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Baryon-Baryon Baryon-Baryon Interactions From Lattice Interactions From Lattice

QCDQCD

Martin SavageUniversity of Washington

K K

(Hyperons 2006, Mainz, Germany)

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A Grand Challenge for A Grand Challenge for QQCCDD and and Nuclear PhysicsNuclear Physics

MuQCD

MdQCD

MsQCD

e ( MZ )

g ( MZ ), , ,QCD ,

How do the properties and interactions How do the properties and interactions of nuclei depend upon the fundamental of nuclei depend upon the fundamental parameters of nature ?parameters of nature ?

Fundamental physics and intellectual curiosityFine-tunings

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The Strategy : The Strategy : QQCCDD to Nuclei to Nuclei

QCD Lagrangian

N, 2N , 3N, 4N, … Effective Interactions

Low-Momentum Interactions For Nuclei

EFT and RG

Lattice QCD

A

Exact methods A≤12GFMC, NCSM,

Lattice EFT

Shell Model, Coupled Cluster, …

A<100

Density Functional Theory ??

Lattice EFTA>100

( HYP 2006 )

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Chiral Symmetry and the Chiral Symmetry and the 2N, 3N and 4N Interactions2N, 3N and 4N Interactions

Low energy EFT of QCD

Quark mass dependence

Softer interaction

Counterterms !!!!

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ggAA from Lattice QCD from Lattice QCD (LHPC)(LHPC)

JLab Lattice

Chroma

PT : V

Mq

a

SciDAC

Mixed Action: DWF on Staggered Lattices

(R. Edwards, B. Joo)

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Strong Isospin Breaking from Strong Isospin Breaking from Isospin Symmetric LatticesIsospin Symmetric Lattices

Neutron-Proton Mass Difference : Quark mass differences , md-mu

Electromagnetism

Partially-Quenched Lattice Calculations + TheoryPartially-Quenched Lattice Calculations + Theory

Mn - Mp= 2.26+-0.57+-0.42+-0.10 MeV

expt = 2.05 +- 0.3 MeV

Electromagnetism

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Maiani-Testa: End of the InnocenceMaiani-Testa: End of the Innocence

(s) ?

GNN (s)Euclidean = GNN (s)Minkowski

One Hopes that Away from Kinematic Thresholds

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aa from Lattice QCD from Lattice QCD(S. Beane, P. Bedaque, K. Orginos, mjs ; PRD73, 054503 (2006))

JLab Lattice

Chroma

PT : V

Mq

aMixed-Action(Chen, O’Connel Van de Water, Walker-Loud)

SciDAC

(R. Edward, B. Joo)

Nf = 2+0

Nf = 2+1

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

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K K Scattering Lengths Scattering LengthsLattice QCD + Chiral Symmetry

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NN CorrelatorsNN Correlators

1S0

3S1 - 3D1

G

Fully-Dynamical QCDDomain-Wall Valence on rooted-Staggered Sea

Cn Exp[-En t]nC0 Exp[-E0 t]

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Two-Particle Energy Levels Two-Particle Energy Levels (Luscher)(Luscher)

UV regulator

Below Inelastic Thresholds : Measure on lattice

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NN Scattering: Chiral ExtrapolationNN Scattering: Chiral Extrapolation(S.R. Beane, P.F. Bedaque, K. Orginos, mjs ; PRL97, 012001 (2006))

1S0 : pp , pn , nn 3S1-3D1 : pn : deuteron

a ~ 1/m

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-- n n 11SS0 0 --- I=3/2, J=0, s=1--- I=3/2, J=0, s=1

a (t)Log[ G ]

Fully-Dynamical QCDDomain-Wall Valence on rooted-Staggered Sea

(S.Beane, P.Bedaque, T.Luu, K.Orginos, E.Pallante, A.Parreno, mjs )

M = 497 MeV

PRELIMINARYPRELIMINARY PRELIMINARYPRELIMINARY

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Interactions --- I=0, J=0, s=2Interactions --- I=0, J=0, s=2

-ve Energy Shift ?

M = 590 MeV

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Ql – Ql Potentials .. A toy for NN Ql – Ql Potentials .. A toy for NN e.g. B-mesonse.g. B-mesons

Q Q Q QDirect Exchange

QuenchedM ~ 420 MeVM ~ 700 MeV

Light d.o.f : S=1/2 , I=1/2 (I,S) = (0,0) , (0,1) , (1,0) , (1,1)

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Quenched : Quenched : a=0.10 fm, L=1.6 fma=0.10 fm, L=1.6 fm150 cfgs150 cfgs

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Tensor Force ?Tensor Force ?

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Summary and OutlookSummary and Outlook

Lattice Lattice QQCCDD is an important part of the future of is an important part of the future of (Hyper-) Nuclear Physics(Hyper-) Nuclear Physics

1/ Reproduce what is known1/ Reproduce what is known 2/ Calculate quantities that are poorly known or not known at all!2/ Calculate quantities that are poorly known or not known at all!

n , n , n ,n ,

First motion toward rigorous QCD calculations (via First motion toward rigorous QCD calculations (via EFT’s) of properties and interactions of nuclei.EFT’s) of properties and interactions of nuclei.

Coherent effort between numerical and analytic Coherent effort between numerical and analytic investigations.investigations.

n n

, K , K

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MM = 350 MeV 2.5 fm lattices... = 350 MeV 2.5 fm lattices...

TODAY !!TODAY !!

NN on the Lattice: NN on the Lattice: Unnatural Scattering Lengths Unnatural Scattering Lengths

(Beane, Bedaque, Parreno, mjs)

~E L2~E L2

Deuteron1st continuum

1st continuum2nd continuum

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Energy Scales and QCDEnergy Scales and QCD

8Be + 7.367

12C

0

4.44

7.654MuQCD

MdQCD

MsQCD

QCD f2 ( , , )

MuQCD

MdQCD

MsQCD

QCD f1 ( , , )

MuQCD

MdQCD

MsQCD

QCD f0 ( , , )

Energy levels are …

+ electroweakMc , Mb , Mt ``in’’ QCD

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InteractionsInteractions

-ve Energy Shift ?