nov. 12, haphy. a qcd sum rule analysis of the plb 594 (2004) 87, plb 610 (2005) 50, and...
TRANSCRIPT
Nov. 12, HAPHY.
A QCD sum rule analysis of the
PLB 594 (2004) 87, PLB 610 (2005) 50, and hep-ph/0506250
Hee-Jung LeeVicente Vento
(APCTP & U. Valencia)Nikolai Kochelev (JINR & SNU)
Contents
• Introduction• Interactions induced by Instantons• Diquark-Triquark model for Pentaquark with
in Instanton model for the QCD vac.• QCD sum rule : Triquark correlations and • Discussion
• QCD : The fundamental theory for the strong interaction - Degrees of freedom : quark and gluon • Hadrons = Baryons+Mesons Baryons = 3 quarks Mesons = quark+antiquark • Multiquark hadrons are possible? YES!? (S=+1 Exotic, etc) • Role of Instanton in Multiquark systems?
Quark Model
• T. Nakano et al : PRL 91(2003) 012002 Observed Pentaquark in n →K+K-n Mass=1540MeV, Width < 25MeV
MnK+
LEPS
1540 10MeV
25MeV
M
(LEPS)
nK
0SpK
F. Close and Q. Zhao, hep-ph/0404075
M
Status of
• ... 1997 : Prediction by Diakonov et al in the chiral soliton model, mass about 1530MeV and width < 15MeV.
• 2003 : Observation by LEPS. Following it, many (+) results were reported : Jefferson Lab, Russia, SAPHIR… (from reanalyzing data obtained in 1997-98)
• 2004-2005 : theoretical criticism and (-) results have been emerged.
- Null results : most from experiments with higher energy and large statistics using nuclei, hadrons rather than photons
Production depends on production mechanism strongly(?)
-Jeffeson Lab this year : hep-ex/0510061 : Upper limit for production cross section of < 0.2% (c.f. 40% in LEPS) Summary : hep-ph/0510309 by Burkert
F. Close, Nature,Vol435,19 May 2005
0p K K n
*/ (1520)
from soliton model
• At the top of Antidecouplet :
• Mass : 1540 MeV Width < 30MeV• Parity = +1(?)
ududs
• Simple constituent quark model based on independently moving quarks yields mass of pentaquark around 2 GeV
• Correlations of quarks inside of (?)
Quark model
Two models for pentaquark1. Jaffe and Wilczek, PRL91(2
003)232003• Potential by one gluon excha
nge• Two scalar diquarks (L=1) + a strange antiquark • Parity = +1 • Recent calculation gives
higher mass than observed. (PRL94 (2005) 062001)
2. Karliner and Lipkin, PLB575 (2003) 249
• Triquark + diquark + orbital motion (L=1)
• Interaction by one gluon exchange
• Triquark = diquark =
3 ,6 ,2fC S
,3 ,3 1C f S
• Mass=1385 (quark masses + OGE) + 207 (orbital motion L=1) = 1592 MeV• Parity = +1• Small width : Potential barrier by the orbital motion
• ?? :- Is there another important source for quark correl
ations in hadrons? instanton?- Only one state in 3q cluster in KL’s?
Instanton : Strong fluctuation of gluonic field in QCD v
acuum
Interactions induced by Instanton• Two body + Three body interactions
Some Properties
• Acts on only quarks with different flavors : flavor antisymmetric wave functions (Isospin=0)
• Minimal spin Maximal strength• Three body interaction by Instanton in color
less 3-quarks state vanishes• For interactions with anti-quark:
Our Model
• Interaction by one gluon exchange + Interaction by Instanton• Instanton supplies the much smaller stron
g interaction coupling (~0.5)• For pentaquark : with different flavors Diquark + Triquark : separated enough
Mass Formula for Hadrons
Confinement Masses, mu=md=m0
Diquark + Triquark System
• Diquark is in isospin = 0, spin = 0 : due to instanton • (ud) quarks in Triquark is in isospin = 0 : d
ue to instanton • Triquark is in spin = 1/2 • There are two possibilities in Triquark • Relative orbital motion : L=1
( )ud ( )uds
State of each cluster Diquark :• Flavor space :
• Color space :
• Spin space :
Triquark : - A state • Flavor space :
• Color space :
• Spin space :
3 3 6 3
3 3 6 3
- B state • Flavor space :
• Color space :
• Spin space :
3 3 6 3
6 3 15 3
After diagonalization
Masses of clusters from parameters
• Mass of Pentaquark : - With the energy from orbital motion
• Orbital motion gives Small width• Positive Parity
11 (1420) Me400 VL fM M M
1595 MeVM
3 2 280MeV / 4q qredM M
Short summary I• Instanton Induced Interaction plays a impor
tant role in pentaquark.• By the way, are there really two clusters of
quarks in pentaquark?
• Triquark correlations in a QCD sum rule• Diquark correlation by Schaefer et al NPB 412(1994) 143
QCD sum rules• The Correlator of the interpolating current
with the quantum number of particle (state) under consideration
• Calculating it in deeply Euclidean region by the perturbative OPE
Condensates from the
nonperturbative vacuum
2 4( ) 0 | ( ) (0) | 0iq xHHq i d x e T x
OPE 2( ) :q
Nonperturbative Vacuum
( )H x
• is related to physical region by the dispersion relation
with a narrow resonance approx.
for spin ½ particle case
OPE 2( )q
2OPE 2 2
2 20
1 Im ( )( )
sq ds
s q
2 2 2 2
2 2 2 20 1 2
ˆIm ( ) ( ) ( )
ˆ( )( Im ( ) Im ( ))
H H Hs q M s M
s s q s s
0 | |H H HH u mass
threshold
2 2 2Im ( ) ( ) 0 | (0) | | (0) | 0n H Hn
p p M n n
• With the Borel transformation, the higher state contributions is exponentially suppressed.
• Two QCD sum rules :
• Quark-Hadron duality :
2 22 2
20
2 22 2
20
/OPE 2 2 / 2 211 1
/OPE 2 2 / 2 212 2
( ) Im ( )
( ) Im ( )
H
H
M Ms MHs
M Ms MH Hs
M ds e s e
M ds e s M e
2Im ( )i M
Borel Mass
21( )M
22 ( )M
• Mass of Particle can be determined in the three ways
• In general, if we include all contribution from OPE, the above ways must give same mass independent on .
• Actually, we cannot do it. Up to a certain energy dimension operator,
in some region of
2 1
3
/
( / 2 )
H
M i i
M
M
M
32 2 ( / 2 )H MM M M
• Parity of particle : - With the state of opposite
parity to the current is
-The interpolating current can create a state of opposite parity to the intrinsic parity of the current :
5i
0 | | H HH u
5 50 | | 0 | | H Hii uH H
Left hand side on the 2nd sum rule is + : the same parity as the current Left hand side on the 2nd sum rule is - : opposite parity to the current
2 2 2
22 2 2 2 2
Im ( ) ( ) 0 | (0) | | (0) | 0
( )( ) ( )( )
+higher
n H Hn
H H H H H H
p p M n n
q M q M q M q M
2 2/22 ( ) HM M
H HM M e
• The 2nd sum rule with massless u,d :
• OPE up to d=5 for nucleon & triquarks :
6 4 21 3 5
97 2
OO
OM O M O MM
• Quark Propagator :
By the Wick’s theorem : perturbative vacuum
[ ( )] 0 | ( ) (0) | 0ab
q a bS x i Tq x q
[ ( )] 0 | ( ) (0) | 0
0 |: ( ) (0) :| 0
ab
q a b
a b
S x i Tq x q
i q x q
Perturbative propagator
color spin
Nonperturbative effect : vacuum condensates
flavor
Nucleon and triquark states
• Interpolating current for nucleon of positive parity :
• Energy dimension of correlator for nucleon and color triquark states after the Borel transform : 7
• T-product of currents :
5
1 5
( ) [ ( ) ( )] ( )
( ) [ ( ) ( )] ( )
N abc Ta b c
N abc Ta b c
x u x C d x u x
x u x Cd x u x
1( ) ( ) ( )tot x f x t x
• QCD sum rule without direct instantons:
=+
• Instanton effect : zero mode of quark
*2 2 2Di : 2 / 3 /(2lute Instanton )
Shur
liquid mo
yak, NPB 203(1982) 930
d
el eff q cn m Size of Instan 1/ mton 3 f
• Mass and Residue : With threshold 1.75 GeV and f=1, t=-1
Without Instanton
A state in Triquark
• Interpolating currents of (-) parity :
• QCD sum rule without direct instantons:
1( ) ( ) ( )tot x f x t x
• Interpolating current of (–) parity :
• QCD sum rule without direct instantons
B state in Triquark
Instanton effect
• Two body effects :
• Three body effect : no in B
Masses and residues
• For A state : threshold 1.8 GeV, f~-t
800 , MeV Parity 1AM
• For B state : threshold 1.72 GeV
MeV, Parit930 1yBM
Short summary II• Schaefer et al showed (ud)-diquark correlat
ion with mass around 420MeV.• Are there really three quark correlations in
pentaquark? Two quasi-bound color quark correlations are there.
• These estimation gives the similar value of mass to in our MODEL.
• With a current of 5 quarks ?
uds
QCD sum rule in 5-quarks
• Two color clusters in the model : - Diquark and Triquark clusters• Diquark cluster : Spin(S)=0, Isospin(I)=0, Color(C)= • Triquark cluster : S=1/2, I=0, C=3• Two states in triquark cluster (ud) diquark : in A, S=1/2, I=0, C= in B, S=1, I=0, C=6
3
3
Interpolating currents• Current for 5-quarks without derivative=(current for triquark)*(current for diquark)• With A state : Two currents
1 5 5
5 5
1 1[ ] [ ]
4 21
[ ][ ]4 2
T T TA abc bde d e c afg f g
T T Tabc bde afg d e f g c
u C d Cs u C d
u C d u C d Cs
5 5
5 5
1 1[ ] [ ]
4 21
[ ][ ]4 2
T T TA abc bde d e c afg f g
T T Tabc bde afg d e f g c
u Cd Cs u C d
u Cd u C d Cs
0!
5 5
1 1[ ] [ ]
4 3 2T T T T
B a b b a b afg f gu C d u C d Cs u C d
• With B state :
• Energy dimension of correlator for the 5-quark after the Borel transform : 13
• The 2nd sum rule with massless u,d :
12 1 1501 3 13 2
OOM O M O
M
Sum rules by other authors
1. Shi-Lin Zhu, PRL91 (2003) 232002 : - Current : - Sum rule : 1st sum rule up to d=12 - Mass ~1.56 GeV, Parity = ? 2. R. D. Matheus et al, PLB578(2004) 323 - Two currents : not proper for - Sum rule : 1st sum rule up to d=12 - Mass~1.54, Parity = ?
5 5
1[ ]{ [ ] ( )}
2T
abc a b e e cu C d u s i d u d
3. M. Eidelmuller, PLB 597 (2004) 314 - Current : P-wave current - Sum rule : 1st sum rule up to d=6 - Mass~1.64, Parity = ?4. J. Sugiyama et al, PLB 581 (2004) 167 - Current : - Sum rule : Both sum rules up to d=6 - Mass~1.63, Parity = -1 - Current is very similar to our A state
5[ ][ ] T T Tabc def cfg a b d e gu Cd u C d Cs
2nd sum rule for A up to d=13 :diagrammatic representation
Parameters in Matheus et al, hep-ph/0412063
LHS
+ or - ?
Left hand side (LHS) of 2nd sum rule :
1512 10 8 61 3 5 7 1 23OM O M O M O M
OO
M
0 2.0GeVs
Sign of LHS is
changed with
going from d=5 to d=7 : Parity of state is
changed.
Contribution from Instanton
• Differently from model calculation, there is instanton effect in two quark pairs of
only.• No instanton effect in thre
e quarks by the color-spin structure of the current!!!
• Instanton effect is small in
, us ds
1.0 2.0M
Mass fitting with Instanton
32 2 ( / 2 )H MM M
Final summary
• For parity : higher operators are important since correlator of Pentaquark has higher energy dimension.
• Instanton effect is unexpectively small• Mass is around 1.75MeV• + parity : one quark is in excited state? Tw
o clusters in L=1?• B state in the triquark cluster?