= Four-fermion matching for squark-mediated proton decay
{title2=$C_6=\lambda'\lambda''^*/M_{\widetilde d}^2$}
The <R-parity violation> vertices from $LQD$ and $UDD$ can both contain the same down-type <squark>. Write its linear couplings as $-\widetilde d A-\widetilde d^*A^\dagger$ and its mass term as $-M^2|\widetilde d|^2$. Eliminating it gives $A^\dagger A/M^2$. The cross term is $(\lambda'\lambda''^*/M^2)(\nu d_L-eu_L)(u^{c\dagger}d^{c\dagger})+\mathrm{h.c.}$, with the color <Levi-Civita symbol> contracting the three quarks. It changes <baryon number> and <lepton number> together and supplies the dimension-six <proton-decay operator> for $p\to e^+\pi^0$. The two down-flavor indices in $UDD$ must differ, so strange- or bottom-squark exchange is allowed but identical down flavors vanish.
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