/*
Matrice de Rotation standard
*/

R12:Matrix(
[cos(t12),sin(t12),0],
[-sin(t12),cos(t12),0],
[0,0,1]
);

R13:Matrix(
[cos(t13),0,sin(t13)*%e^(-%i*delta)],
[0,1,0],
[-sin(t13)*%e^(-%i*delta),0,cos(t13)]
);

R23:Matrix(
[1,0,0],
[0,cos(t23),sin(t23)],
[0,-sin(t23),cos(t23)]
);

R= R23 . R13 . R12 ;


/*
Cabibbo
*/

sin(t12)=lambda;

R12:Matrix(
[sqrt(1-lambda^2),lambda,0],
[-lambda,sqrt(1-lambda^2),0],
[0,0,1]
);

R13:Matrix(
[sqrt(1-(A*lambda^3*(rho-%i*eta))^2),0,A*lambda^3*(rho-%i*eta)],
[0,1,0],
[-A*lambda^3*(rho-%i*eta),0,sqrt(1-(A*lambda^3*(rho-%i*eta))^2)]
);

R23:Matrix(
[1,0,0],
[0,sqrt(1-(A*lambda^2)^2),A*lambda^2],
[0,-A*lambda^2,sqrt(1-(A*lambda^2)^2)]
);

R : R23 . R13 . R12 ;

/*
Matrice CKM
*/

CKM:Matrix(
[Vud,Vus,Vub],
[Vcd,Vcs,Vcb],
[Vtd,Vts,Vtb]
);

Vud:R[1,1];
Vus:R[1,2];
Vub:R[1,3];
Vcd:R[2,1];
Vcs:R[2,2];
Vcb:R[2,3];
Vtd:R[3,1];
Vts:R[3,2];
Vtb:R[3,3];

CKM,
Vud=R[1,1],Vus=R[1,2],Vub=R[1,3],
Vcd=R[2,1],Vcs=R[2,2],Vcb=R[2,3],
Vtd=R[3,1],Vts=R[3,2],Vtb=R[3,3]
;

Taylor(Vud,lambda,0,9);
Taylor(Vus,lambda,0,9);
Taylor(Vub,lambda,0,9);
Taylor(Vcd,lambda,0,9);
Taylor(Vcs,lambda,0,9);
Taylor(Vcb,lambda,0,9);
Taylor(Vtd,lambda,0,9);
Taylor(Vts,lambda,0,9);
Taylor(Vtb,lambda,0,9);

CKM;
%,numer;

ratio:abs(taylor((Vub * Vcs)/(Vcb * Vus),lambda,0,3));

lambda:0.22;
A:0.83;
rho:0.2;
eta:0.32;

/*
UnitaryTriangle:append([
"NoLines: true",
"LargePixels: true",
"TitleText: Unitary Triangle"
],
[0.,0.,1.,0.,eta,rho]);

xgraph_curves([UnitaryTriangle]);
*/

  Frédéric Machefert

Last Modification : 07/10/2007