BOOTSTRAP EQUATION AND CABIBBO ANGLE

It is conjectured that the weak and electromagnetic properties of hadrons are determined by self-consistency requirements. Possible solutions of the c-number bootstrap equations ai=cdjki(ajak+bjbk) and bi=2cdjkibk are studied, where the amplitudes ai and bi represent the matrix elements of unitary octet vector and axial-vector charges, respectively, djki is the completely symmetric invariant tensor of the third order, the unitary spin indices run from 1 to 8, and c is an arbitrary constant. When all expect the amplitudes a3 and a8 are zero, a solution is a3=3a8, which holds for the isoscalar (a8) and isovector (a3) components of electromagnetic interaction. When slight deviations from a3=3a8 are considered, the physical Cabibbo angle can be artifically obtained. More general solutions are considered in which the relative sizes of the amplitudes are obtained in closed form but the Cabibbo angle is 14π. It appears that one must consider slight deviations from a3=3a8 or include higher-order terms in the amplitudes to obtain the physical Cabibbo angle. © 1969 The American Physical Society.