1. p, KK , BB from Lattice QCD Martin Savage Univ. of Washington
Lattice 2008, July 2008

2. Beane (UNH) Orginos (W+M) Luu (LLNL) Parreno (Barcelona) Detmold (UW)
+ Invisible Collaborators : Chroma :
Robert Edwards and JLab Group
Parreno (Barcelona)
Detmold (UW)
Lattice 2008, July 2008
Walker-Loud (UMD)
Torok (UNH)
me (UW)

3. Configurations and Propagators : NPLQCD (LHPC) Mixed-Action Calculations
Coarse MILC ensembles : b ~ fm
Staggered, Rooted, Isospin-symmetric, asqtad
lattice spacing contributes ~ a b2
203 x x 32 : Dirichlet Boundary
Mp ~ 290, 350, 490, 590 MeV
Fine MILC ensembles : b ~ fm
283 x 96 : Anti-periodic, Mp ~ 350, MeV
Coarse Domain Wall Propagators , Ls = 16
e.g. Mp ~ 290 MeV , t ~ 1hr on 32 dual-Xeon nodes
Pion mass tuned to lightest staggered pseudo-scalar mass
24 source points per lattice
Lattice 2008, July 2008

4. d (s) ? Maiani-Testa Theorem GNN (s)Euclidean GNN (s)Minkowski
Away from Kinematic Thresholds
GNN (s)Euclidean GNN (s)Minkowski
Lattice 2008, July 2008

5. Two-Particle Energy Levels (Luscher)
Below Inelastic Thresholds :
Measure on lattice E = 2 p + m
UV regulator
Lattice 2008, July 2008

6. Non-interacting particles
Luscher Relation
E < 0
E > 0 p c o t ( E ) = 1 L S Ã 2 !
Non-interacting particles k = 2 L n ( x ; y z ) V = ! a r : S ( ) 1
Lattice 2008, July 2008

7. Details Ensemble b ml b ms b mres (10 3) Number ~ Mp (MeV) 0.0081
2064f21b676m007m050
0.0081
0.081
1.604
1038 x 24
290
2064f21b676m010m050
0.0138
1.552
769 x 24
350
2064f21b679m020m050
0.0313
1.239
486 x 24
490
2064f21b681m030m050
0.0478
0.982
564 x 20
590
Lattice 2008, July 2008

8. Single Particle Spectra
Effective Mass
(l.u.) p
Time (l.u.)
Dirchlet Boundary
t= -10
Dirchlet Boundary
t=22
Lattice 2008, July 2008

9. Correlators C ( ) = X h t i u ° d ! A e Interpolating field ¼ x ; y ¡+ ( ) = X x ; y h t i u 5 d ! n A e E
Interpolating field
Large number of gauge configs
Lattice 2008, July 2008

10. Effective Scattering Length Plot
e.g. [ m a + ] ( t ) m 3 5 M e V
Lattice 2008, July 2008

11. pp Results Q u a n t i y m = : 7 1 2 3 F R g e 8 ¡ 9 ( . ) 4 5 f 6 ¢ E: 7 1 2 3 F R g e 8 9 ( . ) 4 5 f 6 E I b d r s j p Q u a n t i y m l = : 7 1 2 3 I . ( ) 5 4 6 8 b ! 9
Lattice 2008, July 2008

12. a p+ p+ (Beane et al, arXiv:0706.3026) + O ( m ¯ n i t e , c a l u b sà = 1 r a
(Beane et al, arXiv: ) E = a
( Nuclear Physics
Sign Convention ) m a I = 2 8 f ( 1 + 6
" 3 l o g ) #
Lattice 2008, July 2008 + O ( m 4 n i t e , c a l u b s p g )

13. Lattice (mp / fp ) is useful !
Two-flavor mixed-action
Chen, O’Connell, Walker-Loud,
van de Water m a I = 2 u 8 f ( 1 + 4 )
" l n ~ j à ! ` # 6 P Q :
Meson Spectrum
-- Calculable m a I = 2 8 f ( 1 + 4 ) 3 l n ~ j u 6
Lattice 2008, July 2008

14. p+ p+ (Beane et al, arXiv:0706.3026) m a ¡ : 4 3 § I = 2 ¼: 4 3
Lattice 2008, July 2008

15. e.g. Kaon Mass G ( t ) = A e l o g µ + 1 ¶ ¡ M
Fully-Dynamical, Domain-Wall on Staggered, Mp ~ 350 MeV
Lattice 2008, July 2008

16. (2007)
K+ K+
(Beane et al, arXiv: )
Lattice 2008, July 2008

17. BB Potentials – well-defined !!
Warm-up ----Quenched : b = 0.1 fm B B B B B - m e s o n h a I = 1 2 ; l
( Setting up to do fully-dynamical Calc. at NERSC)
Lattice 2008, July 2008

18. Periodic Boundary Conditions and Images
Lattice 2008, July 2008

19. B-meson B-meson Potentialsg = : 6 9 3
Lattice 2008, July 2008

20. Conclusions
Pion-pion scattering calculated at 1% level with Mixed-Action Lattice QCD and cPT.
Kaon-Kaon scattering calculated
Both are consistent with tree-level at large quark masses !!
Quenched B- meson-B-meson potentials calculated
Lattice 2008, July 2008