Primordial tensor bispectra in ?-CMB cross-correlations

Cross-correlations between Cosmic Microwave Background (CMB) temperature and polarization anisotropies $\mu$-spectral distortions have been considered to measure (squeezed) primordial scalar bispectra in a range of scales inaccessible primary CMB bispectra. In this work we address whether it is possible constrain tensor non-Gaussianities with these cross-correlations. We find that only statistical leave distinct signatures, while isotropic either vanishing or highly suppressed signatures. discuss how the angular dependence squeezed terms short long momenta determine non-zero also non-vanishing configurations are affected by way which transform under parity. By employing so-called BipoSH formalism capture observational effects anisotropies, make Fisher-forecasts assess detection prospects from $\mu T$, E$ B$ Observing $\langle \gamma \gamma\rangle$ \zeta\rangle$ going be challenging as imprint perturbations on $\mu$-distortions subdominant perturbations, therefore requiring large, independent amplification effect $\mu$-epoch. absence such mechanism, \zeta bispectrum most relevant sources particular, point out anisotropic inflationary models where \rangle$ leaves potentially observable signatures T$ E$, enhanced.