Can one see effective chiral restoration in the high lying baryon spectrum

1
Can one see effective chiral restoration in the
high lying baryon spectrum?

• An intriguing but highly speculative idea

TDC, L. Ya. Glozman
2
Outline

• Introduction
• History of idea (a personal perspective)
• Chiral Symmetry and its representations
• Phenomenological Evidence
• Baryon spectra
• Mesons
• Theoretical Issues

3
Introduction

• Ill 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.

4

• 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.

5

• 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.

6

• 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 cant be seen directly in
  spectra.
• These were the ideas in the paper I rejected.

7

• 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.

8

• 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 Lenyas 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

9

• 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 Bobs 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.

10

• In January 2001 when asked to referee Lenya
  Glozmans 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.

11

• About 20 mins. after sending this I got an e-mail
  from Lenya Ive looked in the particle data
  book and the data looks just like the chiral
  multiplets. Lets write a paper.
• And thus are great collaborations born

12

• 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

13
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 mq0
• Hey Im a theorist
• Ultimately add quark mass in perturbatively

14

• 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

15

• 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)

16

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

Note that if we use operators with good parity
the representations are not always single irreps
of chiral group hence chiral/parity irreps.
17

• 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. (Glozmans initial motivation)
• Chiral symmetry is spontaneously broken(cSB )
  the ground state of the theory (vacuum) is not
  invariant under the symmetry.

18

• 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

19

• 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 r(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.

20

• 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)

21

• 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 Ds
• (3/2, 0) ? (0 , 3/2) parity doublet of Ds
• Conjecture of effective chiral restoration
  high in spectrum implies that baryons will fall
  approxiamtely into these multiplets.
• Do they?

22

• 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 cSB becomes progressively less
  important. The spectrum becomes progressively
  better described by chiral multiplets with
  increasing mass.

23
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 youve 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?

24

• 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?

25

• 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 doesnt exist or merely hasnt been
  seen?
• The absence of proof is not proof of absence
• ---Donald Rumsfeld on Iraqs WMD

26
From PDG High mass baryons , 1 and 2 star
resonances in PDG ? missing states
Consistent with (½, 1) ? (1 , ½) representation
27
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)
Consistent with (½, 0) ? (0 , ½) representation
28

• 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

29

• 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.

30

• 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.B58769-77,2004 )
• J1 States
• (1/2,1/2) Reps
• ?(0, 1--) b1(1, 1-) h1(0, 1-) ?(1, 1--)
• 1960 25 1960 35 1965 45 1970 30
• 2205 30 2240 35 2215 40 2150 ?
• (0,1)(1,0) Reps
• a1(1, 1) ?(1, 1--)
• 1930 70 1900 ?
• 2270 55 40 2265 40

31

• J2 States
• (0,0) Reps (0,1)(10) Reps
• ?2(0, 2--) f2(0, 2) a2(1, 2) ?2(1, 2--)
• 1975 20 1934 20 1950 70 1940 40
• 2195 30 2240 15 2175 40 2225 35
• (1/2,1/2) Reps
• p2(1,2-) f2(0, 2) a2(1,2) h2(0, 2-)
• 2005 15 2001 10 2030 20 2030 ?
• 2245 60 2293 13 2255 20 2267 14

Similar for J0,3
32

• How compelling is this data?
• It is certainly suggestive

33
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?

34
Symmetries can slowly turn off

• Consider explicit symmetry breaking (which seems
  even less likely)
• Consider the 2-d system H HHO VSB

35

• HHo is invariant under U(2)

with
36

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

Numerical solutions for R1, A4 in natural units
Effective U(2) Symmetry Restoration high in the
spectrum
37
Another Example
(Scale exaggerated)
SO(4) Symmetry
Effective SO(4) Symmetry Restoration high in the
spectrum
38
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.

39

• This correlator is basic object in lattice QCD
  QCD sum rules.
• Writable in a dispersion relation form

K is a kinematic factor which depends on spin of
current.
40

• Spectral density, r(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 r(s).
  

41

• r(s), is the basic QCD tool for exploring
  resonances.
• We know on very general grounds that r(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).

42

• Perturbative calculations respect chiral
  symmetry cSB 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

43
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?

44

• 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. (CohenGlozman 2001)
• Misha Shifman has recently analyzed the meson
  spectrum at large Nc and shown in detail how
  chiral restoration must be approached. (Shifman
  2005)

45

• 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 Nc3.
• 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 Nc3 can only be
  answered empirically

46
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.