Quarkgluon mixed matrix elements

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PNU NuRI
Quark-gluon mixed matrix elements within the
framework of the nonlocal chiral quark
model Seung-il Nam Hyun-Chul Kim and
Hui-Young Ryu Department of Physics and
Nuclear Physics Radiation Technology Institute
(NuRI), Pusan National University (PNU), Korea
2007 APCTP workshop at POSTECH 2628 Feb. 2007
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PNU NuRI
Introduction
How the universe created?
2007 APCTP workshop at POSTECH 2628 Feb. 2007
What the universe made of?
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PNU NuRI
Introduction
Strong force Prediction of mesons by
Yukawa Conception of partons Group theoretical
analyses of hadron families by Gell-Mann String-li
ke objects (Reggization) Advent of QCD
Confinment, Asymtotic freemdom Transmutation of
dimension ?QCD Chiral symmetry and its
spontaneous breaking
2007 APCTP workshop at POSTECH 2628 Feb. 2007
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Introduction
Quantum ChromoDynamics QCD Quark and gluon
degrees of freedom Gluon interact in non-Abelain
manner with quarks Underlying theory for strong
interaction ARE WE HAPPY WITH THIS? Highly
nonlonear interaction Running coupling depending
on scale ? Renormlaization group
evolution Lattice QCD simulation descrete
space-time Perturbative QCD high energy
machinary
2007 APCTP workshop at POSTECH 2628 Feb. 2007
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PNU NuRI
Introduction
Low energy QCD Perturbation small coupling as
a expamsion parameter High energy ?s lt 1
whereas low energy ?s gt 1 ? Perturbative QCD,
then what for the low energy? As told, lattice
QCD simulation works for all..?? Still more
sofistication necessary in lattice QCD Time,
machine power, large collaboration (matter of
time??)
2007 APCTP workshop at POSTECH 2628 Feb. 2007
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PNU NuRI
Introduction
Effective low energy models for QCD Relatively
simple and easy models mimic QCD Employment of
different D.o.F.s treated easily Guided by
symmetries, constraints, LEC.. In case, several
QCD conditions ignored ? confinment,
renormalizability, anomaly, etc. Focusing on most
relevant conditions Depending much on
scale Better QCD like model building
understanding of QCD
2007 APCTP workshop at POSTECH 2628 Feb. 2007
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PNU NuRI
Introduction
Mass generation of quarks broken symmetry
Flavor SU(3) symmetry mumdms (0, chiral
limit) Broken flavor SU(3) symmetry mumd?ms ?
mumd5 MeV and ms150 MeV Ex) Proton (uud) 15
(940) MeV !? Kaon (us,ds) 155 (495) MeV
!? What happens for these mass differences?
Chiral doublet in the nature
N(940,1/2) vs. N(1535,1/2-) Heavily broken
chiral symmetry from the beginning ?
Spontaneous Chiral Symmetry Breaking (S?SB)
2007 APCTP workshop at POSTECH 2628 Feb. 2007
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PNU NuRI
Introduction
Spontaneous Chiral Symmetry Breaking Nontrivial
vacuum H0??0 Infinitely degenerated
vacuua Realization of S?SB in hadron
physics Continuous symmetry breaking (S?SB) ?
generation of the massless Goldstone boson Pion
(140 MeV) assigned to be the GS boson ? must be
crucial at the low energy hadron phyiscs !! Model
building with ? for the low energy effective
models
2007 APCTP workshop at POSTECH 2628 Feb. 2007
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PNU NuRI
Introduction
Effective models related to pion Hadron physics
filled with pion due to its special natures MIT
bag model naïve treatment of quarks Chiral bag
model MIT bag chiral symmetry with GS
boson Linear and nonlinear ?-models Simple
realization of S?SB Skyrme model only GS boson
in topological soliton Nmabu-Jona-Lasinio (NJL)
quark D.o.F. ? mesonic D.o.F. Nonlocal NJL
nonlocal interaction plays a role Instanton
model quark-instanton D.o.F. instead of gluon
2007 APCTP workshop at POSTECH 2628 Feb. 2007
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Introduction
Instanton vacuum configuration Gluonic potential
of QCD Self-duality condition minimizing the
potential Topological number realted to the
ground state Guage transformation of the ground
state via
2007 APCTP workshop at POSTECH 2628 Feb. 2007
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PNU NuRI
Introduction
Instanton vacuum configuration Winding number
from homotopic SU(N) gaugetransformation Tunnelin
g between vacuua Instanton solution for the
self-duality condition Natural mechanism for S?SB
2007 APCTP workshop at POSTECH 2628 Feb. 2007
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PNU NuRI
Introduction
Merits in instanton model in the large Nc All
relevant QCD symmetries satisfied Only two
phenomenological parameters fixed in the
model Internstanton distance R 1 fm and
Instanton size ? 1/3 fm These values are
supported from the lattice QCD simulations
!!! 1/? 600 MeV plays a role of the model scale
parameter No adjustable free parameters highly
constrained model Intrinsic UV regulator from the
quark-instanton interaction Natural derivation of
nonlocal interactions
2007 APCTP workshop at POSTECH 2628 Feb. 2007
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Introduction
Fermionic zero mode solution A solution for the
Dirac equation with the instanton Fourier
transformation of the wave function Form
factor Natural UV regulator Parameterization
2007 APCTP workshop at POSTECH 2628 Feb. 2007
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Introduction
Quark propagator in broken flavor SU(3) Written
in a iterative integral equation Current quark
mass dependent mass Hadrons with strangeness
quark being able to be studied Then how we
consturct the effective action from
instanton? The action generating the propagator
from its Z-fucntion
2007 APCTP workshop at POSTECH 2628 Feb. 2007
SU(3) correction
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Introduction
Effective QCD partition function via instanton
2Nf-multiquark interaction Employing
Lagrane multiplyer, ?
2007 APCTP workshop at POSTECH 2628 Feb. 2007
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Introduction
Effective QCD partition function via instanton
Variation of Z about to ? Self-consistent
(saddle-point) equation Phenomenological
values Gluon condensate
2007 APCTP workshop at POSTECH 2628 Feb. 2007
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PNU NuRI
Introduction Motivation
Nonperturbative properties of QCD vacuua Nonzero
vacuum expectation value (V.E.V.) of QCD
operators ? Quark (3Dim), gluon (4Dim), Mixed
(5Dim) condensates. Order parameter for the QCD
phase transition ? Order parameter for the
S?SB Input parameter in QCD sumrules (OPE) ?
??(0,x)??an??(x)? Various nonperturbative QCD
vacuum properties ? Resoponse of the V.E.V. to
external EM-field
2007 APCTP workshop at POSTECH 2628 Feb. 2007
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Results
SiNam,H.-Ch.Kim arxivhep-ph/0605041 Accepted
for publication in Phys.Lett.B
Gluon condensate Obvious flavor SU(3)
correction Gluon blind for flavor symmetry
flat gluon condensate Critical effects from the
flavor SU(3) symmetry correction
Without the correction
2007 APCTP workshop at POSTECH 2628 Feb. 2007
With the correction
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PNU NuRI
Results
SiNam,H.-Ch.Kim arxivhep-ph/0605041 Accepted
for publication in Phys.Lett.B
Quark condensate Well produced value The
ratio 0.75 (0.8)
Without the correction
2007 APCTP workshop at POSTECH 2628 Feb. 2007
With the correction
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PNU NuRI
Results
SiNam,H.-Ch.Kim arxivhep-ph/0605041 Accepted
for publication in Phys.Lett.B
Quark-gluon mixed condensate (5dim) Quark-gluon
Yukawa vertex Factorization theorem with
mass2-coefficient Instanton Classical solution
for soft gluon How we can treat gluon operator
consistently??? Convolution of single
quark-instnaton interaction and gluon OP
2007 APCTP workshop at POSTECH 2628 Feb. 2007
G??(instanton) ? dZ Y(quark,instanton) ?G??
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Results
SiNam,H.-Ch.Kim arxivhep-ph/0605041 Accepted
for publication in Phys.Lett.B
Reconstructed gluon operator Single
quark-instanton interaction Gluon operator in
terms of color orientation Gluon operator as a
quark-instanton interaction This reconstructed
operator used for
2007 APCTP workshop at POSTECH 2628 Feb. 2007
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Results
SiNam,H.-Ch.Kim arxivhep-ph/0605041 Accepted
for publication in Phys.Lett.B
Mixed condensate Formula for the
condensate The SU(3) correction effect
manifeted
Without the correction
2007 APCTP workshop at POSTECH 2628 Feb. 2007
With the correction
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Results
SiNam,H.-Ch.Kim arxivhep-ph/0605041 Accepted
for publication in Phys.Lett.B
Factorzation coefficient m20 Less sensitive
effects from the SU(3) correction Using
expansion of Bilocal quark operator and QCD
E.o.M.
2007 APCTP workshop at POSTECH 2628 Feb. 2007
Without the correction
With the correction
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PNU NuRI
Results
SiNam,H.-Ch.Kim arxivhep-ph/0605041 Accepted
for publication in Phys.Lett.B
Factorzation coefficient m20 Relation between
k?and m20
2007 APCTP workshop at POSTECH 2628 Feb. 2007
SiNam et al, Phys.Rev.D74,014019(2006) SiNam et
al, Phys.Rev.D74,076005(2006)
?k2?? 0.2 MeV2 vs. 0.23 MeV2 from pion DA
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PNU NuRI
Results
SiNam,H.-Ch.Kim arxivhep-ph/0605041 Accepted
for publication in Phys.Lett.B
Renormalization group evolution Matching
different scales between models A ratio of the
two different operators Mixed condensate ?1/b
-2/27 -0.07 (insensitive) Quark condensate
?2/b 4/9 0.44 (sensitive) m20 (?1- ?2)/b
-14/27 -0.52 (sensitive)
2007 APCTP workshop at POSTECH 2628 Feb. 2007
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PNU NuRI
Results
H.Y.Ryu, SiNam, H.-Ch.Kim arxivhep-ph/0610348 Sub
mitted to Phys.Revt.D
Electtromagnetic properties of the QCD vacuum QCD
vacuum response to the external EM-field To
obtain the operators, effective partition
function given
H.-Ch.Kim,M.M.Musakhanov,M.Siddikov Phys.Lett.B608
,95(2005)
2007 APCTP workshop at POSTECH 2628 Feb. 2007
Covariant derivative
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PNU NuRI
Results
H.Y.Ryu, SiNam, H.-Ch.Kim arxivhep-ph/0610348 Sub
mitted to Phys.Revt.D
Gluinic magnetic susceptibilities Gauge invariant
forms ? and ? expanded in terms of the
electric charges, e
2007 APCTP workshop at POSTECH 2628 Feb. 2007
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PNU NuRI
Results
H.Y.Ryu, SiNam, H.-Ch.Kim arxivhep-ph/0610348 Sub
mitted to Phys.Revt.D
Gluonic magnetic susceptibilities Absolute values
decreasing as mf increases Vacuum effects
diminished as mf grows general feature?!
2007 APCTP workshop at POSTECH 2628 Feb. 2007
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PNU NuRI
Results
H.Y.Ryu, SiNam, H.-Ch.Kim arxivhep-ph/0610348 Sub
mitted to Phys.Revt.D
Comparison with others Other model calcualtions
moslty coming from QCDSR Comparison via
renormalization group evolution at 600
MeV Inconsistent between the values even in the
same scheme Very different from ?
2007 APCTP workshop at POSTECH 2628 Feb. 2007
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Summary
Strong interaction at nonperturbative
regions Difficulties in applicayion of QCD
(lattice QCD?!) Effective QCD-like models guided
by relevant symmetries S?SB governing low-lying
hadrons critical role of ? Nontrivial QCD
vacuum Instanton vacuum configuration Relatively
sophisticated model highly constrained Broken
flavor SU(3) symmetry taken into account Quark
(3dim), gluon (4dim), mixed (5dim) studied EM
response of QCD vacuum considered In principle,
all kinds of hadronic matrix elements computed
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Thank you very much for your attention !!
2007 APCTP workshop at POSTECH 2628 Feb. 2007