We demonstrate that baryonification algorithms, which displace particles in gravity-only simulations according to physically-motivated prescriptions, can simultaneously capture the impact of baryonic physics on the 2 and 3-point statistics of matter. Specifically, we show that our implementation of a baryonification algorithm jointly fits the changes induced by baryons on the power spectrum and equilateral bispectrum on scales up to k < 5 h/Mpc and redshifts z<2, as measured in six different cosmological hydrodynamical simulations. The accuracy of our fits are typically 1% for the power spectrum, and for the equilateral and squeezed bispectra, which somewhat degrades to 3% for simulations with extreme feedback prescriptions. Our results support the physical assumptions underlying baryonification approaches, and encourage their use in interpreting weak gravitational lensing and other cosmological observables.
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