Primitively divergent diagrams in $\kappa$-deformed scalar field with   quartic self-interaction
  We obtain the primitively divergent diagrams in $\kappa$-deformed scalar field in four-dimensional spacetime with quartic self-interaction in order to investigate the effect of the fundamental length $q=1/(2\kappa)$ on such diagrams. Thanks to $\kappa$-deformation, we find that the dimensionally regularized forms of the diagrams lead to finite results in the limit of space-time dimension four. The effect of the deformation appears as a displacement of the poles in the complex plane. 
M. J. Neves, C. A. A. de Carvalho, C. Farina and M. V. Cougo-Pinto