Data for CP-conserving SO(3) parameterization of the neutrino mixing matrix

S uc u e o SO(3) hypo hesis mixing ma ix
CP-conse ing SO(3) pa ame e iza ion o he neu ino mixing ma ix
Ja osław Duda(Jagiellonian U. (main)), Janusz Gluza(Silesia U.), Biswaji Ka maka (Silesia U.)
Suppo ing Ma hema ica ile o : h ps://a xi .o g/abs/2509.25328
SO3 Gene a o s
In[ ]:= Gx =
0 0 0
0 0 -1
0 1 0
; Gy =
0 0 1
0 0 0
-1 0 0
;Gz=
0-1 0
100
000
;
Ro a ion ec o and ma ix exponen
In[ ]:= A= -θx*Gx -θy*Gy -θz*Gz;
A// Ma ixFo m
UExpA =FullSimpli yMa ixExp[A] /.θx
2+θy
2+θz
2-> θ2,(θx)2+θy2+ (θz)2>1;
Ou [ ]//Ma ixFo m=
0θz-θy
-θz0θx
θy-θx0
SO(3) mixing ma ix
In[ ]:= USO3 =Ma ixFo mUExpA[[1, 1]] /.
θx
2+θy
2+θz
2
-> θ,
UExpA[[1, 2]] /.θx
2+θy
2+θz
2-> θ, UExpA[[1, 3]] /.θx
2+θy
2+θz
2-> θ,
UExpA[[2, 1]] /.θx
2+θy
2+θz
2-> θ, UExpA[[2, 2]] /.θx
2+θy
2+θz
2-> θ,
UExpA[[2, 3]] /.θx
2+θy
2+θz
2-> θ,UExpA[[3, 1]] /.θx
2+θy
2+θz
2-> θ,
UExpA[[3, 2]] /.θx
2+θy
2+θz
2-> θ, UExpA[[3, 3]] /.θx
2+θy
2+θz
2-> θ;
USO3 // Ma ixFo m
Ou [ ]//Ma ixFo m=
θx
2+Cos[θ]θy
2+θz
2
θ2
-((-1+Cos[θ]) θxθy)+θSin[θ]θz
θ2-θSin[θ]θy+(-1+Cos[θ]) θxθz
θ2
-(-1+Cos[θ]) θxθy+θSin[θ]θz
θ2
θy
2+Cos[θ]θx
2+θz
2
θ2
θSin[θ]θx-(-1+Cos[θ]) θyθz
θ2
θSin[θ]θy-(-1+Cos[θ]) θxθz
θ2-θSin[θ]θx+(-1+Cos[θ]) θyθz
θ2
Cos[θ]θx
2+θy
2+θz
2
θ2
2SO3.nb