[Paper Review] On the origin of the narrow peak and the isospin symmetry breaking of the $X$(3872)

S. Takeuchi, Kazuya Shimizu+1 more|arXiv (Cornell University)|Aug 5, 2014

Particle physics theoretical and experimental studies90 references22 citations

TL;DR

This paper proposes a charmonium-two-meson hybrid model to explain the narrow width and large isospin symmetry breaking in the X(3872). By incorporating energy-dependent widths for ρ and ω mesons and a cc(2P) quarkonium component coupled to D0D∗0, D+D∗−, J/ψρ, and J/ψω channels, the model reproduces the observed narrow peak near the D0D∗0 threshold and explains the large J/ψρ/J/ψω branching ratio asymmetry through mass differences in D and D∗ mesons.

ABSTRACT

The $X$(3872) formation and decay processes in the $B$-decay are investigated by a $c\bar c$-two-meson hybrid model. The two-meson state consists of the $D^0{\bar D}^*{}^0$, $D^+D^{*-}$, $J/\psi ho$, and $J/\psi\omega$ channels. The energy-dependent decay widths of the $ ho$ and $\omega$ mesons are introduced. The $D$-${\bar D}^*$ interaction is taken to be consistent with a lack of the $B{\bar B}^*$ bound state. The coupling between the $D{\bar D}^*$ and $J/\psi ho$ or the $D{\bar D}^*$ and $J/\psi\omega$ channels is obtained from a quark model. The $c{\bar c}$-$D{\bar D}^*$ coupling is taken as a parameter to fit the $X$(3872) mass. The spectrum is calculated up to 4 GeV. It is found that very narrow $J/\psi ho$ and $J/\psi\omega$ peaks appear around the $D^0{\bar D}^*{}^0$ threshold. The size of the $J/\psi\pi^3$ peak we calculated is 1.29-2.38 times as large as that of the $J/\psi\pi^2$. The isospin symmetry breaking in the present model comes from the mass difference of the charged and neutral $D$ and $D^*$ mesons, which gives a sufficiently large isospin mixing to explain the experiments. It is also found that values of the ratios of the transfer strengths can give the information on the $X$(3872) mass or the size of the $c{\bar c}$-$D{\bar D}^*$ coupling.

Motivation & Objective

• To explain the extremely narrow width of the X(3872) despite its proximity to multiple two-meson thresholds.
• To understand the large isospin symmetry breaking observed in the X(3872) decay into J/ψρ and J/ψω final states.
• To determine the origin of the narrow peak structure in the J/ψππ spectrum near 3.872 GeV.
• To investigate how the coupling between the cc(2P) state and two-meson channels affects the X(3872) properties.
• To explore whether the ratios of partial decay widths can constrain the cc-DD∗ coupling strength or the X(3872) mass.

Proposed method

• Constructs a c¯c-two-meson hybrid model including D0D∗0, D+D∗−, J/ψρ, and J/ψω channels as two-meson components.
• Introduces energy-dependent decay widths for ρ and ω mesons using monopole form factors to model their P-wave decay into pions.
• Uses a quark model to determine the coupling between DD∗ and J/ψV channels, with the cc-DD∗ coupling treated as a fit parameter.
• Imposes the D-D∗ interaction to be consistent with the absence of a BB∗ bound state.
• Calculates the full mass spectrum up to 4 GeV, including the effects of energy-dependent meson widths on the X(3872) peak.
• Fits the model parameters (ΛV, coupling strength) to experimental data on the X(3872) mass and decay branching ratios.

Experimental results

Research questions

• RQ1 How do energy-dependent widths of ρ and ω mesons lead to a narrow peak in the X(3872) spectrum near the D0D∗0 threshold?
• RQ2 What is the origin of the large isospin symmetry breaking observed in the X(3872) decays to J/ψρ and J/ψω final states?
• RQ3 Can the observed branching ratio ratio rD0D∗0 ≈ 8.9–19.9 be explained by the model’s coupling parameters and mass differences?
• RQ4 How do the ratios of transfer strengths in the decay modes reflect the size of the cc-DD∗ coupling or the X(3872) mass?
• RQ5 To what extent can the X(3872) be described as a superposition of a cc(2P) state and two-meson molecular components?

Key findings

• The model produces very narrow J/ψρ and J/ψω peaks around the D0D∗0 threshold, with a peak width consistent with the experimental observation of less than 1.2 MeV.
• The calculated size of the J/ψπ3 peak is 1.27–2.24 times larger than that of the J/ψπ2 peak, consistent with experimental data.
• Isospin symmetry breaking arises naturally from the mass difference between charged and neutral D and D∗ mesons, which induces sufficient mixing to explain the observed 1:1 branching ratio between J/ψρ and J/ψω final states.
• The ratio of partial decay widths into D0D∗0 and J/ψρ channels varies significantly with the cc-DD∗ coupling strength, indicating that such ratios can constrain the coupling or the X(3872) mass.
• The energy-dependent widths of ρ and ω mesons are essential for generating the narrow peak; without them, the peak would be significantly broader.
• The model successfully explains the absence of a charged X(3872) state and the lack of a χc1(2P) peak in the 1++ spectrum, consistent with experimental observations.