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We compute the tree-level bispectrum of dark matter in the presence ofmassive neutrinos in the mildly non-linear regime in the context of theeffective field theory of large-scale structure (EFTofLSS). For neutrinos,whose typical free streaming wavenumber ($k_{\rm fs}$) is longer than thenon-linear scale ($k_{\mathrm{NL}}$), we solve a Boltzmann equation coupled tothe effective fluid equation for dark matter. We solve perturbatively thecoupled system by expanding in powers of the neutrino density fraction($f_{\nu}$) and the ratio of the wavenumber of interest over the non-linearscale ($k/k_{\mathrm{NL}}$) and add suitable counterterms to remove thedependence from short distance physics. For equilateral configurations, we findthat the total-matter tree-level bispectrum is approximately $16f_{\nu}$ timesthe dark matter one on short scales ($k > k_{\rm fs}$). The largestcontribution stems from the back-reaction of massive neutrinos on the darkmatter growth factor. On large scales ($k < k_{\rm fs}$) the contribution ofneutrinos to the bispectrum is smaller by up to two orders of magnitude.

Tree-Level Bispectrum in the Effective Field Theory of Large-Scale Structure extended to Massive Neutrinos