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The cross-correlation between 21-cm intensity mapping experiments andphotometric surveys of galaxies (or any other cosmological tracer with a broadradial kernel) is severely degraded by the loss of long-wavelength radial modesdue to Galactic foreground contamination. Higher-order correlators are able torestore some of these modes due to the non-linear coupling between them and thelocal small-scale clustering induced by gravitational collapse. We explore thepossibility of recovering information from the bispectrum between a photometricgalaxy sample and an intensity mapping experiment, in the context of theclustering-redshifts technique. We demonstrate that the bispectrum is able tocalibrate the redshift distribution of the photometric sample to the requiredaccuracy of future experiments such as the Rubin Observatory, using futuresingle-dish and interferometric 21-cm observations, in situations where thetwo-point function is not able to do so due to foreground contamination. Wealso show how this calibration is affected by the photometric redshift width$\sigma_{z,0}$ and maximum scale $k_{\mathrm{max}}$. We find that it isimportant to reach scales $k \gtrsim 0.3\,h\,\mathrm{Mpc}^{-1}$, with theconstraints saturating at around $k\sim 1\,h\,\mathrm{Mpc}^{-1}$ fornext-generation experiments.

Clustering redshifts with the 21cm-galaxy cross-bispectrum