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

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:

– 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 8f and _ 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 _ [su][ds] d, ... Ξ _ − − + − − 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 MASS 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 Rooughugh MMassass • 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. Λ Σ 1600 Θ 1540 2 • Σs [us] ¯s – heavy and coupled to ηΣ etc. Ν 1440

R Jaﬀe JLab November, 2003 25 Widths • Mechanism for reduction of widths below KN potential theory estimates: Resonance conﬁguration may have small overlap with KN:

2 ⇔? [ud] ¯s Θ [udd]n [u¯s]K • −− + Relating Γ(Ξ ) to Γ(Θ ) Y Θ+ Θ → K+n/K0p −− → − − − − Ξ Ξ π /Σ K I3

SU(3)f for matrix elements combined with p-wave phase space. Ξ-- Ξ+ −− Predict Γ(Ξ (1750)) ≈ 1.4Γ(Θ) −− [Γ(Ξ (1860)) ≈ 3.5Γ(Θ)] SMALL!.

R Jaﬀe JLab November, 2003 26 Widths II • The widths of the non-exotic [QQ]2Q¯ are complicated by mixing [QQ]2 Q¯ ⇔ Q3 + Θ

N Ns

Λ Σ Σs

− − + Ξ 3/2 Ξ Ξ 3/2

• Width of Roper 150-300 MeV is still a problem.

R Jaﬀe JLab November, 2003 27 −− Exotic Cascades! Ξ (1860)! NA49 in hep-ex/0310014

40 - - 30 a) Ξ π

0 60 a) 15 b) Ξ-π+ 50 40 10 2 2 30

20 5 10

0 0 ± + - 15 c) Ξ π 30 b) 20 Entries / 7.5 MeV/c / 7.5 Entries

10 Entries / 7.5 MeV/c 10 5 0

0 -10 8 ± + + 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 d) Ξ π 2 6 M(Ξπ) [GeV/c ]

0 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 M(Ξπ) [GeV/c2]

R Jaﬀe JLab November, 2003 28 Charm and Bottom Analogues of the Θ+

• 0 ∼ + ∼ ¯ Θc uudd¯c Θb uuddb

• QCD environment of antiquark is familiar: 3¯ 3¯ {[[ud][ud]] cq¯}↔{[ud] cq} Θq ↔ Λq

Except [ud] in Λq has S = J = 0, whereas [ud][ud] in Θq has S =0,J =1.

• Θc − Θs =Λc − Λs ⇒ M(Θc) = 2710 MeV − − ⇒ ± Θb Θs =Λb Λs M(Θb) = 6050 10 MeV

• See Karliner & Lipkin and Fl. Stancu PRD58 (1998)

R Jaﬀe JLab November, 2003 29 • Everything scales linearly except pseudoscalar meson masses, which reﬂect non-linearity due to chiral symmetry.

• So heavier Θ’s are progressively more stable:

→ − Θu,d Nπ Q = 350MeV

Θs → NK − Q = 100MeV

Θc → ND − Q = −100MeV → − − Θb NB Q = 150MeV

− • Searches are possible in hadron and e+e facilities.

R Jaﬀe JLab November, 2003 30 Diquarks Summary

• Accomodates Θ+, Roper

• Predicts N(1700) with hidden strangeness;

−− • Predicts Light, exotic Ξ , Ξ+

• Predicts Π=+, Σ, Λ near 1600 MeV.

• Predicts positive parity for Θ+

• Predicts narrow, possibly stable charm and bottom 0 + analogs, Θc and Θb .

R Jaﬀe JLab November, 2003 31 Diquarks Questions and Problems

• Light negative parity Q4Q¯ cryptoexotic baryons. [qq][qq] Antisymmetric 3 Flavor antisymmetric diquark- diquark s-wave, negative parity [ud][ds] [su][ud] baryons – – However these eﬀective bosons contain identical fermions. Pauli blocking should result in repulsion. [ds][su] Push to higher mass. – Hidden or explicit strangeness throughout Couple to meson nucleon s-wave ⇒ broad. Unless bound. . . Λ(1405)? Further study.

R Jaﬀe JLab November, 2003 32 Negative Parity [ud][ds] [su][ud] Nonet – – Hidden Strangeness

[ud][us]s– [ds][su] – – _ [su][ud]d s } – [ds][su]d _ _ u d

• π 3+ ¯ J = 2 partners of the 10f and 8f.

If spatially antisymmetric diquark-diquark wavefunction has =1then ∃ 3+ + 2 partners of the Θ etc. nearby.

R Jaﬀe JLab November, 2003 33 Mass Spectrum: Diquark versus Soliton • ⊕ CSM: ONLY 10f Diquarks: 8f 10f

• 10f alone seems disfavored now compared with 8f + 10f, which is natural in quark models. – uussd Ξ3/2

Σs Σ

Ξ Ξ3/2 Νs Ν Λ Σ – Θ Θ uudds

Ν SU(3) violation adjusted to fit N(1710) "Reasonable" QUARK SU(3) splittings SOLITON

R Jaﬀe JLab November, 2003 34 Summary: Decision Tree

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 35 + Θ (1540)

Ν(1440)?

+ Ξ − (1860)− Ξ (18−−) 36