Transcript Document

Hadron structure:
quark-model analysis
A. Valcarce
Univ. Salamanca (Spain)
Torino, April 2nd, 2008
Hadron structure: quark model
analysis
1
Outline
• QCD: Hadron physics & constituent quark model
• Multiquarks
• Exotic states.
• Light hadrons
• Light mesons: Scalar mesons.
• Light baryons: Improving its description.
Non-exotic multiquark states
• Heavy hadrons
• Heavy baryons: New bottom states, doubly heavy states.
• Heavy mesons: New open-charm and hidden charm states.
Advances (Exp.)  Challenges (Theor.)
• Summary
Torino, April 2nd, 2008
Hadron structure: quark model
analysis
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QCD. Hadron physics & quark model
QCD is the correct theory of the strong interaction. It has been tested to very high accuracy in the
perturbative regime. The low energy sector (“strong QCD”), i.e. hadron physics, remains challenging
N. Isgur, Overview talk at N*2000, nucl-th/0007008
All roads lead to valence “constituent quarks” and effective forces inspired in the properties of QCD:
asymptotic freedom, confinement and chiral symmetry

Constituent quark models
Constituent quarks (appropriate degrees of freedom) behave in a remarkably simple fashion (CDF)
Effective forces: confining mechanism, a spin-spin force (-, -) and a long-range force
The limitations of the quark model are as obvious as its successes. Nevertheless almost all hadrons can be
classified as relatively simple configurations of a few confined quarks.
Although quark models differ in their details, the qualitative aspects of their spectra are determined by
features that they share in common, these ingredients can be used to project expectations for new sectors.
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Hadron structure: quark model
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Almost all known hadrons can be described as bound states of qqq or qq:
• QCD conserves the number of quarks of each flavor, hadrons can be labeled by their minimun, or
VALENCE, quark content: BARYONS and MESONS. QCD can augment this with flavor neutral pairs
  uds (+ uu + ss + ....)
• NON-EXOTIC MULTIQUARK states do not in general correspond to stable hadrons or even
resonances. Most, perharps even all fall apart into valence mesons and baryons without leaving more than
a ripple on the meson-meson or meson-baryon scattering amplitude. If the multiquark state is unsually
light or sequestered from the scattering channel, it may be prominent. If not, it is just a silly way of
enumerating the states of the continuum.
• Hadrons whose quantum numbers require a valence quark content beyond qqq or qq are termed
EXOTICS (hybrids, qqg)
+  uudds
Exotics are very rare in QCD, perhaps entirely absent. The existence of a handful of exotics has to be
understood in a framework that also explains their overall rarity
We have the tools to deepen our understanding of “strong QCD”
Powerful numerical techniques imported from few-body physics
Faddeev calculations in momentum space [Rept. Prog. Phys. 68, 965(2005)]
Hyperspherical harmonic expansions
Stochastic variational methods
[Phys. Rev. D 73 054004 (2006)]
[Lect. Not. Phys. M 54, 1 (1998)]
Increasing number of experimental data
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Hadron structure: quark model
analysis
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Heavy
baryons
Heavy
baryons
1985 Bjorken: “ We should strive to study triply charmed baryons because their excitation spectrum
should be close to the perturbative QCD regime. For their size scales the quark-gluon coupling
constant is small and therefore the leading term in the perturbative expansion may be enough”
nnQ
nQQ
QQQ
• The larger the number of heavy quarks the simpler the system
• nQQ and QQQ  one-gluon exchange and confinement
• nnQ  there is still residual interaction between light quarks
• nnQ and nQQ  the presence of light and heavy quarks may allow to learn
about the dynamics of the light diquark subsystem
• Ideal systems to check the assumed flavor independence of confinement
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Hadron structure: quark model
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5
State
 (udQ)
S (uuQ)
 (usQ)
JP
Q=Strange
Q=Charm
Q=Bottom
1/2+
1116, 1600
2286, 27651
5625
3/2+
1890
29403
1/2–
1405, 1670
2595
3/2–
1520, 1690
2628, 28801
5/2+
1820
28801
1/2+
1193,1660
2454
58115
3/2+
1385, 1840
2518, 29403
58335
1/2–
1480, 1620
27651
3/2–
1560, 1670
28002
1/2+
1318
2471, 2578
3/2+
1530
2646, 30762
1/2–
3/2–
2792,
1820
CDF, Phys.Rev.Lett.99, 202001 (2007)
29802
2815
5/2+
30553, 31233
 (ssQ)
1/2+
2698
3/2+
1672
27683
 (uQQ)
3/2–
--
35194
Torino, April 2nd, 2008
57925
Hadron structure: quark model
analysis
1
2
3
4
5





CLEO
Belle
BaBar
SELEX
CDF
Regularities  L=1 300 MeV
n=1 500 MeV
6
Heavy baryons: I.a. Spin splitting
Roberts et al., arXiV:0711.2492 Valcarce et al., submitted to PRD
300
M (MeV)
Exp.
c
Sc(3/2+) – c(1/2+)
b
232
200+) – Sc(1/2+)
Sc(3/2
64S
64
Sb(3/2+) – b(1/2+)
209
246
205
Sb(3/2+) – Sb(1/2+)
22
25
22
M (MeV)
S
Full
OPE=0
E
5807
cb
0
Sb(3/2+)
5829
5822
– 15
5844
– 15
b(1/2+)
5819
– 195
M (MeV)
s
100
OGE() s OGE +OPE

S
c
251
217 S
c
b

67 S b
b
Sc
Sb(1/2+)
5624
b(3/2+) 3F (s=0)
6388
6F (s=1)
6387
<1
-100S(1/2+)
1408
1417
–9
S(3/2+)
1/2+ 1454
+
1/2
1462
3/2–+8
(1/2+)
1225
P
J1405
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– 180
Double charm baryons no OPE
M (MeV)
ccLatt.
cc(3/2+) – cc(1/2+)  75
OGE +OPE
3579
 cc(3/2+) – cc(1/2+)  60
3676
OGE()
Latt.
Hadron structure: quark model
analysis
3588
OGE (+ OPE)
cc
77 (77)
3697 (118)
72 (61)
3815 (139)
3698 (110)
7
Heavy baryons: II. Confinement strength
3400
c
(a)
3200
3/2+
Sc
(b)
Mass (MeV)
3/2
3000
1/2-,3/2-
3/2+
2800
1/2+
1/2-,3/21/2+
2600
1/2-,3/2-
1/2-,3/2-
2400
3000
Mass (MeV)
3/2+
+
Valcarce et al., submitted to PRD
3200
2800
3/2+
1/2+
1/2-,3/23/2+
1/2-,3/2-
1/2-,3/2-
1/2+
1/2-,3/2-
2600
3/2+
3/2+
1/2+
1/2+
1/2+
1/2+
2400
2200
[A]
Exp.
[A] Fits the Roper in the light sector
[B] Fits the 1/2– in the light sector
Torino, April 2nd, 2008
[A]
[B]
Exp.
[B]
Flavor independence of confinement
Hadron structure: quark model
analysis
8
CQC Valcarce et al., submitted to PRD
[18] Roberts et al. arXiV:0711.2492
[19] Ebert et al., Phys. Lett. B659, 618 (2008)
Q(3/2+)
S(3/2+) – S(1/2+)  6F – 6F  qQ
S(1/2+) – (1/2+)  6F – 3F  qq
Torino, April 2nd, 2008
CQC
[18]
[19]
c(3/2+)
3061
2887
2874
c(3/2+)*
3308
3073
3262
b(3/2+)
6388
6181
6189
b(3/2+)*
6637
6401
6540
Hadron structure: quark model
analysis
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Heavy mesons
More than 30 years after the so-called November revolution, heavy meson spectrocospy is being again a challenge. The
formerly comfortable world of heavy meson spectroscopy is being severely tested by new experiments
Heavy-light mesons (QCD hydrogren)
DsJ*(2317)
DsJ(2460)
-
JP=1+
-
- P cs ~ 2.48 GeV
- P cs ~ 2.55 GeV
-  < 4.6 MeV
-  < 5.5 MeV
D0*(2308)
-
JP=0+
- P cn ~ 2.46 GeV
-  ~ 276 MeV
X (3872)
DsJ(2632) (Selex)
DsJ
*(2715)
(Belle)
DsJ(2860) (Babar)
.......
JPC=1++ (2–+)
- P cc ~ 3.9-4.0 GeV
Charmonium
Open charm
-
JP=0+
Heavy-heavy mesons
-  < 2.3 MeV
X (3940)
Y (3940):23PJ=1,2,3
Y(4260) : ??
Y(4385) : 43S1,33D1
Z(4433)
X(3876)
....
Z (3940)
• The area that is phenomenologically understood extends to: Heavy-light mesons, states where the quark-antiquark pair
–
–
is in relative S wave; Heavy-heavy mesons: states below the DD (BB) threshold
• In the positive parity sector (P wave, L=1) a number of states have been discovered with masses and widths much
different than expected from quark potential models.
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Hadron structure: quark model
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2007 Close: “I have always felt that this is an example of where naive quarks models are too naive”
When a qq state occurs in L=1 but can couple to hadron pairs in S waves,
the latter will distort the qq picture. The cs states 0+ and 1+ predicted
above the DK (D*K) thresholds couple to the continuum what mixes DK
(D*K) components in the wave function
UNQUENCHING THE NAIVE QUARK MODEL
q
q
q
q
q
q
| B  0  1 | qq   2 | qqqq   ...
qq  J PC  0   S = 1 = L
• S=0
• S=1
h1 (1170)   (550) 


E  L  1  E  L  0   h1 (1595)   '(958)   0.5  0.6 GeV
h (3526)   (2980) 
c

 c
 L  0
  (770)
  L  1 X( J  )  1.3  1.4 GeV

 (782)
qq (~ 2mq)
qqqq (~ 4mq)
Negative parity
0–,1– (L=0)
0–,1– (ℓi0)
Positive parity
0+,1+,2+ (L=1)
0+,1+,2+ (ℓi=0)
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Hadron structure: quark model
analysis
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DsJ mesons: quark-antiquark pairs ?
2800
DsJ*
(2317)
2600
Ds1
(2458)
Ds1
(2460)
DsJ*
(2317)
E (MeV)
D*K
D0K
2400
Chiral gap
2200
2000
1800
Ok!
jq=3/2
{
{
jq=1/2
0–
1–
0+
1+
2+
0–
Bardeen et al.,Phys. Rev. D68, 054024 (2003)
Torino, April 2nd, 2008
Hadron structure: quark model
analysis
1–
0+
1+
2+
Phys. Rev. D73, 034002 (2006)
12
Which is the nature of scalar mesons?
Phys. Lett. B, in press
Torino, April 2nd, 2008
Hadron structure: quark model
analysis
13
Charmonium: playground of new models
Spin-spin interaction:
Spin-orbit interaction:
Torino, April 2nd, 2008
Barnes et al., Phys. Rev. D72, 054026 (2005)
Central potential:
Hadron structure: quark model
analysis
14
Belle, Phys. Rev. Lett. 91, 262001 (2003)
B+ K+ X(3872)  K++-J/
CDF, D0, .. pp
PDG, M = 3871.2 ± 0.5 MeV;  < 2.3 MeV
mD + mD* = (3870.3 ± 2.0)MeV M = (+0.93872
± 2.0)MeV
Production properties very similar to ’(23S1)
Seen in   J/  C = +
Belle rules out 0++ and 0–+, favors 1++
DD
++
–+
CDF only allows for 1 or 2
cc mass spectrum
cc state ?
2–+: is a spin-singlet D wave while J/ is a spin-triplet S wave, so in the NR limit the E1 transition
2–+  J/ is forbidden. D and S radial wave functions are orthogonal what prohibits also M1
1++: Expected larger mass and width ( J/ violates isospin).
Torino, April 2nd, 2008
Hadron structure: quark model
analysis
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Tetraquark ?
Wave function:
• Compact four-quark structure (diquark – antidiquark)
[qq] : color = –
3, flavor= –3, spin = 0
Maiani et al., Phys. Rev. D71, 014028 (2005)
2 neutral states: Xu=[cu][cu] Xd=[cd][cd] M= (72) MeV
2 charged states: X+=[cu][cd] X–=[cd][cu]
No evidence for charged states
Interaction:
• S wave D0 D*0 molecule
Tornqvist, Phys. Lett. B590, 209 (2004)
Long range one-pion exchange B=0.5 MeVM 3870 MeV
Favors JPC = 1++
(X Model
J/) < predictions:
(X  ππJ/)
Binding increases with the mass, 50 MeV for B mesons
• 1++ charmonium mixed with (D D* + D*D)
Suzuki, Phys. Rev.. D72, 114013 (2005)
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Hadron structure: quark model
analysis
16
Solving the Schrödinger equation for cncn : HH
  Color Isospin  Spin  R 
Color   112134 , 812834

JM
3
1
3
1
!
2
2
1,2  c
4
3,4  n
C-parity is a good symmetry of the system
C12 12  1
2
C
12
 12 C21
C1212  C34 I34 

C12  112 ,812  and 12 =+/- S/A
 C34 I34 
 34
1
2
 C  uu
34
 dd

34
C43
 uu
 dd

C34  134 ,834  , 34 =+/- S/A , I34  1/ 0, I34 z  0
Torino, April 2nd, 2008
Hadron structure: quark model
analysis
34
Good symmetry states
C-parity=1234
 12 (1)S12  1  1

S34  3
 1
34 (1)
17
Compact four-quark structure cncn (I=0)
Phys. Rev. D76, 094022 (2007)
CQC
BCN
JPC (Kmax)
E4q (MeV)
EThe
EExp
E4q (MeV)
EThe
EExp
0++ (24)
3779
+ 34
+ 251
3249
+ 75
– 279
0+– (22)
4224
+ 64
+ 438
3778
+ 140
+ 81
1++ (20)
3786
+ 41
+ 206
3808
+ 153
+ 228
1+– (22)
3728
+ 45
+ 84
3319
+ 86
– 325
2++ (26)
3774
+ 29
– 106
3897
+ 23
+ 17
2+– (28)
4214
+ 54
+ 517
4328
+ 32
+ 631
1–+ (19)
3829
+ 84
+ 301
3331
+ 157
– 197
1– – (19)
3969
+ 97
+ 272
3732
+ 94
+ 35
0–+ (17)
3839
+ 94
– 32
3760
+ 105
– 111
0– – (17)
3791
+ 108
+147
3405
+ 172
– 239
2–+ (21)
3820
+ 75
– 60
3929
+ 55
+ 49
2– – (21)
4054
+ 52
+ 357
4092
+ 52
+ 395
0
3!
0
5!
Total
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Hadron structure: quark model
analysis
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Many body forces do not give binding in this case
Torino, April 2nd, 2008
Hadron structure: quark model
analysis
Phys. Rev. D76, 114013 (2007)
19
Exotics
Solving the Schrödinger equation for ccnn : HH
  Color Isospin  Spin  R 

Color  312 334 , 612 634
Spin 
  s ,s  S ,  s ,s  S  S
1
2
12
3
4
34
JM

3
1
  S12 ,S34  S
2
2
1,2  c
Isospin   i3 ,i 4  I34
 R  U n (  ) Y[ K ] ()
    LM L L12
U n (  )  Laguerre functions
Hadron structure: quark model
analysis
4
3,4  n
312 334
 (1)S12  1  1

S34  I  3
(

1)
 1

612 634
 (1)S12  1  1

S34  I  3
(

1)
 1

1 2 3
Y[K]  HH functions
Torino, April 2nd, 2008
3
1
20
––
ccnn
CQC (BCN)
I=0
I=1
JP (Kmax)
E4q (MeV)
EThe
R4q
R4q/(r12q+r22q)
0+ (28)
4441
+ 15
0.624
>1
1+ (24)
3861
– 76
0.367
0.808
2+ (30)
4526
+ 27
0.987
>1
0– (21)
3996
+ 59
0.739
>1
1– (21)
3938
+ 66
0.726
>1
2– (21)
4052
+ 50
0.817
>1
0+ (28)
3905
+ 33
0.752
>1
1+ (24)
3972
+ 35
0.779
>1
2+ (30)
4025
+ 22
0.879
>1
0– (21)
4004
+ 67
0.814
>1
1– (21)
4427
+1
0.516
0.876
2– (21)
4461
– 38
0.465
0.766
Vijande et al., in progress
Torino, April 2nd, 2008
Janc et al., Few Body Syst. 35, 175 (2004)
Hadron structure: quark model
analysis
21
Difference between the two physical systems
c
c
–c
n
n
–c
–n
–
n
J/

c
–c
n
––
cncn
–n
—
D
D
c
–
n
c
–n
–
n
c
––
ccnn
Torino, April 2nd, 2008
D
Hadron structure: quark model
analysis
c
–n
D
22
Behavior of the radius (CQC)
– – PC ++
cncn
J =1
––
ccnn JP=1+
Torino, April 2nd, 2008
Hadron structure: quark model
analysis
23
Light baryons
The effect of the admixture of hidden flavor components in the baryon sector has also been studied. With a 30% of 5q
components a larger decay width of the Roper resonance has been obtained. 10% of 5q components improves the
agreement of the quark model predictions for the octet and decuplet baryon magnetic moments. The admixture is for
positive parity states and it is postulated.
Riska et al. Nucl. Phys. A791, 406-421 (2007)
From the spectroscopic point of view one would expect the effect of 5q components being much more important for low
energy negative parity states (5q S wave)
Takeuchi et al., Phys. Rev. C76, 035204 (2007)
(1405) [1/2–], QM 1500 MeV ((1520) [3/2–])
  |3q [(0s)20p]> +  |5q[(0s)5]>
OGE
=0; QCM S–NK–ud  No resonance found
,   0  A resonance is found
Dynamically generated resonances UPT
Oset et al., Phys. Rev. Lett. 95, 052301(2005)
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Hadron structure: quark model
analysis
24
Torino, April 2nd, 2008
****
Hadron structure: quark model
analysis
1/2(1405)
*
1/2(1900)
3/2(1940)
1400
F35(2000)
1720  60
2200  125
5/2(1930)
1700
N.C.
1/2+(1750)
1900
3/2+(1600)
2000
5/2+(1720)
N 1/2+(1440)
E (MeV)
P. González et al., IFIC-USAL submitted to PRC
2100
***
**
1800
*
***
1600
1500
****
Mixing of 3q plus M-B (5q) a=85 MeV
Meson-baryon S-wave thresholds
Capstick and Isgur, Phys. Rev. D34, 2809 (1986)
Meson-baryon threshold effects in the light-quark baryon spectrum
2200
25
Summary
• There is an increasing interest in hadron spectroscopy due to the advent of a
large number of experimental data in several cases of difficult explanation.
• These data provide with the best laboratory for studying the predictions of
QCD in what has been called the strong limit. We have the methods, so we can
learn about the dynamics. There are enough data to learn about the glue holding
quarks together inside hadrons.
• Simultaneous study of nnQ and nQQ baryons is a priority to understand lowenergy QCD. The discovery Q(3/2+) is a challenge.
• Hidden flavor components, unquenching the quark model, seem to be
neccessary to tame the bewildering landscape of hadrons, but an amazing
folklore is borning around.
• Compact four-quark bound states with non-exotic quantum numbers are hard
to justify while “many-body (medium)” effects do not enter the game.
• Exotic many-quark systems should exist if our understanding of the dynamics
does not hide some information. I hope experimentalists can answer this
question to help in the advance of hadron spectroscopy.
Torino, April 2nd, 2008
Hadron structure: quark model
analysis
26
Acknowledgements
Let me thank the people I collaborated with in the different subjects I covered in
this talk
N. Barnea (Hebrew Univ. Jerusalem, Israel)
J.M. Richard (Grenoble, France)
F. Fernández (Univ. Salamanca, Spain)
B. Silvestre-Brac (Grenoble, France)
H. Garcilazo (IPN, Méjico)
J. Vijande (Univ. Valencia, Spain)
P. González (Univ. Valencia, Spain)
E. Weissman (Hebrew Univ. Jerusalem, Israel)
Thanks!
I tried to cover a wide and very active field, what implies a biased point of view.
So let me apologize with those who have contributed but were not quoted in this
talk. (In the section of relativity time would have been enlarged and the problem, if
any, may have been partially solved)
Torino, April 2nd, 2008
Hadron structure: quark model
analysis
27