Determination of the absolute branching fractions of X(3872) decays

TL;DR

This paper provides the first comprehensive measurement of the absolute branching fractions of X(3872) decays by combining data from multiple experiments, revealing significant unobserved decay modes and estimating the production cross section at 4.226 GeV.

Contribution

It introduces the first global analysis of X(3872) decay modes, providing precise absolute branching fractions and highlighting the potential for discovering new decay channels.

Findings

Branching fraction to pi+pi- J/psi is about 4.1%.

Branching fraction to D*0 D0bar+c.c. is about 52.4%.

Approximately 32% of X(3872) decays remain unobserved.

Abstract

We report the first determination of the absolute branching fractions of the X(3872) decays by globally analyzing the measurements provided by the Belle, BaBar, BESIII, and LHCb experiments. The branching fractions of X(3872) to pi^+pi^- J/psi and D*0D0bar+c.c. are found to be (4.1^{+1.9}_{-1.1})% and (52.4^{+25.3}_{-14.3})%, respectively. The branching fractions of the decays X(3872) to gamma J/psi, gamma psi', omega J/psi, and pi^0 chi_{c1} are also determined. The global fit implies that the fraction of X(3872) decays which are not observed in experiments is (31.9_{-31.5}^{+18.1})%, which indicates that there is still a lot of room for searching for new decay modes of the X(3872). With the branching fraction, we determine the production cross section of e+e- to gamma X(3872) at center-of-mass energy 4.226 GeV.

Tables

Table 1. Table 1: The measurements of the X ​ ( 3872 ) 𝑋 3872 X(3872) decays by Belle, BaBar, BESIII, and LHCb experiments: the product branching fractions of X ​ ( 3872 ) → π + ​ π − ​ J / ψ → 𝑋 3872 superscript 𝜋 superscript 𝜋 𝐽 𝜓 X(3872)\to\pi^{+}\pi^{-}J/\psi , γ ​ J / ψ 𝛾 𝐽 𝜓 \gamma J/\psi , γ ​ ψ ​ ( 3686 ) 𝛾 𝜓 3686 \gamma\psi(3686) , D ∗ 0 ​ D ¯ 0 + c . c . formulae-sequence superscript 𝐷 absent 0 superscript ¯ 𝐷 0 𝑐 𝑐 D^{*0}\bar{D}^{0}+c.c. , and ω ​ J / ψ 𝜔 𝐽 𝜓 \omega J/\psi , the inclusive branching fraction ℬ ​ ( B → X ​ ( 3872 ) ​ K ) ℬ → 𝐵 𝑋 3872 𝐾 {\cal B}(B\to X(3872)K) , the ratios of the branching fractions ℬ ( X ( 3872 ) → γ J / ψ , ω J / ψ , D ∗ 0 D ¯ 0 + c . c . , π 0 χ c ​ 1 ) {\cal B}(X(3872)\to\gamma J/\psi,~{}\omega J/\psi,~{}D^{*0}\bar{D}^{0}+c.c.,~{}\pi^{0}\chi_{c1}) to ℬ ​ ( X ​ ( 3872 ) → π + ​ π − ​ J / ψ ) ℬ → 𝑋 3872 superscript 𝜋 superscript 𝜋 𝐽 𝜓 {\cal B}(X(3872)\to\pi^{+}\pi^{-}J/\psi) . The first uncertainties are statistical and the second systematic.

Index ($i$)	Parameters	Values	Experiments
	$X\left(3872\right)\to {\pi }^{+}{\pi }^{-}J/\psi$	($\times {10}^{-6}$)
1	$B^{+}\to X\left(3872\right)K^{+}$	$8.61\pm 0.82\pm 0.52$	Belle Be2011a
2		$8.4\pm 1.5\pm 0.7$	BaBar Ba2008a
3	$B^0\to X\left(3872\right)K^0$	$4.3\pm 1.2\pm 0.4$	Belle Be2011a
4		$3.5\pm 1.9\pm 0.4$	BaBar Ba2008a
	$X\left(3872\right)\to \gamma J/\psi$	($\times {10}^{-6}$)
5	$B^{+}\to X\left(3872\right)K^{+}$	${1.78}_{-0.44}^{+0.48}\pm 0.12$	Belle Be2011b
6		$2.8\pm 0.8\pm 0.1$	BaBar Ba2009b
7	$B^0\to X\left(3872\right)K^0$	${1.24}_{-0.61}^{+0.76}\pm 0.11$	Belle Be2011b
8		$2.6\pm 1.8\pm 0.2$	BaBar Ba2009b
	$X\left(3872\right)\to \gamma \psi \left(3686\right)$	($\times {10}^{-6}$)
9	$B^{+}\to X\left(3872\right)K^{+}$	${0.83}_{-1.83}^{+1.98}\pm 0.44$	Belle Be2011b
10		$9.5\pm 2.7\pm 0.6$	BaBar Ba2009b
11	$B^0\to X\left(3872\right)K^0$	${1.12}_{-2.90}^{+3.57}\pm 0.57$	Belle Be2011b
12		$11.4\pm 5.5\pm 1.0$	BaBar Ba2009b
	$X\left(3872\right)\to D^{\ast 0}{\overline{D}}^0+c.c.$	($\times {10}^{-4}$)
13	$B^{+}\to X\left(3872\right)K^{+}$	$0.77\pm 0.16\pm 0.10$	Belle Be2010c
14		$1.67\pm 0.36\pm 0.47$	BaBar Ba2008c
15	$B^0\to X\left(3872\right)K^0$	$0.97\pm 0.46\pm 0.13$	Belle Be2010c
16		$2.22\pm 1.05\pm 0.42$	BaBar Ba2008c
	$X\left(3872\right)\to \omega J/\psi$	($\times {10}^{-6}$)
17	$B^{+}\to X\left(3872\right)K^{+}$	$6\pm 2\pm 1$	BaBar Ba2010d
18	$B^0\to X\left(3872\right)K^0$	$6\pm 3\pm 1$	BaBar Ba2010d
	Ratios
19	$\frac{ℬ\left(X\left(3872\right)\to \gamma J/\psi \right)}{ℬ\left(X\left(3872\right)\to {\pi }^{+}{\pi }^{-}J/\psi \right)}$	$0.79\pm 0.28$	BESIII Bs1
20	$\frac{ℬ(X\left(3872\right)\to D^{\ast 0}{\overline{D}}^0+c.c.)}{ℬ\left(X\left(3872\right)\to {\pi }^{+}{\pi }^{-}J/\psi \right)}$	$14.81\pm 3.80$	BESIII Bs1
21	$\frac{ℬ\left(X\left(3872\right)\to \omega J/\psi \right)}{ℬ\left(X\left(3872\right)\to {\pi }^{+}{\pi }^{-}J/\psi \right)}$	${1.6}_{-0.3}^{+0.4}\pm 0.2$	BESIII Bs2
22	$\frac{ℬ\left(X\left(3872\right)\to {\pi }^0{\chi }_{c1}\right)}{ℬ\left(X\left(3872\right)\to {\pi }^{+}{\pi }^{-}J/\psi \right)}$	${0.88}_{-0.27}^{+0.33}\pm 0.10$	BESIII Bs3
23	$\frac{ℬ\left(X\left(3872\right)\to \gamma \psi \left(3686\right)\right)}{ℬ\left(X\left(3872\right)\to \gamma J/\psi \right)}$	$2.46\pm 0.64\pm 0.29$	LHCb Lb1
	$B^{+}\to X\left(3872\right)K^{+}$	($\times {10}^{-4}$)
24		$2.1\pm 0.6\pm 0.3$	BaBar Ba2019d
25		$1.2\pm 1.1\pm 0.1$	Belle Be2018d

Table 2. Table 2: The fitting results of the absolute branching fractions of the X ​ ( 3872 ) 𝑋 3872 X(3872) decays and B → X ​ ( 3872 ) ​ K → 𝐵 𝑋 3872 𝐾 B\to X(3872)K decays. The branching fraction of X ​ ( 3872 ) 𝑋 3872 X(3872) decays into unknown modes is calculated from the fit results.

Parameter index	Decay mode	Branching fraction
1	$X\left(3872\right)\to {\pi }^{+}{\pi }^{-}J/\psi$	$\left({4.1}_{-1.1}^{+1.9}\right)\%$
2	$X\left(3872\right)\to D^{\ast 0}{\overline{D}}^0+c.c.$	$\left({52.4}_{-14.3}^{+25.3}\right)\%$
3	$X\left(3872\right)\to \gamma J/\psi$	$\left({1.1}_{-0.3}^{+0.6}\right)\%$
4	$X\left(3872\right)\to \gamma \psi \left(3686\right)$	$\left({2.4}_{-0.8}^{+1.3}\right)\%$
5	$X\left(3872\right)\to {\pi }^0{\chi }_{c1}$	$\left({3.6}_{-1.6}^{+2.2}\right)\%$
6	$X\left(3872\right)\to \omega J/\psi$	$\left({4.4}_{-1.3}^{+2.3}\right)\%$
7	$B^{+}\to X\left(3872\right)K^{+}$	$\left(1.9\pm 0.6\right)\times {10}^{-4}$
8	$B^0\to X\left(3872\right)K^0$	$\left({1.1}_{-0.4}^{+0.5}\right)\times {10}^{-4}$
	$X\left(3872\right)\to \mathrm{unknown}$	$\left({31.9}_{-31.5}^{+18.1}\right)\%$

Table 3. Table 3: Correlation coefficients of the fit parameters listed in Table  2 .

Parameter index	1	2	3	4	5	6	7	8
1	1	0.87	0.84	0.75	0.64	0.79	-0.95	-0.87
2		1	0.79	0.71	0.56	0.74	-0.90	-0.77
3			1	0.78	0.54	0.73	-0.88	-0.78
4				1	0.49	0.65	-0.79	-0.69
5					1	0.51	-0.61	-0.56
6						1	-0.82	-0.72
7							1	0.84

Equations

$${\chi }^2(x)=\sum _{i=1}^{25}\frac{(x_i-x{)}^2}{{\sigma }_i^2},$$

Full text

††preprint:

Observed in 2003 by the Belle experiment intx1 , the $X(3872)$ has been the most puzzling state among all the so-called charmoniumlike ${\rm XYZ}$ states for all these years PR_review . Being very close to the $D^{*0}\bar{D}^{0}+c.c.$ mass threshold, it is supposed to have a large $D^{*0}\bar{D}^{0}+c.c.$ molecule component intx2 , and its large production rate in $pp$ and $p\bar{p}$ collision experiments suggests that there is a charmonium state $\chi_{c1}(2P)$ core in its wave function lhcpp1 ; lhcpp2 ; lhcpp3 ; d0 . The absolute branching fractions of observed and unknown decays of $X(3872)$ could provide essential information to distinguish the different scenarios absoa1 ; absoa2 ; abso1 ; abso2 .

During the last 16 years, there have been many experimental measurements on the $X(3872)$. Its mass was measured in a high precision of 170 keV pdg and its spin-parity and charge-conjugate parity quantum numbers were determined to be $J^{PC}=1^{++}$ lhcbq ; however, all other quantities are only known with very large uncertainties. Its total width is known to be an upper limit of 1.2 MeV at the 90% confidence level (C.L.), and only $D^{*0}\bar{D}^{0}+c.c.$, $\pi^{+}\pi^{-}J/\psi$, $\omega J/\psi$, $\gamma J/\psi$, and $\pi^{0}\chi_{c1}$ decay modes are observed with more than 5 standard deviation significance Be2011a ; Ba2008a ; Be2010c ; Ba2008c ; Ba2010d ; Bs1 ; Bs2 ; Bs3 ; Be2011b ; Ba2009b , and the existence of the $\gamma\psi(3686)$ decay mode is not confirmed Bs1 ; Be2011b ; Ba2009b ; Lb1 . None of the above modes have measured absolute branching fractions due to the fact that the total number of $X(3872)$ events is very difficult to be determined either in $B$-meson decays or in an $e^{+}e^{-}$ annihilation experiment. As a consequence, only the product branching fractions in $B$ decays or the product of the total cross section and the $X(3872)$ decay branching fraction is reported experimentally.

BaBar and Belle experiments tried to measure ${\cal B}(B^{+}\to X(3872)K^{+})$ by reconstructing inclusive $B^{+}\to K^{+}+\,{anything}$ and searching for the monochromatic $K^{+}$ corresponds to two-body decay $B^{+}\to X(3872)K^{+}$ in the center-of-mass system of the $B^{+}$-meson Ba2005_x ; Be2018d , but no significant signals were observed. By improving the algorithm of signal reconstruction and using the full available data, BaBar is able to improve the sensitivity of the inclusive $X(3872)$ reconstruction, and a $3\sigma$ significance signal of $B^{+}\to X(3872)K^{+}$ is observed, and the branching fraction is determined to be $(2.1\pm 0.6\pm 0.3\pm 0.1)\times 10^{-4}$ Ba2019d , where the three uncertainties are statistical, systematic, and in the quoted ${\cal B}(B^{+}\to J/\psi K^{+})$, respectively. Belle found only a $1.1\sigma$ $X(3872)$ signal, and provided an upper limit ${\cal B}(B^{+}\to X(3872)K^{+})<2.6\times 10^{-4}$ at the 90% C.L., and a central value of $(1.2\pm 1.1\pm 0.1)\times 10^{-4}$, where the uncertainties are statistical and systematic, respectively.

Although neither the BaBar nor the Belle measurement is significant enough to claim observation of $B^{+}\to X(3872)K^{+}$ signal, we do know this decay exists since significant signals have been observed when $X(3872)$ is reconstructed in its exclusive decay modes such as $\pi^{+}\pi^{-}J/\psi$ and $D^{*0}\bar{D}^{0}+c.c.$ This allows us to extract the $X(3872)$ decay branching fractions by using the BaBar and Belle measurements of ${\cal B}(B^{+}\to X(3872)K^{+})$ and the other measurements from Belle, BaBar, BESIII, and LHCb experiments.

The measurements used in this analysis are listed in Table 1. To extract the absolute branching fractions of $X(3872)$ decays we do a least square fit by minimizing

[TABLE]

where $i$ is the index (from 1 to 25) listed in Table 1, $x_{i}$ are the 25 measured values, $x$ is the corresponding values constructed with free parameters, and $\sigma_{i}$ is the sum of the statistical and systematic uncertainties in quadrature.

In the above definition, we assumed that all the measurements follow Gaussian distribution, the statistical uncertainties of different measurements are uncorrelated, and possible correlation among the systematic uncertainties of different measurements in an experiment is neglected since the statistical uncertainties are dominant for most of the measurements. We also assume that there is no correlation between different experiments.

The branching fractions ${\cal B}(X(3872)\to\pi^{+}\pi^{-}J/\psi)$, ${\cal B}(X(3872)\to D^{*0}\bar{D}^{0}+c.c.)$, ${\cal B}(X(3872)\to\gamma J/\psi)$, ${\cal B}(X(3872)\to\gamma\psi(3686))$, ${\cal B}(X(3872)\to\omega J/\psi)$, ${\cal B}(X(3872)\to\pi^{0}\chi_{c1})$, ${\cal B}(B^{+}\to X(3872)K^{+})$, and ${\cal B}(B^{0}\to X(3872)K^{0})$ are free parameters in the fit. By minimizing $\chi^{2}(x)$ with minuit minuit , the fitting results are obtained and listed in Table 2. The fit yields $\chi^{2}/{\rm ndf}$=25.2/17 where ${\rm ndf}$ represents the number of degrees of freedom. The correlation coefficients between the fit parameters are shown in Table 3.

From the fitting results we can see that $D^{*0}\bar{D}^{0}+c.c.$ is the dominant decay mode of the $X(3872)$ with a decay rate of $(52.4^{+25.3}_{-14.3})\%$, and all the other modes with charmonium have branching fraction of a few percent. With all of the known branching fractions, the fraction of $X(3872)$ decays which is not yet observed in experiment is determined to be $(31.9_{-31.5}^{+18.1})\%$, so the search for new decay modes of the $X(3872)$ is still an important task. As free parameters in the fitting, the production rates of the $X(3872)$ in neutral and charged $B$-meson decays are obtained as listed in Table 2.

BESIII measured the product $\sigma(e^{+}e^{-}\to\gamma X(3872)){\cal B}(X(3872)\to\pi^{+}\pi^{-}J/\psi)$ at center-of-mass energies from 4 to 4.6 GeV Bs2 , with known ${\cal B}(X(3872)\to\pi^{+}\pi^{-}J/\psi)$, the production cross section of $e^{+}e^{-}\to\gamma X(3872)$ can be obtained. The peak cross section of $e^{+}e^{-}\to\gamma X(3872)$ is found to be $(5.5^{+2.8}_{-3.6})$ pb at the center-of-mass energy 4.226 GeV. This is obtained by sampling both numerator and denominator with the consideration of their asymmetric uncertainties, the cross section is about an order of magnitude smaller than that of $e^{+}e^{-}\to\pi^{+}\pi^{-}J/\psi$ at the same energy pipijpsi_lineshape .

In summary, we obtain the absolute branching fractions of the $X(3872)$ decays into six modes by globally fitting the measurements provided by Belle, BaBar, BESIII, and LHCb experiments. The branching fraction of $X(3872)\to\pi^{+}\pi^{-}J/\psi$ is determined to be $(4.1^{+1.9}_{-1.1})\%$ which can be used in many measurements where $X(3872)\to\pi^{+}\pi^{-}J/\psi$ is reconstructed and can supply critical input in understanding the nature of the $X(3872)$ ortega . This branching fraction is in good agreement with early estimations in Refs. ycz_pic2009 and Esposito:2014rxa . By combining the branching fractions of the observed modes, we obtain the fraction of the unknown decays of the $X(3872)$ as $(31.9_{-31.5}^{+18.1})\%$, which calls for more experimental efforts in the study of the $X(3872)$ decays.