Pentaquarks from chiral solitons

GRENOBLE, March 24

Maxim V. PolyakovLiege Universitiy & Petersburg NPI

Outline: - Predictions - Post-dictions- Implications

Baryon states

All baryonic states listed in PDG can be made of 3 quarks only* classified as octets, decuplets and singlets of flavour SU(3)* Strangeness range from S=0 to S=-3

A baryonic state with S=+1 is explicitely EXOTIC

• Cannot be made of 3 quarks•Minimal quark content should be , hence pentaquark•Must belong to higher SU(3) multiplets, e.g anti-decuplet

qqqqs

Searches for such states started in 1966, with negativeresults till autumn 2002

observation of a S=+1 baryon implies a new large multiplet of baryons (pentaquark is always ocompanied by its large family!)

important

Possible reason: searches were for heavy and wide states

Theoretical predictions for pentaquarks

1. Bag models [R.L. Jaffe ‘76, J. De Swart ‘80]Jp =1/2- lightest pentaquarkMasses higher than 1700 MeV, width ~ hundreds MeV

2. Soliton models [Diakonov, Petrov ‘84, Chemtob‘85, Praszalowicz ‘87, Walliser ‘92]Exotic anti-decuplet of baryons with lightest S=+1Jp =1/2+ pentaquark with mass in the range

1500-1800 MeV.

Mass of the pentaquark is roughly 5 M +(strangeness) ~ 1800 MeVAn additional q –anti-q pair is added as constituent

Mass of the pentaquark is rougly 3 M +(1/baryon size)+(strangeness) ~ 1500MeVAn additional q –anti-q pair is added in the form of excitation of nearly masslesschiral field

The question what is the width of the exotic pentaquarkIn soliton picture has not been address untill 1997

It came out that it should be „anomalously“ narrow!Light and narrow pentaquark is expected drive for experiments [D. Diakonov, V. Petrov, MVP ’97]

+ + + +….

LEPS@SPring8

SAPHIR @ ELSA CLAS@JLAB

ITEP

HERMES@DESY

DIANA@ITEP

Negative results from HERA-B and BES

What do we know about Theta ?

Mass 1530 – 1540 MeV

Width < 10-20 Mev, can be even about 1 Mev as it follows from reanalysis of K n scattering data [Nussinov; Arndt et al. ; Cahn, Thrilling] see also talk by W. Briscoe

Isospin probably is zero [CLAS, Saphir, HERMES ] Compatible with anti-decuplet interpretation

Spin and parity are not measured yet

Chiral Symmetry of QCD

(2) : ' expu uA AV

d d

SU i

QCD in the chiral limit, i.e. Quark masses ~ 0

QCD 2

1( )

4a aL F F i A

g

5(2) : ' expu uA AA

d d

SU i

Global QCD-Symmetry Lagrangean invariant under:

hadron multiplets

No Multiplets Symmetry is sponteneousl

broken Symmetry of Lagrangean is not the same as the symmetry of eigenstates

Unbroken chiral symmetry of QCD would meanThat all states with opposite parity have equal masses

But in reality: * 1 1( ) ( ) 6002 2

N N MeV

The difference is too large to be explained byNon-zero quark masses

chiral symmetry is spontaneously broken

pions are light [=pseudo-Goldstone bosons]

nucleons are heavy

nuclei exist

... we exist

Three main features of the SCSB

Order parameter: chiral condensate [vacuum is not „empty“ !]

Quarks get dynamical masses: from the „current“ masses of about m=5MeV to about M=350 MeV

The octet of pseudoscalar meson is anomalously light (pseudo) Goldstone bosons.

3(250 ) 0qq MeV

SpontaneousChiral

symmetry breaking5MeV

current-quarks (~5 MeV) Constituent-quarks (~350 MeV)

Particles Quasiparticles

350MeV

0

0

Quark- Model

Nucleon

•Three massive quarks

•2-particle-interactions:

•confinement potential

•gluon-exchange

•meson-exchage

•(non) relativistisc

• chiral symmetry is not respected

•Succesfull spectroscopy (?)

Chiral Soliton

Nucleon

Mean Goldstone-fields (Pion, Kaon)

Large Nc-Expansion of QCD

Chiral Soliton

Nucleon

•Three massive quarks

• interacting with each other

• interacting with Dirac sea

• relativistic field theory

•spontaneously broken chiral symmetry is full accounted

Quantum numbers Quantum #

Quantum #

Quantum #Coherent :1p-1h,2p-2h,.... Quark-anti-quark pairs „stored“ in chiral mean-field

Coupling of spins, isospins etc. of 3 quarks

mean field non-linear system soliton rotation of soliton

Natural way for light baryon exotics. Also usual „3-quark“ baryons should contain a lot of antiquarks

d-bar minus u-

bar

Antiquark distributions: unpolarized

flavour asymmetry

Pobylitsa et al., solitons

( ) ( )d x u x

Soliton picture predicts large polarized flavour asymmetry

Fock-State: Valence and Polarized Dirac Sea

Dirac-Equation: i i ii MU

Quantum numbers originate from 3 valence quarks AND Dirac sea !

Soliton

Quark-anti-quark pairs „stored“ in chiral mean-field

Quantization of the mean field

Idea is to use symmetries

if we find a mean field minimizing the energy

than the flavour rotated mean field

also minimizes the energy

a

ab bR

Slow flavour rotations change energy very little One can write effective dynamics for slow rotations [the form of Lagrangean is fixed by symmeries and axial anomaly ! See next slide] One can quantize corresponding dynamics and get spectrum of excitations [like: rotational bands for moleculae]

Presently there is very interesting discussion whether large Nclimit justifies slow rotations [Cohen, Pobylitsa, Klebanov, DPP....]. Tremendous boost for our understanding of soliton dynamics! -> new predictions

SU(3): Collective Quantization

3 781 2

01 4

3

2 2 2a a a a

colla a

I IL M

ˆ ˆ ˆ,a b abc cJ J if J

8

2 3

aa

c

LJ

N BJ

3 7

1 41 2

8

1 1ˆ ˆ ˆ ˆ ˆ constraint2 2

ˆ2JY' 1

3

a a a acoll

a a

H J J J JI I

Calculate eigenstates of Hcoll and select those, which fulfill the constraint

From Wess-Zumino-term

SU(3): Collective Quantization

3 781 2

01 4

3

2 2 2a a a a

colla a

I IL M

ˆ ˆ ˆ,a b abc cJ J if J

8

2 3

aa

c

LJ

N BJ

3 7

1 41 2

8

1 1ˆ ˆ ˆ ˆ ˆ constraint2 2

ˆ2JY' 1

3

a a a acoll

a a

H J J J JI I

10-8 10-81 2

10-102 1

3, 3, 6 ,8,10,10,27,...

1 3 1J=T ....

2 2 23 3

= =2I 2I

3 3=

2I 2I

Known from delta-

nucleon splitting

Spin and parity are predicted !!!

General idea: 8, 10, anti-10, etc are various excitations of the same mean field properties are interrelated

* *8( ) 3 11 8Nm m m m m

Example [Gudagnini ‘84]

Relates masses in 8 and 10, accuracy 1%

To fix masses of anti-10 one needs to know the value of I2 which is not fixed by masses of 8 and 10

DPP‘97

~180 MeVIn linear order in

ms

Input to fix I2

Jp =1/2+

Mass is in expected range (model calculations of I2)P11(1440) too low, P11(2100) too high

Decay branchings fit soliton picture better

Decays of the anti-decuplet

All decay constants for 8,10 and anti-10 can be expressed in terms of 3 universal couplings: G0, G1 and G2

2decuplet 0 1

1[ ]

2G G 2

anti-decuplet 0 1 2

1[ ]

2G G G

0 1 2

10

2G G G In NR limit ! DPP‘97

< 15 MeV „Natural“ width ~100 MeVCorrecting a mistake in widths of usual decuplet one gets < 30 MeV[Weigel, 98;Jaffe 03] However in these analyses gNN=17.5Model calculations in ChQSM give 5 MeV [Rathke 98]

Where to stop ?

The next rotational excitations of baryons are (27,1/2)and (27,3/2). Taken literary, they predict plenty ofexotic states. However their widths are estimated to be > 150 MeV. Angular velocities increase, centrifugalforces deform the spherically-symmetric soliton.

In order to survive, the chiral soliton has to stretch intosigar like object, such states lie on linear Regge trajectories[Diakonov, Petrov `88]

Very interesting issue! New theoretical tools should be developed!New view on spectroscopy?

CERN NA49 reported evidence for – - with mass around 1862 MeV and width <18 MeV

For symmetry breaking effects expected to be large [Walliser, Kopeliovich]

Update of term gives 180 Mev -> 110 MeV [Diakonov, Petrov]Small width of is trivial consequence of SU(3) symmetry

Are we sure that is observed ?

Non strange partners revisited

N(1710) is not seen anymore in most recent Nscattering PWA [Arndt et al. 03]

If is extremely narrow N* should be alsonarrow 10-20 MeV. Narrow resonance easy to missin PWA. There is a possiblity for narrow N*(1/2+) at1680 and/or 1730 MeV [Arndt et al. 03]

In the soliton picture mixing with usual nucleonis very important. N mode is suppressed,N and modes are enhanced.

Anti-decuplet nature of N* can be checked byphotoexcitation. It is excited much strongerfrom the neuteron, not from the proton [Rathke, MVP]

Non strange partners revisited

3

3

1

4N

N

p

p

0

28

10

8.(1 sin * )

5

G

G

103G Corresponding = 1 MeV

8 18G sin 0.085 [DPP‘ 97]

R. Arndt, Ya. Azimov, MVP, I. Strakovsky, R. Workman 03

284(sin )G

*( ) 0.1 2N N MeV *( ) 3 10N MeV

Cancelation due to mixing !

Possible only due to mixing

Favourable channels to hunt for N* from anti-10 n-> n K

Strength of photoexcitation from the proton targetis expected to be much smaller than from the neuteron![A. Rathke, MVP‘ 03]

See GRAAL results, V. Kuznetsov, talk on Friday

Theory Postdictions

Super radiance resonance

Diamond lattice of gluon strings

+(1540) as a heptaquark

QCD sum rules, parity =- 1Lattice QCD P=-1 or P=+1, see next talk by T. Kovacs

di-quarks + antiquark, P=+1, see talk by C. Semay

colour molecula, P=+1

Constituent quark models, P=-1 or P=+1, review by K. Maltman

Exotic baryons in the large Nc limitAnti-charmed , and anti-beauty produced in the quark-gluon plasma and nuclear matterSU(3) partners of

Rapidly developing theory: >140 papers> 2.5 resubmissionsper paper in hep

Constituent quark models

If one employs flavour independent forces between quarks(OGE) natural parity is negative, although P=+1 possible to

arrangeWith chiral forces between quarks natural parity is P=+1[Stancu, Riska; Glozman]

•No prediction for width•Implies large number of excited pentaquarks

Mass difference 150 MeV

Missing Pentaquarks ? (And their families)

Diquark model [Jaffe, Wilczek]

L=1

(ud)

(ud)

s

No dynamic explanation ofStrong clustering of quarks

Dynamical calculations suggest large mass [Narodetsky et al.; Shuryak, Zahed]

JP=3/2+ pentaquarks should be close in mass [Dudek, Close]

No prediction for width

Mass difference 200 MeV -> Light pentaquark

Anti-decuplet is accompanied by an octet of pentaquarks. P11(1440) is a candidate. It is expected at least 18 (1/2+) pentas.

Views on what hadrons “made of” and how do they “work” may have fundamentally changed

- renaissance of hadron spectroscopy - need to take a fresh look at what we thought we knew well.

Quark model & flux tube models are incomplete and should be revisited

Does start a new Regge trajectory? -> implications for high energy scattering of hadrons ! Can become stable in nuclear matter? -> astrophysics?

Issue of heavy-light systems should be revisited (“BaBar”Resonance, uuddc-bar pentaquarks [H1 results] ). It seems that the chiral physics is important !

Implications of the Pentaquark

uuddc* pentaquark mass is NOT M+ mc –ms like in QMbut rather M+ mc + M, i.e. 3000 – 3200 MeV, 200-300 MeV above QMThe point is that neither c* nor qqqq can be „hidden“in a chiral excitation

Assuming that chiral forces are essential in binding of quarks one gets the lowest baryon multiplets (8,1/2+), (10, 3/2+), (anti-10, 1/2+) whose properties are related by symmetry

Predicted pentaquark is light NOT because it is a sum of 5 constituent quark masses but rather a collective excitation of the mean chiral field. It is narrow for the same reason

Where are family members accompaning the pentaquark Are these “well established 3-quark states”? Or we should look for new “missing resonances”? Or we should reconsider fundamentally our view on spectroscopy?

Summary

Surely new discoveries are waiting us around the corner !