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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
+
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
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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
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Multi-Volume Study by NPLQCD 2009 - 2011
L cfgs srcs
24 2215 390,000
32 739 135,000
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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
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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....
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δE = 2�
p2 + m2 − 2m
Two-Particle Energy Levels (Luscher)
Below Inelastic Thresholds : Measure on lattice
Gives the scattering amplitude at δE
nn nn
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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
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at a pion mass of ~390 MeV
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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)
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Convergence of (Systematic) Expansions of Potentials
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Require regulation - use simple compact shape - square-well, Gaussian, exponential - one length scale, one coupling
LO Weinberg in
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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!
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1S0 : 3-d Schrodinger, Modifications to Luscher’s Relation ?
Attractive core is compact - Luscher’s relation is valid
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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
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Binding in the Singlet Channel
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in Dense Matter Fumi Limit Approx. (assertions)
-
Cancellation between channels in dense matter energy-shift of hyperon
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SU(3) Limit - Isotropic Clover
deuteron nn H�dib n� �1s0� n� �3s1� n� �1s0� n� �3s1� n� �3s1� p� �3s1�
1027
1
10
8A
�100
�80
�60
�40
�20
0
�E�MeV
�
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
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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
