$X$ structures in $B^{+}\to J/\psi \varphi K^{+}$ as one-loop and double-triangle threshold cusps

Abstract

The LHCb data on $B^{+}\to J/\psi \varphi K^{+}$ show four peaks and three dips in the $J/\psi \varphi$ invariant mass distribution, and the peaks are interpreted as $X(4140)$, $X(4274)$, $X(4500)$ and $X(4685)/X(4700)$ resonance contributions. Interestingly, all the peaks and dips are located at (or close to) $D_s^{\ast }{\bar{D}}_s^{(\ast )}$, $D_{s0}^{\ast }(2317){\bar{D}}_s^{(\ast )}$, $D_{s1}(2536){\bar{D}}_s^{(\ast )}$, and ${\psi }^{\prime }\varphi$ thresholds. These coincidences suggest a close connection between the structures and the thresholds, which however has not been seriously considered in previous theoretical studies on the $X$ structures. In fact, if we utilize this connection and interpret the $X$ structures as common $s$-wave threshold cusps, we face a difficulty: $X(4274)$ and $X(4500)$ have spin-parity that conflict with the experimentally determined ones. In this work, we introduce double triangle mechanisms that cause threshold cusps significantly sharper than the ordinary one-loop ones of the same spin-parity. We demonstrate that all the $X$ and dip structures are well described by a combination of one-loop and double-triangle threshold cusps, thereby proposing a novel interpretation of the $X$ and dip structures.

12 pages, 6 figures; (v2) title changed; calculations corrected and all figures updated; 1 figure added; (v3) published version, fitting parameter values corrected

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Cited by in corpus (6)

• An updated review of the new hadron states
• Predicting isovector charmonium-like states from X(3872) properties
• $X$ and $Z_{cs}$ in $B^{+}\to J/\psi \varphi K^{+}$ as $s$-wave threshold cusps and alternative spin-parity assignments to $X(4274)$ and $X(4500)$
• $X(3960)$, $X_0(4140)$, and other compact $cs\bar{c}\bar{s}$ states
• Production of $X_{cs\bar{c}\bar{s}}$ in heavy ion collisions
• Decoding the near-threshold $X_{0,1}(4140)$ and $X_1(4685)$ states via OZI-suppressed coupled-channel scattering