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LatticeLattice QQCCDD and and Nuclear PhysicsNuclear Physics
Martin SavageUniversity of Washington
Lattice 2005, Dublin, July 2005
Emergence of Nuclear Physics Emergence of Nuclear Physics from from QQCCDD
Consistent and rigorous pathway from Consistent and rigorous pathway from QQCCDD
Lattice Lattice QQCCD D EFT Many-BodyEFT Many-Body
Mq - explicit
Calculations where experiments Calculations where experiments are not possibleare not possible
Supernova Remnant ? Supernova Remnant ? neutron starsneutron stars
- decay …- decay …
n n
, K , K
or black holes ,or black holes ,…….. kaon condensation ? ….... kaon condensation ? …..
How does nature depend upon the How does nature depend upon the fundamental constants?fundamental constants?
Quark mass dependence of element productionQuark mass dependence of element production
Dependence upon Dependence upon
Understand the fine-tunings of natureUnderstand the fine-tunings of nature
Deuteron Binding energy is ~2.2 MeVDeuteron Binding energy is ~2.2 MeVa(1s0) ~ -24 fma(1s0) ~ -24 fm Infrared fixed-point of Infrared fixed-point of QQCCDD
3 3 1212CC
Short-range repulsion
Intermediate-range attraction
Long-range attraction (s-wave)
NN Potential
- exchange
- exchange
???
N
N
N
N
N N
N N
~
NN-Scattering (s-wave)NN-Scattering (s-wave)
MMqq–dependence of nuclear properties – Little is –dependence of nuclear properties – Little is
known……..this is all !!!known……..this is all !!!
Quenched Data (Fukugita et al, 1995) , Latt = 204
A Lattice Measurement at this m would fix counterterms : D2
1S03S1
Nuclear Physics with lattice Nuclear Physics with lattice QQCCDD
University of New HampshireUniversity of New Hampshire
Lawrence Berkeley LaboratoryLawrence Berkeley Laboratory
College of William and MaryCollege of William and Mary
University of GroningenUniversity of Groningen
University of BarcelonaUniversity of Barcelona
University of WashingtonUniversity of Washington
Maiani-Testa: End of the InnocenceMaiani-Testa: End of the Innocence
(s) ?
GNN (s)Euclidean = GNN (s)Minkowski
One Hoped that Away from Kinematic Thresholds at infinite volume
Two-Particle Energy Levels Two-Particle Energy Levels (Luscher)(Luscher)
UV regulator
Below Inelastic Thresholds :
Calc. in Pionless EFT :5 fm lattices or larger for MCalc. in Pionless EFT :5 fm lattices or larger for M = 140 MeV = 140 MeV
Need Pionful theory calc. for smaller latticesNeed Pionful theory calc. for smaller lattices
MM = 350 MeV 2.5 fm lattices.... MILC lattices = 350 MeV 2.5 fm lattices.... MILC lattices
NN on the LatticeNN on the Lattice~E L2 ~E L2
Deuteron
1st continuum
1st continuum2nd continuum
Don’t Need Huge Lattices !!!!
np dnp d
N N
N N
N N
1
l1 MEC’s
Asymmetric Lattice
(William Detmold and MJS)
ElectroWeak Matrix ElementsElectroWeak Matrix Elements
L X L/10 X L/10 X T lattice
Hyperon Weak InteractionsHyperon Weak Interactions
S-wave P-wave
Lattice
surface term( Orginos )
QQ QQ Potential Potential
NPLQCDNPLQCD Current Resources : Current Resources : SciDACSciDAC
JLab Clusters JLab Clusters – 8% resources ~ 40 Gflop-yrs– 8% resources ~ 40 Gflop-yrs
Chroma / QDP++Chroma / QDP++MILC staggered LatticesMILC staggered LatticesDWF Propagators of LHPCDWF Propagators of LHPC
Approved Exploratory Approved Exploratory NN , NN , MMN N - - term , strong-isospin-breaking (PQ)term , strong-isospin-breaking (PQ)
scatteringscattering
LHPC’s DWF valence propagators on 20LHPC’s DWF valence propagators on 2033 X 64 MILC X 64 MILC staggered seastaggered sea
MMand 290 MeVand 290 MeV
Chiral-ExtrapolationChiral-Extrapolation
MM a a22 = -0.0426 0.0006 0.0003 0.0018 = -0.0426 0.0006 0.0003 0.0018+- +- +-
( PT for by Bijnens, Colangelo, Gasser, Leutwyler, …)
Prelim.Prelim.
• Coupled Channels ?• | a | < 1 fm
ConclusionConclusion
Lattice Lattice QQCCDD studies of Nuclei and studies of Nuclei and Multi-Hadron Systems are an Multi-Hadron Systems are an important part of the future of Nuclear important part of the future of Nuclear PhysicsPhysics..
Topics that Topics that areare or or cancan or or shouldshould be be tackled todaytackled today
Nucleon Properties …Nucleon Properties … (LHPC) (LHPC) MMNN , , N N , g, gAA , , , as functions of m , as functions of mqq , a , V , a , V
The NN Systems … The NN Systems … (s) , L(s) , LAA
11,, .. ..
Hyperon Properties and Systems… Hyperon Properties and Systems… MM , , N N , , N N N , N , .. ..
V(R) between Hadrons with one Q : DD (Michael, Cook+Fiebig,…)