Triangle singularity appearing as an $X(3872)$-like peak in $B\to (J/\psi {\pi }^{+}{\pi }^{-})K\pi$

Abstract

We consider a triangle diagram for $B^0\to (J/\psi {\pi }^{+}{\pi }^{-})K^{+}{\pi }^{-}$ where an $X(3872)$ peak has been observed experimentally. We demonstrate that a triangle singularity inherent in the triangle diagram creates a sharp peak in the $J/\psi {\pi }^{+}{\pi }^{-}$ invariant mass distribution when the final $(J/\psi {\pi }^{+}{\pi }^{-})\pi$ invariant mass is at and around the $D^{\ast }{\bar{D}}^{\ast }$ threshold. The position and width of the peak is 3871.68 MeV (a few keV above the $D^{\ast 0}{\bar{D}}^0$ threshold) and $\sim$0.4 MeV, respectively, in perfect agreement with the precisely measured $X(3872)$ mass and width: $3871.69\pm 0.17$ MeV and $<1.2$ MeV. This remarkable agreement is virtually parameter-free. The result indicates that the considered mechanism has to be understood in advance when separating an $X(3872)$-pole contribution from $B^0\to (J/\psi {\pi }^{+}{\pi }^{-})K^{+}{\pi }^{-}$ data; the separation yields an $X(3872)\pi$ lineshape that could be used to determine the $X(3872)$ mass. We suggest a method to set a constraint on the triangle mechanism by analyzing a charge analogous process $B^0\to (J/\psi {\pi }^0{\pi }^{-})K^{+}{\pi }^0$ where a similar triangle singularity generates an $X^{-}(3876)$-like peak.

9 pages, 7 figures; In v2, conclusion changed, new contents and figures added

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• Multiquark Resonances
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• Charmonium
• Threshold cusps and triangle singularities in hadronic reactions
• Search for new charmonium states in the processes e+ e- --> J/psi D(*) D(*) at sqrt{s} ~ 10.6 GeV
• A Discussion on Triangle Singularities in the ${\Lambda }_b\to J/\psi K^{-}p$ Reaction
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• Novel Method for Precisely Measuring the $X(3872)$ Mass
• The Spin-orbit force, recoil corrections and possible $B{\bar{B}}^{\ast }$ and $D{\bar{D}}^{\ast }$ molecular states
• How to understand the underlying structures of $X(4140)$, $X(4274)$, $X(4500)$ and $X(4700)$
• Measurement of the B -> Dbar(*)D(*)K branching fractions
• Triangle singularity in the $B^{-}\to K^{-}{\pi }^{0}X(3872)$ reaction and sensitivity to the $X(3872)$ mass

Cited by in corpus (11)

• $P_c(4312{)}^{+}$, $P_c(4380{)}^{+}$, and $P_c(4457{)}^{+}$ as double triangle cusps
• X(3872) Production in Relativistic Heavy-Ion Collisions
• Triangle Singularity in the Production of $T_{cc}^{+}$(3875) and a Soft Pion
• Global coupled-channel analysis of $e^{+}{e}^{-}\to c\bar{c}$ processes in $\sqrt{s}=3.75-4.7$ GeV
• Possible precise measurements of the $X(3872)$ mass with the $e^{+}{e}^{-}\to {\pi }^0\gamma X(3872)$ and $p\bar{p}\to \gamma X(3872)$ reactions
• Heating triangle singularities in heavy ion collisions
• $X$ structures in $B^{+}\to J/\psi \varphi K^{+}$ as one-loop and double-triangle threshold cusps
• $X$ and $Z_{cs}$ in $B^{+}\to J/\psi \varphi K^{+}$ as $s$-wave threshold cusps and alternative spin-parity assignments to $X(4274)$ and $X(4500)$
• Studying triangle singularity through spin observables
• The role of triangle singularity in the decay process $D^0\to {\pi }^{+}{\pi }^{-}{f}_0(980),f_0\to {\pi }^{+}{\pi }^{-}$
• An $X(3872)$-like peak in $B\to (J/\psi {\pi }^{+}{\pi }^{-})K\pi$ due to triangle singularity