Contents ・ Introduction

・ Formalism

・ Results

・ Conclusion

The 17th International Spin Physics Symposium (SPIN 2006)October 2-7, 2006

Kyoto University, Kyoto, Japan

Hideaki IidaProf. Hideo Suganuma

Dr. T.T.Takahashi

Introduction

Origin of the massOrigin of the massMotivation

There are two types of the origin of mass:

current quark ～ 3MeV

constituent quark ～ 350MeV

Strong interaction (QCD)

⇒ Most of the mass in the world is from strong interaction (QCD)

(for light quarks)M ～ (300-400) MeV

Strong-interaction origin … about 99% !

constituent quark mass:

Higgs origin … about 1%

mu (μ=1GeV)= (1.5-3)MeVmd (μ=1GeV)= (3-7)MeVμ: renormalization scale

from the data of Particle Data Group (2006)

current quark mass:

mass of leptons: electron…me=0.51MeV

IntroductionWhat is the mechanism of the generation of such a large constituent quark mass?

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

π

σ

π

σ

Chiral-symmetry is broken Chiral-symmetry is restored

m ～ (1.5-7) MeV:

At high temperature or high density

M ～ (300-400) MeV:

Our present world

Study of partial chiral restoration: (theory) T.Kunihiro, T.Hatsuda (1983) (experiment) H.Enyo group, K.Imai group

One possible answer is

Question:In the strong-interaction world, is chiral symmetry breaking necessary for mass generation?

IntroductionNote however that chiral symmetry is the symmetry for massless fermions

① Gluon (colored vector particle, which is originally massless):

J.E.Mandula and M.Ogilvie (Landau geuge) Phys.Lett.B185(1987),127K.Amemiya, H.Suganuma （ MA gauge ） Phys.Rev.D60(1999)114509

Large mass measured in lattice QCD:

Glueball: hadron made by only gluons

even the lightest glueball (0++) is rather heavy…1.5GeV experimental candidate: f0(1500)

massless massive

…

② Charm quark ・ Current quark mass mc : about 1.2GeV (Particle Data Group)

　　　　・ In the quark model, constituent quark mass is about 1.6GeVThe difference (1.6-1.2)GeV=400MeV is the mass generated by strong interaction without chiral symmetry breaking.

We notice following examples of mass generation without chiral symmetry breaking:

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.

Introduction

colored particles

dressed gluons large mass

In this talk, we study “light” colored scalar particle, which does not have chiral symmetry.

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.

First study for scalar-quark systems in lattice QCDFirst study for scalar-quark systems in lattice QCD

Lattice QCD: first-principle calculation of strong interaction (non-perturbative) ⇒ powerful method in non-perturbative QCD

We call this colored scalar particle as “scalar quark”.Here, the bare scalar-quark mass is set to be almost zero.

Can we observe large mass generation even in this scalar-quark systemwithout chiral symmetry?

Scalar-quark hadron

Scalar-quark hadron is made by two or three scalar quarks.

★ Statistics are different from that of ordinary hadrons

Here, we investigate hadrons made by scalar quarks.

Baryon(Fermion)

Meson(Boson)

: quark

: anti-quark

cf) ordinary hadron

Scalar-quark baryon (Boson)

Scalar-quark meson (Boson)

: scalar quark

:anti scalar-quark

Scalar-quark hadron

Chimera hadronChimera hadron is made by quarks and scalar quarks.

“chimera hadron” is new terminology.

We calculate the masses of scalar-quark hadrons and chimera hadrons in quenched lattice QCD.

chimera baryon (Boson)

chimera meson (Fermion)

: quark

:anti-quark

: scalar quark

:anti scalar-quark

chimera baryon (Fermion)

Chimera hadron

Formalism

： scalar quark （ color triplet ）

QCD

Scalar QCD

: field strength tensor

： quark field （ color triplet ）:covariant derivative

QCD including the quarks and scalar quarks

― continuum （ Minkovsky space ）―

Gauge invariant

Scalar-quark sector

Wilson quark action:Quark sector

Formalism― discretization (Euclid space) ―

： mass of scalar quark

： space coordinate： link variable： hopping parameter

・ scalar-quark meson ：

・ scalar-quark baryon ：

Scalar

Scalar

・ chimera meson ：

・ chimera baryon ：

Spinor

Spinor

Scalar

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: quarkφ: scalar quark

Scalar-quark hadrons

Chimera hadrons

： quark ( 　　 : index of spinor)

・ operators of scalar-quark hadrons

・ operators of chimera hadrons

： scalar quark ( 　 : index of color)

（ scalar-quark baryon ）

（ chimera meson ）

（ chimera baryon ）

（ chimera baryon ）

（ scalar-quark meson ）

Hadronic operators and correlators

⇒ 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

We use the following operators of scalar-quark hadrons and chimera hadrons:

β=5.70 　（　　　　　　　　　　 ）β=5.75 　（ ）β=6.10 　（　　　　　　　　　　 ）

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)

Quenched lattice QCD

Parameters of lattice QCD

: lattice spacing (lattice cutoff)

(corresponding to gauge coupling)

Scalar-quark meson mass M vs bare scalar-quark mass msq

(β=5.75, latt.size: 163×32)

3GeV

M(GeV) (scalar-quark meson mass)Mass generation of scalar quark by gluon

Scalar-quark meson φ†φ

Ψ ： quark φ: scalar quark

msq(GeV)(bare scalar-quark mass)

Important result ：At bare scalar-quark mass msq ～ 0,

scalar-quark meson mass M ～ 3.0GeV.⇒dynamically generated mass of scalar quark Msq is 1.5GeV!!Compared with constituent quark mass ( ～ 300MeV), this mass generation is very large.

Large mass generation by strong interaction (non chiral origin) occurs in the scalar-quarksystem!

Scalar-quark baryon φφφM(GeV) (scalar-quark baryon mass)

scalar-quark baryon mass M vs bare scalar-quark mass msq (β=5.70, latt.size: 163×32)

msq(MeV)(bare scalar-quark mass)

Large mass generation of scalar quark is also seen

At bare scalar-quark mass msq ～ 0,

scalar-quark baryon mass M ～ 4.8GeV.⇒dynamically generated mass of scalar quark Msq is 1.5GeV.

Ψ ： quarkφ: scalar quark

Chimera meson φ†Ψ

chimera meson mass M vs quark mass mq and scalar-quark mass msq

(β=5.70, latt.size: 163×32)

mq(MeV) (bare quark mass)

M(GeV) (chimera meson mass)

msq=120MeV(bare scalar-quark mass)

msq=200MeV

msq=270MeV

Note:Ψ emerges in the following hadrons

Ψ ： quarkφ: scalar quark

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

mq(MeV)(bare quark mass)

M(GeV) (chimera baryon mass)

msq=120MeV(bare scalar-quark mass)

msq=200MeV

msq=270MeV

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 ～ 1.5GeVconstituent quark mass Mq ～ 400MeV

Ψ ： quarkφ: scalar quark

Chimera baryon ΨΨφ

mq(MeV) (bare quark mass)

M(GeV) (chimera baryon mass)

msq=120MeV(bare scalar-quark mass)

msq=200MeVmsq=270MeV

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 ～ 1.5GeVconstituent quark mass Mq ～ 400MeV

Ψ ： quarkφ: scalar quark

⇒ Similar mq-dependence between and is observed.

★Similarity between φφΨ and φ†Ψ

mq(MeV)(bare quark mass)

msq=120MeV(bare scalar-quark mass)

msq=200MeV

msq=270MeV

mq(MeV)(bare quark mass)

M(GeV) (chimera meson mass)

Ψ ： quarkφ: scalar quark

msq=120MeV(bare scalar-quark mass)

msq=200MeV

msq=270MeV

…Slopes (mq-dependence) are almost the same between and

M(GeV) (chimera baryon mass)

Figures of the mass of chimera hadrons

Chimera mesonChimera baryon

Interpretation of the similarity between φ†Ψ and φφΨ

Chimera meson Chimera baryon

Due to the large constituent mass of scalar-quarkφ, the two particles (φφ) are close under Coulomb interaction.

V(r)

r

Energy level of φφ

Similarity of the system between and

Scalar quark φ is very heavy.So, the wave-function of light quark (Ψ) distributes around the scalar-quark φ.

wave functionsΨ ： quarkφ: scalar quark

Chimera meson Chimera baryon

Conclusion

Large mass generation occurs even in the scalar-quark system!(non-chiral origin)

msq ～ 0(bare scalar-quark mass)

Msq 　≧ 1GeV(large mass generation of scalar quark) Dressed gluon effect

…

Dynamically generated mass of scalar quarks ： about 1.5GeV 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.

Similarity between and systems emerges due to the large mass of scalar quark.

msq ～ 0 Msq 　≧ 1GeV

colored-scalarDressed Gluon