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Bound States of (Anti-)Scalar-Quarks in SU(3)c Lattice QCD

Study of bound states made by scalar quarks in lattice QCD, investigating mass generation without chiral symmetry breaking.

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Bound States of (Anti-)Scalar-Quarks in SU(3)c Lattice QCD

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  1. Bound States of (Anti-)Scalar-Quarks in SU(3)c Lattice QCD Hideaki IidaProf.Hideo SuganumaDr. T.T.Takahashi The 17th International Spin Physics Symposium (SPIN 2006) October 2-7, 2006 Kyoto University, Kyoto, Japan Contents ・Introduction ・Formalism ・Results ・Conclusion

  2. Introduction Higgs origin … about 1% mu (μ=1GeV)= (1.5-3)MeV md (μ=1GeV)= (3-7)MeV μ: renormalization scale current quark mass: from the data of Particle Data Group (2006) mass of leptons: electron…me=0.51MeV Strong-interaction origin …about 99% ! (for light quarks) M ～ (300-400) MeV constituent quark mass: ⇒ Most of the mass in the world is from strong interaction (QCD) current quark ～ 3MeV constituent quark ～ 350MeV Strong interaction (QCD) Motivation Origin of the mass There are two types of the origin of mass:

  3. Introduction π σ Chiral-symmetry is restored Chiral-symmetry is broken π σ m ～ (1.5-7) MeV: M ～ (300-400) MeV: Our present world At high temperature or high density Study of partial chiral restoration: (theory) T.Kunihiro, T.Hatsuda (1983) (experiment) H.Enyo group, K.Imai group What is the mechanism of the generation of such a large constituent quarkmass? 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

  4. Introduction ① Gluon (colored vector particle, which is originally massless): Large mass measured in lattice QCD: J.E.Mandula and M.Ogilvie (Landau geuge) Phys.Lett.B185(1987),127 K.Amemiya, H.Suganuma（MA gauge） Phys.Rev.D60(1999)114509 … massless massive 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 : about1.2GeV(Particle Data Group) ・ In the quark model, constituent quark mass is about1.6GeV The difference (1.6-1.2)GeV=400MeV is the mass generated by strong interaction without chiral symmetry breaking. Note however that chiral symmetry is the symmetry for massless fermions Question: In the strong-interaction world, ischiral symmetry breaking necessary for mass generation? We notice following examples of mass generation without chiral symmetry breaking:

  5. Introduction dressed gluons large mass colored particles 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.

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

  7. Scalar-quark hadron cf) ordinary hadron Scalar-quark meson (Boson) Meson (Boson) Scalar-quark baryon (Boson) Baryon (Fermion) : quark : anti-quark : scalar quark :anti scalar-quark Scalar-quark hadron Here, we investigatehadrons made by scalar quarks. Scalar-quark hadron is made by two or threescalar quarks. ★ Statistics are different from that of ordinary hadrons

  8. Chimera hadron Chimera hadron is made by quarksandscalar quarks. “chimera hadron” is new terminology. Chimera hadron chimera meson (Fermion) chimera baryon (Boson) chimera baryon (Fermion) : quark :anti-quark : scalar quark :anti scalar-quark We calculate the masses of scalar-quark hadronsandchimera hadrons in quenched lattice QCD.

  9. 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

  10. ：space coordinate ：link variable ：hopping parameter ：mass of scalar quark Formalism ― discretization (Euclid space) ― Quark sector Wilson quark action: Scalar-quark sector Gauge invariant

  11. Ψ: quark φ: scalar quark Summary of scalar and chimera hadrons For the study of scalar-quark system, we calculate the masses of following scalar hadrons and chimera hadrons: Scalar-quark hadrons Scalar ・scalar-quark meson： Scalar ・scalar-quark baryon： Chimera hadrons Spinor ・chimera meson： Spinor ・chimera baryon： Scalar

  12. ⇒ 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 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)

  13. 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)

  14. Scalar-quark meson φ†φ Mass generation of scalar quark by gluon Important result： At bare scalar-quark massmsq～0, scalar-quark meson massM～3.0GeV. ⇒dynamically generated mass of scalar quark Msq is1.5GeV!! Compared with constituent quark mass (～300MeV), this mass generation is very large. M(GeV) (scalar-quark meson mass) 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) Large mass generation by strong interaction (non chiral origin) occurs in the scalar-quark system!

  15. 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 massmsq～0, scalar-quark baryon mass M～4.8GeV. ⇒dynamically generated mass of scalar quark Msq is1.5GeV. Large mass generation of scalar quark is also seen

  16. Chimera meson φ†Ψ M(GeV) (chimera meson mass) Note: Ψ emerges in the following hadrons Ψ： quark φ: scalar quark 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 massmsq～0 and bare quark mass mq～0, chimera meson mass M～1.9GeV. Msq + Mq ～ Mis formed. (1.5 + 0.4 = 1.9) dynamically generated mass of scalar quark Msq～1.5GeV constituent quark mass Mq～400MeV

  17. 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 massmsq～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

  18. 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 massmsq～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

  19. ⇒ Similar mq-dependence between and is observed. ★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 and

  20. V(r) Due to the large constituent mass of scalar-quarkφ, the two particles (φφ) areclose under Coulomb interaction. Similarity of the system between and r Energy level of φφ Interpretation of the similarity between φ†Ψ and φφΨ Chimera meson Chimera baryon Ψ： quark φ: scalar quark wave functions Chimera meson Chimera baryon Scalar quark φ is very heavy. So, the wave-function of light quark (Ψ) distributes around the scalar-quark φ.

  21. 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)

  22. 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 Generationcan be explained by Dressed Gluon Effect. Similarity between and systems emerges due to the large mass of scalar quark. Dressed Gluon colored-scalar msq～0 Msq≧ 1GeV

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