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Yukawa interaction

{title2=$-\bar f_LM_ff_R+\mathrm{h.c.}$}

After a scalar vacuum expectation value, a <Yukawa matrix> produces a bilinear $-\bar f_LM_ff_R+\mathrm{h.c.}$. Independent unitary left/right rotations diagonalize $M_f$ with nonnegative masses. Extra scalar-dependent operators can make the physical scalar coupling matrix fail to diagonalize with the mass matrix.

Fermion mass matrix

Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 47 / 4 / b / iv / Solution

Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 47 / 4 / c / Solution

Fermion mass matrix ( $- \overset{ˉ}{f}_{L} M_{f} f_{R} + h.c.$ )

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Fermion mass matrix (−fˉ​L​Mf​fR​+h.c.)

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Fermion mass matrix ( $- \overset{ˉ}{f}_{L} M_{f} f_{R} + h.c.$ )

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