MSSM superpotential
= MSSM superpotential
{c}
{title2=$W_{\mathrm{MSSM}}$}
With <hypercharge> normalized by $Q_{\mathrm{em}}=T_3+Y$, the renormalizable <R-parity>-conserving <MSSM> <superpotential> is $W=(y_u)_{ij}U_i^c(Q_j\cdot H_u)+(y_d)_{ij}D_i^c(Q_j\cdot H_d)+(y_e)_{ij}E_i^c(L_j\cdot H_d)+\mu H_u\cdot H_d$, with $A\cdot B=\epsilon_{ab}A^aB^b$. Additional renormalizable <R-parity violation> allows $\tfrac12\lambda_{ijk}(L_i\cdot L_j)E_k^c+\lambda'_{ijk}(L_i\cdot Q_j)D_k^c+\tfrac12\lambda''_{ijk}\epsilon_{abc}U_i^{c,a}D_j^{c,b}D_k^{c,c}+\kappa_iL_i\cdot H_u$. The two antisymmetries are $\lambda_{ijk}=-\lambda_{jik}$ and $\lambda''_{ijk}=-\lambda''_{ikj}$. The first, second and fourth additional terms violate <lepton number>; the third violates <baryon number>.