Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2012/iii/paper-45/2/g/solution

The remaining non-derivative component term in the Lagrangian is the Yukawa interaction
Equivalently the interaction Hamiltonian has the opposite displayed sign. The first term is the two-component fermion mass, and the second its scalar-fermion interaction. A phase redefinition of makes the mass coefficient nonnegative, so the physical Weyl spinor mass is
It is again independent of , the choice of root and any sign of a real . This distinguishes the complex bilinear coefficient from the nonnegative physical mass. In the pure-linear supersymmetry-breaking branch , the fermion is the massless Goldstino.

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