Particle phenomenology on noncommutative spacetime

We introduce particle phenomenology on the noncommutative spacetime called the Groenewold-Moyal plane. The length scale of spacetime noncommutativity is constrained from the $CPT$ violation measurements in the $K^0-{\overline{K}}^0$ system and $g-2$ difference of ${\mu }^{+}-{\mu }^{-}$. The $K^0-{\overline{K}}^0$ system provides an upper bound on the length scale of spacetime noncommutativity of the order of ${10}^{-32}\mathrm{m}$, corresponding to a lower energy bound $E$ of the order of $E\gtrsim {10}^{16}\mathrm{GeV}$. The $g-2$ difference of ${\mu }^{+}-{\mu }^{-}$ constrains the noncommutativity length scale to be of the order of ${10}^{-20}\mathrm{m}$, corresponding to a lower energy bound $E$ of the order of $E\gtrsim {10}^3\mathrm{GeV}$. We also present the phenomenology of the electromagnetic interaction of electrons and nucleons at the tree level on the noncommutative spacetime. We show that the distributions of charge and magnetization of nucleons are affected by spacetime noncommutativity. The analytic properties of electromagnetic form factors are also changed and it may give rise to interesting experimental signals.

Figure 1

A self-energy diagram for $K_L$ with ${\pi }^0$ pole dominance. The coupling constant $\lambda$ has dependence on ${\overrightarrow{\theta }}^0$ and the total incident momentum ${\overrightarrow{P}}_{\mathrm{in}}$.

Figure 2

Lowest order hadronic contribution to $g-2$ of a lepton $l^{\pm }$ (${\mu }^{\pm }$ or $e^{\pm }$) in a uniform magnetic field $B$.

Figure 3

Feynman diagram of electron-nucleon scattering caused by the exchange of a virtual photon.