Muon Anomalous Magnetic Moment in Noncommutative Space-Time

Abstract: The explanation of the muon anomalous magnetic moment ($\mu$-AMM) requires new physics beyond the Standard Model. In this work, we investigate the effects of noncommutative space-time on the $\mu$-AMM within the Seiberg-Witten map framework, analyzing both tree-level and loop-level diagrams. Additionally, we examine the $\mu$-AMM by studying the scattering cross-section of electron-positron annihilation into muon-antimuon pairs $ (e^- e^+ \rightarrow \mu^- \mu^+ ) $. Previous studies have explored the implications of noncommutative space-time through various processes, leading to different bounds on the noncommutative parameter $\theta^{\mu\nu}$. Our analysis estimates $\theta^{\mu\nu} \sim (43 \, \mathrm TeV)^{-2} $ for both tree-level and loop-level contributions when noncommutative space-time accounts for the entire observed $\mu$-AMM. If noncommutative effects are responsible for only 10$\%$ of the $\mu$-AMM, the constraint relaxes to approximately $(136 \, \mathrm TeV)^{-2}$. Furthermore, by comparing the noncommutative cross-section of $ e^- e^+ \rightarrow \mu^- \mu^+ $ with experimental data, we derive an approximate bound of $(90 \, \mathrm TeV)^{-2}$ which corresponds to a 23$\%$ contribution to the $\mu$-AMM.