Reevaluating the $\psi (4160)$ Resonance Parameter Using $B^{+}\to K^{+}{\mu }^{+}{\mu }^{-}$ Data in the Context of Unquenched Charmonium Spectroscopy

Abstract

A puzzling phenomenon, where the measured mass of the $\psi (4160)$ is pushed higher, presents a challenge to current theoretical models of hadron spectroscopy. This study suggests that the issue arises from analyses based on the outdated quenched charmonium spectrum. In the past two decades, the discovery of new hadronic states has emphasized the importance of the unquenched effect. Under the unquenched picture, six vector charmonium states-$\psi (4040)$, $\psi (4160)$, $\psi (4220)$, $\psi (4380)$, $\psi (4415)$, and $\psi (4500)$-are identified in the $4\sim 4.5$ GeV range, contrasting with the three states predicted in the quenched model. We reevaluate the resonance parameters of the $\psi (4160)$ using the di-muon invariant mass spectrum of $B^{+}\to K^{+}{\mu }^{+}{\mu }^{-}$ and unquenched charmonium spectroscopy. Our analysis finds the $\psi (4160)$ mass at $4145.76\pm 4.48$ MeV, indicating previous overestimations. This conclusion is supported by analyzing $e^{+}{e}^{-}\to D_s{\bar{D}}_s^{\ast }$. Our findings have significant implications for both hadron spectroscopy and search for new physics signals by $R_K$.

4 pages, 3 figures and 3 tables. Accepted by Phys. Rev. D

References in corpus (11)

• Precise measurement of the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\psi$ cross section at center-of-mass energies from 3.77 to 4.60 GeV
• Evidence of Two Resonant Structures in $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{h}_c$
• Constructing $J/\psi$ family with updated data of charmoniumlike $Y$ states
• Cross section measurements of $e^{+}{e}^{-}\to \omega {\chi }_{c0}$ from $\sqrt{s}=$4.178 to 4.278 GeV
• Observation of the $Y(4230)$ and a new structure in $e^{+}{e}^{-}\to K^{+}{K}^{-}J/\psi$
• Prediction of a missing higher charmonium around 4.26 GeV in $J/\psi$ family
• Observation of $e^{+}{e}^{-}\to {\chi }_{c0}\omega$ and missing higher charmonium $\psi (4S)$
• Measurement of $e^{+}{e}^{-}\to D_s^{(\ast )+}{D}_s^{(\ast )-}$ cross sections near threshold using initial-state radiation
• Confirming the existence of a new higher charmonium $\psi (4500)$ by the newly released data of $e^{+}{e}^{-}\to K^{+}{K}^{-}J/\psi$
• Measurement of $e^{+}{e}^{-}\to \eta J/\psi$ Cross Section from $\sqrt{s}=$ 3.808 GeV to 4.951 GeV
• How higher charmonia shape the puzzling data of the $e^{+}{e}^{-}\to \eta J/\psi$ cross section

Cited by in corpus (3)

• Colloquium: Hadron Production in Open-charm Meson Pair at $e^{+}{e}^{-}$ Collider
• Is the $3S$-$2D$ mixing strong for the charmonia $\psi (4040)$ and $\psi (4160)$?
• Prospects for observing the missing $2D$ and $1F$ charmonium states around 4 GeV