1. A lattice study of light scalar tetraquarks with I=0, 1/2, 1
Lattice 08, Williamsburg
Sasa Prelovsek
University of Ljubljana
Lattice data from collaboration with
Bern-Graz-Regensburg Coll. (BGR)
(Daniel Mohler, Christian Lang, Christof Gattringer)
Sasa Prelovsek
Lattice 05

2. Outline motivation challenges present simulation and its results
previous lattice simulations
Sasa Prelovsek
Lattice 05

3. Puzzle of light scalar mesons:?
I=1/2
I=1
I=1 I=0 I=1/2
0++ nonet with inverted spectrum
Interpolators used: diquark anti-diquark
[Jaffe, Maiani, t’Hooft, .....]
Sasa Prelovsek
Lattice 05

4. Challenge of the simulation:
to distinguish one-particle (tetraquark) state and scattering states in C(t)
I flavor of source/sink scattering states
udud p p
1/ udds K p
usds K K, p h
Sasa Prelovsek
Lattice 05

5. How to distinguish tetraquark from scattering?
we distinguish one-particle and scattering states by considering: En
volume dependence of wn
properties of scattering: k
Mathur et al.
Kentucky (2006)
property of (one-particle) tetraquark:
Sasa Prelovsek
Lattice 05

6. Lattice simulations of tetraquarks
Previous 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, 1
3x3 correlation matrix evaluated:
3 different smearings at source and the sink:
spatially symmetric Jacobi smearing on quarks: narrow (n) & wide (w)
anti-diquark diquark
variational method
Sasa Prelovsek
Lattice 05

7. Simulation Chirally Improved Fermins [BGR Coll.]
a=0.148 fm, V=163x32, 123x24
ms with physical mass; mu,d correspond to mpi= MeV
As in all previous studies we:
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
Sasa Prelovsek
Lattice 05

8. Results for I=0 E0 close to shifted 2mp
E1,2>2 GeV: to heavy correspond to
s(600), f0(980)
meff of ground state not flat
p(1)p(-1) does not have its own eigenvalue
tower of p(k)p(-k) present
in the ground state eigenvalue
Sasa Prelovsek
Lattice 05

9. Results 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: ground statek
parameters of fit: mpi, w
we can not exclude weakly coupling lighter state at large t
Sasa Prelovsek
Lattice 05

11. Results for I=1/2 similar conclusions as in I=0 channel
parameters of fit: mpi, w
Sasa Prelovsek
Lattice 05

12. 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
Sasa Prelovsek
Lattice 05

13. Summary of our results for I=0,1/2,1?
Sasa Prelovsek
Lattice 05

14. Summary 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= 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 simulations
all quenched, all discard annihilation contr.
study only I=0 channel (Jaffe studies also exotic I=2 channel)
all consider single correlator
I=0
Alford & Jaffe, 2000
pp interpolator
one relatively heavy quark mass
different L
only ground state explored
conclusion: shift does not completely agree with FULL (!) scattering prediction: possible indication of tetraquark
Sasa Prelovsek
Lattice 05

16. Previous tetraquark simulations:
Suganuma, Tsumura, Ishii, Okiharu , 2007
[hep-lat]
diquark antidiquark interpolator
conventional and hybrid boundary conditions
only ground state studied
conclusion: ground state corresponds to scattering
Sasa Prelovsek
Lattice 05

17. Previous tetraquark simulations:
N. Mathur, K.F. Liu et al. (Kentucky, XQCD Collaboration)
[hep-ph/ , PRD, 2006]
pp 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
Sasa Prelovsek
Lattice 05

18. Concusion and outlook the Kentucky group fond indication that
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
s(600) 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)
Sasa Prelovsek
Lattice 05