%0 Journal Article %T Hadronic Light-by-Light Contribution to the Muon $g-2$ %A Johan Bijnens %A Elisabetta Pallante %A Joaquim Prades %J Physics %D 1995 %I arXiv %R 10.1103/PhysRevLett.75.1447 %X Mistake in FORTRAN program corrected. The numerical results and conclusions are changed significantly: We present a calculation of the hadronic light-by-light contributions to the muon $g-2$ in the $1/N_c$ expansion. We have used an Extended NJL model and introduced an explicit cut-off for the high energy region. We have then critically studied the relative size of the high energy contributions. Although we find them large we can give a conservative estimate of the light-by-light contribution to $a_\mu$ which is $-(11\pm5) \cdot 10^{-10}$. This is between two and three sigmas the expected experimental uncertainty at the forthcoming BNL experiment. %U http://arxiv.org/abs/hep-ph/9505251v2