Probing Quark Electric Dipole Moment with Topological Anomalies

TL;DR

This work introduces a novel hadronic-channel probe of the strange-quark EDM $d_s$ by exploiting CP-odd angular observables in $e^+e^-\to K^+K^-\pi^0$ (with potential $J/\psi$ mediation). The SM baseline is fixed by the topological Wess–Zumino–Witten contribution, while a CP-odd interference with the CP-violating tensor operator maps $d_s$ into χPT through leading-order form factors $F_V(0,0,0)$ and $F_A(0,0,0)$. The authors construct a signed interference observable $A_T$ from the transverse components of the hadronic currents and relate it to $d_s$ via $d_s = (-N_c e)/(12\sqrt{2}\pi^2 \Lambda_2) \times (A_T/R(s))$, with $R(s)$ a calculable phase factor. Numerical estimates indicate current CMD-3 data could reach $\delta d_s \sim \mathcal{O}(10^{-16})\,e\cdot\mathrm{cm}$ and BESIII/J/psi data could reach $\mathcal{O}(10^{-18})\,e\cdot\mathrm{cm}$, while future facilities STCF and Belle II could improve by an order of magnitude, offering a robust, detector-agnostic pathway to constrain CP-violating strange-quark dynamics.

Abstract

CP-odd observables originating from the strange-quark electric dipole moment ($d_s$) are identified in $γ^\ast\to K^+K^-π^0$ and evaluated in the chiral limit. A nonzero T-odd asymmetry $A_T$ requires anomalous couplings descending from a five-dimensional Chern-Simons construction. Modeling the running of $F_A$ and $F_V$ with vector-meson dominance, we estimate sensitivities to $d_s$ at the level of $\mathcal{O}(10^{-16})\,e\cdot\mathrm{cm}$ in $e^+e^-$ data at CMD-3 and $\mathcal{O}(10^{-18})\,e\cdot\mathrm{cm}$ using existing $J/ψ$ samples at BESIII. Future experiments at the Super Tau-Charm Facility and Belle~II can further improve the reach by an order of magnitude.

Figures (2)

• Figure 1: Schematic structure of the amplitudes for $\gamma^\ast\!\to K^+K^-\pi^0$. The left panel shows the SM contribution mediated by three-gluon annihilation. The right panel shows the EDM-induced contribution, where the boxed cross denotes the strange-quark EDM $d_s$.
• Figure 2: The definitions of the angles in Eq. \ref{['angles']}. The angle $\theta^0$ is the angle between the momenta of $e^+$ and $\pi^0$ in the center-of-mass frame. The angle $\theta^\ast$ is the angle between $\pi^0$ and $K^+$ in the $K^+K^-$ rest frame. The angle $\phi$ is the dihedral angle between the two planes spanned by $(\pi^0,e^+,e^-)$ and $(\pi^0,K^+,K^-)$.