Probe Noncommutative Space-Time Scale Using $γγ\to Z$ At ILC

Abstract

In the standard model production of on-shell Z boson at a photon collider (or Z decays into $γγ$) is strictly forbidden by angular momentum conservation and Bose statistics (the Yang's Theorem). In the standard model with noncommutative space-time this process can occur. Therefore this process provides an important probe for the noncommutative space-time. The $γγ$ collision at the ILC by laser backscattering of the electron and positron beams offers an ideal place to carry out such a study. Assuming an integrated luminosity of 500 fb$^{-1}$, we show that the constraint which can be achieved on $Γ(Z\to γγ)$ is three to four orders of magnitude better than the current bound of $5.2\times 10^{-5}$ GeV. The noncommutative scale can be probed up to a few TeVs.