Exotic Diquark Spectroscopy JLab R.L. Jaffe November 2003 F. Wilczek hep-ph/0307341 The discovery of the Θ+(1540) this year marks the beginning of a new and rich spectroscopy in QCD. What are the foundations of this physics? Why this channel? What is the underlying dynamics? What implications for QCD? What predictions to test ideas? R Jaffe JLab November, 2003 1 Assumed Properties of the Θ+(1540) 1 It exists ? J = 2 Flat angular distribution Mass 1540 MeV Width 10 MeV ???? How Narrow? Parity Unknown! Very Narrow? + K n quantum numbers: Y Θ+ Y =2 I3 =0 I3 I =0 (no K+p partner) R Jaffe JLab November, 2003 2 First Manifestly Exotic Hadron in 40 Years • What dynamical principles are operating here? • What are the further consequences? • Strong correlation of color, ⇐ THIS TALK flavor, and spin antisymmetric quark pairs into DIQUARKS. Y + _ Θ uudds • Two relatively light, narrow EXOTIC CASCADES await I3 discovery. • -- _ + _ Possible stable? charm and Ξ ssddu Ξ uussd bottom analogues. R Jaffe JLab November, 2003 3 Interpretations of the Θ+ • Chiral Soliton Model (motivated experiments) A narrow K+n resonance generated by chiral dynamics. Chemtob (1984) ; Praszalowicz (1987) Diakonov, Petrov, Polyakov (1997) • Uncorrelated Quark Model Q4Q¯ in the lowest orbital of some mean field: NRQM, bag, . RLJ (1976), Strottman (1978), Wybourne Carlson, Carone, Kwee, & Nazaryan,. • Correlated (Diquark) Description [QQ] correlated in an antisymmetric color, flavor, and spin state. ⇔ Q2Q¯2 mesons, color superconductivity. Jaffe & Wilczek [For a different correlated description, see the talk by M. Karliner.] R Jaffe JLab November, 2003 4 Essential Distinctions These three pictures make strikingly different predictions for the parity of the Θ+ and the spectrum of particles in the same class as the Θ+ CHIRAL SOLITON MODEL + CORRELATED QUARKS PARITY _ UNCORRELATED QUARKS _ CHIRAL SOLITON MODEL 10 HEAVY EXOTIC CASCADES SPECTRUM _ QUARKS 10 + 8 LIGHT EXOTIC CASCADES R Jaffe JLab November, 2003 5 The Θ+ and K+n Scattering • KN non-relativistic at M = 1540 MeV • No other channels until K∆ at 1725 MeV • O 0 No quark annihilation barrier ( (Nc )) • If no hidden structure ⇒ potential theory Parity − ⇒ s-wave ⇒ non-resonant Parity + ⇒ p-wave Try p-wave: What potential generates a resonance at p =270 MeV and Γ <10 MeV? {Range & Depth}⇔{Mass & Width} R Jaffe JLab November, 2003 6 Range/width relation for square well in p-wave EV) 200 Γ ≈ 10 MeV ⇒ 150 Range ≈ 0.05 fm! 100 50 0.2 0.4 0.6 0.8 1.0 WIDTH OF RESONANCE (M RANGE OF INTERACTION (FERMIS) Even in the p-wave, a state this narrow at this mass cannot be explained without either a very high mass scale or suppression by dynamics beyond KN physics. R Jaffe JLab November, 2003 7 Assumptions going forward • Parity of Θ+ is positive • Dynamics beyond KN-scattering. • [QCD ⇒ Quarks!] Uncorrelated quarks: Q4Q¯ ⇒ Negative Parity • Some correlation must be resonsible for switching the parity of the Θ+ R Jaffe JLab November, 2003 8 Strong Correlations in QCD • [QQ¯]1c1f0 (Notation: Color Flavor Spin) Most attractive channel for gluon exchange Condenses in vacuum – drives chiral symmetry breaking ¯ ¯ • [QQ]3c3f0 [ud][ds][su] Color, flavor & spin antisymmetric diquark Next most attractive channel for gluon exchange Favored for instanton mediated interactions Role in QQQ baryon spectroscopy, parton distribution functions, and in exotic spectroscopy R Jaffe JLab November, 2003 9 Correlated Quarks ⇒ Diquarks 3c ⊗ 3c = 3c ⊕ 6c Selects COLOR 3¯c Colorspin: (QQ)3 ˜λj σj × ⇒ ∝− FLAVOR 3f SPIN 0 ∆E 8 ˜λi σi × ⇒ ∝ FLAVOR 6f SPIN 1 ∆E 8/3 So QQ prefer: COLOR 3¯c FLAVOR 3¯f SPIN 0 ⇒ Neither pointlike nor non-relativistic – Energetically favored ⇒ Non-perturbative? R Jaffe JLab November, 2003 10 Diquarks – Some Evidence Diquark correlations have played an important supporting role in QCD cf. Anselmino et al., RMP 65 (1993) • Color superconductivity ¯ ¯ [QQ]3c3f0 condenses at high energy: α α [QQ] a = vδ a Proven at high density, phenomenology in quark matter. • Absence of exotic mesons: 2 2 In principle Q Q¯ could include 10, 10, 27f But ¯ 3f 3f ⇒ [QQ] [Q¯Q¯] 8f + 1f “Crypto”exotic Prediction: Lightest and most prominent Q2Q¯2 states should be nonet of scalar (0++) mesons R Jaffe JLab November, 2003 11 Scalar Mesons 2 – 2 2–2 Q Q Q Q – COLOR 3 ⊗ 3 1 – FLAVOR 3 ⊗ 3 1 ⊕ 8 SPIN 00⊗ 0 ⇒ A nonet of 0++ mesons Scalar Meson [ds] [su] Nonet Hidden Strangeness _ [su][ud] [ud] _ _ [su][ds] [ud] _ } _ [ud][ud] [ds][ds] + _ _ _ [su][su] [su] [ds] R Jaffe JLab November, 2003 12 One Slide Summary of Scalar Mesons – QQ -NONET KNOWN SCALAR MESONS ss– MASS f (1500) – 1500 MeV 0 us a (1450) 0 κ(1430) – f 0 (1370) ud – uu+dd– –– a (98(980) QQQQQQ -NONET NON 1000 MeV 0 f 0 (980) – [su][ds]– κ(800) [su][su]–– –– + – [ud][ds] ( [sd][sd]– ) f 0 (600) – 500 MeV [ud][ud]– -1 0 1 Isospinpin R Jaffe JLab November, 2003 13 Diquarks → Exotics? Diquark correlations predict no exotics in the Q2Q¯2 sector. What about Q4Q¯? • Uniquely predicts 10f ¯ ¯ ¯ [QQ]3f [QQ]3f Q¯3f ⊃ [Q4Q¯]10f • Not recognized before discovery of Θ+ R Jaffe JLab November, 2003 14 Diquarks and Q4Q¯ Construct Θ+ from diquarks — Immediate consequences: • Θ+ must have positive parity • + Θ must lie in a degenerate 8f and 10f • Dramatically fewer associated states compared with uncorrelated quark models. R Jaffe JLab November, 2003 15 ParityofΘ+ [Q1Q2] is a boson • Diquark — diquark – antiquark wavefunction: 3 3¯c 3¯c c 3¯c [Q1Q2] ⊗ [Q3Q4] ⊗ Q¯ Diquarks must couple to 3c to join antiquark in a color singlet hadron. • Consider identical diquarks as in the Θ[ud] − [ud] Antisymmetric in color. ⇒ antisymmetric in space!! ⇒ Q4 has ODD PARITY ⇒ Combine with Q¯ ⇒ Θ+ has EVEN PARITY R Jaffe JLab November, 2003 16 Symmetric Diquark–Diquark Flavor States • Lightest baryons of the form [ud]2¯s have EVEN PARITY • There are six flavor symmetric diquark pairs, degenerate in the SU(3)f symmetry limit 2 2 2 [ud] [ud][ds]+ [ds] [ds][su]+ [su] [su][ud]+ – – [qq][qq] Symmetric 6 Antiquark 3 2 [ud] _ s [ud][ds] [su][ud] + + I 3 _ _ u d 2 [ds] [su] 2 [ds][su]+ Gives 18 states in an SU(3) Octet plus Antidecuplet R Jaffe JLab November, 2003 17 Overall SU(3)f structure: ⊗ ⊕ 6¯f 3¯f = 10f 8f This is a very general result: IN THE QUARK MODEL YOU CANNOT GET A 10f WITHOUT A 8f – – – 6 3 10 8 ⊗ = ⊕ ⎡ ⎤ ¯ ¯ ¯ 6f ⊕ ⎣ ⊗ 3f ⊗ ⊗ 3f ⊗ ⎦ 8f 10f (3f 3f) (3f 3f) 3¯f And they are degenerate in the SU(3)f limit (Same color⊗spin structure) R Jaffe JLab November, 2003 18 [QQ]2Q¯ Octet and Antidecuplet Distinction between (correlated) quark model and chiral soliton model • Quark model: Degenerate 8f and 10f • C. S. M. (see, eg., DPP) 10f, although mixing with other 0 multiplets at order Nc is possible (see, eg., H. Weigel) + + Θ Θ N8 N10− N10− Λ Σ 8 Σ10− Λ Σ10− − − − 0 + − − − 0 + Ξ 3/2 Ξ3/2 Ξ3/2 Ξ 3/2 Ξ 3/2 Ξ3/2 Ξ3/2 Ξ 3/2 − 0 Ξ3/2 Ξ3/2 Octet and Antidecuplet Antidecuplet R Jaffe JLab November, 2003 19 Comparative spectra: Antidecuplet Alone • Degenerate in the SU(3)f limit. 3 • Lowest order in ms equal splitting rule (familiar from old Q decuplet). Note quark content: Θ+ = |[ud][ud]¯s 1 strange quark √ + √1 | | 2 N = 2 [ud][su]+¯s + [ud] d¯ 4/3 strange quark 10 3 √ + √1 | | 2 Σ = 2 [ud][su]+d¯ + [su] ¯s 5/3 strange quark 10 3 Ξ+ = |[us][us]d¯ 2 strange quarks – Ξ3/2 uussd Total Splitting Σ of ~ m s ? Ν Θ uudds– Increasing strange quark mass R Jaffe JLab November, 2003 20 Comparative spectra: Octet Plus Antidecuplet • 10f and 8f mix strongly via degenerate perturbation theory at O(ms) • Schematic model: “ Ideal” mixing, a la ω/φ to diagonalize strange quark content. • More sophisticated treatment allows for 10f/8f mixing angle Diakonov & Petrov hep-ph/0310212 • − O 2 Without 8f 10f a-priori degeneracy, mixing is (ms ) Crucial differences in spectrum: states with same Y and I in 8 and f _ 10f mix and split. Ns uudss For example: _ Θ uudds_ _ N uuddd 10 + 8 R Jaffe JLab November, 2003 21 Schematic Model Rough estimates: Assume ideal mixing – SU(3)f violation diagonalizes strange quark content. + + 2_ Θ Θ [ud] s 2 _ N [ud] d N N _ s N [ud][su] s s _ Σ Σs Λ Σ [ud][su] d, ... Λ 2 _ [us] s Σ _ Ξ [su][ds] d, ... − − + 2 _ Ξ Ξ Ξ − − [su] d Ξ 3/2 3/2 2 _ Ξ+ [ds] u − Corresponds to one choice of 8f 10f mixing angle. [See Diakonov & Petrov hep-ph/0310212 for a more systematic analysis of mixing and masses in light of later discoveries.] R Jaffe JLab November, 2003 22 Identifications and Predictions • Schematic Hamiltonian for SU(3)violation: ∆s — Kinetic cost of strange quark mass. α — Loss in diquark correlation from replacing u, d → s in diquark. Result: s-quark costs more than ¯s-quark. M(ns,n¯s)=M0 + αns +(ns + n¯s)∆s ⇒ Estimate: α ≈ 60 MeV from nucleon octet (Λ, Σ,N). ⇒ Estimate: ∆ ≈ 100 MeV by identifying N with Roper, P11(1440). R Jaffe JLab November, 2003 23 Identifications and Predictions Rough Mass Estimates 1850 M + 3∆ + 2α Σs 1750 18501850 M + 2∆ + 2α Ξ Ξ3/2 M + 2∆ + α Νs 1700 MASS MeV M + ∆ + α Λ Σ 1600 M + ∆ Θ 1540 M Ν 1440 R Jaffe JLab November, 2003 24 Identifications, Postdictions and Predictions • Θ+ – of course • Roper – postdicted Roughough MassMass • Ns ≈ 1700 MeV [ud][ds]¯s EstimatesEstimates 1850 should couple to Nη,KN,...¯ Σs 1750 −− Ξ Ξ • Ξ+, Ξ ≈ 1750 MeV!! 3/2 Νs 1700 • Λ, Σ ≈ 1600 MeV – candidates.