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Baryon-Baryon Interactions From Lattice QCD

Baryon-Baryon Interactions From Lattice QCD. K p. Martin Savage University of Washington. (Hyperons 2006, Mainz, Germany). e ( M Z ). g ( M Z ). M u. M d. M s. L QCD. L QCD. L QCD. L QCD. ,. ,. ,. ,. A Grand Challenge for Q C D and Nuclear Physics.

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Baryon-Baryon Interactions From Lattice QCD

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  1. Baryon-Baryon Interactions From Lattice QCD K p Martin Savage University of Washington (Hyperons 2006, Mainz, Germany)

  2. e ( MZ ) g ( MZ ) Mu Md Ms LQCD LQCD LQCD LQCD , , , , A Grand Challenge for QCD and Nuclear Physics How do the properties and interactions of nuclei depend upon the fundamental parameters of nature ? Fundamental physics and intellectual curiosity Fine-tunings

  3. QCD Lagrangian Lattice QCD Exact methods A≤12GFMC, NCSM, Lattice EFT N, 2N , 3N, 4N, … Effective Interactions A Shell Model, Coupled Cluster, …A<100 EFT and RG Density Functional Theory ?? Lattice EFT A>100 Low-Momentum Interactions For Nuclei The Strategy : QCD to Nuclei ( HYP 2006 )

  4. Chiral Symmetry and the 2N, 3N and 4N Interactions Low energy EFT of QCD Quark mass dependence Softer interaction Counterterms !!!!

  5. gA from Lattice QCD (LHPC) Mixed Action: DWF on Staggered Lattices SciDAC JLab Lattice Chroma (R. Edwards, B. Joo) cPT : V Mq a

  6. Strong Isospin Breaking from Isospin Symmetric Lattices • Neutron-Proton Mass Difference : • Quark mass differences , md-mu • Electromagnetism • Partially-Quenched Lattice Calculations + Theory Mn - Mp= 2.26+-0.57+-0.42+-0.10 MeV expt = 2.05 +- 0.3 MeV Electromagnetism

  7. Maiani-Testa: End of the Innocence d (s) ? Away from Kinematic Thresholds One Hopes that GNN (s)Euclidean= GNN (s)Minkowski

  8. app from Lattice QCD (S. Beane, P. Bedaque, K. Orginos, mjs ; PRD73, 054503 (2006)) I=2 p p p p SciDAC Nf = 2+1 JLab Lattice Chroma (R. Edward, B. Joo) cPT : V Mq a Mixed-Action (Chen, O’Connel Van de Water, Walker-Loud) Nf = 2+0

  9. K+p+ Scattering Length (S.Beane, P.Bedaque, T.Luu, K.Orginos, E.Pallante, A.Parreno, mjs ; hep-lat/0607036)

  10. K p Scattering Lengths Lattice QCD + Chiral Symmetry

  11. NN Correlators = SCnExp[-En t] G C0Exp[-E0 t] n 3S1 -3D1 1S0 Fully-Dynamical QCD Domain-Wall Valence on rooted-Staggered Sea

  12. Two-Particle Energy Levels (Luscher) Measure on lattice Below Inelastic Thresholds : UV regulator

  13. NN Scattering: Chiral Extrapolation (S.R. Beane, P.F. Bedaque, K. Orginos, mjs ; PRL97, 012001 (2006)) a ~ 1/mp 1S0 : pp , pn , nn 3S1-3D1 : pn : deuteron

  14. S- n1S0 --- I=3/2, J=0, s=1 (S.Beane, P.Bedaque, T.Luu, K.Orginos, E.Pallante, A.Parreno, mjs ) Mp = 497 MeV PRELIMINARY PRELIMINARY a (t) Log[ G ] Fully-Dynamical QCD Domain-Wall Valence on rooted-Staggered Sea

  15. LL Interactions --- I=0, J=0, s=2 Mp = 590 MeV -ve Energy Shift ?

  16. Ql – Ql Potentials .. A toy for NN e.g. B-mesons Q Q Q Q Exchange Direct Light d.o.f : S=1/2 , I=1/2 (I,S) = (0,0) , (0,1) , (1,0) , (1,1) Mp ~ 420 MeV Mr ~ 700 MeV Quenched

  17. Quenched : a=0.10 fm, L=1.6 fm150 cfgs L L L L

  18. Tensor Force ?

  19. S , K S , K n n Summary and Outlook • Lattice QCD is an important part of the future of (Hyper-) Nuclear Physics • 1/ Reproduce what is known • 2/ Calculate quantities that are poorly known or not known at all! • Sn , Ln , LL • First motion toward rigorous QCD calculations (via EFT’s) of properties and interactions of nuclei. • Coherent effort between numerical and analytic investigations.

  20. NN on the Lattice: Unnatural Scattering Lengths (Beane, Bedaque, Parreno, mjs) ~E L2 ~E L2 2nd continuum 1st continuum • Mp = 350 MeV 2.5 fm lattices... • TODAY !! Deuteron 1st continuum

  21. 7.654 7.367 8Be + a 4.44 Mu Mu Mu Md Md Md LQCD LQCD LQCD LQCD LQCD LQCD 0 Ms Ms Ms 12C LQCD LQCD LQCD Energy Scales and QCD Energy levels are … LQCD f2 ( , , ) LQCD f1 ( , , ) LQCD f0 ( , , ) Mc , Mb , Mt ``in’’ LQCD + electroweak

  22. LL Interactions -ve Energy Shift ?

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