hyperon nucleon interactions
TRANSCRIPT
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Hyperon Nucleon Interactions and Dense Matter
Martin J. SavageUniversity of Washington
June 2012, Lattice 2012Cairns, Australia
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... 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
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Core-Collapse Supernova and the Heavy Elements
Black-Hole orNeutron Star ?
SN1987a(Mezzacappa et al)
Y nnK
Nuclear EoSWednesday, June 27, 2012
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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
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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
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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
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Hyperon Nucleon Interactions
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NSC97fJuelich '04EFT
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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
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Closing Remarks
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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
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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
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