Conventions for the Standard Model Effective Field Theory in the Warsaw basis The conventions used in the default model file ("SMEFT_Warsaw"Standard Model Effective Field Theory in the Warsaw basis are the following:
The renormalizable part of the Lagrangian ($\mathcal{L}_{\mathrm{SM}}$) agrees with the "SM" model file
The dimension-six Warsaw basis Lagrangian is then given by \(\mathcal{L}_{\mathrm{Warsaw}}=\mathcal{L}_{\mathrm{SM}}+\sum_{k}{c_k}{Q_k},\) where the sum runs over all dimension-six operators ($Q_k$) listed below and their Wilson coefficients are denoted $c_k$.
The key differences with respect to the conventions chosen originally for the Warsaw basis [arXiv:1008.4884] are:
We use a different gauge field normalization. Therefore, for every field-strength tensor contained in an operator, we divide this operator by the corresponding gauge coupling. Since we use the minus sign convention for covariant derivatives, we include a minus sign for every gauge coupling in an operator. Our definition of the Levi-Civita symbol ($\epsilon^{\mu\nu\rho\sigma}$) has opposite sign. Thus, we include a minus sign for all operators containing a dual field-strength tensor. This choice ensures that the values of the Wilson coefficients in [arXiv:1008.4884] with their conventions exactly agree with the values of the Wilson coeffiecients determined by Matchete with our convention.
The full list of Baryon- and Lepton-number conserving dimension-six operators defined in the Matchete version of the Warsaw basis is given below. Note: Baryon- and Lepton-number violating operators are also included in the model file but not listed here.
\[\begin{align*} Q_{G} &= -\frac{1}{g_s^3} f^{ABC} G_\mu^{A\nu} G_\nu^{B\rho} G_\rho^{C\mu} \\ Q_{\tilde G} &= \frac{1}{g_s^3} f^{ABC} \tilde G_\mu^{A\nu} G_\nu^{B\rho} G_\rho^{C\mu} \\ Q_{W} &= -\frac{1}{g_L^3} \varepsilon^{IJK} W_\mu^{I\nu} W_\nu^{J\rho} W_\rho^{K\mu} \\ Q_{\tilde W} &= \frac{1}{g_L^3} \varepsilon^{IJK} \tilde W_\mu^{I\nu} W_\nu^{J\rho} W_\rho^{K\mu} \end{align*}\] \[Q_{H}=(H^\dagger H)^3\] \[\begin{align*} Q_{H\Box} &= (H^\dagger H) \Box (H^\dagger H) \\ Q_{HD} &= (H^\dagger D_\mu H)^\ast (H^\dagger D^\mu H) \end{align*}\] \[\begin{align*} Q_{HG} &= \frac{1}{g_s^2} (H^\dagger H) G_{\mu\nu}^A G^{A\mu\nu} \\ Q_{H\tilde G} &= -\frac{1}{g_s^2} (H^\dagger H) \tilde G_{\mu\nu}^A G^{A\mu\nu} \\ Q_{HW} &= \frac{1}{g_L^2} (H^\dagger H) W_{\mu\nu}^I W^{I\mu\nu} \\ Q_{H\tilde{W}} &= -\frac{1}{g_L^2} (H^\dagger H) \tilde W_{\mu\nu}^I W^{I\mu\nu} \\ Q_{HB} &= \frac{1}{g_Y^2} (H^\dagger H) B_{\mu\nu} B^{\mu\nu} \\ Q_{H \tilde B} &= -\frac{1}{g_Y^2} (H^\dagger H) \tilde B_{\mu\nu} B^{\mu\nu} \\ Q_{H W B} &= \frac{1}{g_L g_Y} (H^\dagger \sigma^I H) W_{\mu\nu}^I B^{\mu\nu} \\ Q_{H \tilde W B} &= -\frac{1}{g_L g_Y} (H^\dagger \sigma^I H) \tilde W_{\mu\nu}^I B^{\mu\nu} \end{align*}\] \[\begin{align*} Q_{uH}^{pr} &= (H^\dagger H)(\bar q_p u_r H^c) \\ Q_{dH}^{pr} &= (H^\dagger H)(\bar q_p d_r H) \\ Q_{eH}^{pr} &= (H^\dagger H)(\bar\ell_p e_r H) \end{align*}\] \[\begin{align*} Q_{uG}^{pr} &= -\frac{1}{g_s} (\bar q_p \sigma^{\mu\nu}T^A u_r) H^c G_{\mu\nu}^A \\ Q_{uW}^{pr} &= -\frac{1}{g_L} (\bar q_p \sigma^{\mu\nu}u_r)\sigma^I H^c W_{\mu\nu}^I \\ Q_{uB}^{pr} &= -\frac{1}{g_Y} (\bar q_p \sigma^{\mu\nu}u_r) H^c B_{\mu\nu} \\ Q_{dG}^{pr} &= -\frac{1}{g_s} (\bar q_p \sigma^{\mu\nu}T^A d_r)H G_{\mu\nu}^A \\ Q_{dW}^{pr} &= -\frac{1}{g_L} (\bar q_p \sigma^{\mu\nu}d_r)\sigma^I H W_{\mu\nu}^I \\ Q_{dB}^{pr} &= -\frac{1}{g_Y} (\bar q_p \sigma^{\mu\nu}d_r) H B_{\mu\nu} \\ Q_{eW}^{pr} &= -\frac{1}{g_L} (\bar\ell_p \sigma^{\mu\nu}e_r)\sigma^I H W_{\mu\nu}^I \\ Q_{eB}^{pr} &= -\frac{1}{g_Y} (\bar\ell_p \sigma^{\mu\nu}e_r) H B_{\mu\nu} \end{align*}\] \[\begin{align*} Q_{Hq}^{(1)\,pr} &= (H^\dagger i \overleftrightarrow{D}_\mu H)(\bar q_p \gamma^\mu q_r) \\ Q_{Hq}^{(3)\,pr} &= (H^\dagger i \overleftrightarrow{D}_\mu^I H)(\bar q_p \sigma^I\gamma^\mu q_r) \\ Q_{H u}^{pr} &= (H^\dagger i \overleftrightarrow{D}_\mu H)(\bar u_p \gamma^\mu u_r) \\ Q_{H d}^{pr} &= (H^\dagger i \overleftrightarrow{D}_\mu H)(\bar d_p \gamma^\mu d_r) \\ Q_{Hl}^{(1)\,pr} &= (H^\dagger i \overleftrightarrow{D}_\mu H)(\bar\ell_p \gamma^\mu \ell_r) \\ Q_{Hl}^{(3)\,pr} &= (H^\dagger i \overleftrightarrow{D}_\mu^I H)(\bar\ell_p \sigma^I\gamma^\mu \ell_r) \\ Q_{H e}^{pr} &= (H^\dagger i \overleftrightarrow{D}_\mu H)(\bar e_p \gamma^\mu e_r) \\ Q_{Hud}^{pr} &= i(H^{c\,\dagger} D_\mu H)(\bar u_p \gamma^\mu d_r) \ \ [+\mathrm{H.c.}] \end{align*}\] \[\begin{align*} Q_{qq}^{(1)\,prst} &= (\bar q_p \gamma_\mu q_r)(\bar q_s \gamma^\mu q_t) \\ Q_{qq}^{(3)\,prst} &= (\bar q_p \gamma_\mu \sigma^I q_r)(\bar q_s \gamma^\mu \sigma^I q_t) \\ Q_{ll}^{prst} &= (\bar\ell_p \gamma_\mu \ell_r)(\bar\ell_s \gamma^\mu \ell_t) \\ Q_{l q}^{(1)\,prst} &= (\bar\ell_p \gamma_\mu \ell_r)(\bar q_s \gamma^\mu q_t) \\ Q_{l q}^{(3)\,prst} &= (\bar\ell_p \gamma_\mu \sigma^I \ell_r)(\bar q_s \gamma^\mu \sigma^I q_t) \end{align*}\] \[\begin{align*} Q_{uu}^{prst} &= (\bar u_p \gamma_\mu u_r)(\bar u_s \gamma^\mu u_t) \\ Q_{dd}^{prst} &= (\bar d_p \gamma_\mu d_r)(\bar d_s \gamma^\mu d_t) \\ Q_{ee}^{prst} &= (\bar e_p \gamma_\mu e_r)(\bar e_s \gamma^\mu e_t) \\ Q_{ud}^{(1)\,prst} &= (\bar u_p \gamma_\mu u_r)(\bar d_s \gamma^\mu d_t) \\ Q_{ud}^{(8)\,prst} &= (\bar u_p \gamma_\mu T^A u_r)(\bar d_s \gamma^\mu T^A d_t) \\ Q_{eu}^{prst} &= (\bar e_p \gamma_\mu e_r)(\bar u_s \gamma^\mu u_t) \\ Q_{ed}^{prst} &= (\bar e_p \gamma_\mu e_r)(\bar d_s \gamma^\mu d_t) \end{align*}\] \[\begin{align*} Q_{qu}^{(1)\,prst} &= (\bar q_p \gamma_\mu q_r)(\bar u_s \gamma^\mu u_t) \\ Q_{qu}^{(8)\,prst} &= (\bar q_p \gamma_\mu T^A q_r)(\bar u_s \gamma^\mu T^A u_t) \\ Q_{qd}^{(1)\,prst} &= (\bar q_p \gamma_\mu q_r)(\bar d_s \gamma^\mu d_t) \\ Q_{qd}^{(8)\,prst} &= (\bar q_p \gamma_\mu T^A q_r)(\bar d_s \gamma^\mu T^A d_t) \\ Q_{qe}^{prst} &= (\bar q_p \gamma_\mu q_r)(\bar e_s \gamma^\mu e_t) \\ Q_{lu}^{prst} &= (\bar\ell_p \gamma_\mu \ell_r)(\bar u_s \gamma^\mu u_t) \\ Q_{ld}^{prst} &= (\bar\ell_p \gamma_\mu \ell_r)(\bar d_s \gamma^\mu d_t) \\ Q_{le}^{prst} &= (\bar\ell_p \gamma_\mu \ell_r)(\bar e_s \gamma^\mu e_t) \end{align*}\] \[\begin{align*} Q_{quqd}^{(1)\,prst} &= (\bar q_p^i u_r)\varepsilon_{ij}(\bar q_s^j d_t) \\ Q_{quqd}^{(8)\,prst} &= (\bar q_p^i T^A u_r)\varepsilon_{ij}(\bar q_s^j T^A d_t) \\ Q_{lequ}^{(1)\,prst} &= (\bar \ell_p^i e_r)\varepsilon_{ij}(\bar q_s^j u_t) \\ Q_{l equ}^{(3)\,prst} &= (\bar \ell_p^i \sigma_{\mu\nu} e_r)\varepsilon_{ij}(\bar q_s^j \sigma^{\mu\nu} u_t) \end{align*}\] \[Q_{ledq}^{prst}=(\bar \ell_p^i e_r)(\bar d_s q_{ti})\]