Observation of $\psi(3686)\rightarrow\Xi(1530)^{-}\bar\Xi(1530)^{+}$ and $\Xi(1530)^{-}\bar\Xi^{+}$

TL;DR

This paper reports the first observation of specific decay modes of the $oldsymbol{\psi(3686)}$ particle into baryon-antibaryon pairs, measuring their branching fractions and angular distribution parameters with high statistical significance.

Contribution

It presents the first observation and measurement of branching fractions for $oldsymbol{\psi(3686)}$ decays into $oldsymbol{\Xi(1530)}$ baryon pairs using a large data sample and a novel single-baryon tagging technique.

Findings

First observation of $oldsymbol{\psi(3686)}$ decays to $oldsymbol{\Xi(1530)}$ pairs.

Measured branching fractions: (11.45 ± 0.40 ± 0.59)×10^{-5} and (0.70 ± 0.11 ± 0.04)×10^{-5}.

Angular distribution parameter $oldsymbol{\alpha}$ = 0.40 ± 0.24 ± 0.06, consistent with theoretical predictions.

Abstract

Using 448.1 $\times$ $10^{6}$ $\psi(3686)$ events collected with the BESIII detector at BEPCII, we employ a single-baryon tagging technique to make the first observation of $\psi(3686)\rightarrow\Xi(1530)^{-}\bar\Xi(1530)^{+}$ and $\Xi(1530)^{-}\bar\Xi^{+}$ decays with a statistical significance of more than 10$\sigma$ and 5.0$\sigma$, respectively. The branching fractions are measured to be $\cal{B}$$[\psi(3686)\rightarrow\Xi(1530)^{-}\bar\Xi(1530)^{+}] $ = (11.45 $\pm$ 0.40 $\pm$ 0.59) $\times$ $10^{-5}$ and $\cal{B}$$[\psi(3686)\rightarrow\Xi(1530)^{-}\bar\Xi^{+}]$ = (0.70 $\pm$ 0.11 $\pm$ 0.04) $\times$ $10^{-5}$. The angular distribution parameter for $\psi(3686)\rightarrow\Xi(1530)^{-}\bar\Xi(1530)^{+}$ is determined to be $\alpha$ = 0.40 $\pm$ 0.24 $\pm$ 0.06, which agrees with the theoretical predictions within 1$\sigma$. The first uncertainties are statistical, and the second systematic.

Tables

Table 1. TABLE 1: The number of the extracted events ( N obs subscript 𝑁 obs N_{\rm obs} ), efficiencies ( ϵ 1 subscript italic-ϵ 1 \epsilon_{1} is for π − ​ Ξ 0 superscript 𝜋 superscript Ξ 0 \pi^{-}\Xi^{0} mode, ϵ 2 subscript italic-ϵ 2 \epsilon_{2} is for π 0 ​ Ξ − superscript 𝜋 0 superscript Ξ \pi^{0}\Xi^{-} mode), statistical significance ( S 𝑆 S ), the angular distribution parameter ( α 𝛼 \alpha ) and branching fractions ( ℬ ℬ {\cal B} ), where ℬ com superscript ℬ com {\cal B}^{\rm com} and α com superscript 𝛼 com \alpha^{\rm com} denote the combined branching fraction and angular distribution parameters. The first uncertainties are statistical, and the second systematic.

	$\psi \left(3686\right)\to \Xi {\left(1530\right)}^{-}\overline{\Xi }{\left(1530\right)}^{+}$		$\psi \left(3686\right)\to \Xi {\left(1530\right)}^{-}{\overline{\Xi }}^{+}$
Tag mode	$\Xi {\left(1530\right)}^{-}$	$\overline{\Xi }{\left(1530\right)}^{+}$	$\Xi {\left(1530\right)}^{-}$	$\overline{\Xi }{\left(1530\right)}^{+}$
$N_{\mathrm{obs}}$	2664 $\pm$ 114	2403 $\pm$ 132	152 $\pm$ 37	247 $\pm$ 48
${ϵ}_1$(%)	7.85 $\pm$ 0.09	7.16 $\pm$ 0.08	8.89 $\pm$ 0.09	8.42 $\pm$ 0.09
${ϵ}_2$(%)	8.91 $\pm$ 0.09	8.17 $\pm$ 0.09	10.58 $\pm$ 0.10	9.82 $\pm$ 0.10
$S\left(\sigma \right)$	23.0	18.2	4.4	5.3
$\alpha$	$0.43\pm 0.30\pm 0.09$	$0.36\pm 0.35\pm 0.08$	…	…
$ℬ\left({10}^{-5}\right)$	11.51 $\pm$ 0.49 $\pm$ 0.92	11.36 $\pm$ 0.62 $\pm$ 1.14	0.57 $\pm$ 0.14 $\pm$ 0.05	0.93 $\pm$ 0.18 $\pm$ 0.10
${\alpha }^{\mathrm{com}}$	$0.40\pm 0.24\pm 0.06$		…
${ℬ}^{\mathrm{com}}\left({10}^{-5}\right)$	11.45 $\pm$ 0.40 $\pm$ 0.59		0.70 $\pm$ 0.11 $\pm$ 0.04

Table 2. TABLE 3: Systematic uncertainties (absolute) on the measurement of α 𝛼 \alpha value for ψ ​ ( 3686 ) → Ξ ​ ( 1530 ) − ​ Ξ ¯ ​ ( 1530 ) + → 𝜓 3686 Ξ superscript 1530 ¯ Ξ superscript 1530 \psi(3686)\rightarrow\Xi(1530)^{-}\bar{\Xi}(1530)^{+} decay.

Source	$\Xi {\left(1530\right)}^{-}$	$\overline{\Xi }{\left(1530\right)}^{+}$
$M_{\pi \Xi }^{\mathrm{recoil}}$ fitting range	0.05	0.02
Background shape	0.03	0.02
Signal shape	0.06	0.04
Wrong combinations	0.01	0.04
$\cos {\theta }_B$ binning	0.02	0.01
$\cos {\theta }_B$ fitting range	0.03	0.04
Total	0.09	0.08

Equations

$$\frac{dN}{d\cos {\theta }_B}\propto 1+\alpha {\cos }^2{\theta }_B,$$

$$M_{\pi \Xi }^{\mathrm{recoil}}=\sqrt{(E_{\mathrm{CM}}-E_{\pi \Xi }{)}^2-|{\vec{p}}_{\pi \Xi }{|}^2},$$

$$\mathcal{B}[\psi (3686)\to X]=\frac{N_{\mathrm{obs}}}{N_{\psi (3686)}\cdot {\sum }_i{ϵ}_i{\mathcal{B}}_i},$$

Full text

The decays of the charmonium resonances, such as $\psi(3686)$, into baryon anti-baryon pairs ($B\bar{B}$) have been extensively studied as a useful test of perturbative quantum chromodynamics (QCD) Farrar01 ; Farrar . They proceed via the annihilation of the $c\bar{c}$ pair into three gluons for strong decays or a virtual photon for electromagnetic decays. Within the context of SU(3) flavor symmetry, decays of charmonium to $B\bar{B}$ (i.e., $B_{1}\bar{B}_{1}$, $B_{8}\bar{B}_{8}$ and $B_{10}\bar{B}_{10}$, where $B_{1}$ is for baryon singlet, $B_{8}$ is for baryon octet and $B_{10}$ is for baryon decuplet) are allowed, but decays into octet-decuplet baryonic pairs ($B_{10}\bar{B}_{8}$) are forbidden Asner:2008nq ; KWetc . However, many experimental results on $J/\psi\rightarrow B_{10}\bar{B}_{8}$ decay SU3B ; Ablikim:2012uqz indicate the presence of flavor SU(3) symmetry breaking. There is no previous experimental information on $\psi(3686)\rightarrow B_{10}\bar{B}_{8}$, such as $\psi(3686)\rightarrow\Xi(1530)^{-}\bar{\Xi}^{+}$ decay.

Due to hadron helicity conservation Farrar01 ; Pais:1971wu , the angular distributions for the process $e^{+}e^{-}\rightarrow\psi(3686)\rightarrow B\bar{B}$ are given by

[TABLE]

where $\theta_{B}$ is the angle between one of the baryons and the $e^{+}$ beam direction in the $e^{+}e^{-}$ center-of-mass (CM) system, and the $\alpha$ is the angular distribution parameter, which is widely investigated in theory and experiment Franklin:1983ve ; ppbref ; angularSig . Many theoretical models, such as those considering quark mass effects ppbref02 , and electromagnetic effects ppbref01 , predict that the angular distribution parameter obeys $\alpha<1$. The BES and BESIII collaborations measured the angular distribution of $J/\psi\rightarrow\Sigma^{0}\bar{\Sigma}^{0}$, $\Sigma(1385)\bar{\Sigma}(1385)$ and obtained a negative $\alpha$ value, but with poor precision angularSig ; Ablikim:2016iym . H. Chen et al. Chen:2006yn noted that the angular distribution parameter for $J/\psi$ and $\psi(3686)\rightarrow B\bar{B}$ could be negative when re-scattering effects of $B\bar{B}$ in heavy quarkonium decays are taken into account. Additional measurements of the $\alpha$ parameter are of interest to confront the various theoretical approaches. In other experiments, the angular distributions for charmonium decays to baryon pairs, such as $J/\psi$ and $\psi(3686)\rightarrow p\bar{p},\Lambda\bar{\Lambda},\Sigma^{0}\bar{\Sigma}^{0}$, $\Xi\bar{\Xi}$, $\Sigma(1385)\bar{\Sigma}(1385)$ ppbref ; Ablikim:2006aw , were reported. Negative $\alpha$ values were found for the processes $J/\psi\rightarrow\Sigma^{0}\bar{\Sigma}^{0}$, $\Sigma(1385)\bar{\Sigma}(1385)$, while for other processes $\alpha$ was either measured to be positive, or not measured. The BESIII experiment has a large data sample at the $\psi(3686)$ resonance, which can be used to verify the theoretical models for the process like $\psi(3686)\rightarrow\Xi(1530)^{-}\bar{\Xi}(1530)^{+}$, for which the $\alpha$ value is predicted to be 0.18 and 0.31 ppbref02 ; ppbref01 .

In this paper, the observation of $\psi(3686)\rightarrow\Xi(1530)^{-}\bar{\Xi}(1530)^{+}$ and $\Xi(1530)^{-}\bar{\Xi}^{+}$ decays is presented based on $448.1\times 10^{6}$ $\psi(3686)$ events Ablikim:2017wyh collected with the BESIII detector at the BEPCII in 2009 and 2012. Selection of $\psi(3686)\rightarrow\Xi(1530)^{-}\bar{\Xi}(1530)^{+}$ and $\Xi(1530)^{-}\bar{\Xi}^{+}$ events via full reconstruction suffers from low efficiency. To achieve a higher efficiency, we first reconstruct a $\Xi(1530)^{-}$, referred to as a $\Xi(1530)^{-}$ tag, and then search for a recoiling $\bar{\Xi}(1530)^{+}$ or $\bar{\Xi}^{+}$ signal (unless otherwise noted, charge conjugation ($c.c.$) is implied throughout the paper).

To determine the detection efficiencies for $\psi(3686)\rightarrow\Xi(1530)^{-}\bar{\Xi}(1530)^{+}$ and $\Xi(1530)^{-}\bar{\Xi}^{+}$, 100,000 simulated events are generated for each reconstructed mode. For the $\Xi(1530)^{-}\bar{\Xi}(1530)^{+}$ final state, the angular distribution is generated with the $\alpha$ value measured in this analysis, while for $\Xi(1530)^{-}\bar{\Xi}^{+}$ we use $\alpha=1$ based on theory Pang . The $\Xi(1530)^{-}$ decays to the $\pi^{0(-)}\Xi^{-(0)}$ modes, with $\Xi^{0(-)}\to\pi^{0(-)}\Lambda$, $\Lambda\to p\pi^{-}$ and $\pi^{0}\to\gamma\gamma$, are simulated using evtgen evt2 , and the response of the BESIII detector is modeled with Monte Carlo (MC) simulations using a framework based on geant4 geant4 . A detailed description of the BESIII detector is given in Ref. BESIII . To study the potential backgrounds, an inclusive MC sample of 350 $\times$ $10^{6}$ $\psi(3686)$ decays is generated, where the production of the $\psi(3686)$ resonance is simulated with the kkmc generator kkmc , the subsequent decays are processed via evtgen evt2 according to the measured branching fractions provided by the Particle Data Group (PDG) PDG2016 , and the remaining unmeasured decay modes are generated with lundcharm lund . Data collected at the CM energy of 3.65 GeV (off-peak data sample, 44 pb*-1*) Ablikim:2017wyh is used to estimate the contamination from the continuum processes $e^{+}e^{-}\rightarrow\Xi(1530)^{-}\bar{\Xi}(1530)^{+}$ and $\Xi(1530)^{-}\bar{\Xi}^{+}$.

Charged tracks are reconstructed in the main drift chamber (MDC) within an angular range of ($|\cos\theta|<0.93$, where $\theta$ is the polar angle with respect to the $e^{+}$ beam direction). Information on the specific energy deposition ($dE/dx$) in the MDC and from the time-of-flight (TOF) counters are combined to form particle identification (PID) confidence levels (CLs) for pion, kaon, and proton hypotheses. Each track is assigned to the particle type with the highest CL. At least two negatively-charged pions and one proton are required. Photons are reconstructed from isolated showers in the electromagnetic calorimeter (EMC). Energy deposited in the nearby TOF counters is included to improve the reconstruction efficiency and energy resolution. Photon energies are required to be greater than 25 MeV in the EMC barrel region ($|\cos\theta|<0.80$) or greater than 50 MeV in the EMC end caps ($0.86<|\cos\theta|<0.92$). Showers in between these angular regions are poorly reconstructed and are excluded. The EMC shower timing is required to be within the range [0, 700] ns, relative to the event start time, to suppress electronic noise and energy deposits unrelated to the analyzed event. The number of good photon candidates, $N_{\gamma}$, must satisfy $2\leq N_{\gamma}\leq 15$ based on a simulated signal MC study.

In order to reconstruct $\pi^{0}$ candidates, a one-constraint (1C) kinematic fit is applied to all $\gamma\gamma$ combinations, constraining the two-photon invariant mass to the nominal $\pi^{0}$ mass PDG2016 . To suppress non-$\pi^{0}$ backgrounds, only combinations with $\chi^{2}_{1C}<20$ are retained by optimizing the figure of merit FOM = $\frac{S}{\sqrt{S+B}}$, where $S$ is the number of signal events and $B$ is the number of background events, based on the MC simulation. The $\Lambda$ candidates are reconstructed from $p\pi^{-}$ pairs with an invariant mass within 5 MeV/$c^{2}$ of the nominal $\Lambda$ mass. This interval is determined by optimizing FOM. A secondary vertex fit Xu:2009zzg is performed on all $p\pi^{-}$ combinations; those with $\chi^{2}<500$ are kept for further analysis. To further suppress the background, the decay length of the $\Lambda$ is required to be positive. In the case of multiple candidates, the one with an unconstrained mass closest to the nominal mass is retained as used in Refs. Ablikim:2016iym . The $\Xi$ candidates are reconstructed by considering all $\pi\Lambda$ combinations within 10 MeV/$c^{2}$ of the nominal $\Xi$ mass. For $\Xi^{-}$ candidates, a secondary vertex-constrained fit is used, while for both charged and neutral $\Xi$, only the candidate closest to the nominal mass is retained when there is more than one per event. The decay length of the $\Xi^{-}$ is required to be positive to further suppress the backgrounds. The $\Xi(1530)^{-}$ candidates are reconstructed in the $\pi^{0}\Xi^{-}$ and $\pi^{-}\Xi^{0}$ modes and the candidate closest to the nominal mass is retained when there is more than one per event.

The anti-baryon candidates $\bar{\Xi}^{+}$ and $\bar{\Xi}(1530)^{+}$ are inferred by the mass recoiling against the selected $\pi\Xi$ system,

[TABLE]

where $E_{\pi\Xi}$ and $\vec{p}_{\pi\Xi}$ are the energy and momentum of the selected $\pi\Xi$ system, and $E_{\rm CM}$ is the CM energy. Figure 1 shows the scatter plot of $M_{\pi\Xi}$ versus $M^{\rm recoil}_{\pi\Xi}$. To determine signal yields, the mass of the $\pi\Xi$ is required to be within 15 MeV/$c^{2}$ of the nominal mass of $\Xi(1530)^{-}$.

Our inclusive MC sample reveals that the main background for $\psi(3686)\rightarrow\Xi(1530)^{-}\bar{\Xi}(1530)^{+}$ and $\Xi(1530)^{-}\bar{\Xi}^{+}$ decays comes from $\psi(3686)\rightarrow\pi^{+}\pi^{-}(\pi^{0}\pi^{0})J/\psi$ with $J/\psi\rightarrow\Xi^{-}\bar{\Xi}^{+}$; it is distributed smoothly in the signal region of $M^{\rm recoil}_{\pi\Xi}$. Only a few events in the off-peak data sample survive and do not form any obvious peaking structures in the $\Xi(1530)$ signal region of the corresponding $M^{\rm recoil}_{\pi\Xi}$ distribution. Taking into account the normalization of the luminosity and CM energy dependence of the cross section, the contribution from continuum processes is expected to be small and is neglected in the further analysis. There are transition $\pi^{0}$s with similar momenta in both the baryon and anti-baryon decay chains within the signal events. Incorrect use of these in the $\Xi^{0}$ or $\Xi(1530)^{-}$ reconstruction leads to a wrong combination background (WCB).

The signal yields for the two decays $\psi(3686)\rightarrow\Xi(1530)^{-}\bar{\Xi}(1530)^{+}$ and $\Xi(1530)^{-}\bar{\Xi}^{+}$ are determined by performing an extended maximum likelihood fit to the $M^{\rm recoil}_{\pi\Xi}$ spectrum. In the fit, the signal shapes for the two decays are represented by the simulated MC shape convolved with a Gaussian function to take into account the mass resolution difference between the data and the MC simulation, where the parameters of the Gaussian function are left free but are shared by the two decay modes. The WCB is described by the simulated MC shape, and the corresponding numbers of events are fixed according to the MC simulation. The other remaining backgrounds (Other-Bkg) are found to distribute smoothly in the $M_{\pi\Xi}^{\rm recoil}$ spectrum and are therefore described by a third-order Chebychev function. Figure 2 shows the $M^{\rm recoil}_{\pi\Xi}$ distributions for the $\Xi(1530)^{-}$ and $\bar{\Xi}(1530)^{+}$ tags, respectively, with $\Xi$ and $\Xi(1530)$ peaks evident in each. Including systematic uncertainties, the significance for $\psi(3686)\rightarrow\Xi(1530)^{-}\bar{\Xi}^{+}$ is calculated to be more than $5.0\sigma$ for the $\Xi(1530)^{-}\bar{\Xi}$ mode and its $c.c.$ mode combined. The individual significances are calculated from the change in log likelihood and degrees of freedom with and without the signal in the fit.

The branching fraction is calculated as

[TABLE]

where $X$ stands for $\Xi(1530)^{-}\bar{\Xi}(1530)^{+}$ or $\Xi(1530)^{-}\bar{\Xi}^{+}$, $N_{\rm obs}$ is the number of extracted signal events, $N_{\psi(3686)}$ is the total number of $\psi(3686)$ events Ablikim:2017wyh , $i$ runs over the $\pi^{-}\Xi^{0}$ and $\pi^{0}\Xi^{-}$ modes, $\epsilon_{i}$ denotes the detection efficiency obtained with the measured $\alpha$ value for both modes, ${\cal B}_{i}$ denotes the product of branching fractions of $\Xi(1530)\rightarrow\pi\Xi$ and $\Xi\rightarrow\pi\Lambda$. Table 1 summarizes the numerical results for the various modes studied. The angular distribution parameter for $\psi(3686)\rightarrow\Xi(1530)^{-}\bar{\Xi}(1530)^{+}$ decay is determined by performing a least squares fit to the $\cos\theta_{B}$ distribution in the range from $-0.8$ to $0.8$ by Eq. (1), divided into 8 equidistant intervals; this is done separately for $\Xi(1530)^{-}$ and $\bar{\Xi}(1530)^{+}$ tags. The signal yield in each $\cos\theta_{B}$ bin is obtained with the aforementioned fit method in the $M^{\rm recoil}_{\pi\Xi}$ range of 1.4 GeV/$c^{2}$ to 1.7 GeV/$c^{2}$. The distributions of the efficiency-corrected signal yields together with the fit curves are shown in Fig. 3. The $\alpha$ values obtained are summarized in Table 1.

Systematic uncertainties on the branching fractions measurements are mainly due to differences of detection efficiency between data and MC simulation. The uncertainties associated with the efficiencies of tracking and PID for the pion from the mother particle $\Xi(1530)^{-}$ in the $\pi^{-}\Xi^{0}$ decay mode, are investigated with the control sample $J/\psi\rightarrow p\bar{p}\pi^{+}\pi^{-}$. The uncertainty due to the 1C kinematic fit for the $\pi^{0}$ reconstruction is estimated with the control sample $J/\psi\rightarrow\rho\pi$. The uncertainties related to the $\Xi^{0}$ and $\Xi^{-}$ reconstruction efficiency combined with tracking, PID, and the $\Lambda$ reconstruction efficiencies are estimated using the control sample $\psi(3686)\rightarrow\Xi^{0}\bar{\Xi}^{0}$ and $\Xi^{-}\bar{\Xi}^{+}$. A detailed description of our methods can be found in Ref. wangxf ; Ablikim:2016iym . The uncertainties due to the requirements for mass window and decay length of $\Xi$, $\Lambda$ are estimated with the control sample $J/\psi\rightarrow\Xi^{0}\bar{\Xi}^{0}$ and $\Xi^{-}\bar{\Xi}^{+}$. The uncertainty related to the mass window of $\Xi(1530)^{-}$ is estimated by varying the half-width of 15 MeV/$c^{2}$ by $\pm 1$ MeV/$c^{2}$. The largest difference of the efficiency between data and MC simulation is taken as the systematic uncertainty. The uncertainty due to the signal shape is estimated by changing the nominal signal function to the Breit-Wigner function; the difference of the signal yields is taken as the systematic uncertainty. The parameters of the Gaussian signal function for the $\Xi(1530)^{-}\bar{\Xi}^{+}$ final state are fixed in the fit; uncertainties are estimated by varying the nominal values by 1$\sigma$. The uncertainty due to the $M^{\rm recoil}_{\pi\Xi}$ fitting range is estimated by varying the mass range by $\pm$10 MeV/$c^{2}$. The uncertainties due to the assumed polynomial background shape are estimated by alternate fits using a second or a fourth-order Chebychev function. The uncertainty due to the WCB is estimated by comparing the signal yields between the fits with and without the corresponding component included in the fit. The uncertainty related with the detection efficiency due to the modeling of the angular distribution of the baryon pairs, represented by the parameter $\alpha$, is estimated for the $\Xi(1530)^{-}\bar{\Xi}(1530)^{+}$ mode by varying the measured $\alpha$ values by 1$\sigma$ in the MC simulation. For the $\Xi(1530)^{-}\bar{\Xi}^{+}$ mode, $\alpha$ is set to zero. The uncertainties due to the branching fractions of the intermediate states, $\Xi\rightarrow\pi\Lambda$ and $\Lambda\rightarrow p\pi$ are taken to be $0.1$% and 0.8% according to the PDG PDG2016 . The uncertainty of the branching fraction of $\Xi(1530)\rightarrow\pi\Xi$ is taken conservatively according to the branching fraction of $\Xi(1530)\rightarrow\gamma\Xi$, 4.0% from the PDG PDG2016 . The uncertainties due to the total number of $\psi(3686)$ events (Nψ(3686)) are determined with inclusive hadronic $\psi(3686)$ decays Ablikim:2017wyh . The various systematic uncertainties on the branching fraction measurements are summarized in Table 2. The total systematic uncertainty is obtained by summing the individual contributions in quadrature.

Systematic issues for the measurement of the $\alpha$ include the determinations of signal yields in $\cos\theta_{B}$ intervals and the $\cos\theta_{B}$ fitting procedure. Signal yield systematic uncertainties arise from the fit range, the background shape, signal shape and WCB. These are evaluated with a method similar to the one described above; the resulting differences with respect to the nominal $\alpha$ values are taken systematic uncertainties. The $\cos\theta_{B}$ fitting uncertainties are estimated by re-fitting the $\cos\theta_{B}$ distribution with a different binning and fit range. We divide $\cos\theta_{B}$ into five intervals instead of eight, and the change in $\alpha$ is taken as the systematic uncertainty. We also repeat the fit after altering the $\cos\theta_{B}$ range to [$-$0.9, 0.9] or [$-$0.7, 0.7], with the same bin size as the nominal fit. The largest changes of $\alpha$ with respect to the nominal fit are taken as systematic uncertainties. All the systematic uncertainties for the $\alpha$ measurement are summarized in Table 3, where the total systematic uncertainty is the quadratic sum of the contributions.

Combined branching fractions and $\alpha$ values are calculated according to the unconstrained averaging introduced in the PDG PDG2016 . Note that the single-baryon recoil mass method leads to some double-counting of the $\Xi(1530)^{-}\bar{\Xi}(1530)^{+}$ final-state; MC studies indicate this occurs at a rate of about 10%. This is taken into account when combining branching fractions and angular distribution parameters. The systematic uncertainties are weighted to properly account for common and uncommon systematic uncertainties using $\frac{1}{2}\sum_{i,j(i\neq j)}$ $\frac{\sigma^{\prime}_{i}\sigma_{j}}{\sqrt{\sigma^{\prime 2}_{i}+\sigma^{2}_{j}}}$, where $\sigma$ ($\sigma^{\prime}$) is the systematic uncertainty with (without) common sources, and $i,j$ run over the baryon and anti-baryon tags.

In summary, using 448.1 million $\psi(3686)$ events collected with the BESIII detector at the BEPCII, we present the observation of $\psi(3686)\rightarrow\Xi(1530)^{-}\bar{\Xi}(1530)^{+}$ and $\Xi(1530)^{-}\bar{\Xi}^{+}$ decays with the statistical significances of more than 10$\sigma$ and 5.0$\sigma$, respectively, based on a single baryon tag strategy. The branching fractions for $\psi(3686)\rightarrow\Xi(1530)^{-}\bar{\Xi}(1530)^{+}$ and $\Xi(1530)^{-}\bar{\Xi}^{+}$ are measured to be (11.45 $\pm$ 0.40 $\pm$ 0.59) $\times$ $10^{-5}$ and (0.70 $\pm$ 0.11 $\pm$ 0.04) $\times$ $10^{-5}$, where the first (second) uncertainty is statistical (systematic). The corresponding results are summarized in Table 1. The observation of the decay $\psi(3686)\rightarrow\Xi(1530)^{-}\bar{\Xi}^{+}$ indicates that the SU(3) flavor symmetry is still broken in the $\psi(3686)$ case, which further validates the generality of SU(3) flavor symmetry breaking. The measured angular distribution parameter $\alpha$ for $\psi(3686)\rightarrow\Xi(1530)^{-}\bar{\Xi}(1530)^{+}$ decay agrees with the theoretical prediction ppbref02 ; ppbref01 with our current errors. This offers support, within our limited statistics, for these models which include quark mass and electromagnetic effects.

I Acknowledgement

The BESIII collaboration thanks the staff of BEPCII and the IHEP computing center for their strong support. This work is supported in part by National Key Basic Research Program of China under Contract No. 2015CB856700; Postdoctoral Natural Science Foundation of China under Contract Nos. 2018M630206, 2017M622347; National Natural Science Foundation of China (NSFC) under Contracts Nos. 11335008, 11425524, 11521505, 11605042, 11625523, 11635010, 11675184, 11705209, 11735014, 11875115, 11905236; Chinese Academy of Science Focused Science Grant; National 1000 Talents Program of China; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; the CAS Center for Excellence in Particle Physics (CCEPP); Joint Large-Scale Scientific Facility Funds of the NSFC and CAS under Contracts Nos. U1532257, U1532258, U1732263; CAS Key Research Program of Frontier Sciences under Contracts Nos. QYZDJ-SSW-SLH003, QYZDJ-SSW-SLH040; 100 Talents Program of CAS; INPAC and Shanghai Key Laboratory for Particle Physics and Cosmology; German Research Foundation DFG under Contract No. Collaborative Research Center CRC 1044, FOR 2359; Istituto Nazionale di Fisica Nucleare, Italy; Koninklijke Nederlandse Akademie van Wetenschappen (KNAW) under Contract No. 530-4CDP03; Ministry of Development of Turkey under Contract No. DPT2006K-120470; National Science and Technology fund; The Swedish Research Council; U. S. Department of Energy under Contracts Nos. DE-FG02-05ER41374, DE-SC-0010118, DE-SC-0012069; University of Groningen (RuG) and the Helmholtzzentrum fuer Schwerionenforschung GmbH (GSI), Darmstadt; Post-doctoral research start-up fees of Henan Province under Contract No. 2017SBH005; Ph.D research start-up fees of Henan Normal University under Contract No. qd16164; Program for Innovative Research Team in University of Henan Province (Grant No.19IRTSTHN018).