Conventions for the Standard Model

The conventions used in the default Matchete model file for the Standard Model ("SM") yield the following Lagrangian density:

\[\begin{align*} \mathcal{L}_{\mathrm{SM}}=&-\frac{1}{4g_Y^2}B^{\mu\nu}B_{\mu\nu}-\frac{1}{4g_s^2}G^{\mu\nu\,A}G_{\mu\nu}^A-\frac{1}{4g_L^2}W^{\mu\nu\,I}W_{\mu\nu}^I+(D_{\mu}H)^\dagger(D^{\mu}H)+\mu^{2}H^{\dagger}H-\frac{\lambda}{2}(H^{\dagger}H)^2 \\ &+i(\bar{q}\gamma^{\mu}D_{\mu}q)+i(\bar{u}\gamma^{\mu}D_{\mu}u)+i(\bar{d}\gamma^{\mu}D_{\mu}d)+i(\bar{\ell}\gamma^{\mu}D_{\mu}\ell)+i(\bar{e}\gamma^{\mu}D_{\mu}e) \\ &-\big[(\bar{q}_{i}Y_{u}u)\varepsilon^{ij}H_{j}^{\ast}+(\bar{q}Y_{d}d)H+(\bar{\ell}Y_{e}e)H+\mathrm{H.c.}\big] \end{align*}\]

Note the:

• normalization of the gauge fields;
• tachyonic sign of Higgs doublet mass term;
• normalization of the Higgs quartic;
• definition of the Yukawas.