ssstr t - PowerPoint PPT Presentation

■s♦s♣✐♥✲❆s②♠♠❡tr② ❉❡♣❡♥❞❡♥❝❡ ♦❢ t❤❡ ❚❤❡r♠♦❞②♥❛♠✐❝ ◆✉❝❧❡❛r ❊q✉❛t✐♦♥ ♦❢ ❙t❛t❡ ❈♦r❜✐♥✐❛♥ ❲❡❧❧❡♥❤♦❢❡r ❚❡❝❤♥✐❝❛❧ ❯♥✐✈❡rs✐t② ▼✉♥✐❝❤ ✇✐t❤✿ ❏❡r❡♠② ❲✳ ❍♦❧t✱ ◆♦r❜❡rt ❑❛✐s❡r✱ ❲♦❧❢r❛♠ ❲❡✐s❡ P✉❜❧✐❝❛t✐♦♥s✿ P❘❈ ✽✾ ✱ ✵✻✹✵✵✾ ✭✷✵✶✹✮❀ P❘❈ ✾✷ ✱ ✵✶✺✽✵✶ ✭✷✵✶✺✮❀ P❘❈ ✾✸ ✱ ✵✺✺✽✵✷ ✭✷✵✶✻✮ ■❈◆❚ Pr♦❣r❛♠ ❛t ❋❘■❇ ❆♣r✐❧ ✺✱ ✷✵✶✼ ❲♦r❦ s✉♣♣♦rt❡❞ ✐♥ ♣❛rt ❜② ❉❋● ❛♥❞ ◆❙❋❈ ✭❈❘❈ ✶✶✵✮

❝❤❛♥❞r❛✳❤❛r✈❛r❞✳❡❞✉

❚❤❡ ◆✉❝❧❡❛r ❊♦❙✿ ■♥t❡r♣❧❛② ♦❢ ◆✉❝❧❡❛r P❤②s✐❝s ❛♥❞ ❆str♦♣❤②s✐❝s ❇✐♥❛r② ▼❡r❣❡rs✿ ❚ � ✺✵ ▼❡❱ ◆❡✉tr♦♥ ❙t❛rs✿ ❚ ∼ ✵ ✇✇✇✷✳❛str♦✳♣✉❝✳❝❧ ❘♦ss✇♦❣✿ P❤✐❧✳ ❚r❛♥s✳ ❘✳ ❙♦❝✳ ❆ ✸✼✶ ✭✷✵✶✸✮ ❛str♦♣❤②s✐❝❛❧ ❝♦♥str❛✐♥ts ♦♥ t❤❡ ❊♦❙ ❢r♦♠ ✭❡✳❣✳✱✮ ♥❡✉tr♦♥✲st❛r ♠❛ss❡s ❛♥❞ r❛❞✐✐✱ ♠♦♠❡♥ts ♦❢ ✐♥t❡rt✐❛✱ . . . t❛s❦ ♦❢ ♥✉❝❧❡❛r t❤❡♦r②✿ ❝♦♠♣✉t❛t✐♦♥ ♦❢ t❤❡ ❊♦❙ ❢r♦♠ ♠✐❝r♦♣❤②s✐❝s → ❊♦❙ ♥✉♠❡r✐❝❛❧ ✐♥♣✉t ❢♦r s✐♠✉❧❛t✐♦♥s ♦❢ s✉♣❡r♥♦✈❛❡ ❛♥❞ ♥❡✉tr♦♥✲st❛r ♠❡r❣❡rs ◆♦✈❡❧ ❞❡✈❡❧♦♣♠❡♥ts ✐♥ t❤❡♦r❡t✐❝❛❧ ♥✉❝❧❡❛r ♣❤②s✐❝s✿ ❝❤✐r❛❧ ❊❋❚ ✱ r❡♥♦r♠❛❧✐③❛t✐♦♥ ❣r♦✉♣ → ❧♦✇✲♠♦♠❡♥t✉♠ ✐♥t❡r❛❝t✐♦♥s ✭♥♦ ✏❤❛r❞ ❝♦r❡✑✮ → ❡♥❛❜❧❡s t❤❡ ✉s❡ ♦❢ ▼❛♥②✲❇♦❞② P❡rt✉r❜❛t✐♦♥ ❚❤❡♦r② t♦ ❝♦♠♣✉t❡ t❤❡ ❊♦❙

▼♦❞❡r♥ ❚❤❡♦r② ♦❢ ◆✉❝❧❡❛r ■♥t❡r❛❝t✐♦♥s ❝❤✐r❛❧ ❊❋❚✿ ❣❡♥❡r❛❧ ❧♦✇✲❡♥❡r❣② ❡✛❡❝t✐✈❡ ✜❡❧❞ t❤❡♦r② ❝♦♥s✐st❡♥t ✇✐t❤ s②♠♠❡tr✐❡s ♦❢ ◗❈❉✱ ❞❡❣r❡❡s ♦❢ ❢r❡❡❞♦♠✿ ♥✉❝❧❡♦♥s ✫ ♣✐♦♥s s②st❡♠❛t✐❝ ❤✐❡r❛r❝❤② ♦❢ ♥✉❝❧❡❛r ✐♥t❡r❛❝t✐♦♥s ❝♦♥tr♦❧❧❡❞ ❜② ❡①♣❛♥s✐♦♥ ♣❛r❛♠❡t❡r ◗ /Λ χ = s♦❢t s❝❛❧❡ / ❤❛r❞ s❝❛❧❡✱ ✇❤❡r❡ Λ χ ∼ ✶ ●❡❱ NN Force 3N Force 4N Force LO ( Q/ Λ χ ) 0 NLO ( Q/ Λ χ ) 2 c E c D NNLO ( Q/ Λ χ ) 3 + . . . c 1 , c 3 , c 4 N 3 LO + . . . + . . . ( Q/ Λ χ ) 4 + . . . not considered here not considered here r❡str✐❝t r❡s♦❧✉t✐♦♥ ✈✐❛ ❯❱ ❝✉t♦✛ Λ < Λ χ ✐♥ ♠♦♠❡♥t✉♠ s♣❛❝❡ ▲❊❈s ❝ ✐ ( Λ ) ✜①❡❞ ❜② ❤✐❣❤✲♣r❡❝✐s✐♦♥ ✜ts t♦ ❢❡✇✲♥✉❝❧❡♦♥ ♦❜s❡r✈❛❜❧❡s → ◆◆ ❛♥❞ ✸◆ ♥✉❝❧❡❛r ♣♦t❡♥t✐❛❧s ❢♦r ♠❛♥②✲❜♦❞② ❝❛❧❝✉❧❛t✐♦♥s ◆✉❝❧❡❛r ♣♦t❡♥t✐❛❧s ❛r❡ ♥♦t ✉♥✐q✉❡✦ → ✉♥❝❡rt❛✐♥t② ❡st✐♠❛t✐♦♥s ✭❜✉t✿ ❛rt✐❢❛❝ts ♣♦ss✐❜❧❡✮ ▲♦✇✲♠♦♠❡♥t✉♠ ♣♦t❡♥t✐❛❧s Λ � ✹✺✵ ▼❡❱✿ ▼❇P❚ ❜❡❝♦♠❡s ✈❛❧✐❞ ❛♣♣r♦❛❝❤✦

▼❛♥②✲❇♦❞② P❡rt✉r❜❛t✐♦♥ ❚❤❡♦r② ✭▼❇P❚✮ ❧✐♥❦❡❞✲❝❧✉st❡r ❡①♣❛♥s✐♦♥ ✭✏●♦❧❞st♦♥❡ ❡①♣❛♥s✐♦♥✑✮ ❢♦r ❣r♦✉♥❞ st❛t❡ ❡♥❡r❣② ✭ ❚ = ✵✮ t❡①t❜♦♦❦ ❛♣♣r♦❛❝❤ ❛t ✜♥✐t❡ ❚ ✿ ❡①♣❛♥s✐♦♥ ♦❢ ❣r❛♥❞✲❝❛♥♦♥✐❝❛❧ ♣♦t❡♥t✐❛❧ Ω ( ❚ , µ ) = Ω ✵ ( ❚ , µ ) + Ω ✶ ( ❚ , µ ) + Ω ✷ ( ❚ , µ ) + K ❛♥♦♠ ( ❚ , µ ) + . . . ❇✉t✿ ♥♦t ❝♦♥s✐st❡♥t ✇✐t❤ ●♦❧❞st♦♥❡ ❡①♣❛♥s✐♦♥✱ ❝❛♥♥♦t ❞❡s❝r✐❜❡ s♣✐♥♦❞❛❧ ✐♥st❛❜✐❧✐t② Pr♦♣❡r ✜♥✐t❡✲t❡♠♣❡r❛t✉r❡ ▼❇P❚✿ ❝❛♥♦♥✐❝❛❧ ❡♥s❡♠❜❧❡✱ ❡①♣❛♥s✐♦♥ ❢♦r ❢r❡❡ ❡♥❡r❣② ✏♥❛✐✈❡✑ ❛♣♣r♦❛❝❤✿ ❧✐♥❦❡❞✲❝❧✉st❡r ❡①♣❛♥s✐♦♥ ♦❢ ❢r❡❡ ❡♥❡r❣②❀ ❞♦❡s ♥♦t ✇♦r❦ ❜❡❝❛✉s❡ ❝❛♥♦♥✐❝❛❧✲❡♥s❡♠❜❧❡ ❛✈❡r❛❣❡s ❛r❡ ❝♦♥str❛✐♥❡❞ ✭✜①❡❞ ◆ ✮ ✐♥st❡❛❞✿ ❡✈❛❧✉❛t❡ ❡♥s❡♠❜❧❡ ❛✈❡r❛❣❡s ✈✐❛ ▲❡❣❡♥❞r❡ tr❛♥s❢♦r♠ ♦❢ ❝✉♠✉❧❛♥ts ❀ ❣✐✈❡s ❋ ( ❚ , ˜ µ ) = ❋ ✵ ( ❚ , ˜ µ ) + ❆ ✶ ( ❚ , ˜ µ ) + ❆ ✷ ( ❚ , ˜ µ ) + K ❛♥♦♠ ( ❚ , ˜ µ ) + K ❝♦rr ( ❚ , ˜ µ ) + . . . ˜ µ ✜①❡❞ ❜② ρ ( ❚ , ˜ µ ) = ∂ ❋ ✵ /∂ ˜ µ → ❝♦♥s✐st❡♥t ✇✐t❤ ●♦❧❞st♦♥❡ ❡①♣❛♥s✐♦♥✦ ❛❞❞✐t✐♦♥❛❧ ❝♦♥tr✐❜✉t✐♦♥s ❢r♦♠ ✉♥❧✐♥❦❡❞ ❞✐❛❣r❛♠s K ❝♦rr ✱ r❡♥♦r♠❛❧✐③❡ ˜ µ ❝❛♥♦♥✐❝❛❧ s❡r✐❡s ❝❛♥ ❜❡ ❛❧s♦ ❞❡r✐✈❡❞ ✈✐❛ r❡♦r❣❛♥✐③❛t✐♦♥ ♦❢ ❣r❛♥❞✲❝❛♥♦♥✐❝❛❧ s❡r✐❡s ✭❑♦❤♥✲▲✉tt✐♥❣❡r ♠❡t❤♦❞✮✱ ❜✉t ❡q✉✐✈❛❧❡♥❝❡ ✐s ♦♥❧② ❢♦r♠❛❧ ✭❛s②♠♣t♦t✐❝ s❡r✐❡s✦✮ free HF ▼❡❛♥✲✜❡❧❞ ❜❡♥❝❤♠❛r❦ HF (G.C.) 5 HF+ K SCHF HF+ K (G.C.) ❢✉❧❧② r❡♥♦r♠❛❧✐③❡❞ ▼❇P❚✿ ❙❈❍❋ 0 F [MeV] ❧❛r❣❡ K ❛♥♦♠ ✭ ε r❡♥♦r♠❛❧✐③❛t✐♦♥✮✱ ❜✉t K ❛♥♦♠ + K ❝♦rr ✭ ε ❛♥❞ ˜ µ -5 0 r❡♥♦r♠❛❧✐③❛t✐♦♥✮ ✐s s♠❛❧❧ -25 K anom. -10 T=15 MeV s♣✐♥♦❞❛❧ r❡❣✐♦♥ ♦♥❧② ❢r♦♠ ❝❛♥♦♥✐❝❛❧ K anom. + K corr. -50 ❛♥❞ ❢✉❧❧② r❡♥♦r♠❛❧✐③❡❞ ▼❇P❚ 0 0.05 0.1 0.15 0.2 0.25 0 0.05 0.1 0.15 0.2 0.25 ρ [fm -3 ]

❈❤✐r❛❧ ◆✉❝❧❡❛r ❊♦❙✿ ❖r❞❡r✲❇②✲❖r❞❡r ❘❡s✉❧ts ❢♦r ✈❛r✐♦✉s ◆◆✰✸◆ P♦t❡♥t✐❛❧s ■s♦s♣✐♥✲s②♠♠❡tr✐❝ ♥✉❝❧❡❛r ♠❛tt❡r✿ δ := ( ρ ♥ − ρ ♣ ) /ρ = ✵✱ ❨ := ρ ♣ /ρ = ✶ / ✷ 0 0 T=0 MeV -10 -10 T=0 MeV n3lo414 n3lo450 -20 -20 n3lo500 [MeV] [MeV] n3lo414 -30 -30 VLK21 n3lo450 VLK23 n3lo500 _ F -40 _ F -40 VLK21 VLK23 T=25 MeV -50 -50 T=25 MeV -60 -60 -70 -70 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 0.3 ρ [fm -3 ] ρ [fm -3 ] (a) NN first order, no 3N (b) NN second order, no 3N 0 0 T=0 MeV T=0 MeV -10 -10 n3lo414 n3lo414 -20 -20 n3lo450 n3lo450 [MeV] [MeV] n3lo500 n3lo500 -30 -30 VLK21 VLK21 _ F _ F -40 VLK23 -40 VLK23 -50 -50 T=25 MeV T=25 MeV -60 -60 -70 -70 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 0.3 ρ [fm -3 ] ρ [fm -3 ] (c) NN second order, 3N first order (d) NN second order, 3N second order ♥✸❧♦✹✶✹ ✫ ♥✸❧♦✹✺✵✿ ❣♦♦❞ ♣❡rt✉r❜❛t✐✈❡ ❜❡❤❛✈✐♦r ❋ ✶ > ❋ ✷ ≫ ❋ ✸ ✭t❤✐r❞ ♦r❞❡r✿ ❍♦❧t ✫ ❑❛✐s❡r✿ ✶✻✶✷✳✵✹✸✵✾ ✭✷✵✶✻✮ ✮ ♥✸❧♦✺✵✵✿ ❧❡ss ♣❡rt✉r❜❛t✐✈❡ ✭ ❋ ✶ , ◆◆ ✫ ❋ ✷ , ◆◆ s✐♠✐❧❛r ♠❛❣♥✐t✉❞❡✮ ❱▲❑✷✶ ✫ ❱▲❑✷✸✿ ◆◆ ♣❡rt✉r❜❛t✐✈❡✱ ❜✉t ❧❛r❣❡ ❝♦♥tr✐❜✉t✐♦♥s ❢r♦♠ ✸◆ ♣♦t❡♥t✐❛❧