Low-energy constraints on kappa-Minkowski extension of the Standard   Model
  We investigate the phenomenological consequences of kappa-Minkowski extension of the Standard Model, working in the linear order in inverse $\kappa$. At this order the *-deformed Lagrangian can be expanded in the series of dimension five operators that have non-trivial transformation properties under the ordinary Lorentz invariance. Such operators cause the Lorentz-violating signatures at low energies, and in particular lead to the anomalous spin precession linked to the external direction. The experimental bounds on this phenomenon then restrict parameter $\kappa$ to be above 10^{23} GeV, making it difficult to impose a direct connection between this theory and quantum gravity. 
Pavel A. Bolokhov and Maxim Pospelov