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Baryon-Baryon Interactions From Lattice QCD

Explore the complexities of baryon-baryon interactions using lattice QCD calculations. Investigate properties and behaviors of nucleons based on fundamental physics parameters. Analyze the effects of quark mass variations and electromagnetic interactions on nuclear structures. Collaborate between numerical simulations and analytical studies to unravel the mysteries of nuclear forces. Address gaps in existing knowledge and aim to predict unknown quantities crucial for nuclear physics advancements.

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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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