Lattice QCD and Nuclear Physics Martin Savage University of Washington Lattice 2005, Dublin, July 2005

Emergence of Nuclear Physics from QCD Consistent and rigorous pathway from QCD Lattice QCD EFT Many-Body Lattice QCD EFT Many-Body M q - explicit

Calculations where experiments are not possible Supernova Remnant ? neutron stars  - decay …  - decay … nn , K or black holes, or black holes, ….. kaon condensation ? …..

How does nature depend upon the fundamental constants? Quark mass dependence of element production Dependence upon 

Understand the fine-tunings of nature Deuteron Binding energy is ~2.2 MeV a(1s0) ~ -24 fm Infrared fixed-point of QCD Infrared fixed-point of QCD 3  12 C Short-range repulsion Intermediate-range attraction Long-range attraction (s-wave) NN Potential  - exchange  - exchange ??? N N N N NN NN  ~

NN-Scattering (s-wave) M q –dependence of nuclear properties – Little is known……..this is all !!! Quenched Data (Fukugita et al, 1995), Latt = 20 4 A Lattice Measurement at this m  would fix counterterms : D 2 1S01S0 3S13S1

Nuclear Physics with lattice QCD University of New Hampshire Lawrence Berkeley Laboratory College of William and Mary University of Groningen University of Barcelona University of Washington

Maiani-Testa: End of the Innocence  (s) ? G NN (s) Euclidean = G NN (s) Minkowski One Hoped that Away from Kinematic Thresholds at infinite volume

Two-Particle Energy Levels (Luscher) UV regulator Below Inelastic Thresholds :

Calc. in Pionless EFT :5 fm lattices or larger for M = 140 MeV Calc. in Pionless EFT :5 fm lattices or larger for M  = 140 MeV Need Pionful theory calc. for smaller lattices M = 350 MeV 2.5 fm lattices.... MILC lattices M  = 350 MeV 2.5 fm lattices.... MILC lattices NN on the Lattice ~E L 2 Deuteron 1st continuum 2nd continuum Don’t Need Huge Lattices !!!!

np d  NN NN NN  11 l1l1 MEC’s Asymmetric Lattice (William Detmold and MJS)

ElectroWeak Matrix Elements L X L/10 X L/10 X T lattice

Hyperon Weak Interactions S-waveP-wave Lattice surface term ( Orginos )

 Q  Q Potential

NPLQCD Current Resources : SciDAC JLab Clusters – 8% resources ~ 40 Gflop-yrs Chroma / QDP++ MILC staggered Lattices DWF Propagators of LHPC Approved Exploratory NN,  NN,  M N -  term, strong-isospin-breaking (PQ) M N -  term, strong-isospin-breaking (PQ)

 scattering LHPC’s DWF valence propagators on 20 3 X 64 MILC staggered sea M   and 290 MeV

Chiral-Extrapolation M  a 2 = (  PT for  by Bijnens, Colangelo, Gasser, Leutwyler, …)

 Prelim. Coupled Channels ? | a | < 1 fm

Conclusion Lattice QCD studies of Nuclei and Multi-Hadron Systems are an important part of the future of Nuclear Physics. Lattice QCD studies of Nuclei and Multi-Hadron Systems are an important part of the future of Nuclear Physics.

Topics that are or can or should be tackled today Nucleon Properties … (LHPC) M N,  N, g A,  , as functions of m q, a, V M N,  N, g A,  , as functions of m q, a, V The NN Systems …  (s), L A 1,..  (s), L A 1,.. Hyperon Properties and Systems… M ,  N ,  N  N,   .. M ,  N ,  N  N,   .. V(R) between Hadrons with one Q : DD (Michael, Cook+Fiebig,…) 