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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

Goldstino null vector with F-term and D-term breaking

Past exam of the gauge field theory course of the University of Cambridge / 2014 / Paper 1 / 2 / Solution

Past exam of the gauge field theory course of the University of Cambridge / 2014 / Paper 1 / 3 / c / Solution

Past exam of the groups and representations course of the University of Oxford / 2021 / 2 / e / Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 53 / 3 / Solution

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

Past exam of the quantum field theory course of the University of Oxford / 2022 / 3 / d / Solution

Quark mixing

S3-invariant Yukawa matrix for a doublet and a sign singlet

Unitary flavour symmetry of degenerate Dirac fields

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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