Can one see effective chiral
restoration in the high lying
baryon spectrum?
An intriguing but highly
speculative idea
TDC, L. Ya. Glozman
Outline
• Introduction
– History of idea (a personal perspective)
– Chiral Symmetry and its representations
• Phenomenological Evidence
– Baryon spectra
– Mesons
• Theoretical Issues
2
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.
3
• 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.
4
• 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.
5
• 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.
6
• 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.
7
• 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”
8
• 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.
9
• 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.
10
• About 20 mins. after sending this I got an email 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
11
• 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… ”
12
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
13
• In this world, QCD is invariant under
q  q'  e
q  q'  e
 
i 
q (vector)
 
i 5 
q (axial)
• Or equivalently
q  q'  e
q  q'  e

i (1 5 )  

i (1 5 )  
q (right)
q (left)
• Hence “Chiral”
• Only term in QCD Lagrangian not invariant
under axial transformation is the (very
14
small) mass term
• 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)
15
• QCD operators transform into one another
under chiral transformation. Fall into
representations under the chiral group. Eg.
operators
q

iq γ 5 τ q , q q


q γ μ τ q , iq γ 5 γ μ τ q
qγμ q

iq γ 5 q , q τ q
quantum #s chiral/par ity repres entation
 12 ,0  0, 12 
quark

1 1

π,σ
2 ,2
 
1,0  0,1
ρ,A1

0,0
ω

 12 , 12 
η, a 0
Note that if we use operators with good parity
the representations are not always single irreps
of chiral group; hence chiral/parity irreps.
16
• 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(cSB ):
the ground state of the theory (vacuum) is not
invariant under the symmetry.
Eg. classical “Mexican hat” potential
17
• 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
18
• 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.
19
• 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)
20
• 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?
21
• 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.
22
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?
23
• 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?
24
• 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
25
From PDG
High mass baryons
*, ** = 1 and 2 star resonances in PDG
? =“missing states
Consistent with (½, 1)  (1 , ½) representation
26
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
27
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… ”
28
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.
29
– 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) Reps
ω(0, 1−−) b1(1, 1+−)
h1(0, 1+−)
ρ(1, 1−−)
1960 ± 25 1960 ± 35
2205 ± 30 2240 ± 35
1965 ± 45
2215 ± 40
1970 ± 30
2150 ± ?
(0,1)+(1,0) Reps
a1(1, 1++) ρ(1, 1−−)
1930 ± 70 1900 ± ?
2270 ± 55 40 2265 ± 40
30
J=2 States:
(0,0) Reps
(0,1)+(10) Reps
ω2(0, 2−−)
f2(0, 2++)
a2(1, 2++)
ρ2(1, 2−−)
1975 ± 20
2195 ± 30
1934 ± 20
2240 ± 15
1950 ± 70
2175 ± 40
1940 ± 40
2225 ± 35
(1/2,1/2) Reps
p2(1,2-+)
f2(0, 2++)
a2(1,2++)
h2(0, 2-+)
2005 ± 15
2245 ± 60
2001 ± 10
2293 ± 13
2030 ± 20
2255 ± 20
2030 ± ?
2267 ± 14
Similar for J=0,3
31
How compelling is this data?
It is certainly suggestive
32
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?
33
Symmetries can “slowly turn off”
• Consider explicit symmetry breaking
(which seems even less likely)
• Consider the 2-d system H
= HHO +VSB
34
HHo is invariant under U(2)
with
U  U (2)
Neglecting VSB the spectrum has significant
degeneracy due to the symmetry
35
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
36
Another Example
SO(4) Symmetry
(Scale exaggerated)
Effective SO(4) Symmetry
Restoration high in the spectrum
37
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.

J p (x) : iq γ5 τ q(x)
J  (x) : q q(x)
38
p (q)   d x e
4
iqx
T J (x ) J (0) 
• This correlator is basic object in lattice
QCD & QCD sum rules.
• Writable in a dispersion relation form:
p ( s)  K  ds
r ( s)
q  s  i
2
 subtractio ns
K is a kinematic factor which depends
on spin of current.
39
• 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).
40
• 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).
41
• 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
42
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?
43
• 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
44
restoration must be approached. (Shifman 2005)
• 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
45
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.46