Searching for light scalar tetraquarks on the lattice

Sasa Prelovsek Bled 2008 1

Searching for light scalar tetraquarks Searching for light scalar tetraquarks on the latticeon the lattice

Bled, september 2008Bled, september 2008

Sasa Prelovsek Sasa Prelovsek University of Ljubljana

[email protected]

Lattice data from collaboration with

Bern-Graz-Regensburg Coll. (BGR)

(Daniel Mohler, Christian Lang, Christof Gattringer)


OutlineOutline

motivation challenges present simulation and its results previous lattice simulations


Puzzle of light scalar mesons:Puzzle of light scalar mesons:?or qqqqqq

2/11 II mm2/11 II mm 2/11 II mm

Model independent determination of poles from exp:

sigma: Leutwyler & Caprini 2006

kappa: Descotes-Genon & Moussallam 2006


Tetraquark with diquark anti-diquark structureTetraquark with diquark anti-diquark structure The most titly bound diquark is SCALAR (“GOOD”) diquark

acTbc

Tbabca suCddCuud as transforms][][ 55

acTbc

Tbabca dsCdsCuus as transforms][][ 55

acTbc

Tbabca udCssCdds as transforms][][ 55

Jaffe 1977

Jaffe & Wilczek PRL 2003

Jaffe, “Exotica”, 2004

SCALAR (“GOOD”) anti-diquark :

aTcb

Tcbabca

aTcb

Tcbabca

aTcb

Tcbabca

udCssCdsd

duCssCusu

suCddCudu

as transforms

as transforms

as transforms

][][

][][

][][

55

55

55

nonet of SCALAR and color singlet states:

)1(]][[

)2/1(]][[

)0(]][[

Iudsdus

Iussdud

Issduud

as transforms

as transforms

as transforms

8133

133

][][ 3,33,3

x

x

qqqqfcfc

:flavor

:color


Arguments in favor of tetraquark interpretationArguments in favor of tetraquark interpretation L=1 quark-antiquark mesons expected to be above 1GeV:

scalar mesons, axial mesons, tensor mesons

observed m(I=1)>m(I=1/2) for states below and above

1 GeV not possible to explain with pure quark-antiquark states.

This ordering is natural in tetraquark picture.

- states below 1 GeV could be “pure” tetraquarks

- states above 1 GeV could be lin. combinations of (mixing via t’Hooft vertex): t’Hooft, Maiani, Polosa, Isidori, Riquer 2008

a0(980) strongly couples to KK:

qqqqqq and

rearrang.quark

suppressed Zweig

KK]sd[us][

KKud


Related observations in favor of tetraquarks:Related observations in favor of tetraquarks:

observed observed X,Y,ZX,Y,Z states with charm quarks states with charm quarks

SuccuuccuX

SdccddccdX

PsccsY

SdccudccuJZ

SSSS

SSSS

SS

SSSS

1][][][][:)3875(

1][][][][:)3872(

][][:)4260(

2,][][][][:/)4430(

0110

0110

00

0110

Experiment: Belle, BaBar, BES, Cleo ....

Possible interpreations: tetraquarks [Maiani, Polosa, ...]


- discard disconnected diagrams

- quenched approximation (we needed two different volumes and different shapes of interpolators)

above two approximations (used in all previous tetraquark simulations)

allow definite quark assignment, no mixing

Present simulation: Present simulation: searching tetraquarks below 1GeV searching tetraquarks below 1GeV a0,f0)a0,f0)

x

xpi uddutxuddue

)0,0](][[),](][[

Calculation of the correlator on the lattice: Calculation of the correlator on the lattice: a=0.15 fm, V=16a=0.15 fm, V=1633 32 , 12 32 , 1233 24 24

.vacqqqqqq


Present simulation:Present simulation:

- Chirally Improved quarks (BGR Coll.) : ms: physical value

mu,d : mp= 340, 470, 570 MeV

- we study I=0,1/2,1; all previous simulations only I=0


to distinguish one-particle (tetraquark) state and scattering states in C(t)

I flavor of source/sink scattering states

0 [ud][ud] sigma

1/2 [ud][ds] kappa K

us][ds] a0 K K,

0

0

IC

p

0 t

,..2,1,0

2

nL

nk

Challenge is analysis of correlator:Challenge is analysis of correlator:

tE

n nn

tE nn ewuddunenudduuddutuddutC ]][[]][[)0](][[)](][[)(

222

,2

km

mE


we distinguish one-particle and scattering states by considering:

En

volume dependence of wn

How to distinguish tetraquark from scattering?How to distinguish tetraquark from scattering?

tEtE ewewtC 1010)(

properties of scattering:

3

32

32

222

221

1

1)(,)(:2/1

4

7)(,)(2:0

Lw

LfLdELdEmmEI

LfLdELdEmEI

kmkmE

treeK

tree

PP

property of (one-particle) tetraquark:

)( 0LOw


How to extract several states ?How to extract several states ?

Ground state: straight forward!

Excited states: challenge! - fitting two exponentials is VERY unstable; fitting more is impossible

- All previous tetraquark simulations calculated only a single correlator

tmeff ewtCm

tC

tCLogtm 0

00 )()1(

)()(

if

tEtE ewewtC 10

10)(


Extracting several states:Extracting several states: variational method variational methodIn each flavour channel I=0, 1/2, 1I=0, 1/2, 1

3x3 correlation matrix3x3 correlation matrix evaluated:

3 different smearings at source and the sink:

spatially symmetric Jacobi smearing on quarks: narrow (n) & wide (w)

]][[

]][[

]][[

3

2

1

wnwn

wwww

nnnn

qqqqO

qqqqO

qqqqO

,..1,0)()()()( ntvttvtC nnn

ii

in

tEn

tEtEnn OvneweOew nn )](1[


Results for I=0Results for I=0

)](1[ tEEnn eOew n

Lnkkkuddu

2)()(:]][[

??)980(,)600( 0f

tmeff ewtm

t

tLogtm 0

00 )()1(

)()(

if


Results for I=0: ground stateResults for I=0: ground state

if all tree sources behave close to point-like:

then three eigenvalues of 3x3 matrix are:

the whole tower of scattering states comes in a single eigenvalue!


I=0 ground state as tower of I=0 ground state as tower of


Results for I=0: Results for I=0: ground stateground state

scattering

particle-one

: weightsspectral

3

0

/1

)(

Lw

LOw

kL

dk

tkfL

tkfkd

tC

i

k

2

),(1

),()2(

)( 33

3


Results for I=1/2 Results for I=1/2 similar conclusions similar conclusions

as in I=0 channelas in I=0 channel

)800(

2)()(:]][[

L

nkkkKdsdu


Results for I=1 Results for I=1 analysis of ground state is more complicated:

two towers of scattering states KK, pi etass:

conventional fit of mass at large t

)980(0

)()(

2)()(:]][[

a

kk

LnkkkKdssu

ss


Summary of our results for I=0,1/2,1Summary of our results for I=0,1/2,1


Summary of our results for I=0,1/2,1Summary of our results for I=0,1/2,1 excited states:

to heavy to correspond to light tetraquark candidates:

I was not looking for interpretation of these states

(they may be also some excited scattering states) ground state:

effective mass and volume dependence of spectral weights

roughly consistent with tower of scattering states

we find no evidence for light tetraquark at mpi=340-570 MeV


Still hopes for finding tetraquarks!Still hopes for finding tetraquarks! There may still exist possibility for finding tetraquarks on lattice: at mpi<340 MeV Kentucky group found I=0 tetraquark only for mpi<300 MeV

with larger/different operator basis

My current simulations:My current simulations:

- mpi=180-400 MeV, overlap fermions, quenched, I=1/2,1,

variational method, with Kentucky group

- mpi~300 MeV, domain wall fermions, dynamical u,d,s quarks

variational method, using RBC/UKQCD propagators


Intermezzo: puzzling mIntermezzo: puzzling meffeff

Effect of finite T on PP state:


Previous tetraquark simulationsPrevious tetraquark simulations all quenched, all discard annihilation contr. study only I=0 channel (Jaffe studies also exotic I=2 channel)

all consider single correlator

Alford & Jaffe, 2000 interpolator one relatively heavy quark mass different L only ground state exploredconclusion: shift does not completely agree with FULL (!) scattering prediction: possible indication of tetraquark

I=0


Previous tetraquark simulations:Previous tetraquark simulations: Suganuma, Tsumura, Ishii, Okiharu , 2007 0707.3309 [hep-lat]

• diquark antidiquark interpolator

• conventional and hybrid boundary conditions

• only ground state studied

• conclusion: ground state corresponds to scattering

physdu

phys mmm 2,


N. Mathur, K.F. Liu et al. (Kentucky, XQCD Collaboration) [hep-ph/0607110, PRD, 2006] interpolator range of very small quark masses (overlap fermions) two volumes three lowest states explored: sequential Bayes method conclusion: indication for tetraquark around sigma mass for mpi<300 MeV

Previous tetraquark simulations:Previous tetraquark simulations:

)0()0(

?)600(

)1()1(

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Searching for light scalar tetraquarks on the lattice

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