Post on 03-Feb-2016
description
Sasa Prelovsek Lattice 05 1
A lattice study of light scalar tetraquarks A lattice study of light scalar tetraquarks with I=0, 1/2, 1with I=0, 1/2, 1
Lattice 08, WilliamsburgLattice 08, Williamsburg
Sasa Prelovsek Sasa Prelovsek University of Ljubljana
sasa.prelovsek@ijs.si
Lattice data from collaboration with
Bern-Graz-Regensburg Coll. (BGR)
(Daniel Mohler, Christian Lang, Christof Gattringer)
Sasa Prelovsek Lattice 05 2
OutlineOutline
motivation challenges present simulation and its results previous lattice simulations
Sasa Prelovsek Lattice 05 3
Puzzle of light scalar mesons:Puzzle of light scalar mesons:
2/11 II mm
2/11 II mm
2/11 II mm
[Jaffe, Maiani, t’Hooft, .....]
?
?or qqqqqq
Interpolators used: Interpolators used: diquark anti-diquarkfcfc
qqqq 3,33,3 ][][
2/11 II mm
0++ nonet with inverted spectrum
][][ 55 cTbc
Tbabca dCssCdds
I=1 I=0 I=1/2
0PCJ
I=1
I=1/2
Sasa Prelovsek Lattice 05 4
Challenge of the simulation:Challenge of the simulation:to distinguish one-particle (tetraquark) state and scattering states in C(t)
0
0
IC
p
I flavor of source/sink scattering states
0 udud
1/2 udds K
usds K K,
,..2,1,0
2
nL
nk
Sasa Prelovsek Lattice 05 5
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
1
1)(,)(:2/1
4
7)(,)(2:0
Lw
LfLdELdEmmEI
LfLdELdEmEI
treeK
tree
property of (one-particle) tetraquark:
)( 0LOw
),(1
),()2(
)( 33
3
tkfL
tkfkd
tCk
Mathur et al.
Kentucky (2006)
k
Sasa Prelovsek Lattice 05 6
Lattice simulations of tetraquarksLattice simulations of tetraquarksPrevious studies (briefly reviewed at the end): [BGR Coll, PRD 73 (2006)]
only I=0 channel (Jaffe studied also I=2) all consider a single correlator
Present study:
a whole flavour pattern: 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)
]][[
]][[
]][[
wnwn
wwww
nnnn
qqqq
qqqq
qqqq
tEn
tn
nnn
newt
ntvttvtC
)(
,..1,0,)()()()(
anti-diquark diquark
variational method
Sasa Prelovsek Lattice 05 7
use quenched approximation:
discard single and double annihilation contractions
There is a good excuse to use these two approximations as we are interested in state with 4 valence quarks: these two
approximations discard
Chirally Improved Fermins [BGR Coll.]
a=0.148 fm, V=163x32, 123x24
ms with physical mass; mu,d correspond to mpi= 340-570 MeV
As in all previous studies we:
SimulationSimulation
.vacqqqqqq
Sasa Prelovsek Lattice 05 8
E0 close to shifted 2m
E1,2>2 GeV: to heavy correspond to
f0(980)
meff of ground state not flat
does not have its own eigenvalue
tower of (k)(-k) present
in the ground state eigenvalue
Results for I=0Results for I=0
)](1[ tEEnn eOew n
Lnkkk
2)()(
324
72
Lfm
)](1[ tEEnn eOew n
??)980(,)600( 0f
Sasa Prelovsek Lattice 05 9
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!
Sasa Prelovsek Lattice 05 10
Results for I=0: Results for I=0: ground stateground state
parameters of fit: mpi, w
0)(22 ELdEmm treefitted
we can not exclude weakly coupling lighter state at large t
scattering
particle-one
: weightsspectral
3
0
/1
)(
Lw
LOw
k
),(1
),()2(
)( 33
3
tkfL
tkfkd
tCk
Sasa Prelovsek Lattice 05 11
Results for I=1/2 Results for I=1/2 similar conclusions as in I=0 channelsimilar conclusions as in I=0 channel
parameters of fit: mpi, w
LnkkkK
2)()(
Sasa Prelovsek Lattice 05 12
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
)()(
2)()(
kk
LnkkkK
ss
Sasa Prelovsek Lattice 05 13
Summary of our results for I=0,1/2,1Summary of our results for I=0,1/2,1
?
ss
ssdudssu
KK
dssudssu
)()(
)()(
Sasa Prelovsek Lattice 05 14
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
slight fall of meff at large times: we can not completely exclude possibility of very light weakly coupling tetraquark;
requires further study with larger time extent and larger operator basis
there may still exist possibility for tetraquarks at mpi<340 MeV (Kentucky group found I=0 tetraquark only for mpi<300 MeV)
Sasa Prelovsek Lattice 05 15
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
Sasa Prelovsek Lattice 05 16
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,
Sasa Prelovsek Lattice 05 17
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(
Sasa Prelovsek Lattice 05 18
Concusion and outlookConcusion and outlook I did not find indication for tetraquarks in I=0, ½, 1
channels at mpi>300 MeV. There are still hope to find tetraquark on the lattice !!
Prompts for tetraquark search with dynamical simulation, light quark masses, preferably on various volumes and using variational method !!
the Kentucky group fond indication that
is tetraqurk at mpi<300 MeV
our ground state in I=1 channel seems to be
slightly below the scattering state (at lightest quark mass)