Glueball Searches and PWA at BESIII

Shan JINInstitute of High Energy Physics (IHEP)

jins@mail.ihep.ac.cn

PWA Workshop

Beijing, January 26, 2006

Outline

Physics goal of hadron spectroscopy at BESIII

What can we learn from BESII results?

Selected topics on glueball searches

PWA at BESIII (with discussions)

Physics goal of hadron spectroscopy at BESIII

Multi-quark State, Glueball and Hybrid

Hadrons consist of 2 or 3 quarks ：

Naive Quark Model ：

New forms of hadrons:• Multi-quark states ： Number of quarks > ＝ 4 • Hybrids ： qqg ， qqqg …

• Glueballs ： gg ， ggg …

Meson （ q q ）

Baryon （ q q q ）

How quarks/gluons form a hadron is far from being well understood.

Multi-quark states, glueballs and hybrids have been searched for experimentally for a very long time, but none is established.

J/ decays are an ideal factory to search for and study light exotic hadrons:

The production cross section of J/ is high.

The production BR of hadrons in J/ decays are one order higher than ’ decays (“12% rule”).

The phase space to 1-3 GeV hadrons in J/ decays are larger than decays.

Exotic hadrons are naively expected to have larger or similar production BR to conventional hadrons in J/ decays.

Clean background environment compared with hadron collision experiments, e.g., “JP, I” filter.

Physics Goal (I)

With 1010 J/psi events, we hope to answer: Whether glueballs exist or not?

• Naively, we estimate in each exclusive decay mode:

• If the eff. is about 20%, we would have 20000 events for each decay mode

we should observe a relative narrow (width: 50~200MeV) glueball if it exists.

510~)()/( hhGBRGJBR

310 210

Physics Goal (II)

Is there any gluon content in hadrons – hybrid mesons and baryons?

Whether multiquark mesons and baryons exist in the nature?

Understanding conventional mesons and baryons

How quark/gluon form a hadron?

QCD cannot “escape” from answering these fundamental questions finally.

Difficulties (I)

Theoretically (glueball as an example)

• Predictions on glueball masses from LQCD may be unreliable due to quench approximation.

• No predictions on the widths so far (even the order).

• No prediction on the production rate (J/ G).

• Mix with qqbar mesons or even with 4q, qqg mesons? (dirty?)

Difficulties (II) Experimentally:

• Data sample is not big enough (it is not a problem for BESIII)

• No good way modeling background at low energy, in many cases we have to study bck via data.

• Interferences among mesons make the mass/Dalitz plots very complicated

PWA is a must for hadron spectroscopy at BESIII

But PWA face many uncertainties (see the discussions on PWA)

What can we learn from BESII results?

A number of unexpected new observations at BESII

A possible bound state: mass threshold enhancement in and new observation of X(1835).

mass threshold enhancement in

mass threshold enhancement in

mass threshold enhancement in J/

New observation of a broad 1- - resonance in J/ K+K- 0

ppppJ /

pKJ /K

p pKJ /

pp

Observation of an anomalous enhancement near the threshold of mass spectrum at BES II

M=1859 MeV/c2

< 30 MeV/c2 (90% CL)

J/pp

M(pp)-2mp (GeV)

0 0.1 0.2 0.3

3-body phase space acceptance

2/dof=56/56

acceptance weighted BW +3 +5

10 25

pp

BES II

Phys. Rev. Lett. 91, 022001 (2003)   

Observation of X(1835) in

The +- mass spectrum for decaying into +- and

Statistical Significance 7.7

J

J

Mass spectrum fitting

54264obsN

MeVm 7.21.67.1833

MeV7.73.207.67

410)4.04.02.2()()( XBXJB

7.7The +- mass spectrum for decaying into +- and

BESII Preliminary

Re-fit to J/p pbar including FSI

Include FSI curve from A.Sirbirtsev et al. ( Phys.Rev.D71:054010, 2005 ) in the fit (I=0)

M = 1830.6 6.7 MeV

= < 153 MeV @90%C.L.

ppp mM 2

In good agreement with X(1835)

A Possible ppbar Bound State

X(1835) could be the same structure as ppbar mass threshold enhancement.

It could be a ppbar bound state since it dominantly decays to ppbar when its mass is above ppbar mass threshold.

Its spin-parity should be 0-+: this would be an important test PWA is needed

Observation of an anomalous enhancement near the threshold of mass spectrum at BES IIp

BES II pKJ /

3-body phase space

For a S-wave BW fit: M = 2075 12 5 MeV Γ = 90 35 9 MeV

Phys. Rev. Lett. 93, 112002 (2004)   

)(GeV/c2

ΛKM

PS, eff. corrected

MMM KΛK

Observation of a strong enhancement near the threshold of mass spectrum at BES IIK

(Arbitrary normalization)

BES II pKJ /

NX*

A strong enhancement is observed near the mass threshold of MK at BES II.

Preliminary PWA with various combinations of possible N* and Λ* in the fits —— The structure Nx*has:

Mass 1500~1650MeV

Width 70~110MeV

JP favors 1/2-

The statistics is not high enough to tell what it is.

The most important is:

It has large BR(J/ψ pNX*) BR(NX* KΛ) 2 X 10-4 ,

suggesting NX* has strong coupling to KΛ. It could be

an KΛ bound/resonant state (5-quark system).

M2()

M2 (

) backgroundX(1810)

An mass threshold enhancement is observed

M()

Phys. Rev. Lett., 96 (2006) 162002

2

21926

MeV/c 2820105

MeV/c 181812

M

JPC favors 0++

It could be a multiquark/hybrid/glueball state.

)1580(X

Background

0)1580(X

New observation of a broad 1- - X(1580) in J/ K+K- 0

1

MeV/c )818(2

)1576(2

264 22133 23

98 4991 55

PCJ

iiM

Phys. Rev. Lett. 97 (2006) 142002

How to understand broad X(1580)?

Search of a similar structure in J/ KSK will help to determine its isospin.

X(1580) could have different nature from conventional mesons:

• There are already many 1- - mesons nearby.

• Width is much broader than other mesons.

• Broad width is expected for a multiquark state.

J/ψ decay is an ideal place to study exotic structures.

The statistics at BESII is not high enough yet.

We would expect: more unexpected discoveries on hadron spectroscopy at BESIII —— the more, the better !

What do we learn from BESII results

Selected topics on glueball searches

Selected topics on glueball searches

J/ ,

2++ glueball candidates

Where to search for the 0-+ glueball?

J/ ,

These two processes are believed to be an ideal place to tag the flavor of mesons.

BESII studied these two channels (PLB549, 47(2004)):

'

)1285(1f)1440(

)(GeVM )(GeVM(1440) from J/0KK bck

J/ ,

At BESII, we only observe ’, (1440) , f1(1285) in J/ , no clear peak in J/

At BESIII:

• The background could be very high when searching for other glueball candidates. Hope BESIII much better detector can strongly suppress the background we will perform MC studies on this.

• PWA is needed.

2++ glueball candidates

Lattice QCD predicts the 2++ glueball mass in the range of 2.2~2.4 GeV

(2230) was a candidate of 2++ glueball:• It was first observed at MARKIII in J/KK• It was observed at BES I in J/KK, , ppbar• It was not observed at DM2.

BES-I (2230) Result

(2230)

The situation at BESII

The mass plots shows no evident (2230) peaks in J/KK, , ppbar, which is different from BESI.

Difficult to draw firm conclusion at present.

PWA is needed to draw firm conclusion on it.

00/ ss KKJ

KKJ /

(2230) could be similar to f0(980) at BESII

We saw a clear f0(980) mass peak in J/ at BESI, but we do not see a clear f0(980) peak in the mass plot at BESII.

However, we need a significant contribution of f0(980) in PWA of J/ at BESII

BESIIM(+-

)

J/

?)980(0f

Other 2++ glueball candidates

No other obvious good candidates have been observed in J/psi radiative decays in the mass range predicted by LQCD.

What does it mean:• LQCD prediction is not very reliable, or• BR(J/ G)xBR(Ghh) is small ( <10-4 ) so that we

don’t have the sensitivity to observe it ( quite possible ), or,

• The width of a glueball is very large ( ~1GeV, E.Klepmt ).

Where to search for the 0-+ glueball?

Lattice QCD predicts the 0-+ glueball mass in the range of 2.3~2.6 GeV.

(1440) and X(1835) were suggested being possible candidates, but their masses are much lower than LQCD predictions.

No 0-+ glueball candidate observed in the mass range 2.3~2.6 GeV

No evidence for a relatively narrow state ( 100 ~ 200 MeV width ) above 2GeV in

Again:• LQCD reliable?• Production rate could be v

ery low.• Glueball width could be ve

ry large.

...',

*,*,,/

KKKKJ

'M

)1835(X

PWA at BESIII

PWA is crucial to most analyses at BESIII

Not only to the spin-parity determination of new hadrons

But also to the measurement of decay BR:

e.g.: BR(J/K*K)

BR(J/K*(1410) K)

Also for D decays…

0/ KKJ

From interference

With huge data samples at BESIII, PWA is possible.

However , there are many difficult problems to be solved.

How to obtain robust PWA results with high speed ?

Q1: How to speed up the PWA fit?

We will have 200 times larger data sample at BESIII:

• Typical size of a data sample at BESII: 10000 events. Usually it takes 1- 3 years to publish one PWA result (with more than 20 CPU fully used).

From previous talks at BESII, we have leant how we obtained the PWA results, including how we dealt with systematic uncertainties

• Naively, we would have 2M events for one data sample at BESIII The speed will be about 100 times slower How many years do we need?

Q1: How to speed up the PWA fit?

PWA procedure at BESII: Global fit

• The PWA input contains 4-momentum of all events (the whole mass range).

• Various fits are tried with different combinations of the possible components/resonances/amplitudes, finding minimum –lnL of all these combinations.

One possible solution at BESIII: bin-by-bin fit

• Divide the mass spectrum into many (~100) bins.

• In each bin, we only fit various JPC components without BW structure.

• We can perform PWA fits for all bins on 100 CPU.

Bin-by-Bin Fit

Advantages• Model independent for each JPC component in each

mass bin.• Phase shift measured automatically• Fast

Disadvantages• Detail mass information lost• The constraint on the phase in nearby mass bin

lost.

MC Input/Output Checks of Bin-by-Bin Fit

We have a working group to check whether the bin-by-bin fit can reproduce the input values based on extensive MC studies.

Here I would only show some examples

Example 1: One 0++ resonance & one 2++ resonance

2++0++

intAll

Generated KK mass plot in J/KK (160K evts)

MeV

MeVM

200

1750

MeV

MeVM

80

1790

Error bar: bin-by-bin fit resultHistogram: generated mass plot

0++ 2++

MKK

0++ Gen Fit Dif

Nevent

65567 63874±814 2.2σ

Mass 1750 1753.3±1.6 2.1σ

Width

200 186.5±3.9 3.5σ

2++ Gen Fit Dif

Nevent

38099 39322±814 1.5σ

Mass 1790 1690.1±1.1 0.1σ

Width

80 83.4±2.8 1.2σ

Fit mass plot based on bin-by-bin fit

2++ B

2++ AAll

Example 2: Two 2++ resonances

Generated KK mass plot in J/KK (140K evts)

0++ is not significant

2++ 0++

Gen Fit Dif

Nevent A 104514 100936±793 4.5σ

Mass A 1950 1947.5±0.6 4.2σ

Width A 150 144.3±1.6 3.6σ

Nevent B 7746 6759±375 2.6σ

Mass B 2100 2099.7±0.9 0.3σ

Width B 40 34.7±2.8 1.9σ

Output (fitting the phase shift curve):

=61.49±6.90

M(0++)=2.5012±0.005GeV

(0++)=0.206±0.012GeV

M(2++)=1.227±0.403GeV

(2++)=32.273±17.906GeV

0++

2++

Input : 0++: m=2.5GeV, =0.2GeV, =60 2++: Phase Space =0

Example 3: Phase Shift Measurement

Bin-by-bin approach looks promising…

However

2++

Example 4: Two 2++ resonances (300K events)

Error bar: bin-by-bin fit resultHistogram: generated mass plot

2++ component cannot be reproduced.

Resonance 1:

M=1970 MeV

Г=180 MeV

Resonance 2:

M=2040 MeV

Г=20 MeV

0++

0++ component is significantly inconsistent with zero.

Given this MC study, we really worry about bin-by-bin fit result (Fortunately, BESII did not have official results based on bin-by-bin analysis).

But in this case, global fit can well reproduce the Inputs.

2++

Global fit results are more reliable than bin-by-bin fit.

More study are needed to understand this.

If bin-by-bin approach cannot obtain robust PWA results, what’s other solutions to speed up PWA fit? – Questions still remains.

Q2: How to treat background?

MC• No reliable inclusive generator at low energy.

Sidebands• More reliable than MC• In some cases, maybe unreliable due to kine

matic limits.

Q3: How to parameterizethe intermediate states?

e.g., the mass shape in J/ process, FSI…

M

In the mass range of (1760)

Q4: How to treat small components?

From PWA of J/ K+K- 0 at BESII, we see that small components could have big interference so as to affect the results significantly.

Q5:How can we include data/MC differences in the PWA fit?

Such differences may results in fake resonances in PWA based on our MC studies.

Example:

• Testing sample: J/+-0 with two intermediate states (770) and (1450)

• Simulation of data/MC difference from MDC wire resolution two different algorithms at BESII

• We add in (1700), (2100) , 3(1690) one by one and then check the significance ( -2lnL ) of each resonance

1.3M J/+-0 events ~ BESII data sample

Δs= -2lnL as a function of the size of data sample

When the data sample is as large as twice of the BESII sample, (1700), (2100) , 3(1690) will have a significance > 5 due to the data/MC difference from MDC wire resolution

They are fake resonances needed in PWA fit.

So We need to find a way to include the data/MC difference in our fit, or at least we need to make the correct judgment that whether the resonances are from the data/MC difference rather than physics resonance.

Q5:How can we include data/MC differences in the PWA fit?

Q6: How to judge whether we have reached a real minimum in the PWA fit rather than local ones?

Especially when there are many resonances (parameters) in one fit.

Currently at BESII, we just tried hundreds of different combinations of initial values of the fitted parameters very time consuming.

Summary

Based on the experience of BESII, we can expect much more unexpected discoveries and much more opportunities at BESIII on hadron spectroscopy.

With huge data samples at BESIII, we hope to answer some fundamental questions such as whether glueball/hybrids/multiquarks exist or not.

PWA is a crucial to most physics results at BESIII. There are many difficult problems to be solved in PWA

—— Suggestions of the solutions are welcome!

谢 谢！Thank You!

With threshold kinematic contributions removed, there are very smooth threshold enhancements in elastic “matrix element” and very small enhancement in annihilation “matrix element”:

much weaker than what BES observed !

NO strong dynamical threshold enhancement in cross sections (at LEAR)

pp

pp

pmppM 2)(

|M|2 |M|2BES BES

elasticelasticM ~|| 2 annlabann PM ~|| 2

Both arbitrary normalization Both arbitrary normalization

Any inconsistency? NO!

For example: with Mres = 1859 MeV, Γ = 30 MeV, J=0, BR(ppbar) ~ 10%, an estimation based on:

At Ecm = 2mp + 6 MeV ( i.e., pLab = 150 MeV ), in elastic process, the resonant cross section is ~ 0.6 mb : much smaller than the continuum cross section ~ 94 20 mb .

Difficult to observe it in cross sections experimentally.

4/)(4

)(4

)12)(12(

)12(22

2

22

2

21

rescm

outin

pcmres mE

BB

mE

c

SS

J

pp

Pure FSI disfavored (I)

1. Theoretical calculation (Zou and Chiang, PRD69 034004 (2003)) shows: The enhancement caused by one-pion-exchange (OPE) FSI is too small to explain the BES structure.

2. The enhancement caused by Coulomb interaction is even smaller than one-pion-exchange FSI.

BES

one-pion-exchange FSI

|M|2 |M|2

Both arbitrary normalization

BES

pmppM 2)(

Both arbitrary normalization

Coulomb interaction

FSI Factors

Most reliable full FSI factors are from A.Sirbirtsev et al. ( Phys.Rev.D71:054010, 2005 ) ， which fit ppbar elastic cross section near threshold quite well.

ppbar elastic cross section near threshold

I=1 S-wave

I=0 S-waveP-wave

pmppM 2)(

J/ decays do not suffer large t-channel “background” as ppbar collision.

>>

p p p p

p

p p p p

p

/J

In ppbar collision, the background is much lager (I)

A.Sibirtsev, J. Haidenbauer, S. Krewald, Ulf-G. Meißner, A.W. Thomas, Phys.Rev.D71:054010, 2005

P-waveI=0 S-wave

I=1 S-wave

In ppbar elastic scattering, I=1 S-wave dominant,while in J/ radiative decays I=0 S-wave dominant.

ppbar elastic cross section near threshold

In ppbar collision, the background is much lager (II)

So, the mechanism in ppbar collision is quite different from J/ decays and the background is much smaller in J/ decays

It would be very difficult to observe an I=0 S-wave ppbar bound state in ppbar collisions if it exists.

J/ decays (in e+e- collider) have much cleaner environment: “JP, I” filter

pp near threshold enhancement is very likely due to some broad sub-threshold 0-+ resonance(s) plus FSI.

From B.S. Zou, Exotics 05:

From A. Sirbirtsev :

FSI factors should be included in BW fit.

Discussion on I=1 S-wave FSI

Pure FSI disfavored (III) — I = 1

Pure I=1 S-wave FSI is disfavored by more than 3 .

ppp mM 2

Pure FSI FSI + BW

M = 1773 21 MeV

= 0 191 MeV

3.85ln2 L 8.65ln2 L

I=0 dominant in J/ radiative decays

Most I = 0 states have been observed in J/ radiative decays with big production rate ( especially for 0-+ mesons ) such as , ’, (1440), (1760), f2(1270), f2(1525), f0

(1500), f0(1710).

The only observed I=1 meson in J/ radiative decays is 0 with low production rate 4*10– 5, e.g., no evidence for (1800) in J/ 3 process.

It is unlikely to be from (1800) .

I=1 S-wave FSI seems unlikely.

ppbar bound state in NNbar potential

Paris NNbar potential: ( Paris 93, B. Loiseau et al., hep-ph/0411218, 0501112 )• For 11S0 , there is a bound state: E = - 4.8 - i 26.3 MeV quite close to the BES observation.

However, Julich NNbar model: ( A. Sibirtsev et al., hep-ph/0411386 )• For 11S0 : E = - 104 - i 413 MeV seems quite far away from BES observation.

They both predict an 11S0 ppbar bound state, although they are quantitatively different.

0/ J

/J

0/ J

)('/ J

BES II Preliminary

No (1800)

With threshold kinematic contributions removed, there are very smooth threshold enhancements in elastic “matrix element” and very small enhancement in annihilation “matrix element”:

much weaker than what BES observed !

NO strong dynamical threshold enhancement in cross sections (at LEAR)

pp

pp

pmppM 2)(

|M|2 |M|2BES BES

elasticelasticM ~|| 2 annlabann PM ~|| 2

Both arbitrary normalization Both arbitrary normalization

The large BR to ppbar suggest it could be an unconventional meson

For a conventional qqbar meson, the BRs decaying into baryons are usually at least one order lower than decaying into mesons.

• There are many examples in PDG.

E.g.

So the large BR to ppbar (with limited phase space from the tail of X(1860)) seems very hard to be explained by a conventional qqbar meson.

310)4.03.1()(

)%9.06.2()(

ppBR

BR

c

c

Analysis of )( J

' X(1835)5.1

Analysis of )( J

'X(1835)6.0

Comparison of two decay modes

Mass and width from m=1827.48.1MeV/c2 , =54.234.5MeV/c2

Mass and width from m=1836.37.9MeV/c2 , =70.323.1MeV/c2

)( J

)( J

)( J410)7.08.1()()( XBXJB

)( J410)5.03.2()()( XBXJB

The mass, width and branching fractions obtained from two different decay modes are consistent with each other.

Similar enhancement also observed in pK'

4 away from phase space.

This enhancement is NOT observed in process at SAPHIR Kp

pKJ

BES

/

Discussion on KΛ mass threshold enhancement NX(1610)

NX(1610) has strong coupling to KΛ:• From (S&D-wave d

ecay) and is a P-wave decay, we can estimate

• From BESII,

• The phase space of NX to KΛ is very small, so such a big BR shows NX has very strong coupling to KΛ, indicating it has a big hidden ssbar component. (5-quark system)

3102)/( ppJBR )1600(/ XpNJ

3100.1)/( XpNJBR

4102~)()/( KNBRpNJBR XX

%20)( KNBR X

Non-observation of NX in suggests an evidence of new baryon :

It is unlikely to be N*(1535). If NX were N*(1535), it should be observed

in process, since:

•

• From PDG, for the N* in the mass range 1535~1750 MeV, N*(1535) has the largest , and from previous estimation, NX would also have almost the largest BR to KΛ.

Also, the EM transition rate of NXto proton is very low.

Kp

Kp)*()*()*( KNBRpNBRKNp

)*( pNBR

Clear and signals

recoiling against

Side-bands do not have mass threshold enhancement

Side-bands

Four decay modes are included :

Amplitudes are defined by Covariant tensor formalism B.S. Zhou and D.V. Bugg, Eur. Phys. J. A16, 537(2003)

BW with energy-dependent width

J.H. Kuhn, A. Satamaria, Z. Phys. C48, 445 (1990).

fitPWA :hist

data : points

0*

0*

)1410(

)890(

: 1

KK

KK

component

)1410( ),890(

)(,)(/

),( ,))1700(,(/

***

0**

0

KKKwhere

KKKKJ

KKXXJ

122

22

2

))(

)(()()(

;)(

1)(

l

R

RRRR

RR

Mp

sp

s

MMs

ssiMssBW

PS

KK

KKX

component

)1700(

: 1

Partial Wave Analysis of J/ K+K- 0 events

Angular distributions for events withfrom PWA fit

Figures on the right: (a),(c),(e) are polar angles in lab. reference frame (b),(d),(f) are polar angles in CM frames of respectively

2/ 7.1 cGeVMKK

fitPWA :hist data, : points

KKandK 0

Broad X cannot be fit with known mesons or their interference

It is unlikely to be (1450), because:

• The parameters of the X is incompatible with (1450).

(1450) has very small fraction to KK. From PDG:

It cannot be fit with the interference of (770) , (1900) and (2150):

• The log-likelihood value worsens by 85 (2=170).

.).%95( 106.1))1450(( 3 LCKKBr

Summary (I)

BES II has observed several strong mass threshold enhancements in J/ decays.

Why strong mass threshold structures are important?

Multiquark states may be only observable near mass thresholds with limited decay phase space.

Otherwise, it might be too wide to be observed as a resonance s

ince it can easily fall apart into two or more mesons.

I can see f0(980)

broadresonance or phase space?

any broadresonanceunder other peaks?

I can see broad under other peaks

Summary (II)

A very narrow and strong mass threshold enhancement is uniquely observed in decays at BES II:• It is NOT observed in B or Y(1S) decays.• Its large BR to suggests it be a bound

state.

X(1835) is observed in It could be same structure as the ppbar mass threshold enhancement, i.e., it could be a ppbar bound state.

pp

ppJ /

pp pp

J