Scalar Mesons in Lattice QCD Kobayashi Maskawa Institute - PowerPoint PPT Presentation

Scalar Mesons in Lattice QCD Kobayashi Maskawa Institute Department of Physics, Nagoya University Chiho NONAKA for the SCALAR Collaboration T.Kunihiro(Kyoto U.), S.Muroya(Matsumoto U.), A.Nakamura(Far Eastern Federal U.), M.Sekiguchi(Kokushikan U.), H.Wada(Kokushikan U.), M.Wakayama (Far Eastern Federal U.) May 19, 2017@Strangeness and charm in hadrons and dense matter

What is the s ? • Re identification of s in 1996 The pole of the s in S-wave is extracted from re-analyses of pp scattering. Igi and Hikasa, PRD59(1999)034005 I. Caprini, G. Colangelo and H. Leutwyler, Phys. Rev. Lett. 96 (2006) 132001 C. NONAKA (SCALAR Collaboration)

I=J=0 pp pp Phase Shift r exchange only degenerate s and r exchanges Chiral low-energy expansion N/D method: unitarity, analyticity, approximate crossing symmetry C. NONAKA (SCALAR Collaboration)

What is the s ? • Re identification of s in 1996 The pole of the s in S-wave extracted from re-analyses of pp scattering. Igi and Hikasa, PRD59(1999)034005 I. Caprini, G. Colangelo and H. Leutwyler, Phys. Rev. Lett. 96 (2006) 132001 non-relativistic Light sigma meson consistent quark model m σ ∼ m ρ P-wave GeV m σ ∼ 1 . 2 − 1 . 6 C. NONAKA (SCALAR Collaboration)

What is the s ? Lattice QCD • Re identification of s in 1996 The pole of the s in S-wave extracted from re-analyses of pp scattering. Igi and Hikasa, PRD59(1999)034005 I. Caprini, G. Colangelo and H. Leutwyler, Phys. Rev. Lett. 96 (2006) 132001 non-relativistic Light sigma meson consistent quark model m σ ∼ m ρ P-wave GeV m σ ∼ 1 . 2 − 1 . 6 C. NONAKA (SCALAR Collaboration)

1996 2002 2016 C. NONAKA (SCALAR Collaboration)

What is the s ? q meson? q ¯ qq ¯ q ¯ q σ tetra quark? mixing? p - p molecule? resonances? glueballs mixing ? G C. NONAKA (SCALAR Collaboration)

Scalar Mesons in Lattice QCD as q ¯ q meson σ quench screening mass 1987 DeTar and Kogut, PRD36(1987)2828 ≈ q 2 ¯ q 2 2000 Alford and Jaffe, NPB578(2000)367 mixing with glueball Lee and Weingarten, PRD61(2000)014015 dynamical 2001 +glueball McNeile and Michael, PRD63(2001)114503 m σ < m π ?? 2002 disconnected diagram SCALAR ,NPProc.Suppl.106(2002)272 domain wall fermions, propagators in quench 2003 Prelovsek and Orginos, NPProc.Suppl.119(2003)822 2004 disconnected diagram SCALAR,PRD70 (2004)034504 C. NONAKA (SCALAR Collaboration)

What is the s ? q meson? q ¯ qq ¯ q ¯ q σ tetra quark? mixing? p - p molecule? resonances? glueballs mixing ? G C. NONAKA (SCALAR Collaboration)

Sigma Meson as Two Quark State SCALAR, Phys. Rev. D70 (2004)034504 • Operator (two flavor) Quark model color Dirac • Propagator �� Tr W − 1 ( x, y ) W − 1 ( y, x ) � G ( y, x ) = connected + 2 � ( σ ( y ) � � σ ( y ) � )( σ ( x ) � � σ ( x ) � ) � disconnected Connected diagram Disconnected diagram q - Vacuum contribution q C. NONAKA (SCALAR Collaboration)

Simulation Setup SCALAR, Phys. Rev. D70 (2004)034504 • Full QCD, Hybrid Monte Carlo Plaquette gauge action, Wilson Fermion • β = 4 . 8 κ = 0 . 1846 , 0 . 1874 , 0 . 1891 CP-PACS, Phys. Rev. D60 (1999)114508 • Lattice size , lattice spacing 0.207(9) fm 8 3 × 16 • Disconnected diagrams Z 2 noise method (number of noise: 1000) CP-PACS our results C. NONAKA (SCALAR Collaboration)

Disconnected Diagrams • Propagators SCALAR, Phys. Rev. D70 (2004)034504 disconnected • Due to the existence of disconnected diagram, m s becomes smaller. connected C. NONAKA (SCALAR Collaboration)

Light Scalar Meson SCALAR, Phys. Rev. D70 (2004)034504 • Propagators p s m σ ∼ m ρ r C. NONAKA (SCALAR Collaboration)

Light Scalar Meson SCALAR,Phys. Rev. D70 (2004)034504 • Only connected diagrams m σ > 2 m ρ 2 m π a σ • Disconnected diagrams ρ m σ ∼ m ρ ρ • At chiral limit m 2 π m σ < m ρ σ C. NONAKA (SCALAR Collaboration)

Sigma Meson Sigma meson as two quark state SCALAR, Phys. Rev. D70 (2004)034504 For light sigma meson, the disconnected diagram is important. If the glueball states Disconnected diagram were not heavy... mixing with glueballs and 4 quark state.... - Vacuum contribution qq − ¯ q ¯ q C. NONAKA (SCALAR Collaboration)

Low Lying Scalar Mesons • Light scalar Mesons s meson , I =0, J PC = 0 ++ : light s , Quark model m σ ∼ m ρ – Nuclear force, important for low energy hadron physics – re-identification of the s : “f 0 (400-1200) ” in PDG1996 existence of s pole: reanalysis of p - p scattering phase shift Igi and Hikasa, PRD59(1999)034005 I. Caprini, G. Colangelo and H. Leutwyler, Phys. Rev. Lett. 96 (2006) 132001 k meson, I =1/2, J PC = 0 ++ : 800 MeV m κ ∼ C. NONAKA (SCALAR Collaboration)

Kappa Meson • flavor non-singlet, strangeness • experiments – E791 collaboration Phys. Rev. Lett.89(2002)121801 m: G : – BES Collaboration BES, Phys. Lett. B633(2006)681 m: G : BES, Phys. Lett. B633(2006)681 k C. NONAKA (SCALAR Collaboration)

Low Lying Scalar Mesons • Light scalar Mesons s meson , I =0, J PC = 0 ++ : light s , Quark model m σ ∼ m ρ – Nuclear force, important for low energy hadron physics – re-identification of the s : “f 0 (400-1200) ” in PDG1996 existence of s pole: reanalysis of p - p scattering phase shift Igi and Hikasa, PRD59(1999)034005 I. Caprini, G. Colangelo and H. Leutwyler, Phys. Rev. Lett. 96 (2006) 132001 k meson, I =1/2, J PC = 0 ++ : 800 MeV m κ ∼ • Nonet scalar states C. NONAKA (SCALAR Collaboration)

Simulation Setup PLB652 (2007)250 • Quenched QCD calculation Plaquette gauge action, Wilson fermions • β = 5 . 9 Chiral limit m 2 κ u/d = 0 . 1589 , 0 . 1583 , 0 . 1574 π κ s = 0 . 1566 , 0 . 1557 CP-PACS, Phys. Rev. D67 (2003)034503 Heavy quark mass: m p /m r =0.467~ 0.686 • Lattice spacing a=0.1020(8) fm from m r in the chiral limit • Lattice size 20 3 × 24 • 80 configurations • Interpolator: C. NONAKA (SCALAR Collaboration)

Effective masses of k and K * PLB652 (2007)250 • k crit =0.1598: from m 2 p k K * k ud dependence is small. K*: error bar is small. k : error bar is large. C. NONAKA (SCALAR Collaboration)

Mass of Kappa Meson PLB652 (2007)250 physical value of k s 1/ k s =6.396(13) from m f /m K* m k /m K* 1/ k s =6.3452(80) from m K /m K* m f /m K* m K /m K* m k ~ 1.7 GeV Larger than M exp ~800 MeV 1/ k s C. NONAKA (SCALAR Collaboration)

Scalar Mesons as Two Quarks • Sigma mesons Other than two – Disconnected diagram is important quark states may for light sigma meson be important. • k mesons – Disconnected diagram does not exist. Four quark state? Glueball? – Heavier mass in quenched QCD Their mixing? – Dynamical quark may be important. C. NONAKA (SCALAR Collaboration)

Phenomenology Jaffe, NPB578(2000)367 Alford and Jaffe, NPB578(2000)367 qqqq nonet qq nonet Inverted mass spectrum ex. vector channel k ? s ? light s and k masses ? C. NONAKA (SCALAR Collaboration)

Scalar Mesons in Lattice QCD s : SCALAR, PRD70(2004)034504 2004 s , k , a 0 : 2006 UKQCD,PRD74(2006)114505 G UKQCD,PRD74(2006)014508 2007 k : SCALAR, PLB652(2007)250 s , k , a 0 : 2009 S.Prelovsek et al, PRD79(2009)014503 connected diagrams 2010 S.Prelovsek et al, PRD82(2010)094507 2012 k , a 0 : BGR,PRD85(2012)034508 k , a 0 : 2013 ETM,JHEP1304(2013)137 s : 2014 SCALAR, PRD91(2015)094508 connected + singly disconnected diagrams C. NONAKA (SCALAR Collaboration)

What is the s ? q meson? q ¯ qq ¯ q ¯ q σ tetra quark? mixing? p - p molecule? resonances? glueballs mixing ? G C. NONAKA (SCALAR Collaboration)

Molecule • Operator (two flavor) The lightest pseudoscalar mesons Jaffe, Phys.Rept.409(2005) 1 • Propagators Singly doubly connected diagrams disconnected diagram disconnected diagram C. NONAKA (SCALAR Collaboration)

Molecule • Operator (two flavor) The lightest pseudoscalar mesons Jaffe, Phys.Rept.409(2005) 1 • Propagators Large Nc limit PRD 88, 074506 (2013) Singly doubly connected diagrams disconnected diagram disconnected diagram C. NONAKA (SCALAR Collaboration)

Tetra • Operator (two flavor) The lightest diquarks Jaffe, Phys.Rept.409(2005) 1 • Propagators Singly doubly connected diagrams disconnected diagram disconnected diagram C. NONAKA (SCALAR Collaboration)

Tetra • Operator (two flavor) The lightest diquarks Jaffe, Phys.Rept.409(2005) 1 • Propagators Large Nc limit PRD 88, 074506 (2013) PRD 88, 074506 (2013) Singly doubly connected diagrams disconnected diagram disconnected diagram C. NONAKA (SCALAR Collaboration)

Simulation Setup SCALAR,PRD91(2015)094508 • 2 flavor full QCD: CP-PACS Phys. Rev. D 63, 034502 (2001) Hybrid Monte Carlo (HMC) with Iwasaki gauge action and the clover Wilson action Lattice size: 8 3 × 16 β = 1 . 7 C SW = 1 . 68 • Heavy quark masses, large statistics • Disconnected diagrams: Z 2 noise method with truncated eigenmode approach eigenvector : 12 noise: 120 X 16 κ c = 0 . 152(6) , a = 0 . 269(9) fm C. NONAKA (SCALAR Collaboration)

Caveat • “Molecule” contains mixing with tetra and two quark state • “Tetra” contains mixing with molecule and two quark state • Application of the variational method for the possible interpolators is needed. C. NONAKA (SCALAR Collaboration)