Can one see effective chiral restoration in the high lying

baryon spectrum?

An intriguing but highly speculative idea

TDC, L. Ya. Glozman

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Outline

• Introduction– History of idea (a personal perspective)– Chiral Symmetry and its representations

• Phenomenological Evidence– Baryon spectra– Mesons

• Theoretical Issues

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Introduction

• I’ll introduce the subject in terms of my personal odyssey in the field

• My experience in this field borders on the surreal– My presence in the field began late in 2000

when serving as a referee and turning down a paper by soon-to-be collaborator Leonid (Lenya) Glozman.

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• I had met Lenya during the summer of 2000 at a workshop in Bled, Slovenia.

• My take on him at the time was that

– He is a very creative theorist with a real passion for doing physics.

– He is also a bit of a wild man intellectually. – He is apt to pull together ideas from many different

places and the different pieces do not always fit together very well.

– He is very sloppy in his use of scientific language---often describing things using word in nonstandard ways. This leads to making very misleading statements.

My present take is far more positive but not so dissimilar in nature.

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• In Bled, Glozman talked about the problem of “parity doublets” which are prominent high in the baryon spectrum

Eg. N*(1675) I(Jp)= ½(5/2+) , N*(1680) I(Jp)= ½(5/2-) N*(1700) I(Jp)= ½(3/2-) , N*(1720) I(Jp)=

½(3/2+)

N*(2220) I(Jp)= ½(9/2+) , N*(2250) I(Jp)= ½(9/2-)

– This phenomenon not easily understood in terms of conventional quark models

• He took this as an indication of chiral restoration.

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• I found the central idea intriguing, but…

• The idea was cast in terms of a quark model based on pion exchange which Lenya had developed with Dan Riska. In my view, the model was quite questionable and in case is totally irrelevant to the central issue.

• The idea was discussed in terms of a “chiral phase transition” which occurs in the baryon spectrum. It was even suggested that the baryon spectrum was a cheaper way to study the phase transition then RHIC. I felt that, this was a profound misunderstanding of the nature of a phase transition which after all is a thermodynamic idea and can’t be seen directly in spectra.

• These were the ideas in the paper I rejected.

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• My next exposure to some of these issues was at “Workshop on Key Issues in Hadron Physics”

Nov 5-10, 2000 Duck North Carolina

• This meeting took place at a truly surreal time: election day 2000.

Frank Wilczek and I watched the returns together and saw the great state of Florida turn blue then not blue.

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• In Duck, the problem of “parity doublets” was raised as an outstanding problem in the field. The comment was made “There are no ideas to explain this”

– In this context I raised Lenya’s idea while neither endorsing or criticizing it.

• Bob Jaffe then said: “Glozman must be wrong. If chiral symmetry were responsible one would have chiral multiplets not parity doublets”

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• He went on to say that it looks like the restoration of UA(1) i.e. the effect of the anomaly turning off and not chiral restoration.

• On reflection it is easy to see that Bob’s second point was wrong--- UA(1) restoration does not lead to parity doublets of the type seen in the baryon spectrum.

• The first point, however is on the mark. One would generally expect full chiral multiplets as opposed to doublets if chiral restoration occurs.

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• In January 2001 when asked to referee Lenya Glozman’s paper, I turned it down for the reasons mentioned above and noted that, “In a recent workshop in Duck, Bob Jaffe remarked….”

• About 2 weeks later I got an e-mail from Lenya. He wrote that the referee quoted Jaffe and knowing I was at the meeting wanted to know exactly what Jaffe had said.

• I repeated what Jaffe said; Lenya asked what the representations would look like. X. Ji and I had worked out some of these for looking at the chiral phase transition; I was immediately able to send him some multiplet structures.

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• About 20 mins. after sending this I got an e-mail from Lenya: “I’ve looked in the particle data book and the data looks just like the chiral multiplets. Let’s write a paper.”

• And thus are great collaborations born

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• The collaboration proceeded as might have been expected.

A (slight) caricature of the writing of the paper:– Glozman: “ … and thus we have a complete and

total, 100% ironclad proof that….”

– Cohen: “ … and thus we have a faint hint of a whisper of the suggestion of the possibility that perhaps… ”

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Chiral Symmetry

• The up and down quark masses in QCD (current quark masses) are very small mq ≈ 5 Mev which is much smaller than all other scales in hadronic physics

• Consider a world where mq=0

– Hey I’m a theorist– Ultimately add quark mass in perturbatively

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• In this world, QCD is invariant under

• Or equivalently

• Hence “Chiral” • Only term in QCD Lagrangian not invariant

under axial transformation is the (very small) mass term

(axial)'

(vector)'

5 qeqq

qeqqi

i

(left)'

(right)')1(

)1(

5

5

qeqq

qeqqi

i

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• Chiral transformations form a group

• Representations of the chiral group are given in terms of the left SU(2) and a right SU(2)

Eg. (½,0) means the lefthanded quarks transform as a doublet (spin ½) while the righthanded quarks transform as a singlet (spin 0)

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• QCD operators transform into one another under chiral transformation. Fall into representations under the chiral group. Eg.

2121

05

15

21

21

5

21

21

00

1001

00

,aη,qτq,qγqi

,ωqγq

,,A,ρqτγγqi,qτγq

,,σπqq,qτγqi

,,quarkq

entationity represchiral/parquantum #soperators

μ

μμ

Note that if we use operators with good parity the representations are not always single irreps of chiral group; hence chiral/parity irreps.

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• Note representations generally mix parity. All representations of QCD operators which are not entirely isosinglet mix parity. Connection of parity multiplets to chiral symmetry is essential. (Glozman’s initial motivation)

• Chiral symmetry is spontaneously broken(SB ): the ground state of the theory (vacuum) is not invariant under the symmetry.

Eg. classical “Mexican hat” potential

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• The evidence that chiral symmetry is spontaneously broken.– Pions are nearly massless

• Goldstones theorem: associated with each spontaneously broken generator is a massless particle.

• Pions have a non-vanishing mass because the quarks not massless but only very small

• Scattering length of pions off of hadrons is very small empirically. If exact, Goldstone boson have zero scattering length.

Strong evidence both for approximate chiral symmetry of QCD and for its spontaneous breaking

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• Further evidence that chiral symmetry is spontaneously broken.– Parity doubling is not seen in low spectrum

• Recall all chiral representations which contain non-isosinglets have both positive and negative parity members.

• Nucleon is not nearly degenerate with N(1535) the lightest negative parity nucleon resonance.

• Similarly in the meson sector the 770) is not nearly degenerate with A1(1535) .

Glozman conjecture (2000) : the observed parity doublets in the nucleon spectrum are a result of “chiral restoration” high in the spectrum.

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• One problem with this: one expects chiral multiplets not mere parity doubling (Jaffe).

• Obvious question: how would it look if the spectrum had chiral multiplets? (TDC, L Ya Glozman, PR D65 (2002) 016006; Int. J. Mod. Phys. A17 (2002) 1327. )

• Easy to classify for “nonexotic” states with quantum numbers made from three quarks:

(½, 0) (0 , ½)

(½, 1) (1 , ½)

(3/2, 0) (0 , 3/2)(Actually there is a small subtlety here in that usually

“nonexotic” means made from three constituent quarks while chirality is based on current quarks)

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• Representations found by trivial group theory: Combine 3 spin ½ objects which can be either L or R

• Physical content:

(½, 0) (0 , ½) parity doublet of nucleon

(½, 1) (1 , ½) parity doublet of nucleon +degenerate parity doublet of s

(3/2, 0) (0 , 3/2) parity doublet of s

Conjecture of “effective chiral restoration” high in spectrum implies that baryons will fall approxiamtely into these multiplets.

Do they?

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• Important point: the “effective restoration” is not a phase transiton. It is a gradual phenomena.

• Linguistic Question: what do you call this

Glozman: “Chiral restoration of the second kind”

Cohen: “Effective chiral restoration high in the spectrum”

• As one goes higher in the spectra the effect of spontaneous SB becomes progressively less important. The spectrum becomes progressively better described by chiral multiplets with increasing mass.

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Phenomenological evidence

• Very difficult to get unequivocal “smoking gun” type evidence by looking at resonances– The idea is qualitative: How close must the

resonances be to be “nearly degenerate”?

How many glasses of beer do you need to drink before convincing yourself that you’ve seen a multiplet?

– The ability to pick out resonances becomes increasingly difficult as one goes higher in the spectrum. Can we still find resonances when we are high enough for the effect to be unambigous?

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• The possibility of accidental matches:

The spectrum becomes increasingly dense as one increases the mass.

How do we know that near degeneracies are not just accidents given many states in the neighborhood?

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• The missing state problem: It is not easy to pick out high lying resonances. Resonances may exist but not yet seen.

How can we tell if a state needed to fill it out a multiplet doesn’t exist or merely hasn’t been seen?

“The absence of proof is not proof of absence”---Donald Rumsfeld on Iraq’s WMD

26Consistent with (½, 1) (1 , ½) representation

From PDG High mass baryons

*, ** = 1 and 2 star resonances in PDG? =“missing states

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Consistent with (½, 0) (0 , ½) representation

From PDG Lower mass baryons

N*(1675) I(Jp)= ½(5/2+) , N*(1680) I(Jp)= ½(5/2-) N*(1700) I(Jp)= ½(3/2-) , N*(1720) I(Jp)= ½(3/2+)

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Is this compelling empirical data?

– Glozman: “ … and thus we have a complete and total, 100% ironclad proof that….”

– Cohen: “ … and thus we have a faint hint of a whisper of the suggestion of the possibility that perhaps… ”

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If idea is correct should be seen in meson spectra as well.

– At the time of our initial work the meson spectroscopy at ~2 GeV was quite sketchy.

– The states included by the PDG were insufficient to see patterns of chiral restoration, so we did not comment.

– There has been extensive recent partial wave analysis of proton-antiproton data from LEAR ( A. V. Anisovich et al, Phys. Lett. B491 (2000) 47;.B517 (2001) 261;

B542 (2002) 8; B542 (2002) 19; B513 (2001) 281) which identified numerous mesons in this region.

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– These are generally still not in PDG listings.• How reliable are they?

– Using these new states Lenya Glozman repeated the same type of analysis that was done for the baryons (Phys.Lett.B587:69-77,2004 )

J=1 States:

(1/2,1/2) Repsω(0, 1−−) b1(1, 1+−) h1(0, 1+−) ρ(1, 1−−)

1960 ± 25 1960 ± 35 1965 ± 45 1970 ± 302205 ± 30 2240 ± 35 2215 ± 40 2150 ± ?

(0,1)+(1,0) Repsa1(1, 1++) ρ(1, 1−−)

1930 ± 70 1900 ± ?2270 ± 55 40 2265 ± 40

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J=2 States:

(0,0) Reps (0,1)+(10) Repsω2(0, 2−−) f2(0, 2++) a2(1, 2++) ρ2(1, 2−−)

1975 ± 20 1934 ± 20 1950 ± 70 1940 ± 40 2195 ± 30 2240 ± 15 2175 ± 40 2225 ± 35

(1/2,1/2) Reps2(1,2-+) f2(0, 2++) a2(1,2++) 2(0, 2-

+)

2005 ± 15 2001 ± 10 2030 ± 20 2030 ± ?2245 ± 60 2293 ± 13 2255 ± 20 2267 ± 14

Similar for J=0,3

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How compelling is this data?

It is certainly suggestive

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Theory Issues

• Short of fully solving QCD for its resonant states, one cannot demonstrate theoretically that the scenario occurs.– Focus here will be on whether it might occur;

i.e. is the idea totally nuts?

• Eg. Can spontaneously symmetry breaking slowly turn off as on goes to higher states in the spectrum?

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Symmetries can “slowly turn off”

• Consider explicit symmetry breaking (which seems even less likely)

• Consider the 2-d system H = HHO +VSB

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HHo is invariant under U(2)

)2(UU with

Neglecting VSB the spectrum has significant degeneracy due to the symmetry

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VSB is not invariant under U(2) but only under a U(1); this breaks degeneracy pattern into doublets of ±m.

Numerical solutions for R=1, A=4 in natural units

Low Lying States High Lying States

Effective U(2) Symmetry Restoration high in the spectrum

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SO(4) Symmetry (Scale exaggerated)

Effective SO(4) Symmetry Restoration high in the spectrum

Another Example

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Does one expect the spectrum to exhabit effective chiral restoration?

• On very general grounds the answer is “yes”.– There is an important caveat, however.

• A useful tool is the study of correlation functions of currents constructed from local gauge invariant operators with quantum numbers of interest. Eg.

)(:)()(:)( 5 xxxx qqJqτγqiJ

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• This correlator is basic object in lattice QCD & QCD sum rules.

• Writable in a dispersion relation form:

)()()( 4 0xq xq JJTexd i

nssubtractio)(

)(2

isq

sdsKs

K is a kinematic factor which depends on spin of current.

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• Spectral density, (s), is the square of the amplitude of making a physical state by acting with the current on the vacuum.– Both the continuum and resonances

appear in (s).

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• (s), is the basic QCD tool for exploring resonances.

• We know on very general grounds that (s), for corellators for operators in a chiral-parity multiplet become degenerate at large s.

• The reason is trivial: the correlators can be expressed in an operator product expansion (OPE) and this is dominated by the perturbative result at large Q2. (Consquence of Assymptotic freedom).

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• Perturbative calculations respect chiral symmetry: SB is intrinsically nonperturbative.

• At large space-like Q2 correlators of operators in a chiral/parity multiplet are identical.

• Given the dispersion relation, this is only possible if the spectral functions are identical at asymptotically large s.

• Ergo: at asymptotically large s chiral/parity multiplets become degenerate

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The key issue

• We know that the spectrum will be chirally symmetric at large masses.

• We also know at very high masses the spectrum looks like the QCD continuum; discrete hadrons states are not seen.

• Does effective chiral restoration set in a regime where we can still resolve hadrons?

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• We do not know a priori.

• One can take the phenomenological situation as evidence that it does but at present it is suggestive rather than compelling.

• Theoretically we do not have a good way to assess this except in one limit of QCD: mesons in the large Nc limit. – At large Nc the mesons remain discrete high in the

spectrum but the general perturbative argument goes thru. (Cohen&Glozman 2001)

– Misha Shifman has recently analyzed the meson spectrum at large Nc and shown in detail how chiral restoration must be approached. (Shifman 2005)

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• This large Nc argument showing that the meson spectrum has effective chiral restoration setting in while hadrons are still observable tell us nothing direct about baryons for Nc=3.

• It is, however, a proof of principle: hadrons can exist as discernable resonances high enough in the spectrum for effective chiral restoration to take place.

• Whether they do for baryons at Nc=3 can only be answered empirically

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Summary

• There is some evidence from the spectrum of excited baryons for effective chiral restoration. – Clearly, to make a more compelling case it

would be helpful to find “missing states” to fill out multiplets

• Theoretically, the spectral functions must exhibit effective chiral restoration, but the question of whether hadrons are still discernable in the region it occurs is open.