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Multi-field inflation models and non-Bunch-Davies vacuum initial conditionsboth predict sizeable non-Gaussian primordial perturbations and anisotropic$\mu$-type spectral distortions of the cosmic microwave background (CMB)blackbody. While CMB anisotropies allow us to probe non-Gaussianity atwavenumbers $k\simeq 0.05\,{\rm Mpc^{-1}}$, $\mu$-distortion anisotropies arerelated to non-Gaussianity of primordial perturbation modes with much largerwavenumbers, $k\simeq 740\,{\rm Mpc^{-1}}$. Through cross-correlations betweenCMB and $\mu$-distortion anisotropies, one can therefore shed light on theaforementioned inflation models. We investigate the ability of a future CMBsatellite imager like LiteBIRD to measure $\mu T$ and $\mu E$ cross-powerspectra between anisotropic $\mu$-distortions and CMB temperature and $E$-modepolarization anisotropies in the presence of foregrounds, and derive LiteBIRDforecasts on ${f_{\rm NL}^\mu(k\simeq 740\,{\rm Mpc^{-1}})}$. We show that $\muE$ cross-correlations with CMB polarization provide more constraining power on$f_{\rm NL}^\mu$ than $\mu T$ cross-correlations in the presence offoregrounds, and the joint combination of $\mu T$ and $\mu E$ observables addsfurther leverage to the detection of small-scale primordial non-Gaussianity. Wefind that LiteBIRD would detect ${f_{\rm NL}^\mu}=4500$ at $5\sigma$significance after foreground removal, and achieve a minimum error of${\sigma(f_{\rm NL}^\mu=0) \simeq 800}$ at 68\% CL by combining CMB temperatureand polarization. Due to the huge dynamic range of wavenumbers between CMB and$\mu$-distortion anisotropies, such large $f^\mu_{\rm NL}$ values would stillbe consistent with current CMB constraints in the case of very mildscale-dependence of primordial non-Gaussianity. Anisotropic spectraldistortions thus provide a new path, complementary to CMB $B$-modes, to probeinflation with LiteBIRD.

Leverage on small-scale primordial non-Gaussianity through cross-correlations between CMB $E$-mode and $\mu$-distortion anisotropies