Bulk graphs

D04: literature. M. B. Fröb, CQG 35 (2018) 055006 (arXiv:1710.00839), works in flat space, in a general gauge, in $n$ dimensions. The de Donder part of the graviton-loop scalar self-energy (his eq. inv2pf_termsumint_grav) has an integrand bracket proportional to $m^2$ or $\xi$, and “vanishes identically” for $\xi =0$, $m=0$, in accordance with Kahya and Woodard (2007). For $m=0$ his ${\xi }^2$ terms vanish, and the gauge-parameter pieces contribute. All three statements agree with our results. The 1PI self-mass is gauge dependent; D04 $=0$ holds in the declared gauge only.

E7. The symmetry factor of D04 is $1$. XVI-O's “$\frac{1}{2}$” was marked Unverified and never used for a value. XVI-P never evaluated D04, and its D11, which has two identical $\varphi$ lines, keeps $\frac{1}{2}$. No earlier value changes.

D05a, D12. These are genuine one-propagator tadpoles: no external momentum flows through the loop line. They are pure power divergences ($\omega =2$, and $2,4$ for D12) with no logarithmic member, so there is no pole on either side, and the zero is not a cancellation between UV and IR poles. Fröb also notes that graviton tadpoles vanish in dimensional regularisation around flat space.

D06. This is the full $\bar{c}c$ two-point function. MS-bar poles: $-3/8$, $1/4$, $-1/8$. Local finite parts: $-2/3$, $5/12$, $-1/3$. Coefficients of $L$: $3/8$, $-1/4$, $1/8$. It is identical in $d$ to the ghost self-energy $\Sigma$ of XVI-P P15, for which the ghost equation against D13 is verified.

D12 reconciliation. XVI-O never labels D12 “Missing”. The word survives only as stale p14r text in XVI-P's P23 O.5 line. XVI-P p15 derived D12 $=0$, and Q02 confirms this independently. The value is derived, never set by convention; this is erratum E6.