E. Notations from section 6

In this Appendix we list the concrete form of the various notations made in section 6.

The polynomials denoted by $\bar{X}_{p}^{\left( i\right) }$ that enter $\bar{\Delta}^{\mathrm{int}}$ given in (137) read as

$$\bar{X}_{0}^{\left( 1\right) } = 6S^{\ast }\eta C+12t^{\ast \mu }\left( V_{\mu }C+\eta C_{\mu }\ri... ... }^{\ast }C+V_{[\mu }C_{\nu ]}-\phi _{\mu \nu }\eta \right) F^{\mu \nu } \notag$$ (366)

$$-2\left( 2\eta _{\mu \nu \rho }^{\ast }C+2B_{[\mu \nu }^{\ast }C_... ...\right) \tilde{D}_{\lambda \sigma }\varepsilon ^{\mu \nu \rho \lambda \sigma },$$ (367)

$$\bar{X}_{1}^{\left( 1\right) } = \left[ \left( -2C_{\mu \nu \rho }^{\ast }\eta -2C_{[\mu \nu }^{\ast }V_{\rho ]}-4H_{[\mu }^{\ast }B_{\nu \rho ]}^{\ast }\right) C\right. \notag$$ (368)

$$\left. +\left( -2H_{[\mu }^{\ast }V_{\nu }C_{\rho ]}+2H_{[\mu }^{... ...] \tilde{D}_{\lambda \sigma }\varepsilon ^{\mu \nu \rho \lambda \sigma } \notag$$ (369)

$$-12H_{\mu }^{\ast }t^{\ast \mu }\eta C+6\left( H_{[\mu }^{\ast }V... ...+2H_{\mu }^{\ast }\eta C_{\nu }+C_{\mu \nu }^{\ast }\eta C\right) F^{\mu \nu },$$ (370)

$$\bar{X}_{2}^{\left( 1\right) } = \left[ \left( -2H_{[\mu }^{\ast }C_{\nu \rho ]}^{\ast }\eta -2H_{[\mu }^{\ast }H_{\nu }^{\ast }V_{\rho ]}\right) C\right. \notag$$ (371)

$$\left. +2H_{[\mu }^{\ast }H_{\nu }^{\ast }C_{\rho ]}\eta \right] ... ... \nu \rho \lambda \sigma }+6H_{\mu }^{\ast }H_{\nu }^{\ast }\eta CF^{\mu \nu },$$ (372)

$$\bar{X}_{3}^{\left( 1\right) }=4H_{\mu }^{\ast }H_{\nu }^{\ast }H_{\rho }^{\ast }\eta CD^{\mu \nu \rho },$$ (373)

$$\bar{X}_{0}^{\left( 2\right) } = -12\cdot 5!\left( S^{\ast }\eta +2t^{\ast \mu }V_{\mu }+2B_{\mu \... ... }\tilde{D}_{\lambda \sigma }\mathcal{G} ^{\mu \nu \rho \lambda \sigma } \notag$$ (374)

$$+4!\cdot 4!t^{\ast \mu }\eta \mathcal{\tilde{G}}_{\mu }-4!\cdot 4... ...\mu \nu \rho \lambda }+6\cdot 4!\left( \phi ^{\ast \mu \nu }\eta \right. \notag$$ (375)

$$\left. -K^{\mu \nu \rho }V_{\rho }\right) \tilde{D}_{\mu \nu }-3\... ...e{K}_{\mu \nu }\eta -4V_{[\mu }\mathcal{\tilde{G}}_{\nu ]}\right) F^{\mu \nu },$$ (376)

$$\bar{X}_{1}^{\left( 2\right) } = -4\cdot 5!\left( C_{\mu \nu \rho }^{\ast }\eta +C_{[\mu \nu }^{\a... ...t) \tilde{D}_{\lambda \sigma }\mathcal{G}^{\mu \nu \rho \lambda \sigma } \notag$$ (377)

$$-12\cdot 5!\left( C_{\mu \nu }^{\ast }F^{\mu \nu }\eta -2H_{\mu }... ...-12\cdot 4!H_{[\mu }^{\ast }\mathcal{\tilde{G}}_{\nu ]}\eta F^{\mu \nu } \notag$$ (378)

$$-12\cdot 4!\left( C_{\mu \nu }^{\ast }\eta +H_{[\mu }^{\ast }V_{\... ...\lambda }-6\cdot 4!H_{\mu }^{\ast }K^{\mu \nu \rho }\eta \tilde{D}_{\nu \rho },$$ (379)

$$\bar{X}_{2}^{\left( 2\right) } = -4\cdot 5!\left( H_{[\mu }^{\ast }C_{\nu \rho ]}^{\ast }\eta +H_{... ...t) \tilde{D}_{\lambda \sigma }\mathcal{G}^{\mu \nu \rho \lambda \sigma } \notag$$ (380)

$$-12\cdot 4!H_{\mu }^{\ast }H_{\nu }^{\ast }\eta \tilde{D}_{\rho \... ...12\cdot 5!H_{\mu }^{\ast }H_{\nu }^{\ast }\eta F^{\mu \nu }\mathcal{\tilde{G}},$$ (381)

$$\bar{X}_{3}^{\left( 2\right) }=-4\cdot 5!H_{\mu }^{\ast }H_{\nu }... ...st }\eta \tilde{D}_{\lambda \sigma }\mathcal{G}^{\mu \nu \rho \lambda \sigma },$$ (382)

$$\bar{X}_{0}^{\left( 3\right) }=-6\cdot 5!S^{\ast }\tilde{\eta}+12... ...mu }+4!B^{\mu \nu }\tilde{D}_{\mu \nu }-36 \tilde{\eta}_{\mu \nu }F^{\mu \nu },$$ (383)

$$\bar{X}_{1}^{\left( 3\right) } = 2\cdot 5!C_{\mu \nu \rho }^{\ast }\tilde{D} _{\lambda \sigma }\et... ...\ast }t^{\ast \mu }-C_{\mu \nu }^{\ast }F^{\mu \nu }\right) \tilde{\eta} \notag$$ (384)

$$+6\cdot 4!C_{\mu \nu }^{\ast }\tilde{D}_{\rho \lambda }\eta ^{\mu... ...ta ^{\mu \nu \rho }+6\cdot 4!H_{[\mu }^{\ast }\tilde{\eta}_{\nu ]}F^{\mu \nu },$$ (385)

$$\bar{X}_{2}^{\left( 3\right) }=2\cdot 5!H_{[\mu }^{\ast }C_{\nu \... ...{\rho \lambda }\eta ^{\mu \nu \rho \lambda }-5F^{\mu \nu }\tilde{\eta}\right) ,$$ (386)

$$\bar{X}_{3}^{\left( 3\right) }=2\cdot 5!H_{\mu }^{\ast }H_{\nu }^... ...{\rho }^{\ast }\tilde{D}_{\lambda \sigma }\eta ^{\mu \nu \rho \lambda \sigma }.$$ (387)

The functions appearing in (146) and denoted by $U_{p}^{\left( i\right) }$ are of the form

$$U_{0}^{\left( 1\right) }=-9\left( 2k_{1}\phi ^{\mu \nu }-\tfrac{k... ...\left( 2B_{\mu \nu }^{\ast }C+V_{[\mu }C_{\nu ]}-\phi _{\mu \nu }\eta \right) ,$$ (388)

$$U_{1}^{\left( 1\right) }=-9\left( k_{1}\phi ^{\mu \nu }-\tfrac{k_... ...}^{\ast }\eta C-H_{\mu }^{\ast }\left( V_{\nu }C+\eta C_{\nu }\right) \right] ,$$ (389)

$$U_{2}^{\left( 1\right) }=-9\left( k_{1}\phi ^{\mu \nu }-\tfrac{k_{2}}{20} \tilde{K}^{\mu \nu }\right) H_{\mu }^{\ast }H_{\nu }^{\ast }\eta C,$$ (390)

$$U_{0}^{\left( 2\right) }=108\left( k_{1}\phi ^{\mu \nu }-\tfrac{k... ...lde{G}} +\eta \tilde{K}_{\mu \nu }-8V_{\mu }\mathcal{\tilde{G}}_{\nu }\right) ,$$ (391)

$$U_{1}^{\left( 2\right) } = 18\varepsilon ^{\alpha \beta \gamma \delta \varepsilon }\left( C_... ...^{\mu \nu }\right) \mathcal{G}_{\alpha \beta \gamma \delta \varepsilon } \notag$$ (392)

$$-36\varepsilon _{\rho \alpha \beta \gamma \delta }H_{\mu }^{\ast ... ...20}\tilde{K}^{\mu \rho }\right) \eta \mathcal{G}^{\alpha \beta \gamma \delta },$$ (393)

$$U_{2}^{\left( 2\right) }=18\varepsilon _{\alpha \beta \gamma \del... ...st }H_{\nu }^{\ast }\eta \mathcal{G}^{\alpha \beta \gamma \delta \varepsilon },$$ (394)

$$U_{0}^{\left( 3\right) }=9\varepsilon _{\nu \rho \alpha \beta \ga... ...o }-\tfrac{k_{2}}{20}\tilde{K}^{\nu \rho }\right) \eta ^{\alpha \beta \gamma },$$ (395)

$$U_{1}^{\left( 3\right) } = \tfrac{9}{4}\varepsilon _{\alpha \beta \gamma \delta \varepsilon ... ...lde{K}^{\mu \nu }\right) \eta ^{\alpha \beta \gamma \delta \varepsilon } \notag$$ (396)

$$-18\varepsilon _{\rho \beta \gamma \delta \varepsilon }H_{\mu }^{... ..._{2}}{20}\tilde{K}^{\mu \rho }\right) \eta ^{\beta \gamma \delta \varepsilon },$$ (397)

$$U_{2}^{\left( 3\right) }=9\varepsilon _{\alpha \beta \gamma \delt... ...20}\tilde{K}^{\mu \nu }\right) \eta ^{\alpha \beta \gamma \delta \varepsilon }.$$ (398)