Progresses on light hadron physics from BESIII

Higgs decaying into Zγ

Yanping Huang

IHEP, CHINA
g Huang1,2, Shan Jin2, Kerstin Tackmann1
For BESIII Collaboration

1 DESY, 2 IHEP China

Shuo Han (IHEP, China & DESY)

1

20th Lomonosov Conference on Elementary Particle Physics
August 23th, 2021

BEPCIIBESIIIII (BEPC II)
Beijing Electron
Positron/ Collider
Storage ring ~240m
Linac ~200m

IP

BESIII Detector

MDC: σp/p ~0.5% @ 1GeV
σdE/dx ~ 6%
TOF: σT ~90 ps (barrel)
110 ps (endcap)
SCS: 1.0T (2009)
0.9T (2012)
EMC: σE/√E ~ 2.5%@1GeV

3

2

Datasetsof BESIIIBESIII Datasets
10 billion

3 billion

PRD
98 (2018) 030001
PRD.98.030001(2018)

Largest !/# and #(%&) dataset in the world!!
World largest J/ψ, ψ(3686), ψ(3770)
2021/7/29

Wujf

3

3

New forms of hardons◈

In quark model:◈ New forms of hardrons in QCD predictionғ
✦Multi-quark: quark number >= 4✦

Hybrid state: the mixture of quark and gluon✦

Glueball: composed of gluons◈ Light hadron spectroscopy is a key tool to test anddevelop theory. Highlights from BESIII:✦ X(1835) / X(ppb) studies✦ Search for the glueball✦ a0(980)-f0(980) mixing✦ PWA in ψ(3686)→K+K-η

4Xð1835Þ and Xð1870Þ, the short-dashed curves are the f 1 ð1510Þ,the dash-dotted curves are the Xð2120Þ, the long-dashed curves
are nonresonant η0 π þ π − fit results, and the shaded histograms arebackground events. The inset shows the data and the global fit
between 1.8 and 1.95 GeV=c2 .

Anomalous ππη’ line shape near M

thresholdFirst establish the direct link between the X(1835) and X(ppb)

gives B½J=ψ →γXð1835Þ$B½Xð1835Þ→η0 π þ π − $¼ð3.72'
0.21Þ×10−4 ,andB½J=ψ → γXð1870Þ$B½Xð1870Þ →η0 π þ π − $ ¼ ð1.57 ' 0.09Þ × 10−5 . In this model, theXð1920Þ is not included in the fit because its significanceis just 3.9σ. Considering systematic uncertainties (see below),
the significance of Xð1870Þ is larger than 7σ.
The systematic uncertainties come from data-MC
differences in the tracking, photon detection and particle
weekfit, ending
requirements
R E V I E W L Eidentification
T T E R S efficiencies, the kinematic
22 JULY 2016
on the invariant mass distribution of γγ, signal selection ofρ0 , η, and η0 , total number of J=ψ events, branching
TABLE I. Fit results of using the Flatté formula. The first errors
fractions for intermediate states decays, fit ranges, backare statistical errors, and the second errors are systematic errors;
ground descriptions, mass resolutions, and the intermediate
the Model
branching Iratiois the product offormulaBðJ=ψ → γXÞ and(9.6σ):of π þ π − . InFlatte
the first model, the dominant terms are
0 structureþ −BðX → η π π Þ.
70)
the fit range, the background description, and the interþ −mediatestructureofπ
π GeV=c. Considering
all systematict
2
The state around 1.85
uncertainties, the final result is shown in Table I. For theþ127.82
1638.0' 121:9sources
M (MeV=csecond)
model, the dominant two
systematic−254.3 are the
þ47.6
2
2
2
' 35:4−43.9structure ofg0 [ðGeV=cbackgroundÞ ]description and the93.7
intermediateþ0.83
2.31uncertainties,' 0.37−0.60
π þ π − . Considering all systematicthe final
g2pp̄ =g20
2 is shown in Table II.
result1909.5 ' 15:9þ9.4
M pole (MeV=c)−27.5
2 summary, the J=ψ → γη0 π þ π − process þ6.1
Inisstudied withΓpole (MeV=c )273.5 ' 21:4−64.0−4the þ0.31
BESIII
experiment
Branching 1.09
ratio × 109 J=ψ events collected
ð3.93 'at0.38
Þ × 10−0.84
in 2012. We observed a significant distortion of the η0 π þ π −line shape
the pforp̄ massthat cannot
befunction. Twotypicalnear
modelssuch thresholda line shapeare117, 042002
accommodated by an ordinary PRL
Breit-Wigner
resonance

2

1909.5 ' 15.9ðstatÞ−27.5 ðsystÞ MeV=c
andΓpole ¼
2
273.5 ' 21.4ðstatÞþ6.1−64.0 ðsystÞ MeV=c . The second model
assumes the distortion reflects interference between theppbXð1835Þ and anotherresonance with mass close to the pp̄
mass threshold. A fit with this model uses a coherent sumof two interfering Breit-Wigner amplitudes to describe theη0 π þ π − mass spectrum around 1.85 GeV=c2 . This fit yields
a narrow resonance below the pp̄ mass threshold with2
M ¼ 1870.2 ' 2.2ðstatÞþ2.3−0.7 ðsystÞ MeV=c and Γ ¼ 13.0'2
6.1ðstatÞþ2.1−3.8 ðsystÞ MeV=c , with a statistical significancelarger than 7σ. With current data, both models fit the datawell with fit qualities, and both suggest the existence of astate, either a broad state with strong couplings to the pp̄, ora narrow state just below the pp̄ mass threshold. For thebroad state above the pp̄ mass threshold, its strong
TABLE II. Fit results using a coherent sum of two Breit-Wigner
amplitudes. The first errors are statistical errors, and the second
errors are systematic errors; the branching ratio (B.R.) is the
product of BðJ=ψ → γXÞ and BðX → η0 π þ π − Þ.

Model II: 2 resonances

Xð1835Þ
Mass (MeV=c2 )Width (MeV=c2 )B.R. (constructive interference)
B.R. (destructive interference)

þ17.3
1825.3 ' 2.4−2.4
þ4.6
245.2 ' 13:1−9.6−4
ð3.01 ' 0.17þ0.26−0.28 Þ × 10
−4
ð3.72 ' 0.21þ0.18−0.35 Þ × 10

Xð1870Þ
Mass (MeV=c2 )Width (MeV=c2 )B.R. (constructive interference)
B.R. (destructive interference)

1870.2 ' 2.2þ2.3
−0.7
þ2.1
13.0 ' 6.1−3.8−7
ð2.03 ' 0.12þ0.43−0.70 Þ × 10
−5
ð1.57 ' 0.09þ0.49−0.86 Þ × 10

used to fit the data. The first model assumes the statearound 1.85 GeV=c2 couples with the pp̄ and the dis◈with almost
equally good fit quality
042002-6
tortion Bothreflects models
the openingdescribeof the pp̄ data
decay channel.
The fit result for this model yields a strong coupling◈
ppb structure
threshold
2 ¼a molecule state or a bound state?
betweenThethe broadand thestructurepp̄ of g2pp̄ =gis
0

5

0
s

0
s

0
s

0
s

Events / 0.02 GeV/c

E

region. The statistical significance of a contribution isestimated inby thedifference indecay
NLL withmodes
and without the
Search for the X(1835)
different
particular contribution, taking the change in degrees of
MK K (GeV/c2
freedom into account.
Dominant decays: X(1835)→f0(980)η
70
Our initial PWA fits include an Xð1835Þ resonance in60+16-25 MeV
theMf=0 ð980Þηand a nonresonant component in one
1844±9channel
50of the possible decay channels f 0 ð980Þη, f 0 ð1500Þη orJ/ψ→γKsK sη
40= 192+20-17+62-43 MeVf 2Γð1525Þη.
All
possible
J PC combinations of the Xð1835Þ
30
and the nonresonant component are tried. We then extend
B(J/ψ→γX(1835))B(X(1835)→f0(980)η)20
the fits by including an additional resonance at lower
10
K 0S K=0S η3.31
mass.
additional
component, denoted here as+0.33This-0.30+1.96-1.29 ×10-5
theXð1560Þ,
improves the fit quality when
it isD allowed
STUDY
OFηð1475Þ
AND
Xð1835Þ
IN
…
PHYS.
REV.
97, 051101 (2
MK K η (GeV/c
to interfere with the Xð1835Þ. Our final fits show that
TABLE I. Mass, width, and BðJ/ψ → γX → γγϕÞ of each component in the two solutions (I) and (II). The firstthe data can be best described with three components:
PRL 115, 091803 uncertainties
are statistical and the second ones are systematic.
ariant mass distributions for selectedXð1835Þ
→ f 0 ð980Þη,
Xð1560Þ Γ→
f ð980Þη, anda nonResonancemR (MeV/c2 )(MeV)0B (10−6 )0 00Solution
0PC
ctra of (a) K S K S η and (b) K S K S ;resonantf
ð1500Þη
component.
TheJof the0Iηð1475Þ
1477 % 7 % 13
118 % 22 % 17
7.03 %Xð1835Þ,
0.92 % 0.91
J/ψ→γγΦ00ersus MK0S K0S η ; (d) K S K S η invariant
Xð1835Þ
1839 % 26 % 26
175 % 57 % 25
1.77 % 0.35 % 0.25
theXð1560Þ,andthenonresonant
component
are%allfoundIIηð1475Þ
1477
%
7
%
13
118
%
22
%
17
10.36
1.51
% 1.54
with the requirement M K0S K0S <−þXð1835Þ
1839 %
26 % 26
175 % 57 % 25 and f8.09% 1.99 % 1.36
to
be
0
.
The
Xð1835Þ,
Xð1560Þ,
ð1500Þ
are0bars are data; the shaded histograms
described by nonrelativistic Breit-Wigner functions, where
stimated by the η sideband; the solidTwosolutionswithdiﬀerent
interference
options0
theintrinsic
widthsdependent.
the Xð1835Þ
decaying into γϕThe
final masses
state indicat
all sources
to be independent,
the aretotal notof energy
MC events of J=ψ → γK 0S KAssuming
ηwithS
this resonancealso containsare
a sizabless̄ component
systematic uncertainties
on theproduct branching
fractionsandwidthsoftheXð1835Þ
andXð1560Þ
derivedbyseems therefore unlikely to be a pure N N̄ bound sof the ηð1475Þ and Xð1835Þ
aredeterminedbycombining
The X(1835) may contain a sizable ss component
all the individual ones in quadrature. The total systematic
50

uncertainty on the product branching fraction of theηð1475Þ is determined to be 12.9% and 14.9% for solution
091803-4
I and solution
II, respectively. And it is determined to be
PRD 97, 051101
14.2% and 16.8% for the two solutions of Xð1835Þ. The

ACKNOWLEDGMENTS

We extend our special thanks to J. J. Wu of the S
Research Centre for the Subatomic Structure of
6(CSSM) for many helpful discussions. The BESI

used to optimize the event selection and to determ
theoretical speculations on their nature, such as a pp̄
the selection efficiency. For the J/ψ → ωX(1835)
bound state [11–13], a pseudo-scalar glueball [14–16], aradial excitation of the η " meson [17], etc. Thanks to
nal simulation we also take into account the J P C =quantum numbers.
the world’s largest e+ e− → J/ψ data set collected by
6
BESIII, it has been possible to study in detail the significant abrupt change in the line shape of the X(1835) →ω sig, η’sigη " π + π − in correspondenceof the pp̄ mass threshold [18],ω sig, η’
2500
Data
bkg
which could beω originatedfrom the opening of the pp̄ ad400,
η’Inclusive MC
bkg
2000
sig
ditional decayωchannel(threshold
effect)orbytheinterJ/ ψ →ω X(1835),
bkg , η’bkg+
2000
X(1835)→η’π πference between two different resonances. However, none
300
of
the
hypotheses
couldbeexcluded
and
no
final
conclu1500
sion has been made. In1500
order to extract additional in200
formation about the states around 1.85 GeV/c2 with thepresent BESIII statistics, additional decay modes must
1000
1000
be investigated.
100
In this paper, we report on the search for X(1835)
500
in the J/ψ → ωη " π + π −500process. The comparison of0
the production rates between J/ψ → ωX(1835) and
1.4
1.6
1.8
2
2.2
2.4
2
Mη’π+π- (GeV/ c )J/ψ → γX(1835) could also
0 help to get information on
00.92
0.94 [13,0.96 14],0.98
0.7
0.75
or gluon0.85
componentof X(1835)
i.e. if 12
the qq 0.8
2
PRD 99 (2019)! + 071101−"
Mπ+πcontainsMηπlike- 0 (GeV/c )+ - (GeV/c
X(1835)substantial qq components,π
π the η ) FIG. 1. (color online). η π π invariant mass distributio
data (black points), inclusive MC sample (yellow histogr
meson, it should be observed in J/ψ → ωX(1835). Using− 0+ −J/ψ → ωX(1835), X(1835) → η ! π + π − signal MC sam(color online). One-dimensional
projectionsfractionof two dimensional
to" ,theπ + πbranching
π (left) and ηπand
π (right)
the branchingof J/ψ fit→results
ω(φ)η
themass distributions. Blue curves refer to the final fit result, while the other fit components are represented
by coloredwith
an arbitrary normalization (blue line).
"""
fractionofJ/ψ→ω(φ)X(1835)isestimatedtobein
rves: red for ω and η signals, green for ω signal and η background, magenta for ω background and η signal, andoth ω and η " backgrounds.
the order of 10−5 [14]. On the other hand, a very small◈
branching fraction is expected for larger gluon compoFor each candidate event, we select charged tracks
nent. effects
Another
estimation was done in Ref. [13], wherereconstructed in the MDC detector with the polar ang
the background. Systematicare evalu→theωX(1835))is expected to be two orders ofsatisfying the condition | cos θ| < 0.93. The tracks arhanging
range andbin size,◈the η!π+ π− fitB(J/ψby varying the fit parameters
withinless
one thanstan- that of J/ψ → γX(1835) decay.
magnitudequired to pass the interaction point within ±10 cm a
! + −
9
2000
ation. Since the η π π Thisbackground-corrected
analysis is based on 1.31×10
J/ψ events-5 collected the beam direction and within 1 cm in the plane
on is extracted from a two-dimensional fit to
by BESIII during 2009 and 2012. The BESIII detecpendicular to the beams. Photon candidates are reπ 0 and ηπ + π − invariant mass spectra, we needtor [19]Onis thisa magnetic
structed using clusters of energy deposited in the EM
1500 operating at BEPCII,e its systematic contribution.
purpose, spectrometere+ e− collider with center-of-mass energies
The energy deposited in the TOF is also included in E
erent signal functions a
aredouble-ringused to parametrized η ! signal: (1) a BWranging
convolvedfrom
with 2.0
a douto 4.6 GeV. The geometrical accepmeasurements in order to improve the reconstruction!
1000
ian for ω and a doubletance
Gaussianfor η , is(2)93%
the of a 4π solid angle. From the innercoveredficiency and the energy resolution. Good photon ca
MC shapes, and (3) the convolution of the ωto the outer side, it consists of a helium-based main drift
dates are required to have a deposited energy larger
7 t
C shapes with a double Gaussian. The resultEvents/(0.011 GeV/ c 2)

Events / ( 1 MeV/c2 )2-dimension fit is used for the signal extraction.

No obvious signal of the X(1835), the corresponding B.R.
rate is measured: <6.2×10 @ 90% CL
nts / (100 MeV/c2)

Events / (2 MeV/c2)

Search for the X(1835) in J/ψ→ωππη’

Search for glueball◈ Possible potential glueball candidates:◈ 0++: f0(1700) f0(1500)•

J/ψ→γηη, γKsKs, γπ0π0◈ 0-+: X(2370)•

J/ψ→γππη’, γKKη◈ 2++: f2(2340)•

J/ψ→γηη, γKsKs, γΦΦRadiative J/ψ decays are ideal for searching for glueballs — oneof the BESIII advantages with the world largest J/ψ data sample.
8

&4
and BðJ= c ! $f0 ð2100Þ ! $##Þ ¼ ð1:13þ0:09
significance of 0:4! is ignored. There are six resonances,&0:10 Þ ' 10 ,where the errors are statistical only.
f0 ð1500Þ, f0 ð1710Þ, f0 ð2100Þ, f20 ð1525Þ, f2 ð1810Þ,The f0 ð1500Þ is observed with a statistical significancef2 ð2340Þ, as well as 0þþ phase space and J= c ! "#of 8:2!, but its production rate, BðJ= c ! $f0 ð1500Þ !
included in the basic solution. Although most of the&5$##Þ ¼ ð1:65þ0:26
J= c ! "# events have been rejected by the above "&0:31 Þ ' 10 , is about one order of magni++
tude lower than ++that of f0 ð1710Þ and f0 ð2100Þ since its
mass window requirement, J= c ! "# is included in
NALYSISOF . .to. evaluate its impact from the interference
PHYSICALREVIEWD&&
87,[16].
092009(2013)
dominant
decay modes
are 4& andThe massandthe PWA2
width obtained from the global fit are 1468þ14
between the tail of " and other components from J= c !
&15 MeV=c◈resonances,2
Large production
rateof f0(1710)$XðX ! ##Þ. The masses and widths of theand 136þ41&26 MeV=c , respectively, which are consistentbranchingratios of J= c 2radiative decaying to X 150
and thewith the BESII measurements in J= c ! $&& [24].
200χ /nbin=1.72
statistical significances are summarized in Table I.
The first experimental evidence for the f0 ð1790Þ (M ¼✦
Comparable
with2 the LQCD
þ60 prediction
2
The comparisons of the ## invariant mass spectrum,
1790þ40&30 MeV=c and " ¼ 270&30 MeV=c ) was observed
150%# , cos %$ and "# distributions between the data andcos
in J= c ! "&& [29]. Of interest is that no evidence was100
the PWA fit projections (weighted by MC efficiencies) are
observed in J= c ! "KK! [29]. In this analysis, if the✦ Large overlap
with
other
scale
glueball2/nbin=1.19
displayedinFigs.
3(a)–3(d),
where
%
is
the
polar
angle
of
ð1710Þ
inthebasic
solutionis replaced withdominant
f
χ
$
0
100
"#
the radiative photon in the J= c rest frame, and %# andthe log-likelihoodf0 ð1790Þ,[e.g.
candidates
f0(1500)]is worse by 30. If the f0 ð1790Þ
50 ##is included as an additional resonance in the fit, the sigare the polar angle and azimuthal angle of # in the50
nificance of f0 ð1790Þ is only 1:8!, which indicates that
helicity
frame. The PWA results provide a good description◈component,
is either fsuppressedin radiative
uncoupled f0 ð1790Þ fromof data. To illustrate the contributions from each
A strongthecontribution
2(2340):
the0 projections for each specific resonance are plotted
decays or not coupled strongly to ##.
0

PWA of J/ψ→γηηand 2state search

EventsEvents / 0.020 GeV/c 2

A good channel for the 0

1. 5(a) I.
TABLE

2

2. 5

3

candidatelowestlying
tensor glueball-1-0.5for the
0
0.5
1

2
θγ
M
(GeV/c(b) and widths forcos
ηηSummary of the PWA) results, including the masses
resonances,branching ratios of J= c ! $X, as well asf0 ð1500Þ
f600
0 ð1710Þ
f0 ð2100Þ
f20 ð1525Þ
400
f2 ð1810Þ
f2 ð2340Þ
200

χ2/nbin=0.69
1468þ14þ23&15&741759 % 6þ14&252081 % 13þ24&361513 % 5þ4&101822þ29þ66&24&572362þ31þ140&30&63

EventsEventsthe significance.
first errors
are statistical and the second ones are systematic. The statistical significances here are obtained
PRD 87The(2013)
092009according to the changes of the log-likelihood.
800
600
Width (MeV=c2 )BðJ= c ! $X ! $##ÞSignificanceResonance
Mass (MeV=c2 )þ41þ28136&26&100
172 % 10þ32&16400
273þ27þ70&24&2375þ12þ16&10&8
þ52þ88229&42&155
þ62þ165
334&54&100
200&5
ð1:65þ0:26þ0:51&0:31&1:40 Þ ' 10
&4
ð2:35þ0:13þ1:24&0:11&0:74 Þ ' 10
&4
ð1:13þ0:09þ0:64&0:10&0:28 Þ ' 10
&5
ð3:42þ0:43þ1:37&0:51&1:30 Þ ' 10
χ2/nbin=0.68&5ð5:40þ0:60þ3:42&0:67&2:35 Þ ' 10
&5
ð5:60þ0:62þ2:37&0:65&2:07 Þ ' 10

8:2!
25:0!
13:9!
11:0!
6:4!
7:6!

9

the measured branching fraction is 6.28−0.17−0.52 × 10 ,described by phase space, are also included.
which is about 3σ away from the product branching
The resonance parameters, i.e., masses and widths, of thefractions taken from the PDG, 10.8 & 1.2 × 10−6 . The
dominant 0þþ and 2þþ resonances are optimized in the MD
overall branching fraction for radiative J=ψ decays toanalysis. The resonance parameters are listed in Table I,
where the parameterswith uncertainties
M. listed
ABLIKIMet al. are opti- KS K S is determined to be ð8.29 & 0.02Þ × 10−4 , where
PHYS. REVthe uncertainty
is statistical only.
mized while the other parameters are Model
fixed to their
PDG
dependent
analysis
The projections of the K S K S and γK S invariant mass
values. The systematic uncertainties, which are discussed
spectra and the angular distributions of the globalare(a)below, include only those related
4000 fit(a)6000 to the MD analysis. In the
shown
in Figs. 3 and 4, respectively. The pull 3500
distributions
resonance parameter optimization, the mass and width of
χ2/nbin=1.45
5000by scanning. The valuesof the fit relative to the data are also shown. Given
the smalleach resonance are optimized
3000
Data
statisticaluncertainties for such a large data sample, thecorresponding to the minimum
S are taken as the optimized
4000
Global Fit
2500
pulls tend to fluctuate above one. A series ofadditional
values. The product branching fraction for an intermediate
2000
3000 tochecks are also performed for the nominal solution. If thestate X is determined accordingf 0 ð1710Þ and f 0 ð1790Þ are replaced with a1500
single reso2000
PRD
98(2018)
072003NX
nance whose mass and width are optimized, S1000
increases byBðJ=ψ → γXÞ × BðX → K S1000
KSÞ ¼
72.9, indicating that the model of two resonances
N J=ψ × ϵ × B2KS →πþ π −500 in thisvicinity is preferred over the single resonance model.
The
4
4
ð5Þ
f 0 ð2200Þ is also replaced by f 0 ð2100Þ and f 0 ð2200Þ
2 states,
2

Events / 20 MeV/c2

EventsPull

Pull

PWA of J/ψ→γKsKs

00-2-2 in the optimal solution. The columns labeled M
TABLE I. The resonance parametersparameters
PDG and ΓPDG give the corresponding-4-4-1 for-0.8a -0.6
from the PDG [5]. The branching fractions
significancefor each
are also
1
1.2and 1.4
1.6 1.8
2.2 2.4
2.6 given.
2 resonance
2.8 When
3 two uncertainties are given

branching fraction, the first and second uncertainties are statistical and systematic,
respectively. The systematic uncertainties due to2)[GeV/c]K
Mass(KS S effect on the mass and width parameters.
overall normalization affect the branching fractions, but have little
M (MeV=c2 )MPDG (MeV=c2 )Γ (MeV=c2 )ΓPDG (MeV=c2 )Branching fraction

K % ð892Þ
K 1 ð1270Þ
f0 ð1370Þ
f0 ð1500Þ
f0 ð1710Þ
f0 ð1790Þ
f0 ð2200Þ
f0 ð2330Þ
f2 ð1270Þ
f02 ð1525Þ
f2 ð2340Þ
0þþ PHSP
2þþ PHSP(b) & 0.198963000 895.81
1272
1272 & 7
2500
1350 & 9þ121200 to 1500
−2
2000 1504 & 61505
1765 & 2þ11723þ6−1 1500−5
þ21870 & 7−3'''
10002184 & 5þ42189 & 13−22411 & 10 & 7 500'''
1275
1275.5 & 0.8
421516 & 1
1525 & 5
02233 & 34þ92345þ50
−40
−25
-2
-4
'''
'''
0.6 0.8
1
'''
'''

48
90
231 & 21þ28−48
109
146 & 3þ7
−1
146 & 14þ7−15
þ4364 & 9−7
349 & 18þ23−1
185
75 & 1 & 1
507 & 37þ18−21'''
1.2 1.4 1.6'''

47.4 & 0.6
2/nbin=1.41
χ90& 20
200 to 500
109 & 7139 & 8Data
Fit
'Global''
238 & 50'''186.7þ2.2
−2.5
þ6
73−5
322þ70−60'''
2.2 2.4
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2
2 '''

þ0.16þ0.59
ð6.28−0.17−0.52
Þ × 10−6−7
ð8.54þ1.07þ2.35−1.20−2.13 Þ × 10
þ0.08þ0.36
ð1.07−0.07−0.34
Þ × 10−5
þ0.16þ0.18
ð1.59−0.16−0.56
Þ × 10−5
þ0.03þ0.31
ð2.00−0.02−0.10
Þ × 10−4
þ0.06þ0.19
ð1.11−0.06−0.32
Þ × 10−5
þ0.08þ0.17
ð2.72−0.06−0.47
Þ × 10−4
þ0.21þ0.66
ð4.95−0.21−0.72
Þ × 10−5
þ0.08þ0.59
ð2.58−0.09−0.20
Þ × 10−5
þ0.03þ0.69
ð7.99−0.04−0.50
Þ × 10−5
þ0.34þ3.82
ð5.54−0.40−1.49
Þ × 10−5
ð1.85þ0.05þ0.68 Þ × 10−5
2.6 −0.05−0.26
þ0.99þ4.18
ð5.73−1.00−3.74
Þ × 10−5

Mass(γ K ) [GeV/c ]

-0.2

0

cos(θ

EventsSignificance

Pull

Pull

Events / 20 MeV/c2

Resonance

-0.4

8000

35σ (b)
χ2/nbin=1.32
16σ
6000
25σ
Data
5000 23σ
Global F
4000≫ 35σ3000 24σ2000≫ 35σ1000 35σ
4 33σ
2≫ 35σ0-2 26σ-4-126σ -0.8 -0.6 -0.4 -0.2
0
13σ
cos
10(θ
7000

Amplitude analysis of J/ψ→γπ0π0
PHYSICAL REVIEW D 92, 052003 (2015)

MPLITUDE ANALYSIS OF THE π 0 π 0 SYSTEM …

dependent assumptions. If more than two solutions arefound in a given bin, all solutions within 1 unit of log
likelihood from the best solution are compared to thepredicted value derived from the best solution and only thatwhich matches the prediction is accepted as the ambiguous
partner.

ut have a degenerate ambiguous pair. A study of thesembiguities (Appendix B) shows consistency between themathematically predicted and experimentally determined
mbiguities. Both ambiguous solutions are presented,
ecause it is impossible to know which represent thehysical solutions without making some additional model
Events / 15 MeV/c 2

18000
16000
14000

(a) 0++

12000
10000
8000
6000
4000
2000
0

0.5

1

1.5

Mass(π0π0)

2

2.5

3

2

[GeV/c ]◈ Model independent analysis:

two distinct sets of solutions
above KK threshold.

Events / 15 MeV/c 2

30000
25000

(b) 2++ E1

20000
15000
10000
5000
0

0.5

1

1.5

2

2.5

3

Events / 15 MeV/c 2

Mass(π0π0) [GeV/c2]
16000
14000

◈ Significance structures in thescalar spectrum near 1.5GeV,
1.7GeV (f0(1500), f0(1710)).

(c) 2++ M2

12000
10000
8000
6000
4000
2000
0

0.5

1

1.5

2

2.5

3

2

2.5

3

Mass(π0π0) [GeV/c2]

Events / 15 MeV/c 2

4500
4000
3500

(d) 2++ E3

3000
2500
2000
1500
1000
500
0

0.5

1

1.5

Mass(π0π0)2[GeV/c ]PRD 92 (2015) 052003

IG. 2 (color online). The intensities for the (a) 0þþ , (b) 2þþ E1, (c) 2þþ M2, and (d) 2þþ E3 amplitudes as a function of M π 0 π 0 for theominal results. The solid black markers show the intensity calculated from one set of solutions, while the open red markers represent its
mbiguous partner. Note that the intensity of the 2þþ E3 amplitude is redundant for the two ambiguous solutions (see Appendix B).
nly statistical errors are presented.

052003-9

11

PWA of J/ψ→γΦΦ
PHYSICAL REVIEW D 93, 112011 (2016)

ABLIKIM et al.

TABLEI. Mass, width, BðJ=ψ → γX → γϕϕÞ (B.F.) andmple of N acc accepted events. The normalization integral-+++
A good channel for 0 and
2 stateabovein 2GeV
significance(Sig.) searchof each component
the baseline solution.
omputed as:(f)Z"
N acc !
X1dσ0dξωðξÞϵðξÞ ¼ σ →:N acc k dΦ k

The first errors are statistical and the second ones are systematic.

ð8Þ

Since data contains the contribution of signal and
kground, the contribution of non-ϕϕ background events
aken into account by subtracting the negative loglihood (NLL) value obtained for events in the ϕϕebands from the NLL value obtained for events in thesignal region, i.e.,
Lsig ¼

Ldata
;
Lbkg

Resonance M (MeV=c2 ) Γ (MeV=c2 )ηð2225Þ
2216þ4þ21−5−11
þ30þ75
ηð2100Þ
2050−24−26
Xð2500Þ
2470þ15þ101−19−23f0 ð2100Þ
2101
f2 ð2010Þ
2011
2297
f2 ð2300Þ
2339
f2 ð2340Þ
0−þ PHSP

185þ12þ43−14−17
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224
202
149
319

B.F. (×10−4 )

Sig.

þ2.47
ð2.40 % 0.10−0.18
Þ 28σ
þ0.18
ð3.30 % 0.09−3.04
Þ 22σ
þ0.02 8.8σ
ð0.17 % 0.02−0.08
Þ
þ0.24
Þ 24σ
ð0.43 % 0.04−0.03
þ0.28 9.5σÞ
ð0.35 % 0.05−0.15
þ0.09 6.4σ
ð0.44 % 0.07−0.15
Þ
þ0.72
Þ 11σ
ð1.91 % 0.14−0.73
þ0.16 6.8σ
ð2.74 % 0.15−1.48
Þð9Þ

PRD 92, (2018)
112011
evaluated.
Given the small phase space of J=ψ → γϕϕ,ð10Þ−ln Lsig ¼ −ðln Ldata − ln Lbkg Þ:J ≥ 4 states should be suppressed. The changes in the NLL
tributions -+of ϕϕ; (b) cos θ of γ in the J=ψ rest
value and the number of free parameters in the fit with and◈ 0 states are dominantazimuthal
the normals
the twoThe
numberangleof thebetween
fitted events
N X for antointermediate
without a resonance are used to evaluate its statisticalundeventssubtracted
solid redpartial
lines areonanceX, which
has Nandindependentwave
W X thesignificance. In the baseline solution, there are three 0−þf2(2340),the large
rate(ηð2225Þ,is compatible
theoneLQCD
plitudesAFor
definedas and green
hered◈dots,boxes
trianglesproduction
withi , isblue
resonancesηð2100Þ, and with
Xð2500Þ),
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resonance(ftoð2100Þ),three
2þþ J/ψ→γηη,
resonances (f 2 ð2010Þ,-independent
fit in eachbin.
Theshort-dashed,0
predictionfortensorglueball,similar
that
in
the
γKsKs
σX
0
f 2 ð2300Þ, and f 2 ð2340Þ), and the direct decay of; , 0þþ and 2þþð11Þ
N X J¼PC 0¼· N0−þW resonances with,σ
J=ψ → γϕϕ, which is modeled by a 0−þ phase space◈
X(2500) is observed with 8.8σ distribution (0−þ PHSP) of the ϕϕ system. The statisticalere N 0 is the number of selected events after backgroundsignificance of each component in the baseline solution is
traction, andlarger than 5σ. The masses and widths of the three 0−þ12The X(2370)

X(2370) could be a good candidate for 0-+ glueballX(1835)

PRL., 106 (2011) 072002

J/ψ→γKKη’(a)

P

Simultaneous fit of(b)z UseX(1835)
1.31 10 J/ events collected by BESIII in 2009 and201• BESIII confirmed
150
400
z Simultaneous
fit is performed onfour decay modes:• BESIII observedX(2120)/X(2370)
+ -

+ -

J/ψ →γ K K η’, η’→ π π η, η→γ γ
Chebychev
Data
PHSP
Fit result
Total bkg
Signal X(2370)

Events/(0.01GeV/c2)

X(2120) X(2370)

200

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J/ψ→γππη’

Eur. Phys. J. C (2020) 80:746

500 J/ψ →γ K+K η’, η’→γρ0, ρ0→ π+π-

Data

Fit result
Signal X(2370)

𝐽/ → 𝐾 𝐾 ′ 300
and 𝐽/J/ψ→ K→K η’+c.c.
𝐾 𝐾 ′, each ′ hη’ sideband
z The mass and width of the X(2370)
are set to be same in four
200
50z
Factor(f) of signal yield between
decay modes is :100two

100

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2

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η’ sideband

2.1

2.2

2.3

2.4

2.5

2.6

0
2

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2.3

2.4

2.5

2.6

2.7

2

MK+K-η’ (GeV/c )
30

-

*+

2

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J/ψ →γ K0 K0S η’, η’→ π+π-η, η → γ γ
S
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Total bkg
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90

𝐵𝑊
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Events/(0.01GeV/c2)

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(d)

0 0
0
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70
60

⨂𝐺𝑎
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20zBackground :Signal X(2370)
50
η’ sideband
η’ sideband
15¾
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5
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polynomial function
10• J/\ Æ JS+S-K is a good place to observe 0-+ glueballz The statistical significance of the X(2370) is 7.6 .
(GeV/c )(GeV/c )M• X(2370) decay pattern seems similar
to KMresults:c ?
z Fitting
7.6σ
0
2

2.1

2.2

2.3

K0SK0Sη’Æ J , more decay modes of X(2370)
PRL 106, 072002

2.5

2

2.6

2.7

Fig. 3 The fit result for X (2370) in the invariant-mass distribution of K K̄ η! for the decays: a J/ψ → γ X (2370), X (2370) →γ K + K − η! , η!
→π + π − η, η→
γ γ , b J/ψ
→
+
−
!
!
0
0
+
−
γ X (2370), X (2370) → γ K K η , η → γρ , ρ → π π , c
J/ψ → γ X (2370), X (2370) → γ K S0 K S0 η! , η! → π + π − η, η → γ γ ,and d J/ψ → γ X (2370), X (2370) → γ K S0 K S0 η! , η! → γρ 0 , ρ 0 →π + π − . The dots with error bars represent the data; the solid curves◈ Firstpc observation of theX(2370) in J/ψ→γππη’

2.4

0
2

2.1

2.2

2.3

K0SK0Sη’

2.4

2.5

2

2.6

2.7

show the fit results; the grid areas represent the signa
dotted lines are the background shapes from J/ψ →the short dashed double dotted lines show the η! sid
dashed lines represent the Chebychev polynomial fu
76
short dashed lines are the contribution from PHSP M
dotted lines show the sum of all backgrounds

EPJC 80 (2020) 746

BESIII Prelimina

0 0 !
−6
and B(J/ψ→ γ XLQCD(2120) → γ Kprediction:
Table 1 Fit results for the structure around 2
S K S η ) < 6.15 × 10 ,0-+Explanation from the comparison
withglueball candidate
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2

X → K + K − η! and X → K S0 K S0 η! , respectively. The
statistical only13

Effici

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Search for the X(2370) in J/ψ→γηηη’
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PRD 103, (2021)
16 012009
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1425-6 @ 96% CL
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12
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2.7 2.75 2.8 2.85 2.9 2.95

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3.05 3.1

FIG. 2. Plots (a) and (b) are efficiency curves for the decays of η0 → γπ þ π − and η0 → π þ π − η obtained from J=ψ → γX → γηηη0 MC
simulation, where X means 0−þ nonresonant state. Plots (c) and (d) are the simultaneous fit results for the Xð2370Þ in the invariant mass
distribution of ηηη0 for the decays of η0 → γπ þ π − and η0 → π þ π − η, respectively. Plots (e) and (f) are the fit results for η in the invariant14

a0(980)-f0(980) mixing
N.N. Achasov, S.A. Devanin & G.N. Shestakov, Phys. Lett. B88, 367 (1979)

isospin violation enhanced by K0 – K+ mass difference

2mK+ = 987.4 MeV
expect a narrow line shape:G≈2(mK0-mK+)=7.8 MeV

2mK0 = 995.2 MeV
PDG2010:
Mf0= 980  10 MeV
Gf0= 40 ~ 100 MeV

2mK+

Ma0= 980  20 MeV
Ga0= 50 ~ 100 MeV

2mK0

15

ae,
k-

was carried out to examine the a00 ð980Þ ↔ f 0 ð980Þ mixing
with the isospin-violating processes of J=ψ →ϕf 0 ð980Þ→
PHYSICAL REVIEW LETTERS 121, 022001 (2018)
ϕa00 ð980Þ→ϕηπ 0 and χ c1 → π 0 a00 ð980Þ → π 0 f 0 ð980Þ →π 0 π þ π − [17–20]. The central masses and couplings of
100
0
−
0
0
0
Þ0
h
have
been
discussed,
such
as
γp
→
pπ
al
η
[7],
π
p
→
π
ηn
a
ð980Þ
→
ηπ
=K
K̄
and
f
ð980Þ
ππ=K
K̄
from
various+0
f →0 a ð980Þ
K (K )
0 the f ð980Þ
rmine
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0
0
],
wo
models
[1–4]andη [10–12],
different dd
experimental
results[21–26]no[8,9],ypn→ dπ→ απ η [13].
However,80
J/
he 0 , were
investigated.
The
mixingintensities,i.e.,firmlyξafa for
the
wo
ηπ
an
unbinned
maximum
likelihood
methodisquantitative
experimental
resulthas
beenestab060
f0transition and ξ for the a0 ð980Þ →
0
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0
yet.
nd
flished
ð980Þ
→
a
ð980Þ
p η
0
0fit the π 0 η massaf
0for the two
multaneously
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Inspiredby Refs.are[14–16],
first
al
40
ce
f 0 ð980Þ
transition,
defineda as
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2 mixing
a- in
was
carriedout toof
examinethe1.25$a0 ð980ÞGeV=c↔ f 0 ð980Þ
to
des
the
range
½0.70;. In the fit,
20
0
0
B½J=ψ
→
ϕf
ð980Þ
→
ϕa
ð980Þ
→
ϕηπ
&
e,
0
with¼0the isospin-violating processesof J=ψ →ϕf; 0 ð980Þ→
en
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ξ
ð1Þ
fa
0Þ
→
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mixingsignal,
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a
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→π →a0 ð980Þ
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he
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2m
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&
SolutionI:
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c1
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PHYSICALÞe,
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3.60
16
s,
18
jA
ðmÞe
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14 (b)
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crucialin modelsf 0 ð980Þ
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Events / (5MeV/c2)

Events / (10MeV/c2)

Mπ+π-π0 (GeV/c2)

Events / (10MeV/c2)

a0(980)-f0(980) mixing

PHYS. REV. D 101, 032008 (2020)

40

(a)

30

data
total fit
sidebandφ(1020)φ(1680)X(1750)ρ(2150)ρ (2250)
3

20
10

50

Events/20MeV/c2

χ2/nbin = 0.95

50

40
30

data
total fit
sidebandK2*(1980)
K3*(1780)(b)

χ2/nbin = 1.22

50

Events/20MeV/c2

M. ABLIKIM et al.

Events/18.5MeV/c2…

PWA in ψ(3686)→K+K-η
40
30

20

20
PHYS. REV. D 101, 032008 (2020)

10

100 intermediate
X for an
1.5

FIG. 3.

TABLE I. Mass, widthand significance of each component in
0
0
2.5
3
1
1.5
2
2.5
3
1
the
baseline
solution.
The
first
uncertainties
arestatisticalandthe
M(K+K ) (GeV/c2)
M(K+η) (GeV/c2)
second are systematic.
2

data
total fit
sidebandK2*(1980)
K3*(1780)(c)

χ2/nbin = 1.25

1.5

2

2.5

3

-

M(K η) (GeV/c2)

Comparisons to the fit projections for the(a) K þ K − , (b) K þ η, and (c) K − η invariant mass distributions.
2

ð11Þ

Resonance

M (MeV=c )Γ (MeV)

Significance# X"
185þ30þ25
14.3σ Xϕð1680Þ11680þ12þ21NN−13−21−26−47ωðξÞ
ipffiffiBWðsÞ ¼ Xð1750Þ
; þ12þ0 ð2Þ 106þ22þ8S ¼ − ln L10.0σ
¼−
−
2
ln
ln εðξi Þ: ð7Þ
1784
0m − s − i sΓðsÞ−12−27−19−36
σ
ξj Þ;
ð12Þ
i
i
þ17þ50þ54þ160
ρð2150Þ
2255
460
23.5σ
−48−90#2lþ1 −18−41" 2 #"
þ31þ17mpðsÞ 2248þ17þ59
185
8.5σterm is a constant and has no impact
2ρ3 ð2250Þ
In
Eq. (7), the second−26−103−17−5;ð3ÞΓðsÞ ¼ Γ0 ðm Þ
2
& s
pðm
Þ 2046þ17þ67
onþ38þ72
the determination
K 2 ð1980Þ
408
19.9σof the amplitude parameters or on theents after background−34−44−16−15relativeþ15þ65
þ43þ3 changes in S. In the fit, − ln L is defined as&ved differential crossKð1780Þ
1813
191
11.2σ
3
−37−81−15−16
where s is the invariant mass squared of the daughter

mediatestate X.
particles, m and Γ0 are the mass and width of the
#
"
N
N
X
X
he intermediate
intermediateresonance,
reso- respectively, l is thePRD
101(2020)
032008ωðξÞi0
orbital angular
−
ln
L
¼
−
¼
−
ln
ln
ωðξ
Þ
þ
N
ln
σ
:
i
0
tedmomentum
MCThesamplethat
2+σ◈Forintheothercomponents
in the fit, a canlarge benumber
dip
the
K K
mass
spectrum
wellofdescribedwith thefor a ~1.7GeV
daughter particle,andpðsÞ
or pðmÞ is theiimomentumof a daughter
particleinarethemaderest frameof theto evaluate
the possible resonanceφ(1680)andptheX(1750)ð8Þ
ffiffi attempts
þ−%resonance with mass s contributionsor m.
in the K K and K η mass spectra [30].
The
probability
to observetheith eventto
characterizedThe
X(1750)
isOnlydetermined
be JaPCstatistical= 1-- ThesignificanceX ðξj Þ◈components
withlarger i.e., the relative magnitudes andcomplexcouplings,
:
ð13Þ
17
by the measurement ξi , i.e., the measured four momenta ofSummary◈ BESIII detector has successfully collected data samples, including 10billion J/ψ events.
◈ A set of interesting and important results from the light hadron spectrum

achieved:✦ Strong correlation between the X(1835) and mppb threshold enhancement.

A molecule state or a bound state?
✦ Wide search for the glueball and current glueball candidates (component):

f0(1710), f2(2340), X(2370)✦ First observation of a0(980)-f0(980) mixing.
✦ The X(1750) was observed with the JPC=1—◈ With the highest J/ψ dataset, the more extensive and intensive investigation is

ongoing, looking forward to new results in the near future.
18