Exotic Diquark Spectroscopy

Transcription

1 Exotic Diquark Spectroscopy JLab November 2003 R.L. Jaffe F. Wilczek hep-ph/ 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,

2 Assumed Properties of the Θ + (1540) It exists Mass 1540 MeV Width 10 MeV How Narrow?? J = 1 2 Flat angular distribution???? Parity Unknown! Very Narrow? K + n quantum numbers: Y =2 Y Θ + I 3 =0 I =0 (no K + p partner) I 3 R Jaffe JLab November,

3 First Manifestly Exotic Hadron in 40 Years What dynamical principles are operating here? What are the further consequences? Strong correlation of color, flavor, and spin antisymmetric quark pairs into DIQUARKS. Two relatively light, narrow EXOTIC CASCADES await discovery. Possible stable? charm and bottom analogues. THIS TALK Y Θ + uudds I 3 Ξ -- ssddu Ξ + uussd R Jaffe JLab November,

4 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 Q 4 Q 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. Q 2 Q 2 mesons, color superconductivity... Jaffe & Wilczek [For a different correlated description, see the talk by M. Karliner.] R Jaffe JLab November,

5 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 + PARITY + CHIRAL SOLITON MODEL CORRELATED QUARKS UNCORRELATED QUARKS SPECTRUM CHIRAL SOLITON MODEL HEAVY EXOTIC CASCADES QUARKS LIGHT EXOTIC CASCADES R Jaffe JLab November,

6 The Θ + and K + n Scattering KN non-relativistic at M = 1540 MeV No other channels until K at 1725 MeV No quark annihilation barrier (O(Nc 0)) 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,

7 Range/width relation for square well in p-wave WIDTH OF RESONANCE (MEV) RANGE OF INTERACTION (FERMIS) Γ 10 MeV Range 0.05 fm! 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,

8 Assumptions going forward Parity of Θ + is positive Dynamics beyond KN-scattering. [QCD Quarks!] Uncorrelated quarks: Q 4 Q Negative Parity Some correlation must be resonsible for switching the parity of the Θ + R Jaffe JLab November,

9 Strong Correlations in QCD [Q Q] 1 c1 f 0 (Notation: Color Flavor Spin) Most attractive channel for gluon exchange Condenses in vacuum drives chiral symmetry breaking [QQ] 3 c 3 f 0 [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,

10 Correlated Quarks Diquarks 3 c 3 c = 3 c 6 c Selects COLOR 3 c Colorspin: (QQ) 3 FLAVOR 3 f SPIN 0 E 8 FLAVOR 6 f SPIN 1 E 8/3 λi σ i λ σ j j So QQ prefer: COLOR 3 c FLAVOR 3 f SPIN 0 Neither pointlike nor non-relativistic Energetically favored Non-perturbative? R Jaffe JLab November,

11 Diquarks Some Evidence Diquark correlations have played an important supporting role in QCD cf. Anselmino et al., RMP 65 (1993) Color superconductivity [QQ] 3 c 3 f 0 condenses at high energy: [QQ] α a = vδ α a Proven at high density, phenomenology in quark matter... Absence of exotic mesons: In principle Q 2 Q 2 could include 10, 10, 27 f But [QQ] 3 f [ Q Q] 3 f 8 f + 1 f Crypto exotic Prediction: Lightest and most prominent Q 2 Q 2 states should be nonet of scalar (0 ++ ) mesons R Jaffe JLab November,

12 Scalar Mesons COLOR FLAVOR SPIN Q 2 Q 2 Q 2 Q A nonet of 0 ++ mesons [ds] [su] Scalar Meson Nonet Hidden Strangeness [su] [ud] [ud] [ds] } [ds][ds] + [su] [su] [su][ud] [su][ds] [ud][ud] R Jaffe JLab November,

13 One Slide Summary of Scalar Mesons QQ -NONET ss MASS KNOWN SCALAR MESONS us ud 1500 MeV f (1500) 0 a (1450) 0 κ(1430) f 0 (1370) QQQQ -NONET [ud][ds] uu+dd [ud][ud] [su][ds] [su][su] [sd][sd] ( + ) 1000 MeV 500 MeV a (980) 0 f (980) 0 κ(800) f (600) Isospin R Jaffe JLab November,

14 Diquarks Exotics? Diquark correlations predict no exotics in the Q 2 Q 2 sector. What about Q 4 Q? Uniquely predicts 10 f [QQ] 3 f [QQ] 3 f Q 3 f [Q 4 Q] 10 f Not recognized before discovery of Θ + R Jaffe JLab November,

15 Diquarks and Q 4 Q Construct Θ + from diquarks Immediate consequences: Θ + must have positive parity Θ + must lie in a degenerate 8 f and 10 f Dramatically fewer associated states compared with uncorrelated quark models. R Jaffe JLab November,

16 ParityofΘ + [Q 1 Q 2 ] is a boson Diquark diquark antiquark wavefunction: [ [Q 1 Q 2 ] 3 c [Q 3 Q 4 ] 3 c] 3 c Q 3 c Diquarks must couple to 3 c to join antiquark in a color singlet hadron. Consider identical diquarks as in the Θ[ud] [ud] Antisymmetric in color. antisymmetric in space!! Q 4 has ODD PARITY Combine with Q Θ + has EVEN PARITY R Jaffe JLab November,

17 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 [ud] 2 [ud][ds] + [ds] 2 [ds][su] + [su] 2 [su][ud] + [qq][qq] Symmetric 6 Antiquark 3 [ud] 2 [ud][ds] + [su][ud] + s I 3 [ds] 2 [ds][su] + [su] 2 u d Gives 18 states in an SU(3) Octet plus Antidecuplet R Jaffe JLab November,

18 Overall SU(3) f structure: 6 f 3 f = 10 f 8 f This is a very general result: IN THE QUARK MODEL YOU CANNOT GET A 10 f WITHOUT A 8 f [ = (3 f 3 f ) 3 f (3 f 3 f ) 3 f ] 6 f 3 f 8 f 10 f And they are degenerate in the SU(3) f limit (Same color spin structure) R Jaffe JLab November,

19 [QQ] 2 Q Octet and Antidecuplet Distinction between (correlated) quark model and chiral soliton model Quark model: Degenerate 8 f and 10 f C. S. M. (see, eg., DPP) 10 f, although mixing with other multiplets at order Nc 0 is possible (see, eg., H. Weigel) + Θ + Θ N N 8 10 N 10 Λ Σ Σ 8 10 Λ Σ 10 Ξ 0 3/2 Ξ 3/2 Ξ3/2 0 Ξ Ξ 3/2 3/2 Octet and Antidecuplet + Ξ 3/2 + Ξ 0 Ξ 3/2 3/2 Ξ 3/2 3/2 Ξ Antidecuplet R Jaffe JLab November,

20 Comparative spectra: Antidecuplet Alone Degenerate in the SU(3) f limit. Lowest order in m s equal splitting rule (familiar from old Q 3 decuplet). Note quark content: Θ + = [ud][ud] s 1 strange quark N + 10 = 1 { 3 2 [ud][su]+ s + [ud] 2 d } 4/3 strange quark Σ + 10 = 1 3 { 2 [ud][su]+ d + [su] 2 s } 5/3 strange quark Ξ + = [us][us] d 2 strange quarks Ξ 3/2 Σ Ν uussd Total Splitting of ~ m s? Increasing strange quark mass Θ uudds R Jaffe JLab November,

21 Comparative spectra: Octet Plus Antidecuplet 10 f and 8 f mix strongly via degenerate perturbation theory at O(m s ) Schematic model: Ideal mixing, a la ω/φ to diagonalize strange quark content. More sophisticated treatment allows for 10 f /8 f mixing angle Diakonov & Petrov hep-ph/ Without 8 f 10 f a-priori degeneracy, mixing is O(m 2 s ) Crucial differences in spectrum: states with same Y and I in 8 f and 10 f mix and split. For example: N s uudss Θ N uuddd uudds R Jaffe JLab November,

22 Schematic Model Rough estimates: Assume ideal mixing SU(3) f violation diagonalizes strange quark content. Ξ + Θ Λ 3/2 Ξ N Ns Σ Σ s + Ξ 3/2 Θ + N Ns Λ Σ Σ Ξ Ξ Ξ + 2 [ud] s 2 [ud] d [ud][su] s [ud][su] d,... 2 [us] s [su][ds] d,... [su] 2 d [ds] 2 u Corresponds to one choice of 8 f 10 f mixing angle. [See Diakonov & Petrov hep-ph/ for a more systematic analysis of mixing and masses in light of later discoveries.] R Jaffe JLab November,

23 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(n s,n s )=M 0 + αn s +(n s + n s ) s Estimate: α 60 MeV from nucleon octet (Λ, Σ,N). Estimate: 100 MeV by identifying N with Roper, P 11 (1440). R Jaffe JLab November,

24 Identifications and Predictions Rough Mass Estimates MASS MeV M + M + M + M + M α 2 + 2α 2 + α + α Σ s Ξ Ξ Ν s Λ Σ Θ 3/ M Ν 1440 R Jaffe JLab November,

25 Identifications, Postdictions and Predictions Θ + of course Roper postdicted N s 1700 MeV [ud][ds] s should couple to Nη, KN,... Ξ +, Ξ 1750 MeV!! Σ s Ξ Ξ 3/2 Ν s Rough Mass Estimates Λ, Σ 1600 MeV candidates. Σ s [us] 2 s heavy and coupled to ησ etc. Λ Σ Θ Ν R Jaffe JLab November,

26 Widths Mechanism for reduction of widths below KN potential theory estimates: Resonance configuration may have small overlap with KN: [ [ud]2 s ] Θ? [udd] n [u s] K Relating Γ(Ξ ) to Γ(Θ + ) Θ K + n/k 0 p Ξ Ξ π /Σ K Y Θ + I 3 SU(3) f for matrix elements combined with p-wave phase space. Predict Γ(Ξ (1750)) 1.4Γ(Θ) [Γ(Ξ (1860)) 3.5Γ(Θ)] Ξ -- SMALL!. Ξ + R Jaffe JLab November,

27 Widths II The widths of the non-exotic [QQ] 2 Q are complicated by mixing [QQ] 2 Q Q 3 + Θ Λ N Ns Σ Σ s Ξ 3/2 Ξ + Ξ 3/2 Width of Roper MeV is still a problem. R Jaffe JLab November,

28 Exotic Cascades! Ξ (1860)! NA49 in hep-ex/ a) Ξ - π Entries / 7.5 MeV/c b) Ξ - π + 15 c) Ξ ± + π - Entries / 7.5 MeV/c a) b) d) Ξ ± + π M(Ξπ) [GeV/c 2 ] M(Ξπ) [GeV/c 2 ] R Jaffe JLab November,

29 Charm and Bottom Analogues of the Θ + Θ 0 c uudd c Θ + b uudd b QCD environment of antiquark is familiar: {[[ud][ud]] 3 c q} {[ud] 3 c q} Θ q Λ q Except [ud] in Λ q has S = J = 0, whereas [ud][ud] in Θ q has S =0,J =1. Θ c Θ s = Λ c Λ s M(Θ c ) = 2710 MeV Θ b Θ s = Λ b Λ s M(Θ b ) = 6050 ± 10 MeV See Karliner & Lipkin and Fl. Stancu PRD58 (1998) R Jaffe JLab November,

30 Everything scales linearly except pseudoscalar meson masses, which reflect non-linearity due to chiral symmetry. So heavier Θ s are progressively more stable: Θ u,d Nπ Q = 350MeV Θ s NK Q = 100MeV Θ c ND Q = 100MeV Θ b NB Q = 150MeV Searches are possible in hadron and e + e facilities. R Jaffe JLab November,

31 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 analogs, Θ 0 c and Θ+ b. R Jaffe JLab November,

32 Diquarks Questions and Problems Light negative parity Q 4 Q cryptoexotic baryons. Flavor antisymmetric diquarkdiquark s-wave, negative parity baryons However these effective bosons contain identical fermions. Pauli blocking should result in repulsion. Push to higher mass. Hidden or explicit strangeness throughout Couple to meson nucleon s-wave broad. Unless bound... Λ(1405)? Further study. [ud][ds] [qq][qq] Antisymmetric 3 [ds][su] [su][ud] R Jaffe JLab November,

33 [ud][ds] [ds][su] u [su][ud] } s d Negative Parity Nonet Hidden Strangeness [ud][us]s [su][ud]d [ds][su]d J π = 3 2+ partners of the 10 f and 8 f. If spatially antisymmetric diquark-diquark wavefunction has l = 1 then 3 2+ partners of the Θ + etc. nearby. R Jaffe JLab November,

34 Mass Spectrum: Diquark versus Soliton CSM: ONLY 10 f Diquarks: 8 f 10 f 10 f alone seems disfavored now compared with 8 f + 10 f, which is natural in quark models. Ξ 3/2 uussd Σ s Ξ Ξ 3/2 Ν s Λ Σ Θ Σ Ν Θ uudds QUARK Ν "Reasonable" SU(3) splittings SU(3) violation adjusted to fit N(1710) SOLITON R Jaffe JLab November,

35 Summary: Decision Tree PARITY + CHIRAL SOLITON MODEL CORRELATED QUARKS UNCORRELATED QUARKS SPECTRUM CHIRAL SOLITON MODEL HEAVY EXOTIC CASCADES QUARKS LIGHT EXOTIC CASCADES?! R Jaffe JLab November,

36 + Θ (1540) Ν(1440)? Ξ (1860) + Ξ (18 ) 36