D^{\mu}(\overline{f}\gamma^{\nu}Mf)-D^{\nu}(\overline{f}\gamma^{\mu}Mf)\,=\,i\,\left[\overline{f}\sigma^{\mu\nu}M\,(/\\!\\!\\!\\!Df)\,-\,(\overline{/\\!\\!\\!\\!Df})\sigma^{\mu\nu}Mf\pm\epsilon^{\mu\nu\rho\eta}\,\overline{f}\gamma_{\rho}M\,\overleftrightarrow{D}_{\eta}f\right]\;.$
(210)

where $M$ can be the identity, a Pauli matrix $\tau^{I}$ or a $T^{A}$ matrix
and the upper (lower) sign corresponds to right (left)-handed fermions.

  * •

Lorentz scalar fermionic Fierz identities:

$\displaystyle(\overline{l}_{a},e_{b})\,(\overline{e}_{c}\,{l_{d}})\,=\,-\,\frac{1}{2}\,(\overline{l}_{a}\,\gamma^{\mu}{l_{d}})\,(\overline{e}_{c}\,\gamma_{\mu}\,e_{b})\;,$
(211)
$\displaystyle(\overline{l}^{j}_{a},e_{b})\,(\overline{e}_{c}\,{l_{d}}_{k})\,=\,-\,\frac{1}{4}\,\left[(\overline{l}_{a}\,\gamma^{\mu}{l_{d}})\,(\overline{e}_{c}\,\gamma_{\mu}\,e_{b})\,\delta^{j}_{k}\,+\,(\overline{l}_{a}\,\gamma^{\mu}\,\tau^{I}{l_{d}})\,(\overline{e}_{c}\,\gamma_{\mu}\,e_{b})\,(\tau^{I})^{j}_{k}\right]\;,$
(212)
$\displaystyle(\overline{q}_{a}\,u_{b})\,(\overline{u}_{c}\,{q_{d}})=-\frac{1}{6}\,(\overline{q}_{a}\,\gamma^{\mu}{q_{d}})\,(\overline{u}_{c}\,\gamma_{\mu}\,u_{b})\,-\;(\overline{q}_{a}\,\gamma^{\mu}T^{A}\,{q_{d}})\,(\overline{u}_{c}\,\gamma_{\mu}\;T^{A}\,u_{b})\;,$
(213)
$\displaystyle(\overline{q}_{a}^{j}\,u_{b})\,(\overline{u}_{c}\,{q_{d}}_{k})=-\,\frac{\delta^{j}_{k}}{2}\,\left[\frac{1}{6}(\overline{q}_{a}\,\gamma^{\mu}{q_{d}})\,(\overline{u}_{c}\,\gamma_{\mu}u_{b})\,+\;(\overline{q}_{a}\,\gamma^{\mu}T^{A}\,{q_{d}})\,(\overline{u}_{c}\,\gamma_{\mu}\;T^{A}u_{b})\,\right]\;,$
$\displaystyle\hskip
71.13188pt-\,\frac{(\tau)^{j}_{k}}{2}\,\left[\frac{1}{6}(\overline{q}_{a}\,\gamma^{\mu}\tau^{I}{q_{d}})\,(\overline{u}_{c}\,\gamma_{\mu}\,u_{b})\,+\;(\overline{q}_{a}\,\gamma^{\mu}T^{A}\,\tau^{I}\,{q_{d}})\,(\overline{u}_{c}\,\gamma_{\mu}\;T^{A}\,u_{b})\,\right]\,\;,$
(214)
$\displaystyle(\overline{f}_{a}\gamma^{\mu}f_{a})\,(\overline{f}_{b}\gamma_{\mu}f_{b})=(\overline{f}_{a}\gamma^{\mu}f_{b})\,(\overline{f}_{b}\gamma_{\mu}f_{a})\;,\hskip
170.71652pt{\rm for}\;f=q,l,u,d,e,$ (215)
$\displaystyle(\bar{l}_{a}\gamma^{\mu}\tau^{I}l_{a})\,(\bar{l}_{b}\gamma_{\mu}\tau^{I}l_{b})=2\;(\bar{l}_{a}\gamma^{\mu}l_{b})\,(\bar{l}_{b}\gamma_{\mu}l_{a})\,-\,(\bar{l}_{a}\gamma^{\mu}l_{a})\,(\bar{l}_{b}\gamma_{\mu}l_{b})\;,$
(216)
$\displaystyle(\overline{f}_{a}\gamma^{\mu}T^{A}f_{a})\,(\overline{f}_{b}\gamma_{\mu}T^{A}f_{b})\,=\,-\,\frac{1}{6}\,(\overline{f}_{a}\gamma^{\mu}f_{a})\,(\overline{f}_{b}\gamma_{\mu}f_{b})\,+\,\frac{1}{2}\,(\overline{f}_{a}\gamma^{\mu}f_{b})\,(\overline{f}_{b}\gamma_{\mu}f_{a})\;,\hskip
28.45274pt{\rm for}\;f=q,u,d\;.$ (217)

  * •

Lorentz tensor fermionic Fierz identities: In the expressions below,
$S^{\mu\nu}$ represent a piece which is symmetric under the exchange
$\mu\leftrightarrow\nu$ and which will not contribute to the operators for
which these relations are being used, so for simplicity we have not included
their explicit forms. They can be found in Ref. [46].

$\displaystyle(\overline{e}_{a}\gamma^{\mu}e_{a})\,(\overline{e}_{b}\gamma^{\nu}e_{b})\,\,=\,S_{e}^{\mu\nu}\,{+}\,\frac{1}{2}\,i\,\epsilon^{\mu\nu\rho\sigma}\,(\overline{e}_{a}\gamma^{\rho}e_{b})\,(\overline{e}_{b}\gamma^{\sigma}e_{a})\;,$
(219)
$\displaystyle(\bar{l}_{a}\gamma^{\mu}l_{a})\,(\bar{l}_{b}\gamma^{\nu}l_{b})\,\,=\,S_{l}^{\mu\nu}\,{-}\,\,\frac{1}{2}\,i\,\epsilon^{\mu\nu\rho\sigma}\,(\overline{l}_{a}\gamma^{\rho}l_{b})\,(\bar{l}_{b}\gamma^{\sigma}l_{a})\;,$
(220)
$\displaystyle(\overline{u}_{a}\gamma^{\mu}u_{a})\,(\overline{u}_{b}\gamma^{\nu}u_{b})\,\,=\,S_{u}^{\mu\nu}\,{+}\,\frac{1}{2}\,i\,\epsilon^{\mu\nu\rho\sigma}\,\left[\frac{1}{3}\,(\overline{u}_{a}\gamma^{\rho}u_{b})\,(\overline{u}_{b}\gamma^{\sigma}u_{b})\,+\,2\,(\overline{u}_{a}\gamma^{\rho}T^{A}u_{b})\,(\overline{u}_{b}\gamma^{\sigma}T^{A}u_{a})\right]\;,$
(221)
$\displaystyle(\overline{q}_{a}\gamma^{\mu}q_{a})\,(\overline{q}_{b}\gamma^{\nu}q_{b})\,\,=\,S_{q}^{\mu\nu}\,{-}\,\frac{1}{2}\,i\,\epsilon^{\mu\nu\rho\sigma}\,\left[\frac{1}{3}\,(\overline{q}_{a}\gamma^{\rho}q_{b})\,(\overline{q}_{b}\gamma^{\sigma}q_{a})\,+\,2\,(\overline{q}_{a}\gamma^{\rho}T^{A}q_{b})\,(\overline{q}_{b}\gamma^{\sigma}T^{A}q_{a})\right]\;,$
(222)
$\displaystyle(\bar{l}_{a}\gamma^{\mu}\tau^{I}l_{a})\,(\bar{l}_{b}\gamma^{\nu}\tau^{J}l_{b})\,\epsilon^{IJK}\,=\,{S^{K}_{l}}^{\mu\nu}\\!{+}\,\,\epsilon^{\mu\nu\rho\sigma}\,(\overline{l}_{a}\gamma^{\rho}\tau^{K}l_{b})\,(\bar{l}_{b}\gamma^{\sigma}l_{b})\;,$
(223)
$\displaystyle(\overline{q}_{a}\gamma^{\mu}\tau^{I}q_{a})\,(\overline{q}_{b}\gamma^{\nu}\tau^{J}q_{b})\,\epsilon^{IJK}\\!\\!={S^{K}_{q}}^{\mu\nu}\\!\\!{+}\,\epsilon^{\mu\nu\rho\sigma}\left[\frac{1}{3}\,(\overline{q}_{a}\gamma^{\rho}\tau^{K}q_{b})\,(\overline{q}_{b}\gamma^{\sigma}q_{b})\,+\,2\,(\overline{q}_{a}\gamma^{\rho}T^{A}\tau^{K}q_{b})\,(\overline{q}_{b}\gamma^{\sigma}T^{A}q_{b})\right]\;,$
(224)
$\displaystyle(\overline{u}_{a}\gamma^{\mu}T^{A}u_{a})\,(\overline{u}_{b}\gamma^{\nu}T^{B}u_{b})\,f^{ABC}=\,{S_{u}^{C}}^{\mu\nu}\,{-}\,\frac{1}{2}\,\epsilon^{\mu\nu\rho\sigma}\,(\overline{u}_{a}\gamma^{\rho}T^{C}u_{b})\,(\overline{u}_{b}\gamma^{\sigma}u_{a})\;,$
(225)
$\displaystyle(\overline{q}_{a}\gamma^{\mu}T^{A}q_{a})\,(\overline{q}_{b}\gamma^{\nu}T^{B}q_{b})\,f^{ABC}=\,{S_{q}^{C}}^{\mu\nu}\,{+}\,\frac{1}{2}\,\epsilon^{\mu\nu\rho\sigma}\,(\overline{q}_{a}\gamma^{\rho}T^{C}q_{b})\,(\overline{q}_{b}\gamma^{\sigma}q_{a})\;.$
(226)

##  Appendix C Relevant fermionic operators in M8B

For convenience and reference, we here list the operators in M8B that contain
fermion and are in the rotation of the bosonic universal operators and,
therefore, appear in Eqs. (101)–(113).

$9:\psi^{2}X^{2}H+\mathrm{h.c.}$ $Q_{leG^{2}H}^{(1)}$
$(\bar{l}_{p}e_{r})HG^{A}_{\mu\nu}G^{A\mu\nu}$ $Q_{leG^{2}H}^{(2)}$
$(\bar{l}_{p}e_{r})H\widetilde{G}^{A}_{\mu\nu}G^{A\mu\nu}$
$Q_{leW^{2}H}^{(1)}$ $(\bar{l}_{p}e_{r})HW^{I}_{\mu\nu}W^{I\mu\nu}$
$Q_{leW^{2}H}^{(2)}$
$(\bar{l}_{p}e_{r})H\widetilde{W}^{I}_{\mu\nu}W^{I\mu\nu}$
$Q_{leW^{2}H}^{(3)}$
$\epsilon^{IJK}(\bar{l}_{p}\sigma^{\mu\nu}e_{r})\tau^{I}HW_{\mu\rho}^{J}W_{\nu}^{K\rho}$
$Q_{quG^{2}H}^{(1)}$
$(\overline{q}_{p}u_{r})\widetilde{H}G^{A}_{\mu\nu}G^{A\mu\nu}$
$Q_{quG^{2}H}^{(2)}$
$(\overline{q}_{p}u_{r})\widetilde{H}\widetilde{G}^{A}_{\mu\nu}G^{A\mu\nu}$
$Q_{quG^{2}H}^{(3)}$
$d^{ABC}(\overline{q}_{p}T^{A}u_{r})\widetilde{H}G^{B}_{\mu\nu}G^{C\mu\nu}$
$Q_{quGBH}^{(3)}$
$(\overline{q}_{p}\sigma^{\mu\nu}T^{A}u_{r})\widetilde{H}G_{\mu\rho}^{A}B_{\nu}^{\,\,\,\rho}$
$Q_{quW^{2}H}^{(1)}$
$(\overline{q}_{p}u_{r})\widetilde{H}W^{I}_{\mu\nu}W^{I\mu\nu}$
$Q_{quW^{2}H}^{(2)}$
$(\overline{q}_{p}u_{r})\widetilde{H}\widetilde{W}^{I}_{\mu\nu}W^{I\mu\nu}$
$Q_{quW^{2}H}^{(3)}$
$\epsilon^{IJK}(\overline{q}_{p}\sigma^{\mu\nu}u_{r})\tau^{I}\widetilde{H}W_{\mu\rho}^{J}W_{\nu}^{K\rho}$
$Q_{quWBH}^{(1)}$
$(\overline{q}_{p}u_{r})\tau^{I}\widetilde{H}W^{I}_{\mu\nu}B^{\mu\nu}$
$Q_{quWBH}^{(2)}$
$(\overline{q}_{p}u_{r})\tau^{I}\widetilde{H}\widetilde{W}^{I}_{\mu\nu}B^{\mu\nu}$
$Q_{quWBH}^{(3)}$
$(\overline{q}_{p}\sigma^{\mu\nu}u_{r})\tau^{I}\widetilde{H}W_{\mu\rho}^{I}B_{\nu}^{\,\,\,\rho}$
$Q_{quB^{2}H}^{(1)}$
$(\overline{q}_{p}u_{r})\widetilde{H}B_{\mu\nu}B^{\mu\nu}$
$Q_{quB^{2}H}^{(2)}$
$(\overline{q}_{p}u_{r})\widetilde{H}\widetilde{B}_{\mu\nu}B^{\mu\nu}$
$9:\psi^{2}X^{2}H+\mathrm{h.c.}$ $Q_{leWBH}^{(1)}$
$(\bar{l}_{p}e_{r})\tau^{I}HW^{I}_{\mu\nu}B^{\mu\nu}$ $Q_{leWBH}^{(2)}$
$(\bar{l}_{p}e_{r})\tau^{I}H\widetilde{W}^{I}_{\mu\nu}B^{\mu\nu}$
$Q_{leWBH}^{(3)}$
$(\bar{l}_{p}\sigma^{\mu\nu}e_{r})\tau^{I}HW_{\mu\rho}^{I}B_{\nu}^{\,\,\,\rho}$
$Q_{leB^{2}H}^{(1)}$ $(\bar{l}_{p}e_{r})HB_{\mu\nu}B^{\mu\nu}$
$Q_{leB^{2}H}^{(2)}$ $(\bar{l}_{p}e_{r})H\widetilde{B}_{\mu\nu}B^{\mu\nu}$
$Q_{qdG^{2}H}^{(1)}$ $(\overline{q}_{p}d_{r})HG^{A}_{\mu\nu}G^{A\mu\nu}$
$Q_{qdG^{2}H}^{(2)}$
$(\overline{q}_{p}d_{r})H\widetilde{G}^{A}_{\mu\nu}G^{A\mu\nu}$
$Q_{qdG^{2}H}^{(3)}$
$d^{ABC}(\overline{q}_{p}T^{A}d_{r})HG^{B}_{\mu\nu}G^{C\mu\nu}$
$Q_{qdGBH}^{(3)}$
$(\overline{q}_{p}\sigma^{\mu\nu}T^{A}d_{r})HG_{\mu\rho}^{A}B_{\nu}^{\,\,\,\rho}$
$Q_{qdW^{2}H}^{(1)}$ $(\overline{q}_{p}d_{r})HW^{I}_{\mu\nu}W^{I\mu\nu}$
$Q_{qdW^{2}H}^{(2)}$
$(\overline{q}_{p}d_{r})H\widetilde{W}^{I}_{\mu\nu}W^{I\mu\nu}$
$Q_{qdW^{2}H}^{(3)}$
$\epsilon^{IJK}(\overline{q}_{p}\sigma^{\mu\nu}d_{r})\tau^{I}HW_{\mu\rho}^{J}W_{\nu}^{K\rho}$
$Q_{qdWBH}^{(1)}$ $(\overline{q}_{p}d_{r})\tau^{I}HW^{I}_{\mu\nu}B^{\mu\nu}$
$Q_{qdWBH}^{(2)}$
$(\overline{q}_{p}d_{r})\tau^{I}H\widetilde{W}^{I}_{\mu\nu}B^{\mu\nu}$
$Q_{qdWBH}^{(3)}$
$(\overline{q}_{p}\sigma^{\mu\nu}d_{r})\tau^{I}HW_{\mu\rho}^{I}B_{\nu}^{\,\,\,\rho}$
$Q_{qdB^{2}H}^{(1)}$ $(\overline{q}_{p}d_{r})HB_{\mu\nu}B^{\mu\nu}$
$Q_{qdB^{2}H}^{(2)}$
$(\overline{q}_{p}d_{r})H\widetilde{B}_{\mu\nu}B^{\mu\nu}$
$11:\psi^{2}H^{2}D^{3}$ $Q_{l^{2}H^{2}D^{3}}^{(1)}$
$i(\bar{l}_{p}\gamma^{\mu}D^{\nu}l_{r})(D_{(\mu}D_{\nu)}H^{{\dagger}}H)$
$Q_{l^{2}H^{2}D^{3}}^{(2)}$
$i(\bar{l}_{p}\gamma^{\mu}D^{\nu}l_{r})(H^{{\dagger}}D_{(\mu}D_{\nu)}H)$
$Q_{l^{2}H^{2}D^{3}}^{(3)}$
$i(\bar{l}_{p}\gamma^{\mu}\tau^{I}D^{\nu}l_{r})(D_{(\mu}D_{\nu)}H^{{\dagger}}\tau^{I}H)$
$Q_{l^{2}H^{2}D^{3}}^{(4)}$
$i(\bar{l}_{p}\gamma^{\mu}\tau^{I}D^{\nu}l_{r})(H^{{\dagger}}\tau^{I}D_{(\mu}D_{\nu)}H)$
$Q_{e^{2}H^{2}D^{3}}^{(1)}$
$i(\bar{e}_{p}\gamma^{\mu}D^{\nu}e_{r})(D_{(\mu}D_{\nu)}H^{{\dagger}}H)$
$Q_{e^{2}H^{2}D^{3}}^{(2)}$
$i(\bar{e}_{p}\gamma^{\mu}D^{\nu}e_{r})(H^{{\dagger}}D_{(\mu}D_{\nu)}H)$
$Q_{q^{2}H^{2}D^{3}}^{(1)}$
$i(\bar{q}_{p}\gamma^{\mu}D^{\nu}q_{r})(D_{(\mu}D_{\nu)}H^{{\dagger}}H)$
$Q_{q^{2}H^{2}D^{3}}^{(2)}$
$i(\bar{q}_{p}\gamma^{\mu}D^{\nu}q_{r})(H^{{\dagger}}D_{(\mu}D_{\nu)}H)$
$Q_{q^{2}H^{2}D^{3}}^{(3)}$
$i(\bar{q}_{p}\gamma^{\mu}\tau^{I}D^{\nu}q_{r})(D_{(\mu}D_{\nu)}H^{{\dagger}}\tau^{I}H)$
$Q_{q^{2}H^{2}D^{2}}^{(4)}$
$i(\bar{q}_{p}\gamma^{\mu}\tau^{I}D^{\nu}q_{r})(H^{{\dagger}}\tau^{I}D_{(\mu}D_{\nu)}H)$
$Q_{u^{2}H^{2}D^{3}}^{(1)}$
$i(\bar{u}_{p}\gamma^{\mu}D^{\nu}u_{r})(D_{(\mu}D_{\nu)}H^{{\dagger}}H)$
$Q_{u^{2}H^{2}D^{3}}^{(2)}$
$i(\bar{u}_{p}\gamma^{\mu}D^{\nu}u_{r})(H^{{\dagger}}D_{(\mu}D_{\nu)}H)$
$Q_{d^{2}H^{2}D^{3}}^{(1)}$
$i(\bar{d}_{p}\gamma^{\mu}D^{\nu}d_{r})(D_{(\mu}D_{\nu)}H^{{\dagger}}H)$
$Q_{d^{2}H^{2}D^{3}}^{(2)}$
$i(\bar{d}_{p}\gamma^{\mu}D^{\nu}d_{r})(H^{{\dagger}}D_{(\mu}D_{\nu)}H)$

Table 2:  The dimension-eight operators in the M8B with particle content
$\psi^{2}X^{2}H$ and $\psi^{2}H^{2}D^{3}$ generated in universal theories. For
the operators in the first two columns their hermitian conjugates are a priori
independent operators. For operators $\psi^{2}H^{2}D^{3}$ their hermitian
conjugates are not independent operators. The subscripts $p,r$ are weak-
eigenstate indices.

$12:\psi^{2}H^{5}+\mathrm{h.c.}$ $Q_{leH^{5}}$
$(H^{\dagger}H)^{2}(\bar{l}_{p}e_{r}H)$ $Q_{quH^{5}}$
$(H^{\dagger}H)^{2}(\overline{q}_{p}u_{r}\widetilde{H})$ $Q_{qdH^{5}}$
$(H^{\dagger}H)^{2}(\overline{q}_{p}d_{r}H)$
$17:\psi^{2}H^{3}D^{2}+\mathrm{h.c.}$ $Q_{leH^{3}D^{2}}^{(1)}$
$(D_{\mu}H^{\dagger}D^{\mu}H)(\bar{l}_{p}e_{r}H)$ $Q_{leH^{3}D^{2}}^{(2)}$
$(D_{\mu}H^{\dagger}\tau^{I}D^{\mu}H)(\bar{l}_{p}e_{r}\tau^{I}H)$
$Q_{leH^{3}D^{2}}^{(5)}$ $(H^{\dagger}D_{\mu}H)(\bar{l}_{p}e_{r}D^{\mu}H)$
$Q_{quH^{3}D^{2}}^{(1)}$
$(D_{\mu}H^{\dagger}D^{\mu}H)(\overline{q}_{p}u_{r}\widetilde{H})$
$Q_{quH^{3}D^{2}}^{(2)}$
$(D_{\mu}H^{\dagger}\tau^{I}D^{\mu}H)(\overline{q}_{p}u_{r}\tau^{I}\widetilde{H})$
$Q_{quH^{3}D^{2}}^{(5)}$
$(D_{\mu}H^{\dagger}H)(\overline{q}_{p}u_{r}D^{\mu}\widetilde{H})$
$Q_{qdH^{3}D^{2}}^{(1)}$
$(D_{\mu}H^{\dagger}D^{\mu}H)(\overline{q}_{p}d_{r}H)$
$Q_{qdH^{3}D^{2}}^{(2)}$
$(D_{\mu}H^{\dagger}\tau^{I}D^{\mu}H)(\overline{q}_{p}d_{r}\tau^{I}H)$
$Q_{qdH^{3}D^{2}}^{(5)}$
$(H^{\dagger}D_{\mu}H)(\overline{q}_{p}d_{r}D^{\mu}H)$ $13:\psi^{2}H^{4}D$
$Q_{l^{2}H^{4}D}^{(1)}$
$i({\bar{l}}_{p}\gamma^{\mu}l_{r})(H^{{\dagger}}\overleftrightarrow{D}_{\mu}H)(H^{{\dagger}}H)$
$Q_{l^{2}H^{4}D}^{(2)}$
$i({\bar{l}}_{p}\gamma^{\mu}\tau^{I}l_{r})[(H^{{\dagger}}\overleftrightarrow{D}_{\mu}^{I}H)(H^{{\dagger}}H)+(H^{{\dagger}}\overleftrightarrow{D}_{\mu}H)(H^{{\dagger}}\tau^{I}H)]$
$Q_{l^{2}H^{4}D}^{(3)}$
$i\epsilon^{IJK}({\bar{l}}_{p}\gamma^{\mu}\tau^{I}l_{r})(H^{{\dagger}}\overleftrightarrow{D}_{\mu}^{J}H)(H^{{\dagger}}\tau^{K}H)$
$Q_{l^{2}H^{4}D}^{(4)}$
$\epsilon^{IJK}({\bar{l}}_{p}\gamma^{\mu}\tau^{I}l_{r})(H^{{\dagger}}\tau^{J}H)D_{\mu}(H^{{\dagger}}\tau^{K}H)$
${Q^{(1)}_{e^{2}H^{4}D}}$
$i({\bar{e}}_{p}\gamma^{\mu}e_{r})(H^{{\dagger}}\overleftrightarrow{D}_{\mu}H)(H^{{\dagger}}H)$
$Q_{q^{2}H^{4}D}^{(1)}$
$i({\bar{q}}_{p}\gamma^{\mu}q_{r})(H^{{\dagger}}\overleftrightarrow{D}_{\mu}H)(H^{{\dagger}}H)$
$Q_{q^{2}H^{4}D}^{(2)}$
$i({\bar{q}}_{p}\gamma^{\mu}\tau^{I}q_{r})[(H^{{\dagger}}\overleftrightarrow{D}_{\mu}^{I}H)(H^{{\dagger}}H)+(H^{{\dagger}}\overleftrightarrow{D}_{\mu}H)(H^{{\dagger}}\tau^{I}H)]$
$Q_{q^{2}H^{4}D}^{(3)}$
$i\epsilon^{IJK}({\bar{q}}_{p}\gamma^{\mu}\tau^{I}q_{r})(H^{{\dagger}}\overleftrightarrow{D}_{\mu}^{J}H)(H^{{\dagger}}\tau^{K}H)$
$Q_{q^{2}H^{4}D}^{(4)}$
$\epsilon^{IJK}({\bar{q}}_{p}\gamma^{\mu}\tau^{I}q_{r})(H^{{\dagger}}\tau^{J}H)D_{\mu}(H^{{\dagger}}\tau^{K}H)$
${Q^{(1)}_{u^{2}H^{4}D}}$
$i({\bar{u}}_{p}\gamma^{\mu}u_{r})(H^{{\dagger}}\overleftrightarrow{D}_{\mu}H)(H^{{\dagger}}H)$
${Q^{(1)}_{d^{2}H^{4}D}}$
$i({\bar{d}}_{p}\gamma^{\mu}d_{r})(H^{{\dagger}}\overleftrightarrow{D}_{\mu}H)(H^{{\dagger}}H)$

Table 3: The dimension-eight operators in the M8B with particle content
$\psi^{2}H^{5}$, $\psi^{2}H^{4}D$ and $\psi^{2}H^{3}D^{2}$ that are generated
in universal theories. For the operators in the first column their hermitian
conjugates are a priori independent operators. Operators in class 13 are
hermitian. For operators $Q^{(1)}_{f^{2}H^{4}D}$, where $f=u,d,e$, we have
added a superscript of $(1)$ to the M8B operators. The subscripts $p,r$ are
weak-eigenstate indices.

$15:(\bar{R}R)XH^{2}D$ $Q_{e^{2}WH^{2}D}^{(1)}$
$(\bar{e}_{p}\gamma^{\nu}e_{r})D^{\mu}(H^{\dagger}\tau^{I}H)W_{\mu\nu}^{I}$
$Q_{e^{2}WH^{2}D}^{(2)}$
$(\bar{e}_{p}\gamma^{\nu}e_{r})D^{\mu}(H^{\dagger}\tau^{I}H)\widetilde{W}_{\mu\nu}^{I}$
$Q_{e^{2}WH^{2}D}^{(3)}$
$(\bar{e}_{p}\gamma^{\nu}e_{r})(H^{\dagger}\overleftrightarrow{D}^{I\mu}H)W_{\mu\nu}^{I}$
$Q_{e^{2}WH^{2}D}^{(4)}$
$(\bar{e}_{p}\gamma^{\nu}e_{r})(H^{\dagger}\overleftrightarrow{D}^{I\mu}H)\widetilde{W}_{\mu\nu}^{I}$
$Q_{e^{2}BH^{2}D}^{(1)}$
$(\bar{e}_{p}\gamma^{\nu}e_{r})D^{\mu}(H^{\dagger}H)B_{\mu\nu}$
$Q_{e^{2}BH^{2}D}^{(2)}$
$(\bar{e}_{p}\gamma^{\nu}e_{r})D^{\mu}(H^{\dagger}H)\widetilde{B}_{\mu\nu}$
$Q_{e^{2}BH^{2}D}^{(3)}$
$(\bar{e}_{p}\gamma^{\nu}e_{r})(H^{\dagger}\overleftrightarrow{D}^{\mu}H)B_{\mu\nu}$
$Q_{e^{2}BH^{2}D}^{(4)}$
$(\bar{e}_{p}\gamma^{\nu}e_{r})(H^{\dagger}\overleftrightarrow{D}^{\mu}H)\widetilde{B}_{\mu\nu}$
$Q_{u^{2}GH^{2}D}^{(1)}$
$(\bar{u}_{p}\gamma^{\nu}T^{A}u_{r})D^{\mu}(H^{\dagger}H)G_{\mu\nu}^{A}$
$Q_{u^{2}GH^{2}D}^{(2)}$
$(\bar{u}_{p}\gamma^{\nu}T^{A}u_{r})D^{\mu}(H^{\dagger}H)\widetilde{G}_{\mu\nu}^{A}$
$Q_{u^{2}GH^{2}D}^{(3)}$
$(\bar{u}_{p}\gamma^{\nu}T^{A}u_{r})(H^{\dagger}\overleftrightarrow{D}^{\mu}H)G_{\mu\nu}^{A}$
$Q_{u^{2}GH^{2}D}^{(4)}$
$(\bar{u}_{p}\gamma^{\nu}T^{A}u_{r})(H^{\dagger}\overleftrightarrow{D}^{\mu}H)\widetilde{G}_{\mu\nu}^{A}$
$Q_{u^{2}WH^{2}D}^{(1)}$
$(\bar{u}_{p}\gamma^{\nu}u_{r})D^{\mu}(H^{\dagger}\tau^{I}H)W_{\mu\nu}^{I}$
$Q_{u^{2}WH^{2}D}^{(2)}$
$(\bar{u}_{p}\gamma^{\nu}u_{r})D^{\mu}(H^{\dagger}\tau^{I}H)\widetilde{W}_{\mu\nu}^{I}$
$Q_{u^{2}WH^{2}D}^{(3)}$
$(\bar{u}_{p}\gamma^{\nu}u_{r})(H^{\dagger}\overleftrightarrow{D}^{I\mu}H)W_{\mu\nu}^{I}$
$Q_{u^{2}WH^{2}D}^{(4)}$
$(\bar{u}_{p}\gamma^{\nu}u_{r})(H^{\dagger}\overleftrightarrow{D}^{I\mu}H)\widetilde{W}_{\mu\nu}^{I}$
$Q_{u^{2}BH^{2}D}^{(1)}$
$(\bar{u}_{p}\gamma^{\nu}u_{r})D^{\mu}(H^{\dagger}H)B_{\mu\nu}$
$Q_{u^{2}BH^{2}D}^{(2)}$
$(\bar{u}_{p}\gamma^{\nu}u_{r})D^{\mu}(H^{\dagger}H)\widetilde{B}_{\mu\nu}$
$Q_{u^{2}BH^{2}D}^{(3)}$
$(\bar{u}_{p}\gamma^{\nu}u_{r})(H^{\dagger}\overleftrightarrow{D}^{\mu}H)B_{\mu\nu}$
$Q_{u^{2}BH^{2}D}^{(4)}$
$(\bar{u}_{p}\gamma^{\nu}u_{r})(H^{\dagger}\overleftrightarrow{D}^{\mu}H)\widetilde{B}_{\mu\nu}$
$Q_{d^{2}GH^{2}D}^{(1)}$
$(\bar{d}_{p}\gamma^{\nu}T^{A}d_{r})D^{\mu}(H^{\dagger}H)G_{\mu\nu}^{A}$
$Q_{d^{2}GH^{2}D}^{(2)}$
$(\bar{d}_{p}\gamma^{\nu}T^{A}d_{r})D^{\mu}(H^{\dagger}H)\widetilde{G}_{\mu\nu}^{A}$
$Q_{d^{2}GH^{2}D}^{(3)}$
$(\bar{d}_{p}\gamma^{\nu}T^{A}d_{r})(H^{\dagger}\overleftrightarrow{D}^{\mu}H)G_{\mu\nu}^{A}$
$Q_{d^{2}GH^{2}D}^{(4)}$
$(\bar{d}_{p}\gamma^{\nu}T^{A}d_{r})(H^{\dagger}\overleftrightarrow{D}^{\mu}H)\widetilde{G}_{\mu\nu}^{A}$
$Q_{d^{2}WH^{2}D}^{(1)}$
$(\bar{d}_{p}\gamma^{\nu}d_{r})D^{\mu}(H^{\dagger}\tau^{I}H)W_{\mu\nu}^{I}$
$Q_{d^{2}WH^{2}D}^{(2)}$
$(\bar{d}_{p}\gamma^{\nu}d_{r})D^{\mu}(H^{\dagger}\tau^{I}H)\widetilde{W}_{\mu\nu}^{I}$
$Q_{d^{2}WH^{2}D}^{(3)}$
$(\bar{d}_{p}\gamma^{\nu}d_{r})(H^{\dagger}\overleftrightarrow{D}^{I\mu}H)W_{\mu\nu}^{I}$
$Q_{d^{2}WH^{2}D}^{(4)}$
$(\bar{d}_{p}\gamma^{\nu}d_{r})(H^{\dagger}\overleftrightarrow{D}^{I\mu}H)\widetilde{W}_{\mu\nu}^{I}$
$Q_{d^{2}BH^{2}D}^{(1)}$
$(\bar{d}_{p}\gamma^{\nu}d_{r})D^{\mu}(H^{\dagger}H)B_{\mu\nu}$
$Q_{d^{2}BH^{2}D}^{(2)}$
$(\bar{d}_{p}\gamma^{\nu}d_{r})D^{\mu}(H^{\dagger}H)\widetilde{B}_{\mu\nu}$
$Q_{d^{2}BH^{2}D}^{(3)}$
$(\bar{d}_{p}\gamma^{\nu}d_{r})(H^{\dagger}\overleftrightarrow{D}^{\mu}H)B_{\mu\nu}$
$Q_{d^{2}BH^{2}D}^{(4)}$
$(\bar{d}_{p}\gamma^{\nu}d_{r})(H^{\dagger}\overleftrightarrow{D}^{\mu}H)\widetilde{B}_{\mu\nu}$
$15:(\bar{L}L)XH^{2}D$ $Q_{l^{2}WH^{2}D}^{(1)}$
$(\bar{l}_{p}\gamma^{\nu}l_{r})D^{\mu}(H^{\dagger}\tau^{I}H)W_{\mu\nu}^{I}$
$Q_{l^{2}WH^{2}D}^{(2)}$
$(\bar{l}_{p}\gamma^{\nu}l_{r})D^{\mu}(H^{\dagger}\tau^{I}H)\widetilde{W}_{\mu\nu}^{I}$
$Q_{l^{2}WH^{2}D}^{(3)}$
$(\bar{l}_{p}\gamma^{\nu}l_{r})(H^{\dagger}\overleftrightarrow{D}^{I\mu}H)W_{\mu\nu}^{I}$
$Q_{l^{2}WH^{2}D}^{(4)}$
$(\bar{l}_{p}\gamma^{\nu}l_{r})(H^{\dagger}\overleftrightarrow{D}^{I\mu}H)\widetilde{W}_{\mu\nu}^{I}$
$Q_{l^{2}WH^{2}D}^{(5)}$
$(\bar{l}_{p}\gamma^{\nu}\tau^{I}l_{r})D^{\mu}(H^{\dagger}H)W_{\mu\nu}^{I}$
$Q_{l^{2}WH^{2}D}^{(6)}$
$(\bar{l}_{p}\gamma^{\nu}\tau^{I}l_{r})D^{\mu}(H^{\dagger}H)\widetilde{W}_{\mu\nu}^{I}$
$Q_{l^{2}WH^{2}D}^{(7)}$
$(\bar{l}_{p}\gamma^{\nu}\tau^{I}l_{r})(H^{\dagger}\overleftrightarrow{D}^{\mu}H)W_{\mu\nu}^{I}$
$Q_{l^{2}WH^{2}D}^{(8)}$
$(\bar{l}_{p}\gamma^{\nu}\tau^{I}l_{r})(H^{\dagger}\overleftrightarrow{D}^{\mu}H)\widetilde{W}_{\mu\nu}^{I}$
$Q_{l^{2}WH^{2}D}^{(9)}$
$\epsilon^{IJK}(\bar{l}_{p}\gamma^{\nu}\tau^{I}l_{r})D^{\mu}(H^{\dagger}\tau^{J}H)W_{\mu\nu}^{K}$
$Q_{l^{2}WH^{2}D}^{(10)}$
$\epsilon^{IJK}(\bar{l}_{p}\gamma^{\nu}\tau^{I}l_{r})D^{\mu}(H^{\dagger}\tau^{J}H)\widetilde{W}_{\mu\nu}^{K}$
$Q_{l^{2}WH^{2}D}^{(11)}$
$\epsilon^{IJK}(\bar{l}_{p}\gamma^{\nu}\tau^{I}l_{r})(H^{\dagger}\overleftrightarrow{D}^{J\mu}H)W_{\mu\nu}^{K}$
$Q_{l^{2}WH^{2}D}^{(12)}$
$\epsilon^{IJK}(\bar{l}_{p}\gamma^{\nu}\tau^{I}l_{r})(H^{\dagger}\overleftrightarrow{D}^{J\mu}H)\widetilde{W}_{\mu\nu}^{K}$
$Q_{l^{2}BH^{2}D}^{(1)}$
$(\bar{l}_{p}\gamma^{\nu}\tau^{I}l_{r})D^{\mu}(H^{\dagger}\tau^{I}H)B_{\mu\nu}$
$Q_{l^{2}BH^{2}D}^{(2)}$
$(\bar{l}_{p}\gamma^{\nu}\tau^{I}l_{r})D^{\mu}(H^{\dagger}\tau^{I}H)\widetilde{B}_{\mu\nu}$
$Q_{l^{2}BH^{2}D}^{(3)}$
$(\bar{l}_{p}\gamma^{\nu}\tau^{I}l_{r})(H^{\dagger}\overleftrightarrow{D}^{I\mu}H)B_{\mu\nu}$
$Q_{l^{2}BH^{2}D}^{(4)}$
$(\bar{l}_{p}\gamma^{\nu}\tau^{I}l_{r})(H^{\dagger}\overleftrightarrow{D}^{I\mu}H)\widetilde{B}_{\mu\nu}$
$Q_{l^{2}BH^{2}D}^{(5)}$
$(\bar{l}_{p}\gamma^{\nu}l_{r})D^{\mu}(H^{\dagger}H)B_{\mu\nu}$
$Q_{l^{2}BH^{2}D}^{(6)}$
$(\bar{l}_{p}\gamma^{\nu}l_{r})D^{\mu}(H^{\dagger}H)\widetilde{B}_{\mu\nu}$
$Q_{l^{2}BH^{2}D}^{(7)}$
$(\bar{l}_{p}\gamma^{\nu}l_{r})(H^{\dagger}\overleftrightarrow{D}^{\mu}H)B_{\mu\nu}$
$Q_{l^{2}BH^{2}D}^{(8)}$
$(\bar{l}_{p}\gamma^{\nu}l_{r})(H^{\dagger}\overleftrightarrow{D}^{\mu}H)\widetilde{B}_{\mu\nu}$
$15:(\bar{L}L)XH^{2}D$ $Q_{q^{2}GH^{2}D}^{(5)}$
$(\bar{q}_{p}\gamma^{\nu}T^{A}q_{r})D^{\mu}(H^{\dagger}H)G_{\mu\nu}^{A}$
$Q_{q^{2}GH^{2}D}^{(6)}$
$(\bar{q}_{p}\gamma^{\nu}T^{A}q_{r})D^{\mu}(H^{\dagger}H)\widetilde{G}_{\mu\nu}^{A}$
$Q_{q^{2}GH^{2}D}^{(7)}$
$(\bar{q}_{p}\gamma^{\nu}T^{A}q_{r})(H^{\dagger}\overleftrightarrow{D}^{\mu}H)G_{\mu\nu}^{A}$
$Q_{q^{2}GH^{2}D}^{(8)}$
$(\bar{q}_{p}\gamma^{\nu}T^{A}q_{r})(H^{\dagger}\overleftrightarrow{D}^{\mu}H)\widetilde{G}_{\mu\nu}^{A}$
$Q_{q^{2}WH^{2}D}^{(1)}$
$(\bar{q}_{p}\gamma^{\nu}q_{r})D^{\mu}(H^{\dagger}\tau^{I}H)W_{\mu\nu}^{I}$
$Q_{q^{2}WH^{2}D}^{(2)}$
$(\bar{q}_{p}\gamma^{\nu}q_{r})D^{\mu}(H^{\dagger}\tau^{I}H)\widetilde{W}_{\mu\nu}^{I}$
$Q_{q^{2}WH^{2}D}^{(3)}$
$(\bar{q}_{p}\gamma^{\nu}q_{r})(H^{\dagger}\overleftrightarrow{D}^{I\mu}H)W_{\mu\nu}^{I}$
$Q_{q^{2}WH^{2}D}^{(4)}$
$(\bar{q}_{p}\gamma^{\nu}q_{r})(H^{\dagger}\overleftrightarrow{D}^{I\mu}H)\widetilde{W}_{\mu\nu}^{I}$
$Q_{q^{2}WH^{2}D}^{(5)}$
$(\bar{q}_{p}\gamma^{\nu}\tau^{I}q_{r})D^{\mu}(H^{\dagger}H)W_{\mu\nu}^{I}$
$Q_{q^{2}WH^{2}D}^{(6)}$
$(\bar{q}_{p}\gamma^{\nu}\tau^{I}q_{r})D^{\mu}(H^{\dagger}H)\widetilde{W}_{\mu\nu}^{I}$
$Q_{q^{2}WH^{2}D}^{(7)}$
$(\bar{q}_{p}\gamma^{\nu}\tau^{I}q_{r})(H^{\dagger}\overleftrightarrow{D}^{\mu}H)W_{\mu\nu}^{I}$
$Q_{q^{2}WH^{2}D}^{(8)}$
$(\bar{q}_{p}\gamma^{\nu}\tau^{I}q_{r})(H^{\dagger}\overleftrightarrow{D}^{\mu}H)\widetilde{W}_{\mu\nu}^{I}$
$Q_{q^{2}WH^{2}D}^{(9)}$
$\epsilon^{IJK}(\bar{q}_{p}\gamma^{\nu}\tau^{I}q_{r})D^{\mu}(H^{\dagger}\tau^{J}H)W_{\mu\nu}^{K}$
$Q_{q^{2}WH^{2}D}^{(10)}$
$\epsilon^{IJK}(\bar{q}_{p}\gamma^{\nu}\tau^{I}q_{r})D^{\mu}(H^{\dagger}\tau^{J}H)\widetilde{W}_{\mu\nu}^{K}$
$Q_{q^{2}WH^{2}D}^{(11)}$
$\epsilon^{IJK}(\bar{q}_{p}\gamma^{\nu}\tau^{I}q_{r})(H^{\dagger}\overleftrightarrow{D}^{J\mu}H)W_{\mu\nu}^{K}$
$Q_{q^{2}WH^{2}D}^{(12)}$
$\epsilon^{IJK}(\bar{q}_{p}\gamma^{\nu}\tau^{I}q_{r})(H^{\dagger}\overleftrightarrow{D}^{J\mu}H)\widetilde{W}_{\mu\nu}^{K}$
$Q_{q^{2}BH^{2}D}^{(1)}$
$(\bar{q}_{p}\gamma^{\nu}\tau^{I}q_{r})D^{\mu}(H^{\dagger}\tau^{I}H)B_{\mu\nu}$
$Q_{q^{2}BH^{2}D}^{(2)}$
$(\bar{q}_{p}\gamma^{\nu}\tau^{I}q_{r})D^{\mu}(H^{\dagger}\tau^{I}H)\widetilde{B}_{\mu\nu}$
$Q_{q^{2}BH^{2}D}^{(3)}$
$(\bar{q}_{p}\gamma^{\nu}\tau^{I}q_{r})(H^{\dagger}\overleftrightarrow{D}^{I\mu}H)B_{\mu\nu}$
$Q_{q^{2}BH^{2}D}^{(4)}$
$(\bar{q}_{p}\gamma^{\nu}\tau^{I}q_{r})(H^{\dagger}\overleftrightarrow{D}^{I\mu}H)\widetilde{B}_{\mu\nu}$
$Q_{q^{2}BH^{2}D}^{(5)}$
$(\bar{q}_{p}\gamma^{\nu}q_{r})D^{\mu}(H^{\dagger}H)B_{\mu\nu}$
$Q_{q^{2}BH^{2}D}^{(6)}$
$(\bar{q}_{p}\gamma^{\nu}q_{r})D^{\mu}(H^{\dagger}H)\widetilde{B}_{\mu\nu}$
$Q_{q^{2}BH^{2}D}^{(7)}$
$(\bar{q}_{p}\gamma^{\nu}q_{r})(H^{\dagger}\overleftrightarrow{D}^{\mu}H)B_{\mu\nu}$
$Q_{q^{2}BH^{2}D}^{(8)}$
$(\bar{q}_{p}\gamma^{\nu}q_{r})(H^{\dagger}\overleftrightarrow{D}^{\mu}H)\widetilde{B}_{\mu\nu}$

Table 4: The dimension-eight operators in the M8B with particle content
$\psi^{2}XH^{2}D$ generated in universal theories. All operators are either
hermitian or anti-hermitian. Once again, the subscripts $p,r$ are weak-
eigenstate indices.

$14:\psi^{2}X^{2}D$ $Q_{l^{2}W^{2}D}^{(2)}$
$\epsilon^{IJK}(\bar{l}_{p}\gamma^{\mu}\tau^{I}\overleftrightarrow{D}^{\nu}l_{r})W_{\mu\rho}^{J}W_{\nu}^{K\rho}$
$Q_{l^{2}W^{2}D}^{(4)}$
$\epsilon^{IJK}(\bar{l}_{p}\gamma^{\mu}\tau^{I}\overleftrightarrow{D}^{\nu}l_{r})(W_{\mu\rho}^{J}\widetilde{W}_{\nu}^{K\rho}+\widetilde{W}_{\mu\rho}^{J}W_{\nu}^{K\rho})$
$Q_{q^{2}W^{2}D}^{(2)}$
$\epsilon^{IJK}(\overline{q}_{p}\gamma^{\mu}\tau^{I}\overleftrightarrow{D}^{\nu}q_{r})W_{\mu\rho}^{J}W_{\nu}^{K\rho}$
$Q_{q^{2}G^{2}D}^{(2)}$
$f^{ABC}(\overline{q}_{p}\gamma^{\mu}T^{A}\overleftrightarrow{D}^{\nu}q_{r})G_{\mu\rho}^{B}G_{\nu}^{C\rho}$
$Q_{q^{2}W^{2}D}^{(4)}$
$\epsilon^{IJK}(\overline{q}_{p}\gamma^{\mu}\tau^{I}\overleftrightarrow{D}^{\nu}q_{r})(W_{\mu\rho}^{J}\widetilde{W}_{\nu}^{K\rho}+\widetilde{W}_{\mu\rho}^{J}W_{\nu}^{K\rho})$
$Q_{q^{2}G^{2}D}^{(5)}$
$f^{ABC}(\overline{q}_{p}\gamma^{\mu}T^{A}\overleftrightarrow{D}^{\nu}q_{r})(G_{\mu\rho}^{B}\widetilde{G}_{\nu}^{C\rho}+\widetilde{G}_{\mu\rho}^{B}G_{\nu}^{C\rho})$
$Q_{u^{2}G^{2}D}^{(2)}$
$f^{ABC}(\bar{u}_{p}\gamma^{\mu}T^{A}\overleftrightarrow{D}^{\nu}u_{r})G_{\mu\rho}^{B}G_{\nu}^{C\rho}$
$Q_{u^{2}G^{2}D}^{(5)}$
$f^{ABC}(\bar{u}_{p}\gamma^{\mu}T^{A}\overleftrightarrow{D}^{\nu}u_{r})(G_{\mu\rho}^{B}\widetilde{G}_{\nu}^{C\rho}+\widetilde{G}_{\mu\rho}^{B}G_{\nu}^{C\rho})$
$Q_{d^{2}G^{2}D}^{(2)}$
$f^{ABC}(\bar{d}_{p}\gamma^{\mu}T^{A}\overleftrightarrow{D}^{\nu}d_{r})G_{\mu\rho}^{B}G_{\nu}^{C\rho}$
$Q_{d^{2}G^{2}D}^{(5)}$
$f^{ABC}(\bar{d}_{p}\gamma^{\mu}T^{A}\overleftrightarrow{D}^{\nu}d_{r})(G_{\mu\rho}^{B}\widetilde{G}_{\nu}^{C\rho}+\widetilde{G}_{\mu\rho}^{B}G_{\nu}^{C\rho})$
$14:\psi^{2}X^{2}D$ $Q_{l^{2}WBD}^{(1)}$
$(\bar{l}_{p}\gamma^{\mu}\tau^{I}\overleftrightarrow{D}^{\nu}l_{r})(B_{\mu\rho}W_{\nu}^{I\rho}-B_{\nu\rho}W_{\mu}^{I\rho})$
$Q_{l^{2}WBD}^{(3)}$
$(\bar{l}_{p}\gamma^{\mu}\tau^{I}\overleftrightarrow{D}^{\nu}l_{r})(B_{\mu\rho}\widetilde{W}_{\nu}^{I\rho}-B_{\nu\rho}\widetilde{W}_{\mu}^{I\rho})$
$Q_{q^{2}WBD}^{(1)}$
$(\overline{q}_{p}\gamma^{\mu}\tau^{I}\overleftrightarrow{D}^{\nu}q_{r})(B_{\mu\rho}W_{\nu}^{I\rho}-B_{\nu\rho}W_{\mu}^{I\rho})$
$Q_{q^{2}WBD}^{(3)}$
$(\overline{q}_{p}\gamma^{\mu}\tau^{I}\overleftrightarrow{D}^{\nu}q_{r})(B_{\mu\rho}\widetilde{W}_{\nu}^{I\rho}-B_{\nu\rho}\widetilde{W}_{\mu}^{I\rho})$
$Q_{q^{2}GBD}^{(1)}$
$(\overline{q}_{p}\gamma^{\mu}T^{A}\overleftrightarrow{D}^{\nu}q_{r})(B_{\mu\rho}G_{\nu}^{A\rho}-B_{\nu\rho}G_{\mu}^{A\rho})$
$Q_{q^{2}GBD}^{(3)}$
$(\overline{q}_{p}\gamma^{\mu}T^{A}\overleftrightarrow{D}^{\nu}q_{r})(B_{\mu\rho}\widetilde{G}_{\nu}^{A\rho}-B_{\nu\rho}\widetilde{G}_{\mu}^{A\rho})$
$Q_{u^{2}GBD}^{(1)}$
$(\bar{u}_{p}\gamma^{\mu}T^{A}\overleftrightarrow{D}^{\nu}u_{r})(B_{\mu\rho}G_{\nu}^{A\rho}-B_{\nu\rho}G_{\mu}^{A\rho})$
$Q_{u^{2}GBD}^{(3)}$
$(\bar{u}_{p}\gamma^{\mu}T^{A}\overleftrightarrow{D}^{\nu}u_{r})(B_{\mu\rho}\widetilde{G}_{\nu}^{A\rho}-B_{\nu\rho}\widetilde{G}_{\mu}^{A\rho})$
$Q_{d^{2}GBD}^{(1)}$
$(\bar{d}_{p}\gamma^{\mu}T^{A}\overleftrightarrow{D}^{\nu}d_{r})(B_{\mu\rho}G_{\nu}^{A\rho}-B_{\nu\rho}G_{\mu}^{A\rho})$
$Q_{d^{2}GBD}^{(3)}$
$(\bar{d}_{p}\gamma^{\mu}T^{A}\overleftrightarrow{D}^{\nu}d_{r})(B_{\mu\rho}\widetilde{G}_{\nu}^{A\rho}-B_{\nu\rho}\widetilde{G}_{\mu}^{A\rho})$

Table 5: The dimension-eight operators in the M8B with particle content
$\psi^{2}X^{2}D$ generated in universal theories. All operators are anti-
hermitian. As before, the subscripts $p,r$ are weak-eigenstate indices.

$18:(\bar{L}L)(\bar{L}L)H^{2}$ $Q_{l^{4}H^{2}}^{(1)}$
$(\bar{l}_{p}\gamma^{\mu}l_{r})(\bar{l}_{s}\gamma_{\mu}l_{t})(H^{\dagger}H)$
$Q_{l^{4}H^{2}}^{(2)}$
$(\bar{l}_{p}\gamma^{\mu}l_{r})(\bar{l}_{s}\gamma_{\mu}\tau^{I}l_{t})(H^{\dagger}\tau^{I}H)$
$Q_{q^{4}H^{2}}^{(1)}$
$(\overline{q}_{p}\gamma^{\mu}q_{r})(\overline{q}_{s}\gamma_{\mu}q_{t})(H^{\dagger}H)$
$Q_{q^{4}H^{2}}^{(2)}$
$(\overline{q}_{p}\gamma^{\mu}q_{r})(\overline{q}_{s}\gamma_{\mu}\tau^{I}q_{t})(H^{\dagger}\tau^{I}H)$
$Q_{q^{4}H^{2}}^{(3)}$
$(\overline{q}_{p}\gamma^{\mu}\tau^{I}q_{r})(\overline{q}_{s}\gamma_{\mu}\tau^{I}q_{t})(H^{\dagger}H)$
$Q_{l^{2}q^{2}H^{2}}^{(1)}$
$(\bar{l}_{p}\gamma^{\mu}l_{r})(\overline{q}_{s}\gamma_{\mu}q_{t})(H^{\dagger}H)$
$Q_{l^{2}q^{2}H^{2}}^{(2)}$
$(\bar{l}_{p}\gamma^{\mu}\tau^{I}l_{r})(\overline{q}_{s}\gamma_{\mu}q_{t})(H^{\dagger}\tau^{I}H)$
$Q_{l^{2}q^{2}H^{2}}^{(3)}$
$(\bar{l}_{p}\gamma^{\mu}\tau^{I}l_{r})(\overline{q}_{s}\gamma_{\mu}\tau^{I}q_{t})(H^{\dagger}H)$
$Q_{l^{2}q^{2}H^{2}}^{(4)}$
$(\bar{l}_{p}\gamma^{\mu}l_{r})(\overline{q}_{s}\gamma_{\mu}\tau^{I}q_{t})(H^{\dagger}\tau^{I}H)$
$18:(\bar{R}R)(\bar{R}R)H^{2}$ $Q_{e^{4}H^{2}}^{(1)}$
$(\bar{e}_{p}\gamma^{\mu}e_{r})(\bar{e}_{s}\gamma_{\mu}e_{t})(H^{\dagger}H)$
$Q_{u^{4}H^{2}}^{(1)}$
$(\bar{u}_{p}\gamma^{\mu}u_{r})(\bar{u}_{s}\gamma_{\mu}u_{t})(H^{\dagger}H)$
$Q_{d^{4}H^{2}}^{(1)}$
$(\bar{d}_{p}\gamma^{\mu}d_{r})(\bar{d}_{s}\gamma_{\mu}d_{t})(H^{\dagger}H)$
$Q_{e^{2}u^{2}H^{2}}^{(1)}$
$(\bar{e}_{p}\gamma^{\mu}e_{r})(\bar{u}_{s}\gamma_{\mu}u_{t})(H^{\dagger}H)$
$Q_{e^{2}d^{2}H^{2}}^{(1)}$
$(\bar{e}_{p}\gamma^{\mu}e_{r})(\bar{d}_{s}\gamma_{\mu}d_{t})(H^{\dagger}H)$
$Q_{u^{2}d^{2}H^{2}}^{(1)}$
$(\bar{u}_{p}\gamma^{\mu}u_{r})(\bar{d}_{s}\gamma_{\mu}d_{t})(H^{\dagger}H)$
$Q_{u^{2}d^{2}H^{2}}^{(2)}$
$(\bar{u}_{p}\gamma^{\mu}T^{A}u_{r})(\bar{d}_{s}\gamma_{\mu}T^{A}d_{t})(H^{\dagger}H)$
$18:(\bar{L}L)(\bar{R}R)H^{2}$ $Q_{l^{2}e^{2}H^{2}}^{(1)}$
$(\bar{l}_{p}\gamma^{\mu}l_{r})(\bar{e}_{s}\gamma_{\mu}e_{t})(H^{\dagger}H)$
$Q_{l^{2}e^{2}H^{2}}^{(2)}$
$(\bar{l}_{p}\gamma^{\mu}\tau^{I}l_{r})(\bar{e}_{s}\gamma_{\mu}e_{t})(H^{\dagger}\tau^{I}H)$
$Q_{l^{2}u^{2}H^{2}}^{(1)}$
$(\bar{l}_{p}\gamma^{\mu}l_{r})(\bar{u}_{s}\gamma_{\mu}u_{t})(H^{\dagger}H)$
$Q_{l^{2}u^{2}H^{2}}^{(2)}$
$(\bar{l}_{p}\gamma^{\mu}\tau^{I}l_{r})(\bar{u}_{s}\gamma_{\mu}u_{t})(H^{\dagger}\tau^{I}H)$
$Q_{l^{2}d^{2}H^{2}}^{(1)}$
$(\bar{l}_{p}\gamma^{\mu}l_{r})(\bar{d}_{s}\gamma_{\mu}d_{t})(H^{\dagger}H)$
$Q_{l^{2}d^{2}H^{2}}^{(2)}$
$(\bar{l}_{p}\gamma^{\mu}\tau^{I}l_{r})(\bar{d}_{s}\gamma_{\mu}d_{t})(H^{\dagger}\tau^{I}H)$
$Q_{q^{2}e^{2}H^{2}}^{(1)}$
$(\overline{q}_{p}\gamma^{\mu}q_{r})(\bar{e}_{s}\gamma_{\mu}e_{t})(H^{\dagger}H)$
$Q_{q^{2}e^{2}H^{2}}^{(2)}$
$(\overline{q}_{p}\gamma^{\mu}\tau^{I}q_{r})(\bar{e}_{s}\gamma_{\mu}e_{t})(H^{\dagger}\tau^{I}H)$
$Q_{q^{2}u^{2}H^{2}}^{(1)}$
$(\overline{q}_{p}\gamma^{\mu}q_{r})(\bar{u}_{s}\gamma_{\mu}u_{t})(H^{\dagger}H)$
$Q_{q^{2}u^{2}H^{2}}^{(2)}$
$(\overline{q}_{p}\gamma^{\mu}\tau^{I}q_{r})(\bar{u}_{s}\gamma_{\mu}u_{t})(H^{\dagger}\tau^{I}H)$
$Q_{q^{2}u^{2}H^{2}}^{(3)}$
$(\overline{q}_{p}\gamma^{\mu}T^{A}q_{r})(\bar{u}_{s}\gamma_{\mu}T^{A}u_{t})(H^{\dagger}H)$
$Q_{q^{2}u^{2}H^{2}}^{(4)}$
$(\overline{q}_{p}\gamma^{\mu}T^{A}\tau^{I}q_{r})(\bar{u}_{s}\gamma_{\mu}T^{A}u_{t})(H^{\dagger}\tau^{I}H)$
$Q_{q^{2}d^{2}H^{2}}^{(1)}$
$(\overline{q}_{p}\gamma^{\mu}q_{r})(\bar{d}_{s}\gamma_{\mu}d_{t})(H^{\dagger}H)$
$Q_{q^{2}d^{2}H^{2}}^{(2)}$
$(\overline{q}_{p}\gamma^{\mu}\tau^{I}q_{r})(\bar{d}_{s}\gamma_{\mu}d_{t})(H^{\dagger}\tau^{I}H)$
$Q_{q^{2}d^{2}H^{2}}^{(3)}$
$(\overline{q}_{p}\gamma^{\mu}T^{A}q_{r})(\bar{d}_{s}\gamma_{\mu}T^{A}d_{t})(H^{\dagger}H)$
$Q_{q^{2}d^{2}H^{2}}^{(4)}$
$(\overline{q}_{p}\gamma^{\mu}T^{A}\tau^{I}q_{r})(\bar{d}_{s}\gamma_{\mu}T^{A}d_{t})(H^{\dagger}\tau^{I}H)$
$18:(\bar{L}R)(\bar{L}R)H^{2}+\mathrm{h.c.}$ $Q_{q^{2}udH^{2}}^{(1)}$
$(\overline{q}_{p}^{j}u_{r})\epsilon_{jk}(\overline{q}_{s}^{k}d_{t})(H^{\dagger}H)$
$Q_{q^{2}udH^{2}}^{(2)}$
$(\overline{q}_{p}^{j}u_{r})(\tau^{I}\epsilon)_{jk}(\overline{q}_{s}^{k}d_{t})(H^{\dagger}\tau^{I}H)$
$Q_{lequH^{2}}^{(1)}$
$(\bar{l}_{p}^{j}e_{r})\epsilon_{jk}(\overline{q}_{s}^{k}u_{t})(H^{\dagger}H)$
$Q_{lequH^{2}}^{(2)}$
$(\bar{l}_{p}^{j}e_{r})(\tau^{I}\epsilon)_{jk}(\overline{q}_{s}^{k}u_{t})(H^{\dagger}\tau^{I}H)$
$Q_{l^{2}e^{2}H^{2}}^{(3)}$ $(\bar{l}_{p}e_{r}H)(\bar{l}_{s}e_{t}H)$
$Q_{leqdH^{2}}^{(3)}$ $(\bar{l}_{p}e_{r}H)(\overline{q}_{s}d_{t}H)$
$Q_{q^{2}u^{2}H^{2}}^{(5)}$
$(\overline{q}_{p}u_{r}\widetilde{H})(\overline{q}_{s}u_{t}\widetilde{H})$
$Q_{q^{2}d^{2}H^{2}}^{(5)}$ $(\overline{q}_{p}d_{r}H)(\overline{q}_{s}d_{t}H)$
$18:(\bar{L}R)(\bar{R}L)H^{2}+\mathrm{h.c.}$ $Q_{leqdH^{2}}^{(1)}$
$(\bar{l}_{p}^{j}e_{r})(\bar{d}_{s}q_{tj})(H^{\dagger}H)$
$Q_{leqdH^{2}}^{(2)}$
$(\bar{l}_{p}e_{r})\tau^{I}(\bar{d}_{s}q_{t})(H^{\dagger}\tau^{I}H)$
$Q_{lequH^{2}}^{(5)}$
$(\bar{l}_{p}e_{r}H)(\widetilde{H}^{\dagger}\bar{u}_{s}q_{t})$
$Q_{q^{2}udH^{2}}^{(5)}$
$(\overline{q}_{p}d_{r}H)(\widetilde{H}^{\dagger}\bar{u}_{s}q_{t})$

Table 6: The dimension-eight operators in the M8B with particle content
$\psi^{4}H^{2}$ generated in universal theories. All operators are either
hermitian or anti-hermitian. For operators $Q^{(1)}_{f^{4}H^{2}}$, where
$f=u,d,e$; and for $Q^{(1)}_{e^{2}u^{2}H^{2}}$ and $Q^{(1)}_{e^{2}d^{2}H^{2}}$
we have added a superscript of $(1)$ to the M8B operators. The subscripts
$p,r,s,t$ are weak-eigenstate indices.

$19:(\bar{L}L)(\bar{L}L)X$ $Q_{l^{4}W}^{(1)}$
$(\bar{l}_{p}\gamma^{\mu}l_{r})(\bar{l}_{s}\gamma^{\nu}\tau^{I}l_{t})W_{\mu\nu}^{I}$
$Q_{l^{4}W}^{(2)}$
$(\bar{l}_{p}\gamma^{\mu}l_{r})(\bar{l}_{s}\gamma^{\nu}\tau^{I}l_{t})\widetilde{W}_{\mu\nu}^{I}$
$Q_{q^{4}G}^{(1)}$
$(\overline{q}_{p}\gamma^{\mu}q_{r})(\overline{q}_{s}\gamma^{\nu}T^{A}q_{t})G^{A}_{\mu\nu}$
$Q_{q^{4}G}^{(2)}$
$(\overline{q}_{p}\gamma^{\mu}q_{r})(\overline{q}_{s}\gamma^{\nu}T^{A}q_{t})\widetilde{G}^{A}_{\mu\nu}$
$Q_{q^{4}G}^{(3)}$
$(\overline{q}_{p}\gamma^{\mu}\tau^{I}q_{r})(\overline{q}_{s}\gamma^{\nu}T^{A}\tau^{I}q_{t})G^{A}_{\mu\nu}$
$Q_{q^{4}G}^{(4)}$
$(\overline{q}_{p}\gamma^{\mu}\tau^{I}q_{r})(\overline{q}_{s}\gamma^{\nu}T^{A}\tau^{I}q_{t})\widetilde{G}^{A}_{\mu\nu}$
$Q_{q^{4}W}^{(1)}$
$(\overline{q}_{p}\gamma^{\mu}q_{r})(\overline{q}_{s}\gamma^{\nu}\tau^{I}q_{t})W^{I}_{\mu\nu}$
$Q_{q^{4}W}^{(2)}$
$(\overline{q}_{p}\gamma^{\mu}q_{r})(\overline{q}_{s}\gamma^{\nu}\tau^{I}q_{t})\widetilde{W}^{I}_{\mu\nu}$
$Q_{q^{4}W}^{(3)}$
$(\overline{q}_{p}\gamma^{\mu}T^{A}q_{r})(\overline{q}_{s}\gamma^{\nu}T^{A}\tau^{I}q_{t})W^{I}_{\mu\nu}$
$Q_{q^{4}W}^{(4)}$
$(\overline{q}_{p}\gamma^{\mu}T^{A}q_{r})(\overline{q}_{s}\gamma^{\nu}T^{A}\tau^{I}q_{t})\widetilde{W}^{I}_{\mu\nu}$
$Q_{l^{2}q^{2}G}^{(1)}$
$(\bar{l}_{p}\gamma^{\mu}l_{r})(\overline{q}_{s}\gamma^{\nu}T^{A}q_{t})G^{A}_{\mu\nu}$
$Q_{l^{2}q^{2}G}^{(2)}$
$(\bar{l}_{p}\gamma^{\mu}l_{r})(\overline{q}_{s}\gamma^{\nu}T^{A}q_{t})\widetilde{G}^{A}_{\mu\nu}$
$Q_{l^{2}q^{2}W}^{(1)}$
$(\bar{l}_{p}\gamma^{\mu}l_{r})(\overline{q}_{s}\gamma^{\nu}\tau^{I}q_{t})W^{I}_{\mu\nu}$
$Q_{l^{2}q^{2}W}^{(2)}$
$(\bar{l}_{p}\gamma^{\mu}l_{r})(\overline{q}_{s}\gamma^{\nu}\tau^{I}q_{t})\widetilde{W}^{I}_{\mu\nu}$
$Q_{l^{2}q^{2}W}^{(3)}$
$(\bar{l}_{p}\gamma^{\mu}\tau^{I}l_{r})(\overline{q}_{s}\gamma^{\nu}q_{t})W^{I}_{\mu\nu}$
$Q_{l^{2}q^{2}W}^{(4)}$
$(\bar{l}_{p}\gamma^{\mu}\tau^{I}l_{r})(\overline{q}_{s}\gamma^{\nu}q_{t})\widetilde{W}^{I}_{\mu\nu}$
$Q_{l^{2}q^{2}W}^{(5)}$
$\epsilon^{IJK}(\bar{l}_{p}\gamma^{\mu}\tau^{I}l_{r})(\overline{q}_{s}\gamma^{\nu}\tau^{J}q_{t})W^{K}_{\mu\nu}$
$Q_{l^{2}q^{2}W}^{(6)}$
$\epsilon^{IJK}(\bar{l}_{p}\gamma^{\mu}\tau^{I}l_{r})(\overline{q}_{s}\gamma^{\nu}\tau^{J}q_{t})\widetilde{W}^{K}_{\mu\nu}$
$19:(\bar{R}R)(\bar{R}R)X$ $Q_{u^{4}G}^{(1)}$
$(\bar{u}_{p}\gamma^{\mu}u_{r})(\bar{u}_{s}\gamma^{\nu}T^{A}u_{t})G^{A}_{\mu\nu}$
$Q_{u^{4}G}^{(2)}$
$(\bar{u}_{p}\gamma^{\mu}u_{r})(\bar{u}_{s}\gamma^{\nu}T^{A}u_{t})\widetilde{G}^{A}_{\mu\nu}$
$Q_{d^{4}G}^{(1)}$
$(\bar{d}_{p}\gamma^{\mu}d_{r})(\bar{d}_{s}\gamma^{\nu}T^{A}d_{t})G^{A}_{\mu\nu}$
$Q_{d^{4}G}^{(2)}$
$(\bar{d}_{p}\gamma^{\mu}d_{r})(\bar{d}_{s}\gamma^{\nu}T^{A}d_{t})\widetilde{G}^{A}_{\mu\nu}$
$Q_{e^{2}u^{2}G}^{(1)}$
$(\bar{e}_{p}\gamma^{\mu}e_{r})(\bar{u}_{s}\gamma^{\nu}T^{A}u_{t})G_{\mu\nu}^{A}$
$Q_{e^{2}u^{2}G}^{(2)}$
$(\bar{e}_{p}\gamma^{\mu}e_{r})(\bar{u}_{s}\gamma^{\nu}T^{A}u_{t})\widetilde{G}_{\mu\nu}^{A}$
$Q_{e^{2}d^{2}G}^{(1)}$
$(\bar{e}_{p}\gamma^{\mu}e_{r})(\bar{d}_{s}\gamma^{\nu}T^{A}d_{t})G_{\mu\nu}^{A}$
$Q_{e^{2}d^{2}G}^{(2)}$
$(\bar{e}_{p}\gamma^{\mu}e_{r})(\bar{d}_{s}\gamma^{\nu}T^{A}d_{t})\widetilde{G}_{\mu\nu}^{A}$
$Q_{u^{2}d^{2}G}^{(1)}$
$(\bar{u}_{p}\gamma^{\mu}u_{r})(\bar{d}_{s}\gamma^{\nu}T^{A}d_{t})G_{\mu\nu}^{A}$
$Q_{u^{2}d^{2}G}^{(2)}$
$(\bar{u}_{p}\gamma^{\mu}u_{r})(\bar{d}_{s}\gamma^{\nu}T^{A}d_{t})\widetilde{G}_{\mu\nu}^{A}$
$Q_{u^{2}d^{2}G}^{(3)}$
$(\bar{u}_{p}\gamma^{\mu}T^{A}u_{r})(\bar{d}_{s}\gamma^{\nu}d_{t})G_{\mu\nu}^{A}$
$Q_{u^{2}d^{2}G}^{(4)}$
$(\bar{u}_{p}\gamma^{\mu}T^{A}u_{r})(\bar{d}_{s}\gamma^{\nu}d_{t})\widetilde{G}_{\mu\nu}^{A}$
$Q_{u^{2}d^{2}G}^{(5)}$
$f^{ABC}(\bar{u}_{p}\gamma^{\mu}T^{A}u_{r})(\bar{d}_{s}\gamma^{\nu}T^{B}d_{t})G_{\mu\nu}^{C}$
$Q_{u^{2}d^{2}G}^{(6)}$
$f^{ABC}(\bar{u}_{p}\gamma^{\mu}T^{A}u_{r})(\bar{d}_{s}\gamma^{\nu}T^{B}d_{t})\widetilde{G}_{\mu\nu}^{C}$
$19:(\bar{L}L)(\bar{R}R)X$ $Q_{l^{2}e^{2}W}^{(1)}$
$(\bar{l}_{p}\gamma^{\mu}\tau^{I}l_{r})(\bar{e}_{s}\gamma^{\nu}e_{t})W^{I}_{\mu\nu}$
$Q_{l^{2}e^{2}W}^{(2)}$
$(\bar{l}_{p}\gamma^{\mu}\tau^{I}l_{r})(\bar{e}_{s}\gamma^{\nu}e_{t})\widetilde{W}^{I}_{\mu\nu}$
$Q_{l^{2}u^{2}G}^{(1)}$
$(\bar{l}_{p}\gamma^{\mu}l_{r})(\bar{u}_{s}\gamma^{\nu}T^{A}u_{t})G^{A}_{\mu\nu}$
$Q_{l^{2}u^{2}G}^{(2)}$
$(\bar{l}_{p}\gamma^{\mu}l_{r})(\bar{u}_{s}\gamma^{\nu}T^{A}u_{t})\widetilde{G}^{A}_{\mu\nu}$
$Q_{l^{2}u^{2}W}^{(1)}$
$(\bar{l}_{p}\gamma^{\mu}\tau^{I}l_{r})(\bar{u}_{s}\gamma^{\nu}u_{t})W^{I}_{\mu\nu}$
$Q_{l^{2}u^{2}W}^{(2)}$
$(\bar{l}_{p}\gamma^{\mu}\tau^{I}l_{r})(\bar{u}_{s}\gamma^{\nu}u_{t})\widetilde{W}^{I}_{\mu\nu}$
$19:(\bar{L}L)(\bar{R}R)X$ $Q_{l^{2}d^{2}G}^{(1)}$
$(\bar{l}_{p}\gamma^{\mu}l_{r})(\bar{d}_{s}\gamma^{\nu}T^{A}d_{t})G^{A}_{\mu\nu}$
$Q_{l^{2}d^{2}G}^{(2)}$
$(\bar{l}_{p}\gamma^{\mu}l_{r})(\bar{d}_{s}\gamma^{\nu}T^{A}d_{t})\widetilde{G}^{A}_{\mu\nu}$
$Q_{l^{2}d^{2}W}^{(1)}$
$(\bar{l}_{p}\gamma^{\mu}\tau^{I}l_{r})(\bar{d}_{s}\gamma^{\nu}d_{t})W^{I}_{\mu\nu}$
$Q_{l^{2}d^{2}W}^{(2)}$
$(\bar{l}_{p}\gamma^{\mu}\tau^{I}l_{r})(\bar{d}_{s}\gamma^{\nu}d_{t})\widetilde{W}^{I}_{\mu\nu}$
$Q_{q^{2}e^{2}G}^{(1)}$
$(\overline{q}_{p}\gamma^{\mu}T^{A}q_{r})(\bar{e}_{s}\gamma^{\nu}e_{t})G^{A}_{\mu\nu}$
$Q_{q^{2}e^{2}G}^{(2)}$
$(\overline{q}_{p}\gamma^{\mu}T^{A}q_{r})(\bar{e}_{s}\gamma^{\nu}e_{t})\widetilde{G}^{A}_{\mu\nu}$
$Q_{q^{2}e^{2}W}^{(1)}$
$(\overline{q}_{p}\gamma^{\mu}\tau^{I}q_{r})(\bar{e}_{s}\gamma^{\nu}e_{t})W^{I}_{\mu\nu}$
$Q_{q^{2}e^{2}W}^{(2)}$
$(\overline{q}_{p}\gamma^{\mu}\tau^{I}q_{r})(\bar{e}_{s}\gamma^{\nu}e_{t})\widetilde{W}^{I}_{\mu\nu}$
$Q_{q^{2}u^{2}G}^{(1)}$
$(\overline{q}_{p}\gamma^{\mu}q_{r})(\bar{u}_{s}\gamma^{\nu}T^{A}u_{t})G^{A}_{\mu\nu}$
$Q_{q^{2}u^{2}G}^{(2)}$
$(\overline{q}_{p}\gamma^{\mu}q_{r})(\bar{u}_{s}\gamma^{\nu}T^{A}u_{t})\widetilde{G}^{A}_{\mu\nu}$
$Q_{q^{2}u^{2}G}^{(3)}$
$(\overline{q}_{p}\gamma^{\mu}T^{A}q_{r})(\bar{u}_{s}\gamma^{\nu}u_{t})G^{A}_{\mu\nu}$
$Q_{q^{2}u^{2}G}^{(4)}$
$(\overline{q}_{p}\gamma^{\mu}T^{A}q_{r})(\bar{u}_{s}\gamma^{\nu}u_{t})\widetilde{G}^{A}_{\mu\nu}$
$Q_{q^{2}u^{2}G}^{(5)}$
$f^{ABC}(\overline{q}_{p}\gamma^{\mu}T^{A}q_{r})(\bar{u}_{s}\gamma^{\nu}T^{B}u_{t})G^{C}_{\mu\nu}$
$Q_{q^{2}u^{2}G}^{(6)}$
$f^{ABC}(\overline{q}_{p}\gamma^{\mu}T^{A}q_{r})(\bar{u}_{s}\gamma^{\nu}T^{B}u_{t})\widetilde{G}^{C}_{\mu\nu}$
$Q_{q^{2}u^{2}W}^{(1)}$
$(\overline{q}_{p}\gamma^{\mu}\tau^{I}q_{r})(\bar{u}_{s}\gamma^{\nu}u_{t})W^{I}_{\mu\nu}$
$Q_{q^{2}u^{2}W}^{(2)}$
$(\overline{q}_{p}\gamma^{\mu}\tau^{I}q_{r})(\bar{u}_{s}\gamma^{\nu}u_{t})\widetilde{W}^{I}_{\mu\nu}$
$Q_{q^{2}d^{2}G}^{(1)}$
$(\overline{q}_{p}\gamma^{\mu}q_{r})(\bar{d}_{s}\gamma^{\nu}T^{A}d_{t})G^{A}_{\mu\nu}$
$Q_{q^{2}d^{2}G}^{(2)}$
$(\overline{q}_{p}\gamma^{\mu}q_{r})(\bar{d}_{s}\gamma^{\nu}T^{A}d_{t})\widetilde{G}^{A}_{\mu\nu}$
$Q_{q^{2}d^{2}G}^{(3)}$
$(\overline{q}_{p}\gamma^{\mu}T^{A}q_{r})(\bar{d}_{s}\gamma^{\nu}d_{t})G^{A}_{\mu\nu}$
$Q_{q^{2}d^{2}G}^{(4)}$
$(\overline{q}_{p}\gamma^{\mu}T^{A}q_{r})(\bar{d}_{s}\gamma^{\nu}d_{t})\widetilde{G}^{A}_{\mu\nu}$
$Q_{q^{2}d^{2}G}^{(5)}$
$f^{ABC}(\overline{q}_{p}\gamma^{\mu}T^{A}q_{r})(\bar{d}_{s}\gamma^{\nu}T^{B}d_{t})G^{C}_{\mu\nu}$
$Q_{q^{2}d^{2}G}^{(6)}$
$f^{ABC}(\overline{q}_{p}\gamma^{\mu}T^{A}q_{r})(\bar{d}_{s}\gamma^{\nu}T^{B}d_{t})\widetilde{G}^{C}_{\mu\nu}$
$Q_{q^{2}d^{2}W}^{(1)}$
$(\overline{q}_{p}\gamma^{\mu}\tau^{I}q_{r})(\bar{d}_{s}\gamma^{\nu}d_{t})W^{I}_{\mu\nu}$
$Q_{q^{2}d^{2}W}^{(2)}$
$(\overline{q}_{p}\gamma^{\mu}\tau^{I}q_{r})(\bar{d}_{s}\gamma^{\nu}d_{t})\widetilde{W}^{I}_{\mu\nu}$

Table 7: The dimension-eight operators in the M8B with particle content
$\psi^{4}X$ generated in universal theories. All operators are either
hermitian or anti-hermitian. The subscripts $p,r,s,t$ are weak-eigenstate
indices.

$20:\psi^{4}HD+\mathrm{h.c.}$ $Q_{l^{3}eHD}^{(1)}$
$i(\bar{l}_{p}\gamma^{\mu}l_{r})[(\bar{l}_{s}e_{t})D_{\mu}H]$
$Q_{l^{3}eHD}^{(2)}$
$i(\bar{l}_{p}\gamma^{\mu}\tau^{I}l_{r})[(\bar{l}_{s}e_{t})\tau^{I}D_{\mu}H]$
$Q_{le^{3}HD}^{(1)}$
$i(\bar{e}_{p}\gamma^{\mu}e_{r})[(\bar{l}_{s}D_{\mu}e_{t})H]$
$Q_{leq^{2}HD}^{(1)}$
$i(\overline{q}_{p}\gamma^{\mu}q_{r})[(\bar{l}_{s}e_{t})D_{\mu}H]$
$Q_{leq^{2}HD}^{(3)}$
$i(\overline{q}_{p}\gamma^{\mu}\tau^{I}q_{r})[(\bar{l}_{s}e_{t})\tau^{I}D_{\mu}H]$
$Q_{leu^{2}HD}^{(1)}$
$i(\bar{u}_{p}\gamma^{\mu}u_{r})[(\bar{l}_{s}e_{t})D_{\mu}H]$
$Q_{led^{2}HD}^{(1)}$
$i(\bar{d}_{p}\gamma^{\mu}d_{r})[(\bar{l}_{s}e_{t})D_{\mu}H]$
$20:\psi^{4}HD+\mathrm{h.c.}$ $Q_{l^{2}quHD}^{(1)}$
$i(\bar{l}_{p}\gamma^{\mu}l_{r})[(\overline{q}_{s}u_{t})D_{\mu}\widetilde{H}]$
$Q_{l^{2}quHD}^{(3)}$
$i(\bar{l}_{p}\gamma^{\mu}\tau^{I}l_{r})[(\overline{q}_{s}u_{t})\tau^{I}D_{\mu}\widetilde{H}]$
$Q_{e^{2}quHD}^{(1)}$
$i(\bar{e}_{p}\gamma^{\mu}e_{r})[(\overline{q}_{s}u_{t})D_{\mu}\widetilde{H}]$
$Q_{q^{3}uHD}^{(1)}$
$i(\overline{q}_{p}\gamma^{\mu}q_{r})[(\overline{q}_{s}u_{t})D_{\mu}\widetilde{H}]$
$Q_{q^{3}uHD}^{(2)}$
$i(\overline{q}_{p}\gamma^{\mu}\tau^{I}q_{r})[(\overline{q}_{s}u_{t})\tau^{I}D_{\mu}\widetilde{H}]$
$Q_{qu^{3}HD}^{(1)}$
$i(\bar{u}_{p}\gamma^{\mu}u_{r})[(\overline{q}_{s}u_{t})D_{\mu}\widetilde{H}]$
$Q_{qud^{2}HD}^{(1)}$
$i(\bar{d}_{p}\gamma^{\mu}d_{r})[(\overline{q}_{s}u_{t})D_{\mu}\widetilde{H}]$
$20:\psi^{4}HD+\mathrm{h.c.}$ $Q_{l^{2}qdHD}^{(1)}$
$i(\bar{l}_{p}\gamma^{\mu}l_{r})[(\overline{q}_{s}d_{t})D_{\mu}H]$
$Q_{l^{2}qdHD}^{(3)}$
$i(\bar{l}_{p}\gamma^{\mu}\tau^{I}l_{r})[(\overline{q}_{s}d_{t})\tau^{I}D_{\mu}H]$
$Q_{e^{2}qdHD}^{(1)}$
$i(\bar{e}_{p}\gamma^{\mu}e_{r})[(\overline{q}_{s}d_{t})D_{\mu}H]$
$Q_{q^{3}dHD}^{(1)}$
$i(\overline{q}_{p}\gamma^{\mu}q_{r})[(\overline{q}_{s}d_{t})D_{\mu}H]$
$Q_{q^{3}dHD}^{(2)}$
$i(\overline{q}_{p}\gamma^{\mu}\tau^{I}q_{r})[(\overline{q}_{s}d_{t})\tau^{I}D_{\mu}H]$
$Q_{qu^{2}dHD}^{(1)}$
$i(\bar{u}_{p}\gamma^{\mu}u_{r})[(\overline{q}_{s}d_{t})D_{\mu}H]$
$Q_{qd^{3}HD}^{(1)}$
$i(\bar{d}_{p}\gamma^{\mu}d_{r})[(\overline{q}_{s}d_{t})D_{\mu}H]$

Table 8: The dimension-eight operators in the M8B with particle content
$\psi^{4}HD$ generated in universal theories. For all operators their
hermitian conjugates are a priori independent operators. The subscripts
$p,r,s,t$ are weak-eigenstate indices.

$21:(\bar{L}L)(\bar{L}L)D^{2}$ $Q_{l^{4}D^{2}}^{(1)}$
$D^{\nu}(\bar{l}_{p}\gamma^{\mu}l_{r})D_{\nu}(\bar{l}_{s}\gamma_{\mu}l_{t})$
$Q_{q^{4}D^{2}}^{(1)}$
$D^{\nu}(\overline{q}_{p}\gamma^{\mu}q_{r})D_{\nu}(\overline{q}_{s}\gamma_{\mu}q_{t})$
$Q_{q^{4}D^{2}}^{(3)}$
$D^{\nu}(\overline{q}_{p}\gamma^{\mu}\tau^{I}q_{r})D_{\nu}(\overline{q}_{s}\gamma_{\mu}\tau^{I}q_{t})$
$Q_{l^{2}q^{2}D^{2}}^{(1)}$
$D^{\nu}(\bar{l}_{p}\gamma^{\mu}l_{r})D_{\nu}(\overline{q}_{s}\gamma_{\mu}q_{t})$
$Q_{l^{2}q^{2}D^{2}}^{(3)}$
$D^{\nu}(\bar{l}_{p}\gamma^{\mu}\tau^{I}l_{r})D_{\nu}(\overline{q}_{s}\gamma_{\mu}\tau^{I}q_{t})$
$21:(\bar{L}R)(\bar{L}R)D^{2}+\mathrm{h.c.}$ $Q_{q^{2}udD^{2}}^{(1)}$
$D_{\mu}(\overline{q}_{p}^{j}u_{r})\epsilon_{jk}D^{\mu}(\overline{q}_{s}^{k}d_{t})$
$Q_{lequD^{2}}^{(1)}$
$D_{\mu}(\bar{l}_{p}^{j}e_{r})\epsilon_{jk}D^{\mu}(\overline{q}_{s}^{k}u_{t})$
$21:(\bar{R}R)(\bar{R}R)D^{2}$ $Q_{e^{4}D^{2}}^{(1)}$
$D^{\nu}(\bar{e}_{p}\gamma^{\mu}e_{r})D_{\nu}(\bar{e}_{s}\gamma_{\mu}e_{t})$
$Q_{u^{4}D^{2}}^{(1)}$
$D^{\nu}(\bar{u}_{p}\gamma^{\mu}u_{r})D_{\nu}(\bar{u}_{s}\gamma_{\mu}u_{t})$
$Q_{d^{4}D^{2}}^{(1)}$
$D^{\nu}(\bar{d}_{p}\gamma^{\mu}d_{r})D_{\nu}(\bar{d}_{s}\gamma_{\mu}d_{t})$
$Q_{e^{2}u^{2}D^{2}}^{(1)}$
$D^{\nu}(\bar{e}_{p}\gamma^{\mu}e_{r})D_{\nu}(\bar{u}_{s}\gamma_{\mu}u_{t})$
$Q_{e^{2}d^{2}D^{2}}^{(1)}$
$D^{\nu}(\bar{e}_{p}\gamma^{\mu}e_{r})D_{\nu}(\bar{d}_{s}\gamma_{\mu}d_{t})$
$Q_{u^{2}d^{2}D^{2}}^{(1)}$
$D^{\nu}(\bar{u}_{p}\gamma^{\mu}u_{r})D_{\nu}(\bar{d}_{s}\gamma_{\mu}d_{t})$
$Q_{u^{2}d^{2}D^{2}}^{(3)}$
$D^{\nu}(\bar{u}_{p}\gamma^{\mu}T^{A}u_{r})D_{\nu}(\bar{d}_{s}\gamma_{\mu}T^{A}d_{t})$
$21:(\bar{L}R)(\bar{R}L)D^{2}+\mathrm{h.c.}$ $Q_{leqdD^{2}}^{(1)}$
$D_{\mu}(\overline{l}_{p}^{j}e_{r})\epsilon_{jk}D^{\mu}(\overline{d}_{s}^{k}q_{t})$
$21:(\bar{L}L)(\bar{R}R)D^{2}$ $Q_{l^{2}e^{2}D^{2}}^{(1)}$
$D^{\nu}(\bar{l}_{p}\gamma^{\mu}l_{r})D_{\nu}(\bar{e}_{s}\gamma_{\mu}e_{t})$
$Q_{l^{2}u^{2}D^{2}}^{(1)}$
$D^{\nu}(\bar{l}_{p}\gamma^{\mu}l_{r})D_{\nu}(\bar{u}_{s}\gamma_{\mu}u_{t})$
$Q_{l^{2}d^{2}D^{2}}^{(1)}$
$D^{\nu}(\bar{l}_{p}\gamma^{\mu}l_{r})D_{\nu}(\bar{d}_{s}\gamma_{\mu}d_{t})$
$Q_{q^{2}e^{2}D^{2}}^{(1)}$
$D^{\nu}(\overline{q}_{p}\gamma^{\mu}q_{r})D_{\nu}(\bar{e}_{s}\gamma_{\mu}e_{t})$
$Q_{q^{2}u^{2}D^{2}}^{(1)}$
$D^{\nu}(\overline{q}_{p}\gamma^{\mu}q_{r})D_{\nu}(\bar{u}_{s}\gamma_{\mu}u_{t})$
$Q_{q^{2}u^{2}D^{2}}^{(3)}$
$D^{\nu}(\overline{q}_{p}\gamma^{\mu}T^{A}q_{r})D_{\nu}(\bar{u}_{s}\gamma_{\mu}T^{A}u_{t})$
$Q_{q^{2}d^{2}D^{2}}^{(1)}$
$D^{\nu}(\overline{q}_{p}\gamma^{\mu}q_{r})D_{\nu}(\bar{d}_{s}\gamma_{\mu}d_{t})$
$Q_{q^{2}d^{2}D^{2}}^{(3)}$
$D^{\nu}(\overline{q}_{p}\gamma^{\mu}T^{A}q_{r})D_{\nu}(\bar{d}_{s}\gamma_{\mu}T^{A}d_{t})$

Table 9: The dimension-eight operators in the M8B with particle content
$\psi^{4}HD$ generated in universal theories. All operators are either
hermitian or anti-hermitian. For the operator $Q^{(1)}_{e^{4}D^{2}}$, we have
added a superscript of $(1)$ to the M8B operator. The subscripts $p,r,s,t$ are
weak-eigenstate indices.

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