Role of electromagnetic corrections in the $\pi \pi$ distributions of ${\psi }^{\prime }\to J/\psi \pi \pi$

Abstract

The cusp structure at the ${\pi }^{+}{\pi }^{-}$ threshold in the ${\pi }^0{\pi }^0$ invariant mass spectrum serves as a sensitive probe for extracting the $S$-wave $\pi \pi$ scattering lengths in processes where an $S$-wave ${\pi }^0{\pi }^0$ pair is produced in the final states. Within the framework of nonrelativistic effective field theory with coupled channels ${\pi }^0{\pi }^0$ and ${\pi }^{+}{\pi }^{-}$, we revisit the near-threshold structures in the ${\pi }^0{\pi }^0$ spectrum of ${\psi }^{\prime }\to J/\psi \pi \pi$. Our analysis incorporates the $\pi \pi$ final-state rescattering, including both strong and Coulomb interactions. It turns out that the cusp near the ${\pi }^{+}{\pi }^{-}$ threshold becomes more prominent when Coulomb interactions are included. The electromagnetic correctionsare found to alter the magnitude of the threshold cusp by about 2%-3%, underscoring the necessity of including these effects in precision determinations of the $\pi \pi$ scattering lengths. The coupled-channel amplitude constructed in this work provides a ready-to-use theoretical framework for experimental analyses of fine structures near $\pi \pi$ thresholds.

13 pages, 7 figures, comments are welcome

References in corpus (15)

• Charmonium
• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• STCF Conceptual Design Report: Volume 1 -- Physics & Detector
• Cusps in K --> 3 pi decays
• Radiative corrections in K --> 3 pi decays
• Cusps in K_L --> 3 pi decays
• Is the existence of a $J/\psi J/\psi$ bound state plausible?
• Determination of the number of $\psi (3686)$ events taken at BESIII
• The cusp effect in eta' --> eta pi pi decays
• Extracting $\pi \pi$ $S$-wave scattering lengths from cusp effect in heavy quarkonium dipion transitions
• Extraction of $ND$ scattering lengths from the ${\Lambda }_b\to {\pi }^{-}p{D}^0$ decay and properties of the ${\Sigma }_c(2800{)}^{+}$
• $D^{+}{D}^{-}$ hadronic atom and its production in $pp$ and $p\bar{p}$ collisions
• Deciphering the mechanism of $J/\psi$-nucleon scattering
• Coupled-channel analysis of the near-threshold $e^{+}{e}^{-}\to N\bar{N}$ cross sections
• Studies on ${\pi }^{+}{\pi }^{-}$ phase motion in the ${\Psi }^{\prime }\to J/\Psi {\pi }^{+}{\pi }^{-}$ process