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We investigate the emergence of a conformal anomaly pole in conformal fieldtheories in the case of the $TJJ$ correlator. We show how it comes to begenerated in dimensional renormalization, using a basis of 13 form factors (the$F$-basis), where only one of them requires renormalization $(F_{13})$,extending previous studies. We then combine recent results on the structure ofthe non-perturbative solutions of the conformal Ward identities (CWI's) for the$TJJ$ in momentum space, expressed in terms of a minimal set of 4 form factors($A-$ basis), with the properties of the $F$-basis, and show how the singularbehaviour of the corresponding form factors in both basis can be related. Theresult proves the centrality of such massless effective interactions induced bythe anomaly, which have recently found realization in solid state, in thetheory of topological insulators and of Weyl semimetals. This pattern isconfirmed in massless abelian and nonabelian theories (QED and QCD)investigated at one-loop.

Renormalization, Conformal Ward Identities and the Origin of a Conformal Anomaly Pole