hyperon nucleon interactions

Hyperon Nucleon Interactions and Dense Matter

Martin J. SavageUniversity of Washington

June 2012, Lattice 2012Cairns, Australia

Wednesday, June 27, 2012

... to make predictions for the structure and interactions of nuclei using lattice QCD.

NPLQCD

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Silas Beane Emmanuel Chang William Detmold Huey-Wen Lin Tom Luu Saul CohenNew Hampshire Barcelona Willam+Mary U. of Washington LLNL U. of Washington

Kostas Orginos Assumpta Parreno Marton Savage Aaron Torok Andre Walker-Loud William+Mary Barcelona U. of Washington Indiana LBNL

Wednesday, June 27, 2012

Core-Collapse Supernova and the Heavy Elements

Black-Hole orNeutron Star ?

SN1987a(Mezzacappa et al)

Y nnK

Nuclear EoSWednesday, June 27, 2012

Core-Collapse Supernova and the Heavy Elements

(Mezzacappa et al)

Y nnK

Nuclear EoS

e- K- + neutrino

n + e- + neutrino

Role depends upon Interactions

Wednesday, June 27, 2012

Hyperons in Matter :Present Predictive Capability

( Schaffner-Bielich (2010) ) ( Schaffner-Bielich (2010) )

(Whittenbury) (2012)

Mean-Field Models

Wednesday, June 27, 2012

Multi-Volume Study by NPLQCD 2009 - 2011

L ∼ 4 fmL ∼ 3 fmL ∼ 2.5 fmL ∼ 2 fm

lattice spacing : b ∼ 0.123 fmpion mass : mπ ∼ 390 MeVfermion action : Cloveranisotropy : ξt ∼ 3.5

mπT ∼ 9 , 9 , 9 , 18mπL ∼ 4 , 5 , 6 , 8resources :∼ 80× 106 core hrs

Wednesday, June 27, 2012

Multi-Volume Study by NPLQCD 2009 - 2011

L cfgs srcs

24 2215 390,000

32 739 135,000

Wednesday, June 27, 2012

Generic Calculations of 2-Body Interactions

nn nn

qqq

qqq

(Derek Leinweber, U. of Adelaide)

qqqqqq

qqqZN

qqqZNN (r,r’)

qqq

1) Maiani-Testa Theorem

2) Luscher : Measure energy-eigenvalues of the two-hadron system

Wednesday, June 27, 2012

A Primer -1990 : Luscher says ....

Taking U to be energy-independent is a model-dependent assertion and not a QCD prediction

It therefore follows that....

Wednesday, June 27, 2012

δE = 2�

p2 + m2 − 2m

Two-Particle Energy Levels (Luscher)

Below Inelastic Thresholds : Measure on lattice

Gives the scattering amplitude at δE

nn nn

Wednesday, June 27, 2012

Luscher Eigenvalue Relation

Non-interacting particles

E < 0 E > 0 Bound-state or Scattering state ?

V = 0 → a = r = 0S =∞

k =2π

Ln

n = (nx, ny, nz)

A1+

nn nn

Wednesday, June 27, 2012

at a pion mass of ~390 MeV

Wednesday, June 27, 2012

QCD-Based Organization of Nuclear Forces

• Low-energy EFT of QCD

• Chiral symmetries of QCD

• Quark mass dependence

• Renormalization Group

• Softer Interactions• Vlowk , SRG

Effective Field Theory introduced by Weinberg in the early 1990’s to systematize nuclear forces

Wednesday, June 27, 2012

LO Weinberg in

1 : local 4-baryon contact interaction (1 parameter)2 : one meson exchange (0 new parameters)

Wednesday, June 27, 2012

Convergence of (Systematic) Expansions of Potentials

Wednesday, June 27, 2012

Require regulation - use simple compact shape - square-well, Gaussian, exponential - one length scale, one coupling

LO Weinberg in

Wednesday, June 27, 2012

3S1 : 3-d Schrodinger, Modifications to Luscher’s Relation ?

• diagonalize H in full 3-d mom. space (constrained by L and a)

• choose R <<1/mmes and fix C0 to energy-eigenvalue• extended repulsive core - Luscher ?• use both Luscher and Weinberg EFT

• phase-shifts are same within uncertainties!

Wednesday, June 27, 2012

1S0 : 3-d Schrodinger, Modifications to Luscher’s Relation ?

Attractive core is compact - Luscher’s relation is valid

Wednesday, June 27, 2012

Hyperon Nucleon Interactions

Haidenbauer and Meissner (2007)Wednesday, June 27, 2012

Hyperon Nucleon Interactions

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NSC97fJuelich '04EFT

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NSC97fJuelich '04EFT

Meissner+Haidenbauer - Experiment + YN-EFT (LO)

1S03S1

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NPLQCD - Lattice QCD + YN-EFT (LO)

Hyperon Nucleon Interactions

1S03S1

Wednesday, June 27, 2012

Binding in the Singlet Channel

Wednesday, June 27, 2012

in Dense Matter Fumi Limit Approx. (assertions)

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Cancellation between channels in dense matter energy-shift of hyperon

Wednesday, June 27, 2012

SU(3) Limit - Isotropic Clover

deuteron nn H�dib n� �1s0� n� �3s1� n� �1s0� n� �3s1� n� �3s1� p� �3s1�

1027

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�E�MeV

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L�48 , �p��2L�48 , �p��1L�48 , �p��0L�32 , �p��2L�32 , �p��1L�32 , �p��0L�24 , �p��0

NPLQCD : e-Print: arXiv:1206.5219 [hep-lat]Wednesday, June 27, 2012

Closing Remarks

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1S0

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3S1

• LQCD calculations of

• Luscher and 3-d SE consistent

• Extrapolation with (W)EFT

• Consistent with phase-shift analysis of (limited) expt data

• Future LQCD calculations will supersede experiment

• Refine understanding of dense matter•Further theoretical developments required

Wednesday, June 27, 2012

END

Wednesday, June 27, 2012

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Hyperon Nucleon Interactions

1S03S1

• LQCD + (W)EFT consistent with limited data sets • Next generation of LQCD will be more precise than expt

Wednesday, June 27, 2012