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We report measurement of the cross section of $e^+e^-\to \pi^+\pi^-\psi(2S)$ between 4.0 and $5.5 {\rm GeV}$, based on an analysis of initial state radiation events in a $980 \rm fb^{-1}$ data sample recorded with the Belle detector.
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M π + π − J / ψ = M π + π − ℓ + ℓ − − M ℓ + ℓ − + m J / ψ M_{\pi^{+}\pi^{-}J/\psi}=M_{\pi^{+}\pi^{-}\ell^{+}\ell^{-}}-M_{\ell^{+}\ell^{-}}+m_{J/\psi} is used to cancel the lepton-pair mass resolution in the π + π − J / ψ \pi^{+}\pi^{-}J/\psi invariant mass spectrum; here, m J / ψ m_{J/\psi} is the nominal mass of J / ψ J/\psi PDG
Cited in the paper.
M π + π − ψ ( 2 S ) = M π + π − π + π − ℓ + ℓ − − M π + π − ℓ + ℓ − + m ψ ( 2 S ) M_{\pi^{+}\pi^{-}\psi(2S)}=M_{\pi^{+}\pi^{-}\pi^{+}\pi^{-}\ell^{+}\ell^{-}}-M_{\pi^{+}\pi^{-}\ell^{+}\ell^{-}}+m_{\psi(2S)} for the π + π − J / ψ \pi^{+}\pi^{-}J/\psi mode and M π + π − ψ ( 2 S ) = M π + π − μ + μ − − M μ + μ − + m ψ ( 2 S ) M_{\pi^{+}\pi^{-}\psi(2S)}=M_{\pi^{+}\pi^{-}\mu^{+}\mu^{-}}-M_{\mu^{+}\mu^{-}}+m_{\psi(2S)} for the μ + μ − \mu^{+}\mu^{-} mode, where m ψ ( 2 S ) m_{\psi(2S)} is the ψ ( 2 S ) \psi(2S) norminal mass PDG
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