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A QCD Sum Rule with An Explicit Di-quark Field . Kyung- il Kim, Su Houng Lee, Daisuke Jido. December 7~11, 2010, BARYONS’10 . Contents. Motivation Di-quark Structures in Hadrons Introduction to QCD Sum Rule(QCDSR) QCDSR with Di-quark Eff. Lagrangian Lambda particles Nucleons - PowerPoint PPT Presentation
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A QCD Sum Rule with An Explicit Di-quark Field
Kyung-il Kim, Su Houng Lee, Daisuke Jido
December 7~11, 2010, BARYONS’10
Contents• Motivation
– Di-quark Structures in Hadrons
• Introduction to QCD Sum Rule(QCDSR)
• QCDSR with Di-quark Eff. Lagrangian– Lambda particles– Nucleons– Scalar meson
• The Summary2/182010 Dec. 7~11 BARYONS’10
Motivation : Di-quark Structures in HadronsSHLee and S.Yasui : EPJ C (2009)
<Diquark inside baryons>
3/18
<Quark-antiquark inside mesons>
2010 Dec. 7~11 BARYONS’10
Motivation : Di-quark Structures in Hadrons
4/18
<Tetraquark> u dq q Vs. u q
d q
<H Dibaryon>
<Pentaquark>
q qq
2010 Dec. 7~11 BARYONS’10
Introduction: QCD Sum Rules<Two-point correlation function>
<The operator product expansion>
5/18
OPE factorizes function into a short- and long-distance pieceExample) for gluon operator
2010 Dec. 7~11 BARYONS’10
Introduction: QCD Sum Rules<Dispersion relation>
∼ Spectral Density
Ex)
6/18
<Optical Theorem>
2010 Dec. 7~11 BARYONS’10
Introduction: QCD Sum Rules
<Borel Transformation>
7/18
By the weight function, high resonances are suppressed.<Sum rule to obtain mass>
2010 Dec. 7~11 BARYONS’10
Λ Baryons
8/18
u d
s
Ref. PDG<Current for Λ mesons>
Scalar diquark fieldGauge invariant Lagrangian for diquark field
2010 Dec. 7~11 BARYONS’10
QCDSR with Di-quark fields
9/18
Effective Lagrangian for Di-quark Field
<Propagator of diquark field>
=0
=0
2010 Dec. 7~11 BARYONS’10
Λ Baryons
10/18
Gauge invariant Lagrangian for diquark field
Propagator of diquark fieldFree parameters!
The relation between diquark condensate and gluon condensate
OPE terms
2010 Dec. 7~11 BARYONS’10
QCDSR with Di-quark fields
11/18
OPE Result
2010 Dec. 7~11 BARYONS’10
Λ Baryons
12/18
Diquark Mass (GeV)
Ratio(λ)
0.2 -0.50.3 -0.20.4 -0.013
0.41 0
Parameter Set ( ms=0.12GeV, mΛ =1.115GeV)
2010 Dec. 7~11 BARYONS’10
Λ Baryons
13/18
mc=1.6 GeV, mΛ =2.284GeV
2010 Dec. 7~11 BARYONS’10
Nucleons
14/18
u
dd
d
u u
Neutron
Proton
The masses of nucleons are over 1GeV -> We didn’t consider the tunneling behavior of quarks!
2010 Dec. 7~11 BARYONS’10
Scalar meson
Scalar meson as a tetraquark
15/18
Can it reproduce sigma(600) meson?(ud-diquark field)
Jaffe(1977) PRD
2010 Dec. 7~11 BARYONS’10
Scalar meson
16/182010 Dec. 7~11 BARYONS’10
Summary• In some hadron configuration, during diquark structures are
not broken, we can regard diquark field as a point particle.
• Two free parameter, diquark mass and condensate can be chosen from Λ sum rules. These parameters give reason-able mass of Λ_c.
• QCD sum rule with diquark field gives nucleon mass as over 1GeV. -> We need to consider tunneling effect of quarks.
• We can not reproduce a sigma(600) meson mass because that has not good diquark structure. -> The scalar meson which has a diquark structure has a mass over 1 GeV.
17/182010 Dec. 7~11 BARYONS’10
Thank you!
