Experimental limits on kappa-Minkowski field theories

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The non-commutative kappa-Minkowski field theory, often tauted as a low-energy candidate for the quantum description of gravity, operates on a spacetime which possesses a modified Lorentz invariance, and as such can be probed in high-precision low-energy experiments. We study the first order corrections in kappa to the Standard Model, and show that they typically induce a coupling of nuclear spin to an external background at low energies. Strong limits on this type of interactions push the scale of non-commutativity to more than 10^7 Planck masses, thus exhibiting a severe naturalness problem for kappa-Minkowski Field Theory viewed as an effective description of quantum gravity.