飯田英明（東工大理）菅沼秀夫（京大理）高橋徹（京大基研）

Hideaki Iida
Prof. Hideo Suganuma
Dr. T.T.Takahashi
The 17th International Spin Physics Symposium (SPIN 2006)
October 2-7, 2006
Kyoto University, Kyoto, Japan
Contents
・Introduction
・Formalism
・Results
・Conclusion
Introduction
Motivation
Origin of the mass
There are two types of the origin of mass:
Higgs origin … about 1%
current quark mass:
mu (μ=1GeV)= (1.5-3)MeV
md (μ=1GeV)= (3-7)MeV
μ: renormalization scale
mass of leptons:
electron…me=0.51MeV
from the data of
Particle Data Group (2006)
Strong-interaction origin … about 99% !
constituent quark mass:
M ～ (300-400) MeV (for light quarks)
⇒ Most of the mass in the world is from strong interaction (QCD)
current quark
～ 3MeV
constituent quark
～ 350MeV
Strong interaction (QCD)
Introduction
What is the mechanism of the generation of
such a large constituent quark mass?
One possible answer is
Spontaneous breaking of chiral symmetry
…Important mechanism of mass generation for light fermions
Y.Nambu, G.Jona-Lasinio,Phys.Rev.122(1961)345: in Nambu-Jona-Lasinio (NJL) model
Chiral-symmetry is broken
π
Chiral-symmetry is restored
π
σ
M ～ (300-400) MeV:
Our present world
σ
m ～ (1.5-7) MeV:
At high temperature or high density
Study of partial chiral restoration: (theory) T.Kunihiro, T.Hatsuda (1983)
(experiment) H.Enyo group, K.Imai group
Introduction
Note however that chiral symmetry is the symmetry for massless fermions
Question:
In the strong-interaction world,
is chiral symmetry breaking necessary for mass generation?
We notice following examples of mass generation without chiral symmetry breaking:
① Gluon (colored vector particle, which is originally massless):
Large mass measured in lattice QCD:
…
massless
massive
J.E.Mandula and M.Ogilvie (Landau geuge)
Phys.Lett.B185(1987),127
K.Amemiya, H.Suganuma（MA gauge）
Phys.Rev.D60(1999)114509
Glueball: hadron made by only gluons
even the lightest glueball (0++) is rather heavy…1.5GeV experimental candidate: f0(1500)
② Charm quark
・Current quark mass mc : about 1.2GeV (Particle Data Group)
・ In the quark model, constituent quark mass is about 1.6GeV
The difference (1.6-1.2)GeV=400MeV is the mass generated by strong interaction
without chiral symmetry breaking.
Introduction
In this way, we conjecture that there should be
other type of mass generation
without chiral symmetry breaking or Higgs mechanism.
(non-chiral origin but strong-interaction origin)
Our conjecture:
Even without chiral symmetry, large mass generation
generally occurs in the strong-interaction world.
In fact, all colored particles (scalar, fermion, vector) have
a large mass generated by dressed gluon effect.
dressed gluons
colored particles
large mass
In this talk, we study “light” colored scalar particle,
which does not have chiral symmetry.
We call this colored scalar particle as “scalar quark”.
Here, the bare scalar-quark mass is set to be almost zero.
We investigate bound states of colored scalar particles,
namely, hadrons made by scalar quarks in lattice QCD
in terms of mass generation of scalar quark.
Can we observe large mass generation even in this scalar-quark system
without chiral symmetry?
Lattice QCD: first-principle calculation of strong interaction
(non-perturbative)
⇒ powerful method in non-perturbative QCD
First study for scalar-quark systems in lattice QCD
Scalar-quark hadron
Here, we investigate hadrons made by scalar quarks.
Scalar-quark hadron is made by two or three scalar quarks.
Scalar-quark hadron
cf) ordinary hadron
Scalar-quark meson
(Boson)
Scalar-quark baryon
(Boson)
Meson
(Boson)
Baryon
(Fermion)
: quark
: scalar quark
:anti scalar-quark
★ Statistics are different from that of ordinary hadrons
: anti-quark
Chimera hadron
Chimera hadron is made by quarks and scalar quarks.
“chimera hadron” is new terminology.
Chimera hadron
chimera meson
(Fermion)
chimera baryon
(Boson)
chimera baryon
(Fermion)
: quark
: scalar quark
:anti-quark
:anti scalar-quark
We calculate the masses of
scalar-quark hadrons and chimera hadrons in quenched lattice QCD.
Formalism
― continuum （Minkovsky space）―
QCD
： quark field （color triplet）
:covariant derivative
: field strength tensor
Scalar QCD
： scalar quark （color triplet）
QCD including the quarks and scalar quarks
Formalism
― discretization (Euclid space) ―
Quark sector
Wilson quark action:
：space coordinate
：link variable
：hopping parameter
Scalar-quark sector
：mass of scalar quark
Gauge invariant
Summary of scalar and chimera hadrons
For the study of scalar-quark system,
we calculate the masses of following scalar hadrons and chimera hadrons:
Ψ: quark
φ: scalar quark
Scalar-quark hadrons
・scalar-quark meson：
Scalar
・scalar-quark baryon：
Scalar
Chimera hadrons
・chimera meson：
Spinor
・chimera baryon：
Spinor
Scalar
Hadronic operators and correlators
We use the following operators of scalar-quark hadrons and chimera hadrons:
・operators of scalar-quark hadrons
（scalar-quark meson）
（scalar-quark baryon）
・operators of chimera hadrons
（chimera meson）
（chimera baryon）
（chimera baryon）
：scalar quark ( : index of color)
：quark (
: index of spinor)
⇒ using these operators, we calculate the correlators of these hadrons
（total momentum is projected to be zero）
from
, we extract the mass of these hadrons
Parameters of lattice QCD
Quenched lattice QCD
β=5.70 （
β=5.75 （
β=6.10 （
）
）
）
(corresponding to gauge coupling)
: lattice spacing (lattice cutoff)
Lattice size: 163×24 (for φ†φ)
163×32 (for other hadrons except)
spatial volume: (2.9fm)3 (β=5.70)
(2.7fm)3 (β=5.75)
(1.8fm)3 (β=6.10)
Scalar-quark meson φ†φ
M(GeV) (scalar-quark meson mass)
Mass generation of scalar quark by gluon
Ψ： quark
φ: scalar quark
3GeV
msq(GeV)
(bare scalar-quark mass)
Scalar-quark meson mass M vs bare scalar-quark mass msq
(β=5.75, latt.size: 163×32)
Important result：
Large mass generation by
At bare scalar-quark mass msq～0,
strong interaction
scalar-quark meson mass M～3.0GeV.
(non chiral origin)
⇒dynamically generated mass of scalar quark Msq is 1.5GeV!!
occurs in the scalar-quark
Compared with constituent quark mass (～300MeV),
system!
this mass generation is very large.
Scalar-quark baryon φφφ
M(GeV) (scalar-quark baryon mass)
Ψ： quark
φ: scalar quark
msq(MeV)(bare scalar-quark mass)
scalar-quark baryon mass M vs bare scalar-quark mass msq
(β=5.70, latt.size: 163×32)
At bare scalar-quark mass msq～0,
scalar-quark baryon mass M～4.8GeV.
⇒dynamically generated mass of scalar quark Msq is 1.5GeV.
Large mass generation of scalar quark is also seen
Chimera meson φ†Ψ
M(GeV) (chimera meson mass)
Ψ： quark
φ: scalar quark
Note:
Ψ emerges in the
following hadrons
msq=270MeV
msq=200MeV
msq=120MeV
(bare scalar-quark mass)
mq(MeV)
(bare quark mass)
chimera meson mass M vs quark mass mq and scalar-quark mass msq
(β=5.70, latt.size: 163×32)
At bare scalar-quark mass msq～0 and bare quark mass mq～0,
chimera meson mass M～1.9GeV.
Msq + Mq ～ M is formed. (1.5 + 0.4 = 1.9)
dynamically generated mass of scalar quark Msq ～1.5GeV
constituent quark mass
Mq～400MeV
Chimera baryon φφΨ
M(GeV) (chimera baryon mass)
Ψ： quark
φ: scalar quark
msq=270MeV
msq=200MeV
msq=120MeV
(bare scalar-quark mass)
mq(MeV)
(bare quark mass)
chimera baryon mass M vs quark mass mq and scalar-quark mass msq
(β=5.70, latt.size: 163×32)
At bare scalar-quark mass msq～0 and bare quark mass mq～0,
chimera baryon mass M～3.7GeV.
2×Msq +Mq ～ M
dynamically generated mass of scalar quark Msq ～1.5GeV
constituent quark mass
Mq～400MeV
Chimera baryon ΨΨφ
M(GeV) (chimera baryon mass)
Ψ： quark
φ: scalar quark
msq=270MeV
msq=200MeV
msq=120MeV
(bare scalar-quark mass)
mq(MeV)
(bare quark mass)
chimera baryon mass M vs quark mass mq and scalar-quark mass msq
(β=5.70, latt.size: 163×32)
At bare scalar-quark mass msq～0 and bare quark mass mq～0,
chimera baryon mass M～2.4 GeV.
Msq + 2×Mq ～ M
dynamically generated mass of scalar quark Msq ～1.5GeV
constituent quark mass
Mq～400MeV
★Similarity between φφΨ and φ†Ψ
Chimera baryon
Chimera meson
Ψ： quark
φ: scalar quark
Figures of the mass of chimera hadrons
M(GeV) (chimera meson mass)
M(GeV) (chimera baryon mass)
msq=270MeV
msq=270MeV
msq=200MeV
msq=200MeV
msq=120MeV
(bare scalar-quark mass)
msq=120MeV
(bare scalar-quark mass)
mq(MeV)
(bare quark mass)
mq(MeV)
(bare quark mass)
…Slopes (mq-dependence) are almost the same between
⇒ Similar mq-dependence between
and
and
is observed.
Interpretation of the similarity between φ†Ψ and φφΨ
Ψ： quark
φ: scalar quark
Chimera meson
Chimera baryon
wave functions
Chimera meson
Scalar quark φ is very heavy.
So, the wave-function of
light quark (Ψ) distributes
around the scalar-quark φ.
Chimera baryon
Due to the large constituent mass of
scalar-quarkφ, the two particles (φφ)
are close under Coulomb interaction.
Similarity of the system between
V(r)
and
r
Energy level
of φφ
Conclusion
Large mass generation occurs
even in the scalar-quark system!
(non-chiral origin)
Dynamically generated mass of scalar quarks：
about 1.5GeV
Dressed gluon effect
…
msq～0
(bare scalar-quark mass)
Msq ≧ 1GeV
(large mass generation of scalar quark)
Dressed gluon effect
QCD (gluon) effect
(non-chiral origin)
Summary and Concluding Remarks
Using Lattice QCD, we have performed the
First Study of scalar-quark (colored-scalar) systems.
We have found Large Mass Generation of
scalar quarks. (This is Non-Chiral Origin)
This Large Mass Generation can be explained by
Dressed Gluon Effect.
Dressed Gluon
colored-scalar
msq～0
Msq ≧ 1GeV
Similarity between
and
systems emerges
due to the large mass of scalar quark.

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