Hadron Spectroscopy
from Strange to Charm/Bottom- Effective theories orandLattice
Lattice? Makoto Oka(Tokyo Institute of Technology)!

03/02/2015!

Hadrons and Hadron Interactions in QCD- Effective theories and Lattice Yukawa Institute Theoretical Physics
HHIQCD2015

Introduction!

HHIQCD2015!2

Nuclear Physics vs Hadron Physics
Nuclear Dynamics

Hadron Dynamics

single particle motions
shell structure

valence quark motions
quark model, symmetries

collective motions
rotations and vibrations

collective motions in field theory
NG bosons, Skyrmion

clusteralpha, di-neutron

di-quarkcolor-non-singlet clusters

exotic nuclei
neutron rich nuclei, halo

exotic hadrons
multi-quark, hybrid hadrons

large amplitude motions,deformation, fission

molecular bound states
resonance statessuperfluidity/dense matter

hot/dense hadronic matter

HHIQCD2015!3

From QCD to Hadron Spectrum
QCD = colored quarks + colored gluons with SU(3)c gauge
symmetry
Quarks have flavor quantum numbers: u, d, s, c, b, t.
QCD Lagrangian is flavor independent, but the coupling
Yruns.
Y
constant
R
P
Δ
Δ
Δ
Δ




The lowest-lying hadrons with u, d, s quarks form complete
Ḙ ḟ
ḟ
ḟ
ḟ
ḟ
ḟ
I
I
patterns of the SU(3)f representations.








3

3

ḛ
ḛ
SU(3)fḛ symmetry
isḛ the basisof the constituent quark model.








Y
-

ḬḬ

ḵ

ḥ
ḵᳩ

ḵ

Y

P

Ḙ

ḟ

Δ

R

ḟ

ḟ

ḟ 

I3
-

-

mesons with qqbar
HHIQCD2015

Δ

Y

Δ

ḟ 

Δ

ḟ

I3
ḛ

I3
ḛ 

ḛ

ḛ 

Y
-

-

ḥ

baryons ḵwith qqq

ḵ

ḬḬ

ḵ

ᳩ

I3

!4

From QCD to Hadron Spectrum
After 50 years since it was born, the quark model gives very
good guidelines to classify and interpret the hadron spectrum.
The charmonium spectrum is a textbook example.
“hydrogen atom” in QCD
The Hamiltonian with a
Linear + Coulomb potentiale+ r
V (r) =
r
E. Eichten, et al., PRL 34 (1975) 369

gives a good fit to the 1S, 1P, 2S, . .
charmonium (and bottomonium)
states.
HHIQCD2015

Lattice QCD
G.S. Bali, Phys. Rept. 343 (2001) 1!5

From QCD to Hadron Spectrum
The color is confined. Effective dynamical degrees of freedom
at low energy are color-singlet hadrons.
In the variety of excited hadrons, can we identify
constituent quark excitations?
hadron molecule states?
di-quark or other clusters of quarks and gluons?
QCD is the judge.
The lattice QCD will be able to help us to understand the(most) effective DOF in the hadron spectrum.
It is important to “derive” effective theories from QCD.
inter-quark potential from lattice QCD or PQCD
comparison of effective theories in a box with LQCD

HHIQCD2015!6

Lattice QCD calculations is reaching state-of-theart stage.
It is very successful for the ground-state hadrons.
For excited states, q-qbar or qqq operators may
not be good enough.

HHIQCD2015!7

Charmonium spectra on Lattice
Liuming Liu, et al. (Hadron Spectrum Collaboration)
JHEP 07, 126 (2012)
exotic states
2D?

1F

3S?
1D

2P

X(3872)2S
1P
1S
HHIQCD2015

LatticeEXP

mπ≃400 MeV!8

New Charmonium-like States
X(3872) found in 2003 by Belle (KEK)
Z(3900), Z(4430) etc. : charged hidden charm states
Zc+(3900)
X(3872)Zc+(4430)
M=4433 MeV
Γ =45 MeV

M=3899 MeV
Γ =46 MeVPRL 110 (2013) 252001
PRL 91 (2003) 262001

PRL 100 (2008) 142001

These states require at least 4 quarks,i.e., tetra-quarks or hadron molecules.
HHIQCD2015!9

Baryons in LQCD
Light baryon spectra by R.G. Edwards et al., PRD84 (2011)074508, are consistent with the SU(6)×O(3) quark model.

2nd 1/2+ ?

70 (1/2-,3/2-,5/2-)
Δ

N

HHIQCD2015

56 (1/2+,3/2+)mπ=396 MeV!10Lattice QCD has confirmed that the overall features ofthe low-lying hadron spectrum are given by theconstituent quark model.
Some (exotic) hadrons are not reproduced by thesimple qqbar or qqq operators. They may be given bymulti-quark or multi-hadron operators.
Which are exotic?
Recent development of analyses of Λ(1405)

HHIQCD2015!11

Λ(1405)
Recent analysis of the lattice QCD data by J.M.M. Hall et al.
ArXiv:1411.3402, claims KbarN dominance.

HHIQCD2015!12

Λ(1405)
Recent analysis of the lattice QCD data by J.M.M. Hall et al.
ArXiv:1411.3402, claims KbarN dominance.

HHIQCD2015!12

Λ(1405) as a hadron moleculeΛ(1405) as a Kbar N “bound” state.

Chiral unitary approaches predict two resonance poles forΛ(1405). (Jido et al., 2003)
They originate from a KbarN bound state and a πΣ resonance.
(Hyodo, Weise)
HHIQCD2015!13

Multi-quark states

Multi-quark exotic hadrons
f0(1710)M (MeV)a0(1450)a2(1320)

f0(1500)
f0(1370)

K0*(1430)

qq+glueballa1(1230)a0(980)f0(980)K0*(800)ρ(770)

scalar nonets

f0(600)

Exotic qqqq nonets
π(137)
HHIQCD2015!15

Multi-quark exotic hadrons
Why is Λ(1405) likely to be a 5-quark state (in the quark model)?
Λ(1405) Jπ= 1/2-, flavor singlet☆ uds L=1 orbital excited state with spin 1/2=> J=1/2- and 3/2- : spin-orbit partner Λ(1520) 3/2-

☆ udsuu, . . L= 0 state, i.e. NO orbital excitation required(ud)s=0 (su)s=0 u (= two di-quarks + an anti-quark)
The total quark spin is S=1/2 so that only a J=1/2- state
exists, i.e. no spin-orbit partner.#
The competition between the kinetic energy (L=1) and the extra
quark masses (qqbar) indicates possible mixing of the two Fockcomponents.
HHIQCD2015!16

QCD sum rule approach
How can we directly determine the Fock components ofhadrons from QCD?
In order to identify 5-quark components, one may use
overlaps of local operators to the hadron states.
Choose two local operators, 3-quark J3 and 5-quark J5
0|J3q (x)| = cos u(x)!
0|J5q (x)| = sin u(x)!
Then one can determine the "mixing angle” ?
J3q (x)J¯3q (0) = 2 cos2
J5q (x)J¯5q (0) = 2 sin2J3q (x)J¯5q (0) = 2 sin cos

HHIQCD2015!17

QCD sum rule approach
Choose some operators for Λ(1/2-)

However, it does not work, as these operators are notnormalized properly (ex. their dimensions are different).
We need to normalize the operators. Two methods were
proposed.
T. Nakamura, J. Sugiyama, T. Nishikawa, N. Ishii, MO, PRD78 (2008) 014010
HHIQCD2015!18

QCD sum rule approach
Choose a J5 and define a genuine 5-quark operator J5’ so that 3quark component of J5 is subtracted.

then one may determine the operator which couples moststrongly to the physical state,!

J (x) = cos J3 (x) + sin J5 (x)This method is "model independent", but it depends on the
choice of the operators.

HHIQCD2015!19

Λ(singlet, 1/2-)
Mass and mixing angle v.s. the Borel mass
mixing angle
mass

T. Nakamura, et al, PRD78 (2008) 014010
HHIQCD2015!20

Number of quarks in QCD"Counting" the number of quarks?
There is no conserved current corresponding to the # ofquarks: N(q)+N(q).
!

It may depend on choices of the quark operator.
Ex. Bogoliubov transformation may change the# of quarks in a hadron.
!

Any observables which can distinguish valence and sea quarks?
Parton distribution in the light-cone frame?
!
!

HHIQCD2015!21

Number of quarks in QCDIn DIS and other high energy processes, one may distinguish andcount "valence" quarks.

sea quarks
HHIQCD2015

valence quarks!22Number of quarks in QCD
Hadronization in heavy ion collisions:
Recombination and fragmentation of partons
R. J. Fries, S. A. Bass, B. Muller, C. Nonaka,
PRL 90 (2003) 202303
meson vs baryon
qq → 2 <pT>
qqq → 3 <pT>

proton anomaly

Then
how do 4 or 5 quark
states behave?

HHIQCD2015!23

Number of quarks in QCD
M.
! Hirai, S. Kumano, MO, K. Sudoh, PR D77 (2008) 017504

We proposed to apply to the fragmentation functions ofresonances.
determined by a global analysis ofe++e−→ h+X experimental data
Favored vs Disfavored FF
Favored F
Disfavored F
Favored FF → valence quarks
constituents of produced
hadrons
peaked at medium to large z
Disfavored FF → sea quarks
peaked at small z
Z=Eh/Eq

HHIQCD2015!24

Number of quarks in QCD
M.
! Hirai, S. Kumano, MO, K. Sudoh, PR D77 (2008) 017504

We proposed to apply to the fragmentation functions ofresonances.
determined by a global analysis ofe++e−→ h+X experimental data
Favored vs Disfavored FF
Favored F
Disfavored F
Favored FF → valence quarks
constituents of produced
hadrons
peaked at medium to large z+ fragmentations
K
Disfavored FF → sea quarks
peaked at small z
Z=Eh/Eq

HHIQCD2015!24

Number of quarks in QCD
Applied to f0(980) (0+, I=0)
- Tetra-quark configuration
favored FF: u and s quarks
Peak at large-z (z~0.85)
zumax ~ zsmax
OR!
- SS configuration
Mu < Ms(Mu/Ms=0.43 ± 6.73)!

Large uncertainty
Need further precise data
χ2/d.o.f. = 0.907
Total Number of data: 23
HHIQCD2015

2nd moments"

Mu=0.0012 ± 0.0107"
Ms=0.0027 ± 0.0183"
Mg=0.0090 ± 0.0046!25

Heavy Quark Hadrons!

Why Heavy Quarks are interesting ?
The c, b, (t) quarks have large masses.
m(ρ/ω): m(K*): m(D*): m(B*)= 1 : 1.15 : 2.59 : 6.87
ΛQCD(~ 300 MeV) ≪ mc(~ 1.3 GeV) ≪ mb(~ 4.2 GeV)
light quarks
1

10
u

d

100 MeV 1schiral symmetry
mq expansion

HHIQCD2015

heavy quarks

ΛQCD

10
c

b

mq

100 GeVtheavy quark symmetry(1/mQ) expansion!27

Why Heavy Quarks are interesting ?
Dynamics of Heavy Quarks
Asymptotic freesmall αs ~ v/c (~ 0.25 for charm)→ Heavy Quark Spin SymmetryNon-relativistic
QQbar mixing is suppressed.
Heavy quarks provide color sources for light quarks.
We can extract the dynamics of light quarks.
Are Strange quarks light or heavy? Or both?
SU(3)f symmetry vs HQ symmetry
HHIQCD2015!28

From Strangeness to Heavy Quarks
Σ* 1385Q-(qq)1

Σav 1321

Σ 1193q
Q-(qq)0*
Σbav 5826 Σ b 5833
Σb 5812 21MeV+

210 MeV

205 MeVΛ 1116

Λc 2286

Λb 5620

isoscalar baryon 1/2+

K* 892

Charm
vector mesons 1D* 2009

142MeV
397MeV

Bottom

310 MeV

323 MeVKav 793Q-qqΣcav 2496

65MeV isovector baryon 1/2

StrangeQΣ*c 2518
Σc 2453

194MeVq

Q

isovector baryon 3/2+

Dav 1974*
Bav 5313 B 5325
B 5279D 1867

46MeV

pseudoscalar mesons 0K 495

HHIQCD2015!29

From Strangeness to Heavy Quarks
φ 1680ss
2Sccψ 3086ηc   3637

f1 1420

1P

φ 1020η' 958HHIQCD2015

f2 1430
h1 1380
f0 1370ηb   9999
hb 9899χb1 9892

χb2 9912
χb0 9859

χc0 3415

J/ψ 3096

1S

Υ 10023
χc2 3556
hc 3525
χc1 3511

η 1475 ?

bbηc 2980

Υ 9460ηb 9398!30

From Strangeness to Heavy Quarks
φ 1680ss
2Sccψ 3086ηc   3637

f1 14201P

Υ 10023
χc2 3556
hc 3525
χc1 3511

η 1475 ?
f2 1430
h1 1380
f0 1370bbηb   9999
hb 9899χb1 9892

χb2 9912
χb0 9859

χc0 3415

The strange quark may be“light” as classified by SU(3),and also“heavy” to be isolated from the u, d quarks.
φ 1020η' 958HHIQCD2015

J/ψ 3096

1Sηc 2980

Υ 9460ηb 9398!30

From Strangeness to Heavy Quarks
e
l
u
c
bar
e
l
o
Λ(1405) as a (K N) molecule
m
n
o
r
d
a
H resonance- the lowest negative parity baryon- significantly lower than the other P-wave baryons
n
o
r
d
a
h
k
r
a
H dibaryon
u
q
i
t
l
u
M
- B=2, Str = -2, J=0+, I=0 resonancepredicted by Jaffe (1977)- Also predicted by the LQCD calculation (HALQCD, etc)
- (strongly) coupled to ΛΛ-NΞ-ΣΣ two-baryon channels

n
o
r
d
a
xotic hΘ+ pentaquark
E- Str = +1 baryon resonance, classified as SU(3) 10bar predictedin the chiral quark model by Diakonov. dron

a
h
r
o
v
ulti-fla

S= -2, -3 baryons M- The available data are very limited.

Are these “novel” features unique to the Strangeness?
Do they persist in the charm/bottom sectors?
HHIQCD2015!31

Heavy Quark Spin Symmetry
Magnetic gluon coupling is suppressed
µ

c

¯

µ⇥

a

2

Aaµ ⇤

†⇥

a

2

a

2

Aa0

†

⇥a
⇤
2

·

1
(⌅ ⇥ Aa )mQ(Color Electric coupling) ≫ (Color Magnetic coupling)
HQ spin-flip amplitudes are suppressed by (1/mQ).
➯ Heavy Quark Spin Symmetry
HHIQCD2015!32

Heavy Quark Spin Symmetry
HQ spin symmetry[SQ , H] = O

Q
q

1
mQ

} J = SQ + jL
J = jL ±jL = Sq + Lq

1states are degenerate in the HQ limit.
2
jL = 1

Σ* 1385
Σav 1321Σ*c 2518
Σc 2453Σ 1193

Σcav 2496

jL = 0Λ 1116

Λc 2286

1+ diquark*Σbav 5826 Σ b 5833
Σb 58120+ diquarkQqq

Λb 5620

Spectroscopy of Light Diquarks
HHIQCD2015

D*s 2112!33*

Charmed Baryons: Ground states
All the ground-state (S-wave) single charm baryons have been
observed, and are consistent with the quark model.
Lattice QCD reproduces the ground state baryon spectrum
fairly well.
Y. Namekawa, et al., (PACS-CS Collaboration)(2+1) flavor with physical quark mass, PRD 87, 094512 (2013)

single charm

HHIQCD2015

double charm!34

Qqq baryon
quark model

Q[qq] baryon
with diquark correlationsqq

P-wave excited statesl

λ modeqh
L=0 Qρ mode

l q
h
Q

L=1

chiralby
partners
A. Hosaka

L=0

L=1
Q

Q

ρ mode33l0,1,2, 61l1

33l0,1,2, 61l1
31h0, 63h0,1,2

33l0,1,2
61l1

P-waveL=01/2-, 1/2-, 3/2-, 3/2-, 5/2P----Q
L=0
1/2-, 3/2V----QΣl modesingle quarkmode

S-wave31S0, 63S1
mQ=mq
HHIQCD2015

λ mode31h1, 63h0,1,2

diquark
motionh mode63h0,1,2
31h1

spin-spin

ground31S0, 63S1 statesmQ ≠ mqΛρ modes

63S1
31S0

L=1

Σ

λ modesA----Q 1/2-, 1/2-, 3/2-, 3/2-, 5/2L=1
1/2-, 3/2S----Q

Λ

L=0
A----Q 1/2+, 3/2+

Σ

L=0
1/2+
S----QΛ

ground states!35P-wave excited states
The “diquark clusters” can be identified with the help of
the heavy quark in the HQ baryon spectroscopy.
The ρ mode excitations of the HQ baryons provide us witha diquark spectrum.
The λ mode excitations reveal the interaction of thediquarks.
The decays of the ρ and λ modes have different properties.
ρ-mode → Heavy baryon (Qqq) + light mesons (qqbar)
λ-mode → Heavy meson (Qqbar) + light baryon (qqq)

HHIQCD2015!36

P-wave excited states
The “diquark clusters” can be identified with the help of
the heavy quark in the
HQ baryon spectroscopy.
ρ modeλ modeThe ρ mode excitations of the HQ baryons provide us witha diquark spectrum.
The λ mode excitations reveal the interaction of thediquarks.
The decays of the ρ and λ modes have different properties.
ρ-mode → Heavy baryon (Qqq) + light mesons (qqbar)
λ-mode → Heavy meson (Qqbar) + light baryon (qqq)

HHIQCD2015!36

P-wave excited states: from s to c

probability

Probabilities of λ and ρ modes v.s. heavy quark massby a Hamiltonian quark model with spin-spin, spin-orbit andtensor forces
λ mode1ΛQ(1/2 )
L=0
λ - mode

0
300

L=1

Ms

Mb

Mc

ρ modeL=1

ρ - mode
600

1200

MQ
2400

L=0

(MeV)

Yoshida, Sadato, Hosaka, Hiyama, MO, in preparation.
HHIQCD2015!37

P-wave excited states: from s to c
sud
(I=0)

sqq
(I=1)

Λ (1830) 5/2(S=1/2)ρ

Λ (1800) 1/2

Σ (2000) 1/2(S=3/2)ρ

Λ (1690) 3/2
Λ (1670) 1/2(S=1/2)ρ

ssq(I=1/2)Σc (2800) ?

Σ (1940) 3/2(S=3/2)λΣ (1775) 5/2

Ξ (2030) ?

HHIQCD2015?

?

Λc (2625) 3/2

Ξc (2815) 3/2

Λc (2595) 1/2

Ξc (2790) 1/2

Ξ (1950) ?

Σ (1750) 1/2
Σ (1670) 3/2

Λ (1405) 1/2

csq (I=1/2)

Λc (2880) 5/2?

Λ (1520) 3/2(S=1/2)λcud (I=0, 1)

Ξ (1820) 3/2(S=1/2)λΞ (1690) ?

(S=1/2)λ!39

P-wave excited states: from s to c
sud
(I=0)

sqq
(I=1)

ssq
(I=1/2)

Λ (1830) 5/2
Λ (1800) 1/2

cud (I=0, 1)

csq (I=1/2)

Λc (2880) 5/2?
Σ (2000) 1/2

Σc (2800) ?

Σ (1940) 3/2
Ξ (2030) ?
Λ (1690) 3/2
Λ (1670) 1/2

Σ (1775) 5/2?

?

Λc (2625) 3/2

Ξc (2815) 3/2

Λc (2595) 1/2

Ξc (2790) 1/2

Ξ (1950) ?

Σ (1750) 1/2
Λ (1520) 3/2
Σ (1670) 3/2

Λ (1405) 1/2
HHIQCD2015

Ξ (1820) 3/2

Ξ (1690) ?
!40

P-wave excited states: from s to cTransition from the SU(3)f to HQ.
Lattice QCD for mQ = mS → mC with mπ2 = 410 MeV
singletoctet-

singlet/octet componentof ground state (1/2 )amplitudes
overlap

1
0.9

SU3 1

mS

0.8

mC

1
2

0.7
0.6

SU3 8

0.5
0.4
0.3
0.2
7.3

7.4

7.5

7.6

7.7

7.8
1/g

7.9

8

8.1

8.2

mQ

P. Gubler, T.T. Takahashi, M.O., preliminary
HHIQCD2015!41

Conclusion and Further possibilities
Going from strange to charm/bottom, we may isolate lightdegrees freedom by using the heavy quark spin symmetry.
This may help extracting inter-quark and di-quarkinteractions in hadrons.
Hadrons and Hadronic Interactions of charmed (heavy)
quarks may show more exotic features than strangeness.
A few interesting problems are:
Where are Ξcc ground and excited states?
Do exotic double charm mesons exist?
Are there any bound states of D mesons to nucleon/nuclei?
How strong are the interactions of charmed baryons with
nucleon? Are there charmed hyper-nuclei?
Many interesting physics subjects are waiting for the newheavy quark projects in J-PARC, GSI and others.
HHIQCD2015!42