Sasa Prelovsek Scadron70, February 2008 1

Simulations of light scalar mesons Simulations of light scalar mesons on the lattice and related difficultieson the lattice and related difficulties

Scadron 70, IST Lisbon, Portugal (February 2008)Scadron 70, IST Lisbon, Portugal (February 2008)

Sasa PrelovsekSasa Prelovsek (sasa.prelovsek@ijs.si) University of Ljubljana and Jozef Stefan Institute

some of the results presented obtained in my collaboration with

RBC, MILC RBC, MILC and and BGR BGR lattice collaborationslattice collaborations(C. Dawson, K. Orginos, T. Izubuchi, A. Soni, C. Bernard, C. Detar, Z. Fu,

C. Lang, C. Gattringer, L. Glozman, D. Mohler, ..)

Sasa Prelovsek Scadron70, February 2008 2

a0: dynamical

quenched

formulations with various unphysical approx.

- tetraquark interpolators

One of the main difficulties to determine scalar masses:

bound states are accompanied by scattering states in lattice correlators

OutlineOutline

orsinterpolatqq

0

*0

,

,

f

K

Extracting scalar meson masses from lattice simulations:

Sasa Prelovsek Scadron70, February 2008 3

JJPP=0=0+ +

I=1I=1

a0a0

C(t)=

point-point correlator),(),( txutxdx

)0()0( du

udJJPP=0=0++ I=1I=1

t=0 t

mma0a0 from scalar correlator from scalar correlator

iiiiii EKKDCaBaAud ')0()0( *

00

Sasa Prelovsek Scadron70, February 2008 4

mma0a0 from scalar correlatorfrom scalar correlator

dunenuddutudtC tE

nn )0()()(

...,',,,, *00 KKaan JJPP=0=0+ + , I=1 :I=1 :

tmae 0tMMtE

ee )(

2222, pMpMMME

dominates if

0amMM nL

p 2

0p

Sasa Prelovsek Scadron70, February 2008 5

extracting hadron masses from extracting hadron masses from lattice correlatorlattice correlator

mte

Sasa Prelovsek Scadron70, February 2008 6

Lattice simulations of a0 Lattice simulations of a0 with u,d,s dynamical quarkswith u,d,s dynamical quarks

• dynamical staggered u,d,s quarksdynamical staggered u,d,s quarks [MILC]

u,d,s close to physical masses

MILC 2001[PRD64]

similar observation UKCD Irving et al.[Pos LAT05:027]

0a

0a ?

Resolving this puzzle:S.P. [PRD 73, 2006]:Prediction for

with Staggered ChPT Taste breaking effects of staggered fermions allow

at finite lattice spacingmE 2

Sasa Prelovsek Scadron70, February 2008 7

Simulation of a0 and f0 correlators with Simulation of a0 and f0 correlators with dynamical staggered u,d,s quarks dynamical staggered u,d,s quarks

C. Bernard, C. Detar, S.P., Z. Fu [PRD76]

Staggered ChPT describes I=0,1 point-point scalar correlators well (with no free parameters) Extracted

point-point scalar correlators

GeVm

GeVma

16.075.0

08.001.10

uncertain due to large unphysical scattering contribution

Staggered ChPT

Sasa Prelovsek Scadron70, February 2008 8

a0 with a0 with u,d u,d dynamical quarksdynamical quarks

3 flavor QCD: KK’

2 flavor QCD ’ ) ’

2 flavor QCD with m0=inf. : none

I=1t=0 t

Sasa Prelovsek Scadron70, February 2008 9

a0 with dynamical u,d : a0 with dynamical u,d : a0(980) or a0(1450) ?a0(980) or a0(1450) ?

group mma0 comment

SCALAR Coll, 2003

S.P. et al [RBC] 2004

1.58 +/- 0.34 GeV

scattering states accounted for; fit of point-point correlators at low t due to

noise; value high possibly due to excited state contribution

Hashimoto, Izubuchi [RBC]

2008, not published yet

1.111 +/- 0.081 GeV

variational method ;

scattering state seems slightly higher

UKQDC 2003 1.0 +/- 0.2 GeV variational method

UKQDC 2006 1.01 +/- 0.04 GeV

deduced from [m(b1)-m(a0)]lat and [m(b1)]exp; scattering state seems

slightly higher

BGR 2007 ~ 1 GeV variational method ;

scattering state seems slightly higher

m4.2~

Sasa Prelovsek Scadron70, February 2008 10

quenched a0: quenched a0: a0(980) or a0(1450) ?a0(980) or a0(1450) ?

tme 2

group mma0

Bardeen et al. 2001

1.34 +/- 0.09 GeV

BGR 2006, 2007 ~ 1.4 GeV

Mathur, Liu et al., 2006

1.42 +/- 0.13 GeV

u

d

scattering states:

S.P. et al [RBC] 2003

Quenched ChPT prediction Bardeen et al. [2001]

Sasa Prelovsek Scadron70, February 2008 11

scalar mesonsscalar mesons: : ?)1430(*0Kordsus ,

Important scattering state in all lattice formulations (even quenched)

Scattering state subtracted (to my knowledge)only in quenched simulation of K.F.Liu, N.Mathur et al. [hep-ph/0607110], PRD:

m=1.41 +/- 0.12 GeV

K

s

Sasa Prelovsek Scadron70, February 2008 12

scattering states vs. bound statesscattering states vs. bound states prediction for scattering state to point-point a0 correlator from corresponding ChPT:

volume dependence: scattering state:

resonant state: small volume dependence

various boundary conditions on quark fields variational method with a number of interpolators

3

)( 21

L

e tEE PP

Quenched: no sea quarks, Bardeen et al [2001]

Staggered: staggered sea and valence quarks, S.P. [2006]

Partially quenched: S.P. et al. [2004]

Mixed: staggered sea and chiral valence qcuarks; S.P. et al. [2006]

Twisted mass: Abdel-Rehim et al., ETM coll.

Sasa Prelovsek Scadron70, February 2008 13

I=0 scalar mesons I=0 scalar mesons disconnected quark contributions mixing with glueballs sizable dependence on lattice spacing

forstatescattering

),( 0f

mm commentSCALAR Coll,

2003 large scale simulation with dynamical u,d

m slightly bellow 2m

Wilson fermions

Lee, Weingarten 99

f0(1710) 74% glueball

mixing of various f0 , sigma and glue

quenched

McNeile, Michael, et al. [UKQCD]

2006

m~ 1 GeVfor lightest

isosinglet state

mixing of various f0 , sigma and glue

dynamical u,d, quarks

mm ~

.simulqq

Sasa Prelovsek Scadron70, February 2008 14

Tetraquark simulations of light scalars:Tetraquark simulations of light scalars:all quenchedall quenched

K.-F.Liu, N. Mathur et al. (Kentucky), hep-ph/0607110, PRD, 2006 - - small u,d quark masses (good chiral properties) - quenched - volume dependence of spectral weight to distinguish between resonance (W~L0) and scattering (W~1/L3):

fororinterpolat)()( 55 qqqq

Sasa Prelovsek Scadron70, February 2008 15

Tetraquark simulations of light scalarsTetraquark simulations of light scalars Alford & Jaffe, 2000

- exotic channel, I=2 of SU(2)flavor

- interpreted as repulsive scattering

relation for scattering at finite volume (Luscher 1986)

- non-exotic channel, I=0 of SU(2)- interpreted as repulsive scattering + possible tetraquark resonance

massesquarkheavyrelativelywithorinterpolat)()( 55 qqqq

Sasa Prelovsek Scadron70, February 2008 16

Tetraquark simulations of light scalarsTetraquark simulations of light scalars

Suganuma et al. , 2007

- quenched

- hybrid boundary coditions

- result: The lowest state found is scattering,

No indication of tetraquark found for

orinterpolatfcfc

qqqq 3,33,3 )()(

physdu

phys mmm 2,

Sasa Prelovsek Scadron70, February 2008 17

Recent reviews: Craig McNeile:

Lattice approach to light scalars, 0710.2470 [hep-lat]

Hard Hadron spectroscopy, Lattice 2007, 0710.0985 [hep-lat]

determining scalar meson spectra on the lattice is not a

simple problem final concusions not ready yet effect of the scattering states has to be disentangeled ! “vague” conclusions for the time beeing:

- a0a0: simulations with dynamical u,d seem to indicate that the lightest state that couples to is perhaps closer to a0(980) than to a0(1450)

- kappakappa: dynamical simulation which dissentangles K

stattering state missing

- sigmasigma:

two indications for light sigma, which take into account scattering:

* K.F. Liu et al., tetraquark, quenched: msigma~600 MeV

* SCALAR Coll, , dynamical: msigma~mrho

SummarySummary

qq

qq