Models of radiative Majorana neutrino masses require new scalars and/or fermions to induce lepton number violating interactions. We show that these new particles also generate observable neutrino nonstandard interactions (NSI) with matter. We classify radiative models as type-I or II, with type-I models containing at least one Standard Model (SM) particle inside the loop diagram generating neutrino mass, and type-II models having no SM particle inside the loop. While type-II radiative models do not generate NSI at tree-level, popular models which fall under the type-I category are shown, somewhat surprisingly, to generate observable NSI at tree-level, while being consistent with direct and indirect constraints from colliders, electroweak precision data and charged-lepton flavor violation (cLFV). We survey such models where neutrino masses arise at one, two and three loops. In the prototypical Zee model which generates neutrino masses via one-loop diagrams involving charged scalars, we find that diagonal NSI can be as large as (8%, 3.8%, 9.3%) for (ε ee , ε µµ , ε τ τ ), while off-diagonal NSI can be at most (1.5 × 10 −3 %, 0.56%, 0.34%) for (ε eµ , ε eτ , ε µτ ). In one-loop neutrino mass models using leptoquarks (LQs), (ε µµ , ε τ τ ) can be as large as (21.6%, 51.7%), while ε ee and (ε eµ , ε eτ , ε µτ ) can at most be 0.6%. Other twoand three-loop LQ models are found to give NSI of similar strength. The most stringent constraints on the diagonal NSI are found to come from neutrino oscillation and scattering experiments, while the off-diagonal NSI are mostly constrained by low-energy processes, such as atomic parity violation and cLFV. We also comment on the future sensitivity of these radiative models in long-baseline neutrino experiments, such as DUNE. While our analysis is focused on radiative neutrino mass models, it essentially covers all NSI possibilities with heavy mediators. arXiv:1907.09498v2 [hep-ph] 3 Oct 2019 Contents 7 Other type-I radiative models 76 7.1 One-loop models 77 7.1.1 Minimal radiative inverse seesaw model 77 7.1.2 One-loop model with vectorlike leptons 80 7.1.3 SU (2) L -singlet leptoquark model with vectorlike quark 82 7.1.4 SU (2) L -doublet leptoquark model with vectorlike quark 83 7.1.5 Model with SU (2) L -triplet leptoquark and vectorlike quark 84 7.1.6 A new extended one-loop leptoquark model 85 7.2 Two-loop models 87 7.2.1 Zee-Babu model 87 7.2.2 Leptoquark/diquark variant of the Zee-Babu model 88 7.2.3 Model with SU (2) L -doublet and singlet leptoquarks 89 7.2.4 Leptoquark model with SU (2) L -singlet vectorlike quark 90 7.2.5 Angelic model 91 7.2.6 Model with singlet scalar and vectorlike quark 92 7.2.7 Leptoquark model with vectorlike lepton 93 7.2.8 Leptoquark model with SU (2) L -doublet vectorlike quark 93 7.2.9 A new two-loop leptoquark model 94 7.3 Three-loop models 95 7.3.1 KNT Model 95 7.3.2 AKS model 96 7.3.3 Cocktail Model 97 7.3.4 Leptoquark variant of the KNT model 98 -ii -7.3.5 SU (2) L -singlet three-loop model 99 7.4 Four-and higher-loop models 100 8 Type II r...