Hadronic Light-by-Light Contribution to the Muong−2

We present a calculation of the hadronic light-by-light contributions to the muon $g-2\mathrm{}$ in the ${1/N}_c$ expansion. We have used an extended Nambu-Jona-Lansinio model and introduced an explicit cutoff for the high energy region. We then have critically studied the relative size of the high energy contributions. Although we find them large, we can give an estimate of the light-by-light contribution to $a_{\mu }$ which is around $1\times {10}^{-10\mathrm{}}$. This is smaller than previous estimates and the expected experimental uncertainty at the forthcoming Brookhaven National Laboratory experiment.