XYZ at Belle

TL;DR

This paper reviews recent experimental results on exotic heavy-quark states, including searches for specific particles, measurements of branching fractions, and new state discoveries in high-energy physics.

Contribution

It provides new experimental data and searches related to XYZ states, including the $Y$(4260), $Y$(4630) spin partner, $P_s^+$ pentaquark, and $X$(3872) branching fractions.

Findings

Search for $Y$(4260) in B decays

Observation of a spin partner of $Y$(4630)

Measurement of $X$(3872) branching fraction

Abstract

Recent results of exotic states with heavy quarks, denoted as $XYZ$ states, are presented. The results include searches for the $Y$(4260) in $B$ meson decays, a spin partner of $Y$(4630), and the strange Pentaquark $P_s^+$. In addition, the measurements of the absolute branching fraction of $X$(3872) and search for double $Z_c$ production is discussed.

Equations

$$\mathcal{B}({\Lambda }_c^{+}\to P_s^{+}\varphi )\times \mathcal{B}(P_s^{+}\to \varphi p)<8.3\times 10^{-5}.$$

Full text

1 Introduction

In recent years, numerous narrow states with heavy quarks ($c$,$b$) have been observed, which do not fit the expected properties for charmonium or bottomonium states from the Cornell potential potential_1978 . For detailed information about the states, their discovery and their properties, we refer to the recent reviews reviews . Throughout this paper below, charge conjugated states and decay modes are implied.

2 $Y$(4260) in $B$ meson decays

The vector state $Y$(4260) has been observed in the ISR (initial state radiation) process e^{+}$$e^{-}$$\rightarrow$$\gamma$$Y(4260)\rightarrow$$J/\psi$$\pi^{+}$$\pi^{-} by BaBar y4260_babar , Belle y4260_belle , CLEO–c y4260_cleo-c and in direct production in e^{+}$$e^{-}$$\rightarrow$$Y(4260) at BESIII y4260_bes3 . Up to date, in total four states $Y$(4008), $Y$(4260), $Y$(4350) and $Y$(4660) have been observed by several experiments, all of them carrying the quantum numbers $J^{PC}$=1*–*. In addition, there are the well known conventional vector charmonium states $\psi$(4040), $\psi$(4140), $\psi$(4400) pdg in the same mass regime, leading to a overpopulation of states and thus pointing to the exotic nature of the $Y$ states.

In literature, the $Y$(4260) has been discussed as a D$$\overline{D}_{1}(2460) molecule and as a $P$-wave tetraquark reviews . In particular, the decay to D^{(*)}$$\overline{D}^{(*)} has not been seen yet pdg , although the phasespace is large. This observation can be explained in the context of a [$$J/\psi$$f_{0}(980)$$] hadrocharmonium state (with dominant decays to ”core" and ”cloud” components) or of a $[$(c$$\overline{c}){}_{8}g$$] hybrid (with open charm decays being blocked by the gluon fluxtube) reviews .

Searches for the $Y$(4260) in $B$ meson decays have started more than a decade ago by BABAR in the decay B^{+}$$\rightarrow$$K^{+}$$Y(4260) with $Y$(4260)\rightarrow$$J/\psi$$\pi^{+}$$\pi^{-}. In a data set of 211 fb*-1*, 128$\pm$42 signal events were observed y4260_in_b_decays_babar , corresponding to a significance of 3.1$\sigma$, and being translated to a range of a branching fraction of 1.2<$${\cal B}$$<2.9$\times$10*-5*.

Recently, the D0 experiment reported the surprising observation with 167$\pm$41 signal events (4.3$\sigma$ significance) in a data set of 10.4 fb*-1* y4260_in_b_decays_D0 . However, different from BABAR , $b$-flavoured hadrons ($B$, $B_{s}$, $B*$, $\Lambda_{b}$, …) were selected inclusively instead of $B$ mesons, by requiring a [$$J/\psi$$\pi^{+}$$\pi^{-}$$] system with a secondary vertex.

A search in Belle was performed y4260_in_b_decays_belle , using the complete Belle $\Upsilon$(4S) data set of 711 fb*-1* and corresponding to a factor  3.3 more data than in case of BABAR . Scaling the signal and background yields would give $S$/$\sqrt{S+B}$=5.7, which would be a clear observation. In addition, neutral B decays with B^{0}$$\rightarrow$$K^{0}_{s}$$Y(4260) were added to the analysis. Fig. 1 shows the $J$/\psi$$\pi^{+}$$\pi^{-} invariant mass distributions for the three different mass regions around the $\psi^{\prime}$, the $X$(3872) and the $Y$(4260). The first two served as control signals. For the $Y$(4260), no signal was observed, with the measured branching fraction reaching the 10*-6* level. The derived upper limit of 1.4$\times$10*-5* for the charged $B$ meson decays is consistent with the BABAR measurement.

3 Search for a spin partner of the $Y$(4630)

The $Y$(4630) was discovered in ISR as well and thus also represents a vector state with $J^{PC}$=1*–. Along with the $Y$(4660) mentioned above in Sec. 2, it represents the highest charmed XYZ state with charm observed so far. If being a pure c$$\overline{c} state, the radius111In the Cornell potential, the radius can be approximated by the turning point of the wavefunction. of can be calculated in the Cornell potential r$$\simeq2.2 fm, far beyond string breaking limit outside the confinement region. In addition, it is the only XYZ state observed so far decaying into baryons. It was recognized early, that the $Y$(4660), decaying to $J$/\psi$$\pi^{+}$$\pi^{-} and already mentioned above, and the $Y$(4630), decaying to \Lambda_{c}^{+}$$\Lambda_{c}^{-}, may represent same state y4660_guo . In the hadrocharmonium model, the X(3872) can be interpreted as a [$$J/\psi$$\rho^{0}$$] state, the $Y$(4260) as a $[$ $J$/$\psi$ $f_{0}$(980)$]$ state and the $Y$(4630) as a [$$\psi^{\prime} $f_{0}$(980)$]$ state. The latter one would imply the existence of a [$$\eta_{c}(2S) $f_{0}$(980)$]$ partner state, called the $Y_{\eta}$, with a mass of 4613$\pm$4 MeV and a width $\simeq$30 MeV, whereas the width is dominated by the $\eta_{c}$(2S). With $L$=0, the quantum numbers would be $J^{PC}$=0-+, and thus it can not be produced in ISR. Therefore a search in $B$ meson decays was performed with the complete Belle $\Upsilon$(4S) data set of 711 fb-1* y4660_spin_partner_belle . No signal was observed yet, leading to an upper limit of ${\cal B}$(B^{+}$$\rightarrow$$K^{+}$$Y_{\eta}) $\times$ ${\cal B}$(Y_{\eta}$$\rightarrow$$\Lambda_{c}^{+}$$\Lambda_{c}^{-})$<$2.0\times$$10^{-4}.

4 Absolute branching fraction of the $X$(3872)

The $X$(3872) has been observed in five different decays pdg . However, all branching fractions are only established as lower limits pdg , because the total branching fraction ${\cal B}_{total}$, being required as normalisation, is not known. There is a way to measure ${\cal B}_{total}$ at $B$ factories, which operate with e^{+}$$e^{-} collisions at the $\Upsilon$(4S) resonance at $\sqrt{s}$=10.58 GeV. The particular situation kinematic situation at the $\Upsilon$(4S) is, that the mass of the $\Upsilon$(4S)) coincides very closely with the sum of the masses of the $B$ meson and the $\overline{B}$ meson, the decay products of the $\Upsilon$(4S). Therefore, the two $B$ mesons are almost at rest in the center-of-mass (cms) system. One of the two $B$ mesons can now be tagged, with a hierarchical full reconstruction of 1104 hadronic decays neurobayes . The other, remaining $B$ meson could be decay into a $K$ meson and a charmonium or charmonium-like, exotic state $X_{c\overline{c}}$. Due to the peculiar kinematic situation, the missing mass $m_{miss}$ of the $K$ meson can be utilized for the measurements of total cross sections of any $X_{c\overline{c}}$, and in particular the X(3872). The missing mass is calculated as $m_{miss}$($K$)=$\sqrt{p^{*}_{e^{+}e^{-}}-p^{*}_{tag}-p^{*}_{K})^{2}}$/$c^{2}$ with cms momenta of the e^{+}$$e^{-} collision system, the tagging side and the $K$ meson, respectively. The recently measured value is ${\cal B}_{total}$=1.2$\pm$1.1$\pm$0.1\times$$10^{-4} belle_x3872_absolute , leading to an upper limit of {\cal B}_{total}$$<2.6\times$$10^{-4}. Interestingly, this value almost reaches the value of the highest known partial product branching fraction pdg for B^{+}$$\rightarrow$$K^{+}$$X(3872) with $X$(3872)\rightarrow$$D^{0}$$\overline{D}^{0}$$\pi^{0} of ${\cal B}_{partial}$=(1.0$\pm$0.4)$\times$10*-4*. Thus, the measurement of ${\cal B}_{total}$ is in close reach for the ongoing data taking at Belle II.

5 Double $Z_{c}$ production

The charged $Z_{c}$ states have been observed in e^{+}$$e^{-}$$\rightarrow$$Z_{c}^{+}(3900)$\pi^{-}$ at BESIII at $\sqrt{s}$=4.26 GeV z3900_bes3 . In addition, the charged $Z_{b}$ states have been observed in e^{+}$$e^{-}$$\rightarrow$$Z_{b}^{+}$$\pi^{-} at Belle at higher $\sqrt{s}$=10.86 GeV in the bottomonium mass regime. Thus, it is intuitive to perform a search for e^{+}$$e^{-}$$\rightarrow$$Z_{c}^{+}$$Z_{c}^{(^{\prime})-} pair production at such higher cms energies of $\sqrt{s}$=10.52 GeV, 10.58 GeV and 10.86 GeV, using the complete Belle data set. This search was performed at Belle zczc_belle , adding even 102 Mill. $\Upsilon$(1S) and 158 Mill. $\Upsilon$(2S) decays at $\sqrt{s}$=9.46 GeV and 10.02 GeV, respectively. $Z_{c}^{+}$ $Z_{c}^{(^{\prime})-}$ refer to any possible combination of the $Z_{c}$(3900) and the $Z_{c}$(4200) states. No signal was observed, resulting, as an example, in an upper limit on the product branching fraction \sigma$$\times$${\cal B}($Z_{c}^{+}$(3900)\rightarrow$$J/\psi$$\pi^{+}) of 2.3 fb for the $Z_{c}$(3900)$Z_{c}$(3900) combination. The order of magnitude of these upper limits is about a factor of 106 smaller than typical cross sections of $\sigma$(e^{+}$$e^{-}$$\rightarrow$$\Upsilon(5S))=0.3 nb at $\sqrt{s}$=10.86 GeV and about a factor 104 smaller than $\sigma$(e^{+}$$e^{-}$$\rightarrowY(4260))$\simeq$65 pb at $\sqrt{s}$=4.26 GeV, with $\Upsilon$(5S)\rightarrow$$Z_{b}^{(^{\prime})+}$$\pi^{-} and $Y$(4260)\rightarrow$$Z_{c}^{+}(3900)$\pi^{-}$.

6 Search for the $P_{s}^{+}$ pentaquark

The charmed pentaquark candidate P_{c}^{+}$$\rightarrow$$J/\psi$$p has been observed in $\Lambda_{b}$ decays at LHCb Pc_lhcb . For Belle (II), the $\Lambda_{b}$ is outside the kinematically accessible range. However, $\Lambda_{c}$ baryons are produced copiously and provide a suitable data set for the search for the strange partner of the $P_{c}^{+}$, called $P_{s}^{+}$, in the decay P_{s}^{+}$$\rightarrow$$\phi$$p in \Lambda_{c}$$\rightarrow$$[$$\phi$$p$$]$$\pi^{0}. The search was performed at Belle Ps_belle in a data set of 915 fb*-1* with total 1.468.435$\pm$4816 $\Lambda_{c}$ candidates. Fig. 2 shows the background subtracted $m$(\phi$$p) distribution. Each data point corresponds to a fitted yield of a 2D fit. For details about the background subtraction and the fit procedure see Ps_belle . No significant signal is observed. The fit result of 77.6$\pm$28.1 $P_{s}$ events at a mass of 2.025$\pm$0.005 GeV/$c^{2}$ and a width of 0.022$\pm$0.012 GeV/$c^{2}$ leads to an upper limit of the product branching fraction of

[TABLE]

The determined upper limit for $P_{s}^{+}$ is still about a factor of 6 higher than measured branching fraction for the $P_{c}^{+}$ at LHCb.

7 Acknowledgement

We would like to warmly thank the colleagues of BINP and Novosibirsk State University for their kind hospitality. This project was supported by the European Unionâs Horizon 2020 research and innovation program under grant agreement No. 644294 and the German Ministry of Education and Research (BMBF) under grant agreements 05H15RGKBA and 05H19RGKBA.