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Precise determination of the properties of $X(3872)$ and of its isovector partner $W_{c1}$
High Energy Physics - Phenomenology · Submitted 6 Feb 2025 · Published version
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim It is found as a virtual state at $\left(3.1\pm0.7+ 1.3^{+1.9}_{-0.6}\,i\right)\ \rm MeV$ relative to the $D^+ D^{*-}$ threshold on an unphysical Riemann sheet, strongly supporting a molecular nature of both $X(3872)$ and $W_{c1}$.
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We perform a simultaneous fit to BESIII data on $e^+e^-\to \gamma (D^0{\bar{D}^{0}}\pi^0/J/\psi\pi^+\pi^-)$ and LHCb data on $B^+\to K^+(J/\psi\pi^+\pi^-)$ to precisely determine the properties of the $X(3872)$, with full consideration of three-body effects from $D^*\to D\pi$ decay, respecting both analyticity and unitarity. The $X(3872)$ is determined to be a quasi-bound state with a significance of $2.7\,\sigma$, representing the most precise determination to date. Its pole is located at $\left(-160^{+57}_{-74}-125^{+23}_{-38}\,i\right) \rm keV$, relative to the nominal $D^0\bar{D}^{*0}$ threshold. Moreover, we confirm the presence of an isovector partner state, $W_{c1}$. It is found as a virtual state at $\left(3.1\pm0.7+ 1.3^{+1.9}_{-0.6}\,i\right)\ \rm MeV$ relative to the $D^+ D^{*-}$ threshold on an unphysical Riemann sheet, strongly supporting a molecular nature of both $X(3872)$ and $W_{c1}$. As a highly nontrivial prediction we show that the $W_{c1}$ leads to nontrivial lineshapes around 3.88 GeV in $B^0\to K^0 X(3872)\to K^0 D^0\bar D^0\pi^0$ and $K^0J/\psi\pi^+\pi^-$ -- thus the scheme presented here can be tested further by improved measurements.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We perform a simultaneous fit to BESIII data on $e^+e^-\to \gamma (D^0{\bar{D}^{0}}\pi^0/J/\psi\pi^+\pi^-)$ and LHCb data on $B^+\to K^+(J/\psi\pi^+\pi^-)$ to precisely determine the properties of the $X(3872)$, with full consideration of three-body effects from $D^*\to D\pi$ decay, respecting both analyticity and unitarity. | method 0.90 | 0.96 | 0.07 | asserted 0.97 |
| s1 | The $X(3872)$ is determined to be a quasi-bound state with a significance of $2.7\,\sigma$, representing the most precise determination to date. | result 1.00 | 0.94 | 0.42 | asserted 0.98 |
| s2 | Its pole is located at $\left(-160^{+57}_{-74}-125^{+23}_{-38}\,i\right) \rm keV$, relative to the nominal $D^0\bar{D}^{*0}$ threshold. | result 1.00 | 0.95 | 0.17 | asserted 1.00 |
| s3 | Moreover, we confirm the presence of an isovector partner state, $W_{c1}$. | result 0.99 | 0.92 | 0.17 | asserted 1.00 |
| s4 | It is found as a virtual state at $\left(3.1\pm0.7+ 1.3^{+1.9}_{-0.6}\,i\right)\ \rm MeV$ relative to the $D^+ D^{*-}$ threshold on an unphysical Riemann sheet, strongly supporting a molecular nature of both $X(3872)$ and $W_{c1}$. | result 0.93 | 0.96 | 0.23 | asserted 0.97 |
| s5 | As a highly nontrivial prediction we show that the $W_{c1}$ leads to nontrivial lineshapes around 3.88 GeV in $B^0\to K^0 X(3872)\to K^0 D^0\bar D^0\pi^0$ and $K^0J/\psi\pi^+\pi^-$ -- thus the scheme presented here can be tested further by improved measurements. | future work 0.50 | 0.92 | 0.08 | asserted 0.98 |
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The paper
Original abstract
We perform a simultaneous fit to BESIII data on $e^+e^-\to \gamma (D^0{\bar{D}^{0}}\pi^0/J/\psi\pi^+\pi^-)$ and LHCb data on $B^+\to K^+(J/\psi\pi^+\pi^-)$ to precisely determine the properties of the $X(3872)$, with full consideration of three-body effects from $D^*\to D\pi$ decay, respecting both analyticity and unitarity. The $X(3872)$ is determined to be a quasi-bound state with a significance of $2.7\,\sigma$, representing the most precise determination to date. Its pole is located at $\left(-160^{+57}_{-74}-125^{+23}_{-38}\,i\right) \rm keV$, relative to the nominal $D^0\bar{D}^{*0}$ threshold. Moreover, we confirm the presence of an isovector partner state, $W_{c1}$. It is found as a virtual state at $\left(3.1\pm0.7+ 1.3^{+1.9}_{-0.6}\,i\right)\ \rm MeV$ relative to the $D^+ D^{*-}$ threshold on an unphysical Riemann sheet, strongly supporting a molecular nature of both $X(3872)$ and $W_{c1}$. As a highly nontrivial prediction we show that the $W_{c1}$ leads to nontrivial lineshapes around 3.88 GeV in $B^0\to K^0 X(3872)\to K^0 D^0\bar D^0\pi^0$ and $K^0J/\psi\pi^+\pi^-$ -- thus the scheme presented here can be tested further by improved measurements.
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References
How the literature uses it
17 arXiv papers cite this in 35 sentences
Papers whose main result relates to this one's
States a conflicting result 1 paper
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Our analysis disfavors the interpretation of X(3872) as a loosely bound molecular state if we use the experimental $D^\ast D\pi$ coupling constant $g=0.59$ and a reasonable cutoff around 1 GeV, which is the typical hadronic scale.
Papers citing it · 21 sentences without a confident label
Uses its method or tool 2 papers
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The effective potential matrix is constructed in terms of the heavy-quark spin (HQS) and light-flavor SU(3) symmetries [ref] ,[The direct $J/ψπ$ and $J/ψK$ transitions are Okubo-Zweig-Iizuka suppressed and are neglected in the present analysis.
A femtoscopic tale of two $C$-parities: the $Z_c(3900)$ and the isovector partner of the $X(3872)$ · Formalism · 0.85
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Therefore, we refrain from considering direct transitions between observation channels, which allows us to reduce the dimension of the potential matrix in Eq. [ref] by introducing an effective potential $V̅$ (Hereinafter, summation over repeated indices is implied unless stated otherwise), [equation] that absorbs the effects of the observation channels [ref] .
Vector charmonium(-like) states in the energy range of 4.1-4.6 GeV · Lippmann-Schwinger equation · 0.81
Uses its data or values 4 papers
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We fix these constants $a_i(μ=1 GeV)$ to the values $-2.77$ for $i=1$, and $-2.5$ for $i=2,3$ [ref] .[These subtraction constants, fixed in the state-of-the-art analyses of the $Z_c(3900)$ and $Z_cs(3985)$ [ref] and of the $W_c1$ [ref] , are intimately related to the UV cutoff used in the wave function in Eq. [ref] [ref] .
A femtoscopic tale of two $C$-parities: the $Z_c(3900)$ and the isovector partner of the $X(3872)$ · Formalism · 0.84
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A direct calculation for the $X(3872)$ system, using the pertinent parameters extracted from data in Ref. [ref] , namely $E_b=160 keV$ below the neutral threshold on RS$_++$ and $=0.26$, leads to a nearby $I=1$ pole on RS$_+-$ close to the charged threshold at [equation] consistent with Refs. [ref] ; see also Ref. [ref] for support from lattice calculations.
Amplified Isospin Breaking from Coupled-Channel Dynamics Near Threshold · From Amplification to Partner Poles · 0.87
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For the effective couplings $g_^'$ of $X(3872)$ to $D^0D̅^*0$ and $D^+D^*-$, we take the values $g_, 0'=(0.26 ±0.02) e^(0.02 ±0.01) i GeV^-1/2$ and $g_, ±' =(0.16 ±0.01) e^(0.02 ±0.01) i GeV^-1/2$ determined recently in Ref. [ref] .
Production of $1^{-+}$ exotic charmonium-like states in electron-positron collisions · Decay width for $ψ(4360)→γX(3872)$ · 1.00
Compares with it 2 papers
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Our results are similar to the one in Ref. [ref] .
Two nearby states in the $X(3872)$ region: Resolving the radiative-decay ratio tension with $\eta_{c2}$ · Introduction · 1.00
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This situation reminds one of similar conclusions obtained for the $X(3872)$ from the study of the line shape for $X(3872)$ production [ref] .
Testing the nature of the $\Sigma^*(1430)$ · results · 0.99
Cites it as support 1 paper
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A recent study of the BESIII data on $e^+e^-→γ(D^0D̅^0π^0)J/ψπ^+π^-$, and LHCb data on $B^+→K^+(J/ψπ^+π^-)$, with full consideration of three-body effects, respecting analyticity and unitarity, provides strong support for the molecular picture [ref] .
$KX(3872)$ interaction and correlation function · Introduction · 0.97
Cites it as background 1 paper
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The possibility of an isotriplet partner was also investigated in Ref. [ref] , where both the isosinglet and isotriplet configurations were treated as molecular states.
Isosinglet-isotriplet mixing and the $X(3872)$ lineshape · Introduction · 0.89
What it cites · 49 sentences without a confident label
Contests 11 papers
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While the Flatté parameterization of Ref. [ref] employed in Refs. [ref] offers improvement by including the nonanalyticity at the $D^0D̅^*0$ threshold, it neglects the three-body effects of the $DD̅π$ system, as discussed in Refs. [ref] for similar systems, which could hinder a precise determination of the $X(3872)$ properties.
Reconciling the X(3872) with the near-threshold enhancement in the D^0\bar{D}^{*0} final state · Introduction · contest 0.71
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While the Flatté parameterization of Ref. [ref] employed in Refs. [ref] offers improvement by including the nonanalyticity at the $D^0D̅^*0$ threshold, it neglects the three-body effects of the $DD̅π$ system, as discussed in Refs. [ref] for similar systems, which could hinder a precise determination of the $X(3872)$ properties.
Three-body $D\bar{D}\pi$ dynamics for the X(3872) · Introduction · contest 0.71
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While the Flatté parameterization of Ref. [ref] employed in Refs. [ref] offers improvement by including the nonanalyticity at the $D^0D̅^*0$ threshold, it neglects the three-body effects of the $DD̅π$ system, as discussed in Refs. [ref] for similar systems, which could hinder a precise determination of the $X(3872)$ properties.
2005.13419 · Introduction · contest 0.71
Uses the method or tool of 14 papers
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The $D^*$ decay widths take the $Dπ$ self-energies into account via the energy-dependent $Γ_α(E;l)$, which introduces the $πDD̅$ three-body cut into the amplitude, and the constant $Γ_α^rad$ is accounting for the radiative $Dγ$ partial width of $D^*$ (see Refs. [ref] for explicit expressions).
Predicting isovector charmonium-like states from X(3872) properties · Framework · 0.91
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The $D^*$ decay widths take the $Dπ$ self-energies into account via the energy-dependent $Γ_α(E;l)$, which introduces the $πDD̅$ three-body cut into the amplitude, and the constant $Γ_α^rad$ is accounting for the radiative $Dγ$ partial width of $D^*$ (see Refs. [ref] for explicit expressions).
Coupled-channel approach to $T_{cc}^+$ including three-body effects · Framework · 0.91
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This can be done in a way consistent with unitarity [ref] , which gives [equation] where the Latin indices $j=ρ,ω$ represent the channels $J/ψρ,J/ψω$, respectively.
A practical parametrization for line shapes of near-threshold states · Framework · 0.92
Uses data or values from 6 papers
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In the BESIII data [ref] for the $J/ψπ^+π^-$ distribution, besides the resonance signal (taken to be from $X(3872)$ in Ref. [ref] ), there is a smooth background.
Observation of $e^{+} e^{-} \to \gamma X(3872)$ at BESIII · Numerical results · 0.99
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In the BESIII data [ref] for the $J/ψπ^+π^-$ distribution, besides the resonance signal (taken to be from $X(3872)$ in Ref. [ref] ), there is a smooth background.
2309.01502 · Numerical results · 0.99
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To include the effect of the additional decay channels of $X(3872)$ in the analysis, we employ the relative branching ratios reported in Refs. [ref] ,[Although the $W_c1$ contribution was not considered there, we expect them to provide reasonable estimates.] which lead to an estimate of the contributions from other inelastic channels to the $X(3872)$ width to be $≲20$ keV.
2001.01156 · Numerical results · 0.99
Compares with 4 papers
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The real part is consistent with the ones obtained in the analyses performed by LHCb [ref] and BESIII [ref] using the generalized Flatté parameterization of Ref. [ref] , but with a significantly reduced uncertainty.
Lineshapes for composite particles with unstable constituents · Numerical results · 1.00
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The real part is consistent with the ones obtained in the analyses performed by LHCb [ref] and BESIII [ref] using the generalized Flatté parameterization of Ref. [ref] , but with a significantly reduced uncertainty.
2005.13419 · Numerical results · 1.00
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The real part is consistent with the ones obtained in the analyses performed by LHCb [ref] and BESIII [ref] using the generalized Flatté parameterization of Ref. [ref] , but with a significantly reduced uncertainty.
2309.01502 · Numerical results · 1.00
Cites as support 4 papers
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Thus the current data are consistent only with a very small or even positive effective range, providing strong support for a molecular nature of $X(3872)$ in line with the reasoning of Refs. [ref] .
From the lineshape of the $X(3872)$ to its structure · Numerical results · 1.00
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Thus the current data are consistent only with a very small or even positive effective range, providing strong support for a molecular nature of $X(3872)$ in line with the reasoning of Refs. [ref] .
Generalization of Weinberg's Compositeness Relations · Numerical results · 1.00
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Thus the current data are consistent only with a very small or even positive effective range, providing strong support for a molecular nature of $X(3872)$ in line with the reasoning of Refs. [ref] .
Effective range expansion for narrow near-threshold resonances · Numerical results · 1.00
Cites as background 16 papers
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The new quest was initiated by the discovery of $X(3872)$ in $B$ decays [ref] , also denoted as $χ_c1(3872)$ [ref] after the quantum numbers were fixed to $J^PC=1^++$ [ref] .
Observation of a narrow charmonium-like state in exclusive B+ -> K+ pi+pi- J/psi decays · Introduction · 0.97
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The new quest was initiated by the discovery of $X(3872)$ in $B$ decays [ref] , also denoted as $χ_c1(3872)$ [ref] after the quantum numbers were fixed to $J^PC=1^++$ [ref] .
Determination of the X(3872) meson quantum numbers · Introduction · 0.97
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The new quest was initiated by the discovery of $X(3872)$ in $B$ decays [ref] , also denoted as $χ_c1(3872)$ [ref] after the quantum numbers were fixed to $J^PC=1^++$ [ref] .
Quantum numbers of the $X(3872)$ state and orbital angular momentum in its $\rho^0 J\psi$ decay · Introduction · 0.97
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