA FINAL IN DEGREES
0.14096653490297417156D+07 0.44800353124935384130D+02 This is angle θ12 after the transformation

θ12 = (0.44800353124935384130D+02) * (5/8) = 28.0002 degrees

θ12 Final = (0.44800353124935384130D+02) * (5/8) = 28.0002 degrees

i.e ("ordinary" angle) * (quantum number) = final angle

The sum of all six Boson Mixing Angles (three "ordinary" and three after the transformation) is:

θ SUM OF BOSON ANGLES = (-28.1209 + 60.2637) + (13.3623 + 1.3316) + (28.0002 + 28.0002) = 102.8371 degrees

This value will form a quadrangle (360+ degrees)  with Neutrino Mixing Angles.