  A new relation between a class of complex polynomials with a good behavior at
infinity studied by A. N\'emethi and A. Zaharia and the cohomology groups of
affine complex hyperplane arrangement complements with rank one local system
coefficients is introduced and explored.
  This approach gives in particular new upper-bounds for the dimension of the
twisted cohomology groups of line arrangement complements in the complex affine
plane.
