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Pentaquarks from Chiral Solitons

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Pentaquarks from Chiral Solitons Pentaquarks from chiral solitons Maxim V. Polyakov Liege Universitiy & Petersburg NPI Outline: -Predictions -Post-dictions -Implications GRENOBLE, March 24 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 •Cannotbemadeof 3 quarks •Minimal quark content should be qqqqs , hence pentaquark •Must belong to higher SU(3) multiplets, e.g anti-decuplet observation of a S=+1 baryon implies a new large multiplet of important baryons (pentaquark is always ocompanied by its large family!) Searches for such states started in 1966, with negative results till autumn 2002 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 pentaquark Masses higher than 1700 MeV, width ~ hundreds MeV Mass of the pentaquark is roughly 5 M +(strangeness) ~ 1800 MeV An additional q –anti-q pair is added as constituent 2. Soliton models [Diakonov, Petrov ‘84, Chemtob‘85, Praszalowicz ‘87, Walliser ‘92] Exotic anti-decuplet of baryons with lightest S=+1 Jp =1/2+ pentaquark with mass in the range 1500-1800 MeV. Mass of the pentaquark is rougly 3 M +(1/baryon size)+(strangeness) ~ 1500MeV An additional q –anti-q pair is added in the form of excitation of nearly massless chiral field The question what is the width of the exotic pentaquark In 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] Θ+ Θ+ Θ+ Θ+…. LEPS@SPring8 ITEP DIANA@ITEP Negative results from HERA-B SAPHIRand @BES ELSA CLAS@JLAB HERMES@DESY 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 QCD in the chiral limit, i.e. Quark masses ~ 0 1 aaµν µ µ LF=− µν F+ψγ()i∂µ +γAµ ψ QCD 4g 2 Global QCD-Symmetry Æ Lagrangean invariant under: ψψ hadron SU(2) : ψψ=→uu' =exp{}−iαAAτ V ψψ dd multiplets ψψ No Multiplets SU(2) : ψψ=→uu' =exp{}−iαAAτγ A ψψ5 Symmetry is dd sponteneousl Symmetry of Lagrangean is not the same broken as the symmetry of eigenstates Unbroken chiral symmetry of QCD would mean That all states with opposite parity have equal masses −+ But in reality: 11 NN* ()−=()600MeV 22 Thedifferenceistoolarge to beexplainedby Non-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 3 Order parameter: chiral condensate<>qq −(250MeV ) ≠0 [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. <>ψψ =0 Spontaneous Chiral symmetry 5MeV breaking <>ψψ ≠0 current-quarks (~5 MeV) Æ Constituent-quarks (~350 MeV) 350MeV Particles Æ Quasiparticles Quark- Model •Three massive quarks •2-particle-interactions: •confinement potential •gluon-exchange •meson-exchage Nucleon •(non) relativistisc • chiral symmetry is not respected •Succesfull spectroscopy (?) Chiral Soliton Mean Goldstone-fields (Pion, Kaon) Large Nc-Expansion of Nucleon QCD Chiral Soliton •Three massive quarks • interacting with each other • interacting with Dirac sea • relativistic field theory •spontaneously broken chiral symmetry is full accounted Nucleon Quantum numbers Quantum # Coupling of spins, isospins etc. of 3 quarks mean field Æ non-linear system Æ soliton Æ rotation of soliton Quantum # Natural way for light baryon exotics. Also usual „3-quark“ Coherent :1p-1h,2p-2h,....baryonsQuark-anti-quark should containpairsa lot„stored“ Quantumof in # antiquarkschiral mean-field Antiquark distributions: unpolarized flavour d-bar minus u- asymmetry bar dx()− u()x Pobylitsa et al., solitons Soliton picture predicts large polarized flavour asymmetry Fock-State: Valence and Polarized Dirac Sea ()−∇α +βφ=ε φ Dirac-Equation: iMUiii Soliton Quark-anti-quark pairs „stored“ in chiral mean-field Quantum numbers originate from 3 valence quarks AND Dirac sea ! Quantization of the mean field Idea is to use symmetries if we find a mean field π a minimizing the energy than the flavour rotated Rabπ b mean field also minimizes the energy 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 Nc limit justifies slow rotations [Cohen, Pobylitsa, Klebanov, DPP....]. Tremendous boost for our understanding of soliton dynamics! -> new predictions SU(3): Collective Quantization 37 =+II12ΩaaΩ+ ΩaaΩ+3 Ω8 LMcoll 0 ∑∑ 22aa==142 ∂L 1137 J a = HJˆˆ=+aaJˆJˆaaJˆ+constraint ∂Ωa coll ∑∑ 22II12aa==14 8 =−NBc ˆ8 From J ≡−2J = 23 Y' 1 Wess- 3 Zumino -term Jˆˆab, Ji= fabcJˆc Calculate eigenstates of Hcoll and select those, which fulfill the constraint SU(3): Collective Quantization 37 =+II12ΩaaΩ+ ΩaaΩ+3 Ω8 LMcoll 0 ∑∑ 22aa==142 ∂L 1137 J a = HJˆˆ=+aaJˆJˆaaJˆ+constraint ∂Ωa coll ∑∑ 22II12aa==14 NB 8 3, 3, 6,8,10,10,27,... J 8 =− c 2Jˆ Y' ≡− =1 +++ 23 131 3 J=T → .... Known from 222 delta-nucleon ab abcc 33 Jˆˆ, Ji= fJˆ splitting ∆∆= = 10-8 10-8 2I122I Spin and parity are predicted !!! ∆−33 10-10 = 2I212I General idea: 8, 10, anti-10, etc are various excitations of the same mean field Æ properties are interrelated Example [Gudagnini ‘84] ++= + 8(mΞΣ**mmmN ) 3 ΣΛ11 8m 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 MeV In 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 π,Κ, η All decay constants for 8,10 and anti-10 can be expressed in terms of 3 universal couplings: G0, G1 and G2 1 Γ+2 Γ−−1 2 decuplet []GG0 1 anti-decuplet []GG0 1 G2 2 2 1 GG−−G→0 In NR limit ! DPP‘97 012 2 ΓΘ < 15 MeV „Natural“ width ~100 MeV Correcting a mistake in widths of usual decuplet one gets < 30 MeV [Weigel, 98;Jaffe 03] However in these analyses gπNN=17.5 Model 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 of exotic states. However their widths are estimated to be > 150 MeV. Angular velocities increase, centrifugal forces deform the spherically-symmetric soliton. In order to survive, the chiral soliton has to stretch into sigar like object, such states lie on linear Regge trajectories [Diakonov, Petrov `88] π,Κ, π,Κ, η η Very interesting issue! New theoretical tools should be developed! New view on spectroscopy? Ξ−− CERN NA49 reported evidence for Ξ–- with mass around 1862 MeV and width <18 MeV For Ξ symmetry breaking effects expected to be large [Walliser, Kopeliovich] Update of π Ν Σ term gives 180 Mev -> 110 MeV [Diakonov, Petrov] Small width of Ξ is trivial consequence of SU(3) symmetry Are we sure that Ξ is observed ? Non strange partners revisited N(1710) is not seen anymore in most recent πN scattering PWA [Arndt et al. 03] If Θ is extremely narrow N* should be also narrow 10-20 MeV. Narrow resonance easy to miss in PWA. There is a possiblity for narrow N*(1/2+) at 1680 and/or 1730 MeV [Arndt et al. 03] In the soliton picture mixing with usual nucleon is very important. π N mode is suppressed, ηNand π∆ modes are enhanced. Anti-decuplet nature of N* can be checked by photoexcitation. It is excited much stronger from the neuteron, not from the proton [Rathke, MVP] Non strange partners revisited R. Arndt, Ya. Azimov, MVP, I. Strakovsky, R. Workman 03 3 Γ 1 p 8. G 2 π N = Θ (1 − sin φ * 8 ) Γ 3 Θ 5 G 4 pπ N 10 ≈ Corresponding ΓΘ= 1 MeV G10 3 ≈ φ ≈ [DPP‘ 97] G8 18 sin 0.085 Γ π∆ = + φ 2 0 4(sin G8 ) ΓΘ Γ→()NN* π =0.1−2MeVCancelation due to mixing ! Γ→()NM* π∆=3−10eVPossible only due to mixing Favourable channels to hunt for N* from anti-10 γ n-> η n (π ∆, KΛ) Strength of photoexcitation from the proton target is 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 latRapidlytice of gluondeveloping strings theory: >140 papers Θ+(1540) >as 2.5 a heptaquark resubmissions QCD sumper rules, paper parity =-in 1hep Lattice 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 limit Anti-charmed Θ , and anti-beauty Θ Θ produced in the quark-gluon plasma and nuclear matter SU(3) partners of Θ Constituent quark models If one employs flavour independent forces between quarks (OGE) natural parity is negative, although P=+1 possible to arrange With chiral forces between quarks natural parity is P=+1 [Stancu, Riska; Glozman] •No prediction for width •Implies large number of excited pentaquarks Missing Pentaquarks ? (And their families) Mass difference Ξ −Θ ∼ 150 MeV Diquark model [Jaffe, Wilczek] No dynamic explanation of Strong clustering of quarks (ud) L=1 Dynamical calculations suggest large mass [Narodetsky et al.; Shuryak, Zahed] s (ud) JP=3/2+ pentaquarks should be close in mass [Dudek, Close] Anti-decuplet is accompanied by an octet of pentaquarks.
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