Study of the lineshape of $X(3872)$ using $B$ decays to ${D}^{0}{\overline{D}}^{*0}K$

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Study of the lineshape of $X (3872)$ using $B$ decays to $D^{0} {\bar{D}}^{* 0} K$

H. Hirata et al. (Belle Collaboration)

Phys. Rev. D 107, 112011 – Published 28 June 2023

Abstract

We present a study of the $X (3872)$ lineshape in the decay $B \to X (3872) K \to D^{0} {\bar{D}}^{* 0} K$ using a data sample of $772 \times 10^{6} B \bar{B}$ pairs collected at the $ϒ (4 S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+} e^{-}$ collider. The peak near the threshold in the $D^{0} {\bar{D}}^{* 0}$ invariant mass spectrum is fitted using a relativistic Breit-Wigner lineshape. We determine the mass and width parameters to be $m_{BW} = 3873.7 1_{- 0.50}^{+ 0.56} (stat) \pm 0.13 (syst) MeV / c^{2}$ and $Γ_{BW} = {5.2}_{- 1.5}^{+ 2.2} (stat) \pm 0.4 (syst) MeV$ , respectively. The branching fraction is found to be $B (B^{+} \to X (3872) K^{+}) \times B (X (3872) \to D^{0} {\bar{D}}^{* 0}) = (0.9 7_{- 0.18}^{+ 0.21} (stat) \pm 0.10 (syst)) \times 10^{- 4}$ . The signal from $B^{0}$ decays is observed for the first time with $5.2 σ$ significance, and the ratio of branching fractions between charged and neutral $B$ decays is measured to be $B (B^{0} \to X (3872) K^{0}) / B (B^{+} \to X (3872) K^{+}) = {1.34}_{- 0.40}^{+ 0.47} (stat)_{- 0.12}^{+ 0.10} (syst)$ . The peak is also studied using a Flatté lineshape. We determine the lower limit on the $D {\bar{D}}^{*}$ coupling constant $g$ to be 0.075 at 95% credibility in the parameter region where the ratio of $g$ to the mass difference from the $D^{0} {\bar{D}}^{* 0}$ threshold is equal to $- 15.11 {GeV}^{- 1}$ , as measured by LHCb.

Received 3 February 2023
Accepted 15 May 2023

DOI:https://doi.org/10.1103/PhysRevD.107.112011

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Exotic mesons

Particles & Fields

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Vol. 107, Iss. 11 — 1 June 2023

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Figure 1
Distributions of $(M_{bc}, Δ E)$ for $B^{+}$ (left) and $B^{0}$ (right) candidates in the $M (D^{0} {\bar{D}}^{* 0}) < 3.88 GeV / c^{2}$ region, where the signal-to-background ratio for $X (3872)$ in data is relatively high. The red solid and blue dashed rectangles show the $(M_{bc}, Δ E)$ signal regions for ${\bar{D}}^{* 0} \to {\bar{D}}^{0} γ$ and ${\bar{D}}^{0} π^{0}$ , respectively.
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Figure 2
The detector response for the signal component. (a) The sum of products of the signal efficiency and the branching fraction of the intermediate states $B_{{\bar{D}}^{* 0}} \sum ε_{i j} \times B_{i j}$ as a function of the $X (3872)$ mass generated in the MC samples for $B^{+} \to X (3872) K^{+}$ ; the blue circles and the red squares are for $D^{* 0} \to D^{0} π^{0}$ and $D^{* 0} \to D^{0} γ$ , respectively. The lines represent the parametrized efficiency functions. For $B^{0} \to X (3872) K^{0}$ , similar structures are obtained with a ratio of $B^{+} \to X (3872) K^{+}$ to $B^{0} \to X (3872) K^{0}$ of almost $4 : 1$ . (b) The $M (D^{0} {\bar{D}}^{* 0})$ spread due to the detector response for the $X (3872)$ lineshape generated with zero width and masses of $3871.9 MeV / c^{2}$ , $3879.0 MeV / c^{2}$ , $3884.0 MeV / c^{2}$ , and $3950.0 MeV / c^{2}$ for the $D^{* 0} \to D^{0} π^{0}$ decay mode. The circles show normalized distributions obtained from the MC sample. The curves show the parametrized resolution functions. Similar results are obtained for $D^{* 0} \to D^{0} γ$ .
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Figure 3
The $M (D^{0} {\bar{D}}^{* 0})$ distributions with the fit result with the relativistic Breit-Wigner lineshape for $B^{+} \to X (3872) K^{+}$ (top) and $B^{0} \to X (3872) K^{0}$ (bottom). The left and right rows are for ${\bar{D}}^{* 0} \to {\bar{D}}^{0} γ$ and ${\bar{D}}^{* 0} \to {\bar{D}}^{0} π^{0}$ , respectively. The points with error bars represent data. The blue solid line shows the total fit result. The blue and green dashed lines show the signal contributions and broken signal contributions, respectively. The red dashed line shows the contribution of generic background.
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Figure 4
The $M (D^{0} {\bar{D}}^{* 0})$ distributions with the fit result with the Flatté lineshape for $B^{+} \to X (3872) K^{+}$ (top) and $B^{0} \to X (3872) K^{0}$ (bottom). The left and right rows are for ${\bar{D}}^{* 0} \to {\bar{D}}^{0} γ$ and ${\bar{D}}^{* 0} \to {\bar{D}}^{0} π^{0}$ , respectively. The points with error bars represent data. The blue solid line shows the total fit result. The blue and green dashed lines show the signal contributions and broken-signal contributions, respectively. The red dashed line shows the contribution of generic background.
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Figure 5
The median of output values of the coupling constant $g$ , as a function of the input $g$ , evaluated using pseudoexperiments. The dotted black line represents perfect linearity $g_{out} = g_{in}$ . The solid blue curve represents the threshold function $g_{out} = 0.14 (1 - \exp (- 9 g_{in}))$ .
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Figure 6
For each of seven parameter sets, the likelihood ratio $L / L_{0}$ is shown, as a function of the coupling constant $g$ , where $L = L (g)$ is the fitted likelihood and $L_{0}$ is the likelihood of the best fit for that parameter set. The solid black line shows the parameter set (1). The red and blue dotted lines show parameter sets (2) and (3), respectively. The red and blue dashed lines show sets (4) and (5), and the red and blue dot-dashed lines show sets (6) and (7), respectively. The parameter sets are described in Table 5. Circles on the lines show the best fit $g$ .
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Physical Review D

covering particles, fields, gravitation, and cosmology

Study of the lineshape of $X (3872)$ using $B$ decays to $D^{0} {\bar{D}}^{* 0} K$

H. Hirata et al. (Belle Collaboration)

Phys. Rev. D 107, 112011 – Published 28 June 2023

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Physical Review D

covering particles, fields, gravitation, and cosmology

Study of the lineshape of X(3872) using B decays to D0D¯*0K

H. Hirata et al. (Belle Collaboration)

Phys. Rev. D 107, 112011 – Published 28 June 2023

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Study of the lineshape of $X (3872)$ using $B$ decays to $D^{0} {\bar{D}}^{* 0} K$