Bounds on the Parameter of Noncommutativity from Supernova SN1987A

We consider supernova SN1987A to find bounds on parameter of noncommutativity, $\th_{\mu\nu}$. Right handed neutrino in the noncommutative standard model, NCSM, can directly couple to the photon and the Z-gauge boson. Therefore the observed flux of neutrinos from SN1987A can constrain the strength of the new couplings in the NCSM. We obtain two bounds on the NC-parameter, $\Lambda_{NC}=1/{\sqrt |\th|}$, with respect to escaping or trapping of the right handed neutrinos inside the supernova which are $\Lambda_{NC}\gtrsim 3.7 TeV$ or $\Lambda_{NC}\lesssim 1 TeV$, respectively. The excluded region $1 TeV\lesssim\Lambda_{NC}\lesssim 3.7 TeV$ for the NC-parameter is obtained for the first time. In fact $\Lambda_{NC}\lesssim 1 TeV$ is consistent with the existing bounds on $\Lambda_{NC}$ and raises our hopes to find the NC-effects in the LHC or even in the LEP. Meanwhile $\Lambda_{NC}\gtrsim 3.7 TeV$ is more stringent than the other bounds obtained from LEP and LHC considerations. Furthermore, since NC-calculations are perturbative and are correct only up to the energy scale of the NC-system $\lesssim\Lambda_{NC}$, therefore these bounds which are obtained from the energy scale considerably less than the energy scale of LEP and LHC are more reliable.