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Changed:  
< < 
Under construction
The CabibboKobayashiMaskawa ( CKM) matrixis a 3x3 unitary matrix which originates from the misalignment in flavour space of the up and down components of the quark doublet of the Standard Model ( SM). In the quark mass eigenstate basis, the CKM matrix appears in the SM chargedcurrent interaction Lagrangianwhere the quark fields are and , while is the weak coupling constant and is the field which creates the vector boson. The CKM matrix elements are the only flavournondiagonal and CPviolating couplings present in the SM. In general, the CKM matrix can be parametrized using three rotation angles and one phase. The parametrization is however not unique. The standard parametrization, advocated by the PDG, uses in and in defined so that  
> > 
 
\sin\theta_{12}\cos\theta_{23}\cos\theta_{12}\sin\theta_{13}\sin\theta_{23}\, e^{i\delta} & \cos\theta_{12}\cos\theta_{23}\sin\theta_{12}\sin\theta_{13}\sin\theta_{23}\, e^{i\delta} & \cos\theta_{13}\sin\theta_{23}\  
Changed:  
< < 
\sin\theta_{12}\sin\theta_{23}\cos\theta_{12}\sin\theta_{13}\cos\theta_{23}\, e^{i\delta} & \cos\theta_{12}\sin\theta_{23}\sin\theta_{12}\sin\theta_{13}\cos\theta_{23}\, e^{i\delta} & \cos\theta_{13}\cos\theta_{23}\end{array}\right)\,. The relations induced by the unitarity of the CKM matrix include six "triangular" relations, among which is referred to as the Unitarity Triangle ( UT). It can be rewritten as with , and , are the nontrivial sides and angles of the normalized UT. The third side is the unit vector and the third angle is given by . The UT is determined by one complex number namely by the coordinates in the complex plane of its only nontrivial apex (the others being (0,0) and (1,0)). Several experimental constraints can be conveniently represented on this plane and used to determine the UT, as shown in section Fit Results. We start extracting the CKM parameters from the measurements of and using
 
> > 
\sin\theta_{12}\sin\theta_{23}\cos\theta_{12}\sin\theta_{13}\cos\theta_{23}\, e^{i\delta} & \cos\theta_{12}\sin\theta_{23}\sin\theta_{12}\sin\theta_{13}\cos\theta_{23}\, e^{i\delta} & \cos\theta_{13}\cos\theta_{23}\end{array}\right)\,.
The relations induced by the unitarity of the CKM matrix include six "triangular" relations, among which
 
\cos\theta_{12}=\frac{\vert V_{ud}\vert}{\cos\theta_{13}}, & \sin\theta_{12}=\sqrt{1\cos^2\theta_{12}},\\sin\theta_{23}=\frac{\vert V_{cb}\vert}{\cos\theta_{13}}, & \cos\theta_{23}=\sqrt{1\sin^2\theta_{23}},\end{array} ~~\delta=2\arctan\left(\frac{1\mp\sqrt{1(a^21)\tan^2\gamma}}{(a1)\tan\gamma}\right), ~a=\frac{\cos\theta_{12}\sin\theta_{13}\sin\theta_{23}}{\sin\theta_{12}\cos\theta_{23}}.  
Changed:  
< < 
The sign in the formula for corresponds to . Additional constraints, discussed in section Constraints, are then applied using the method described in section Statistical Method. Fit Results are also given in the popular Wolfenstein parametrization which allows for a transparent expansion of the CKM matrix in terms of the sine of the small Cabibbo angle . The Wolfenstain parameters are defined by the following equations The CKM matrix can be expanded as The exact and expanded relations between the UT apex coordinates and the Wolfenstein parameters are given by At the lowest order in , and coincide with and .  
> > 
The sign in the formula for corresponds to . Additional constraints, discussed in section Constraints, are then applied using the method described in section Statistical Method. Fit Results are also given in the popular Wolfenstein parametrization which allows for a transparent expansion of the CKM matrix in terms of the sine of the small Cabibbo angle . The Wolfenstain parameters are defined by the following equations

Line: 1 to 1  

Under construction  
Changed:  
< < 
The CabibboKobayashiMaskawa ( CKM) matrixis a 3x3 unitary matrix which originates from the misalignment in flavour space of the up and down components of the quark doublet of the Standard Model ( SM). In the quark mass eigenstate basis, the CKM matrix appears in the SM chargedcurrent interaction Lagrangianwhere the quark fields are and , while is the weak coupling constant and is the field which creates the vector boson. The CKM matrix elements are the only flavour and CPviolating couplings present in the SM. In general, the CKM matrix can be parametrized using three rotation angles and one phase. The parametrization is however not unique. The standard parametrization, advocated by the PDG, uses in and in defined so that  
> > 
The CabibboKobayashiMaskawa ( CKM) matrixis a 3x3 unitary matrix which originates from the misalignment in flavour space of the up and down components of the quark doublet of the Standard Model ( SM). In the quark mass eigenstate basis, the CKM matrix appears in the SM chargedcurrent interaction Lagrangianwhere the quark fields are and , while is the weak coupling constant and is the field which creates the vector boson. The CKM matrix elements are the only flavournondiagonal and CPviolating couplings present in the SM. In general, the CKM matrix can be parametrized using three rotation angles and one phase. The parametrization is however not unique. The standard parametrization, advocated by the PDG, uses in and in defined so that  
\sin\theta_{12}\cos\theta_{23}\cos\theta_{12}\sin\theta_{13}\sin\theta_{23}\, e^{i\delta} & \cos\theta_{12}\cos\theta_{23}\sin\theta_{12}\sin\theta_{13}\sin\theta_{23}\, e^{i\delta} & \cos\theta_{13}\sin\theta_{23}\\sin\theta_{12}\sin\theta_{23}\cos\theta_{12}\sin\theta_{13}\cos\theta_{23}\, e^{i\delta} & \cos\theta_{12}\sin\theta_{23}\sin\theta_{12}\sin\theta_{13}\cos\theta_{23}\, e^{i\delta} & \cos\theta_{13}\cos\theta_{23}\end{array}\right)\,. The relations induced by the unitarity of the CKM matrix include six "triangular" relations, among which is referred to as the Unitarity Triangle ( UT). It can be rewritten as with , and , are the nontrivial sides and angles of the normalized UT. The third side is the unit vector and the third angle is given by . The UT is determined by one complex number namely by the coordinates in the complex plane of its only nontrivial apex (the others being (0,0) and (1,0)). Several experimental constraints can be conveniently represented on this plane and used to determine the UT, as shown in section Fit Results. We start extracting the CKM parameters from the measurements of and using
 
Changed:  
< < 
The sign in the formula for corresponds to . Additional constraints, discussed in section Constraints, are then applied using the method described in section Statistical Method. Fit Results are also given in the popular Wolfenstein parametrization which allows for a transparent expansion of the CKM matrix in terms of the sine of the small Cabibbo angle . The Wolfenstain parameters are defined by the following equations The CKM matrix can be expanded as The exact and expanded relations between and the Wolfenstein parameters are given by At the lowest order in , and coincide with the UT apex coordinates and .  
> > 
The sign in the formula for corresponds to . Additional constraints, discussed in section Constraints, are then applied using the method described in section Statistical Method. Fit Results are also given in the popular Wolfenstein parametrization which allows for a transparent expansion of the CKM matrix in terms of the sine of the small Cabibbo angle . The Wolfenstain parameters are defined by the following equations The CKM matrix can be expanded as The exact and expanded relations between the UT apex coordinates and the Wolfenstein parameters are given by At the lowest order in , and coincide with and . 
Line: 1 to 1  

Under construction  
Changed:  
< < 
The CabibboKobayashiMaskawa ( CKM) matrixis a 3x3 unitary matrix which originates from the disalignment in flavour space of the up and down components of the quark doublet of the Standard Model ( SM). In the quark mass eigenstate basis, the CKM matrix appears in the SM chargedcurrent interaction Lagrangianwhere the quark fields are and , while is the weak coupling constant and is the field which creates the vector boson. The CKM matrix elements are the only flavour and CPviolating couplings present in the SM. In general, the CKM matrix can be parametrized using three rotation angles and one phase. The parametrization is however not unique. The standard parametrization, advocated by the PDG, uses in and in defined so that  
> > 
The CabibboKobayashiMaskawa ( CKM) matrixis a 3x3 unitary matrix which originates from the misalignment in flavour space of the up and down components of the quark doublet of the Standard Model ( SM). In the quark mass eigenstate basis, the CKM matrix appears in the SM chargedcurrent interaction Lagrangianwhere the quark fields are and , while is the weak coupling constant and is the field which creates the vector boson. The CKM matrix elements are the only flavour and CPviolating couplings present in the SM. In general, the CKM matrix can be parametrized using three rotation angles and one phase. The parametrization is however not unique. The standard parametrization, advocated by the PDG, uses in and in defined so that  
\sin\theta_{12}\cos\theta_{23}\cos\theta_{12}\sin\theta_{13}\sin\theta_{23}\, e^{i\delta} & \cos\theta_{12}\cos\theta_{23}\sin\theta_{12}\sin\theta_{13}\sin\theta_{23}\, e^{i\delta} & \cos\theta_{13}\sin\theta_{23}\\sin\theta_{12}\sin\theta_{23}\cos\theta_{12}\sin\theta_{13}\cos\theta_{23}\, e^{i\delta} & \cos\theta_{12}\sin\theta_{23}\sin\theta_{12}\sin\theta_{13}\cos\theta_{23}\, e^{i\delta} & \cos\theta_{13}\cos\theta_{23}\end{array}\right)\,. The relations induced by the unitarity of the CKM matrix include six "triangular" relations, among which is referred to as the Unitarity Triangle ( UT). It can be rewritten as with , and , are the nontrivial sides and angles of the normalized UT. The third side is the unit vector and the third angle is given by . The UT is determined by one complex number namely by the coordinates in the complex plane of its only nontrivial apex (the others being (0,0) and (1,0)). Several experimental constraints can be conveniently represented on this plane and used to determine the UT, as shown in section Fit Results. We start extracting the CKM parameters from the measurements of and using

Line: 1 to 1  

Under construction
The CabibboKobayashiMaskawa ( CKM) matrixis a 3x3 unitary matrix which originates from the disalignment in flavour space of the up and down components of the quark doublet of the Standard Model ( SM). In the quark mass eigenstate basis, the CKM matrix appears in the SM chargedcurrent interaction Lagrangianwhere the quark fields are and , while is the weak coupling constant and is the field which creates the vector boson. The CKM matrix elements are the only flavour and CPviolating couplings present in the SM. In general, the CKM matrix can be parametrized using three rotation angles and one phase. The parametrization is however not unique. The standard parametrization, advocated by the PDG, uses in and in defined so that  
Line: 7 to 7  
\sin\theta_{23}=\frac{\vert V_{cb}\vert}{\cos\theta_{13}}, & \cos\theta_{23}=\sqrt{1\sin^2\theta_{23}},\end{array} ~~\delta=2\arctan\left(\frac{1\mp\sqrt{1(a^21)\tan^2\gamma}}{(a1)\tan\gamma}\right), ~a=\frac{\cos\theta_{12}\sin\theta_{13}\sin\theta_{23}}{\sin\theta_{12}\cos\theta_{23}}.  
Changed:  
< < 
The sign in the formula for corresponds to . Additional constraints, discussed in section Constraints, are then applied using the method described in section Statistical Method. Fit Results are also given in the popular Wolfenstein parametrization which allows for a transparent expansion of the CKM matrix in terms of the small Cabibbo angle . The Wolfenstain parameters are defined by the following equations At the first order, is the Cabibbo angle and and coincide with the UT coordinates and . The exact relation between and is given by </latex></latex>  
> > 
The sign in the formula for corresponds to . Additional constraints, discussed in section Constraints, are then applied using the method described in section Statistical Method. Fit Results are also given in the popular Wolfenstein parametrization which allows for a transparent expansion of the CKM matrix in terms of the sine of the small Cabibbo angle . The Wolfenstain parameters are defined by the following equations The CKM matrix can be expanded as The exact and expanded relations between and the Wolfenstein parameters are given by At the lowest order in , and coincide with the UT apex coordinates and . 
Line: 1 to 1  

Under construction  
Changed:  
< < 
The CabibboKobayashiMaskawa ( CKM) matrixis a 3x3 unitary matrix which originates from the disalignment in flavour space of the up and down components of the quark doublet of the Standard Model ( SM). In the quark mass eigenstate basis, the CKM matrix appears in the SM chargedcurrent interaction Lagrangianwhere the quark fields are and , while is the weak coupling constant and is the field which creates the vector boson. The CKM matrix elements are the only flavour and CPviolating couplings present in the SM. In general, the CKM matrix can be parametrized using three rotation angles and one phase. The parametrization is however not unique. The standard parametrization, advocated by the PDG, uses in and in defined so that  
> > 
The CabibboKobayashiMaskawa ( CKM) matrixis a 3x3 unitary matrix which originates from the disalignment in flavour space of the up and down components of the quark doublet of the Standard Model ( SM). In the quark mass eigenstate basis, the CKM matrix appears in the SM chargedcurrent interaction Lagrangianwhere the quark fields are and , while is the weak coupling constant and is the field which creates the vector boson. The CKM matrix elements are the only flavour and CPviolating couplings present in the SM. In general, the CKM matrix can be parametrized using three rotation angles and one phase. The parametrization is however not unique. The standard parametrization, advocated by the PDG, uses in and in defined so that  
\sin\theta_{12}\cos\theta_{23}\cos\theta_{12}\sin\theta_{13}\sin\theta_{23}\, e^{i\delta} & \cos\theta_{12}\cos\theta_{23}\sin\theta_{12}\sin\theta_{13}\sin\theta_{23}\, e^{i\delta} & \cos\theta_{13}\sin\theta_{23}\  
Changed:  
< < 
\sin\theta_{12}\sin\theta_{23}\cos\theta_{12}\sin\theta_{13}\cos\theta_{23}\, e^{i\delta} & \cos\theta_{12}\sin\theta_{23}\sin\theta_{12}\sin\theta_{13}\cos\theta_{23}\, e^{i\delta} & \cos\theta_{13}\cos\theta_{23}\end{array}\right)\,. We start extracting the CKM parameters from the measurements of and using
 
> > 
\sin\theta_{12}\sin\theta_{23}\cos\theta_{12}\sin\theta_{13}\cos\theta_{23}\, e^{i\delta} & \cos\theta_{12}\sin\theta_{23}\sin\theta_{12}\sin\theta_{13}\cos\theta_{23}\, e^{i\delta} & \cos\theta_{13}\cos\theta_{23}\end{array}\right)\,. The relations induced by the unitarity of the CKM matrix include six "triangular" relations, among which is referred to as the Unitarity Triangle ( UT). It can be rewritten as with , and , are the nontrivial sides and angles of the normalized UT. The third side is the unit vector and the third angle is given by . The UT is determined by one complex number namely by the coordinates in the complex plane of its only nontrivial apex (the others being (0,0) and (1,0)). Several experimental constraints can be conveniently represented on this plane and used to determine the UT, as shown in section Fit Results. We start extracting the CKM parameters from the measurements of and using
 
\cos\theta_{12}=\frac{\vert V_{ud}\vert}{\cos\theta_{13}}, & \sin\theta_{12}=\sqrt{1\cos^2\theta_{12}},\\sin\theta_{23}=\frac{\vert V_{cb}\vert}{\cos\theta_{13}}, & \cos\theta_{23}=\sqrt{1\sin^2\theta_{23}},\end{array} ~~\delta=2\arctan\left(\frac{1\mp\sqrt{1(a^21)\tan^2\gamma}}{(a1)\tan\gamma}\right), ~a=\frac{\cos\theta_{12}\sin\theta_{13}\sin\theta_{23}}{\sin\theta_{12}\cos\theta_{23}}.  
Changed:  
< < 
The sign in the formula for corresponds to . Additional constraints are then applied using the method described in the section Statistical Method. Results are also given in the popular Wolfenstein parametrization which allows for a transparent expansion of the CKM matrix in terms of the small Cabibbo angle . The Wolfenstain parameters are defined by the following equations The relations induced by the unitarity of the CKM matrix include six "triangular" relations, among which is referred to as the Unitarity Triangle ( UT). It can be rewritten as with  
> > 
The sign in the formula for corresponds to . Additional constraints, discussed in section Constraints, are then applied using the method described in section Statistical Method. Fit Results are also given in the popular Wolfenstein parametrization which allows for a transparent expansion of the CKM matrix in terms of the small Cabibbo angle . The Wolfenstain parameters are defined by the following equations At the first order, is the Cabibbo angle and and coincide with the UT coordinates and . The exact relation between and is given by </latex></latex> 
Line: 1 to 1  

Under construction
The CabibboKobayashiMaskawa ( CKM) matrixis a 3x3 unitary matrix which originates from the disalignment in flavour space of the up and down components of the quark doublet of the Standard Model ( SM). In the quark mass eigenstate basis, the CKM matrix appears in the SM chargedcurrent interaction Lagrangianwhere the quark fields are and , while is the weak coupling constant and is the field which creates the vector boson. The CKM matrix elements are the only flavour and CPviolating couplings present in the SM. In general, the CKM matrix can be parametrized using three rotation angles and one phase. The parametrization is however not unique. The standard parametrization, advocated by the PDG, uses in and in defined so that 
Line: 1 to 1  

Under construction
The CabibboKobayashiMaskawa ( CKM) matrixis a 3x3 unitary matrix which originates from the disalignment in flavour space of the up and down components of the quark doublet of the Standard Model ( SM). In the quark mass eigenstate basis, the CKM matrix appears in the SM chargedcurrent interaction Lagrangianwhere the quark fields are and , while is the weak coupling constant and is the field which creates the vector boson. The CKM matrix elements are the only flavour and CPviolating couplings present in the SM. In general, the CKM matrix can be parametrized using three rotation angles and one phase. The parametrization is however not unique. The standard parametrization, advocated by the PDG, uses in and in defined so that  
Line: 7 to 7  
\sin\theta_{23}=\frac{\vert V_{cb}\vert}{\cos\theta_{13}}, & \cos\theta_{23}=\sqrt{1\sin^2\theta_{23}},\end{array} ~~\delta=2\arctan\left(\frac{1\mp\sqrt{1(a^21)\tan^2\gamma}}{(a1)\tan\gamma}\right), ~a=\frac{\cos\theta_{12}\sin\theta_{13}\sin\theta_{23}}{\sin\theta_{12}\cos\theta_{23}}.  
Changed:  
< < 
The sign in the formula for corresponds to . Additional constraints are then applied using the method described in the section Statistical Method. Results are also given in the popular Wolfenstein parametrization which allows for a transparent expansion of the CKM matrix in terms of the small Cabibbo angle . The Wolfenstain parameters are defined by the following equations The relations induced by the unitarity of the CKM matrix include six "triangular" relations, among which is referred to as the Unitarity Triangle ( UT). It can be rewritten as with  
> > 
The sign in the formula for corresponds to . Additional constraints are then applied using the method described in the section Statistical Method. Results are also given in the popular Wolfenstein parametrization which allows for a transparent expansion of the CKM matrix in terms of the small Cabibbo angle . The Wolfenstain parameters are defined by the following equations The relations induced by the unitarity of the CKM matrix include six "triangular" relations, among which is referred to as the Unitarity Triangle ( UT). It can be rewritten as with 
Line: 1 to 1  

Under construction  
Changed:  
< < 
The CabibboKobayashiMaskawa ( CKM) matrixis a 3x3 unitary matrix which originates from the disalignment in flavour space of the up and down components of the quark doublet of the Standard Model ( SM). In the mass eigenstate basis, the CKM matrix appears in the SM charged current interactionThe CKM matrix elements are the only flavour and CPviolating couplings present in the SM.  
> > 
The CabibboKobayashiMaskawa ( CKM) matrixis a 3x3 unitary matrix which originates from the disalignment in flavour space of the up and down components of the quark doublet of the Standard Model ( SM). In the quark mass eigenstate basis, the CKM matrix appears in the SM chargedcurrent interaction Lagrangianwhere the quark fields are and , while is the weak coupling constant and is the field which creates the vector boson. The CKM matrix elements are the only flavour and CPviolating couplings present in the SM. In general, the CKM matrix can be parametrized using three rotation angles and one phase. The parametrization is however not unique. The standard parametrization, advocated by the PDG, uses in and in defined so thatWe start extracting the CKM parameters from the measurements of and using  
\cos\theta_{12}=\frac{\vert V_{ud}\vert}{\cos\theta_{13}}, & \sin\theta_{12}=\sqrt{1\cos^2\theta_{12}},\\sin\theta_{23}=\frac{\vert V_{cb}\vert}{\cos\theta_{13}}, & \cos\theta_{23}=\sqrt{1\sin^2\theta_{23}},\end{array} ~~\delta=2\arctan\left(\frac{1\mp\sqrt{1(a^21)\tan^2\gamma}}{(a1)\tan\gamma}\right), ~a=\frac{\cos\theta_{12}\sin\theta_{13}\sin\theta_{23}}{\sin\theta_{12}\cos\theta_{23}}.  
Changed:  
< <  The sign in the formula for corresponds to .  
> > 
The sign in the formula for corresponds to . Additional constraints are then applied using the method described in the section Statistical Method. Results are also given in the popular Wolfenstein parametrization which allows for a transparent expansion of the CKM matrix in terms of the small Cabibbo angle . The Wolfenstain parameters are defined by the following equations The relations induced by the unitarity of the CKM matrix include six "triangular" relations, among which is referred to as the Unitarity Triangle ( UT). It can be rewritten as with 
Line: 1 to 1  

Under construction  
Changed:  
< < 
 
> > 
The CabibboKobayashiMaskawa ( CKM) matrixis a 3x3 unitary matrix which originates from the disalignment in flavour space of the up and down components of the quark doublet of the Standard Model ( SM). In the mass eigenstate basis, the CKM matrix appears in the SM charged current interactionThe CKM matrix elements are the only flavour and CPviolating couplings present in the SM. 
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Under construction  
Added:  
> > 
