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,…)