t trtr s trst - - PowerPoint PPT Presentation

❋✐♥✐t❡ t❡♠♣❡r❛t✉r❡ ♣❤❛s❡ tr❛♥s✐t✐♦♥ ✐♥ ▲❛tt✐❝❡ ◗❈❉ ✇✐t❤ t✇♦ ✢❛✈♦rs

❱✳ ❇♦r♥②❛❦♦✈

■❍❊P✱ Pr♦t✈✐♥♦ ❛♥❞ ■❚❊P✱ ▼♦s❝♦✇

❉✉❜♥❛ ✷✸✳✵✾✳✶✵

❱✳ ❇♦r♥②❛❦♦✈ ✭■❍❊P✮ ❋✐♥✐t❡ t❡♠♣❡r❛t✉r❡ ▲◗❈❉ ✶✹✳✵✻✳✶✵ ✶ ✴ ✶✼

❉■❑ ❛♥❞ ◗❈❉❙❋ ❝♦❧❧❛❜♦r❛t✐♦♥s ❱❇✱ ❘✳ ❍♦rs❧❡② ✭❊❞✐♥❜✉r❣❤✮✱ ❱✳ ▼✐tr②✉s❤❦✐♥ ✭❉✉❜♥❛✮✱ ❨✳ ◆❛❦❛♠✉r❛ ✭❘❡❣❡♥s❜✉r❣✮✱ ▼✳ P♦❧✐❦❛r♣♦✈ ✭■❚❊P✱ ▼♦s❝♦✇✮✱ P✳ ❘❛❦♦✇ ✭▲✐✈❡r♣♦♦❧✮✱ ●✳ ❙❝❤✐❡r❤♦❧③ ✭❉❊❙❨✮ ❆r❳✐✈✿✵✾✶✵✳✷✸✾✷

❱✳ ❇♦r♥②❛❦♦✈ ✭■❍❊P✮ ❋✐♥✐t❡ t❡♠♣❡r❛t✉r❡ ▲◗❈❉ ✶✹✳✵✻✳✶✵ ✷ ✴ ✶✼

❖✉t❧✐♥❡

✶

■♥tr♦❞✉❝t✐♦♥

✷ ❙✐♠✉❧❛t✐♦♥ ❞❡t❛✐❧s ❛♥❞ r❡s✉❧ts ✸ ❈♦♥❝❧✉s✐♦♥s ❛♥❞ ♦✉t❧♦♦❦

❱✳ ❇♦r♥②❛❦♦✈ ✭■❍❊P✮ ❋✐♥✐t❡ t❡♠♣❡r❛t✉r❡ ▲◗❈❉ ✶✹✳✵✻✳✶✵ ✸ ✴ ✶✼

■♥tr♦❞✉❝t✐♦♥

■♥tr♦❞✉❝t✐♦♥

• ♦❛❧s✿

✕ ♣r❡❝✐s❡ ✈❛❧✉❡ ♦❢ Tc ✕ ♥❛t✉r❡ ♦❢ t❤❡ ♣❤❛s❡ tr❛♥s✐t✐♦♥ ❙♦♠❡ ♥♦t❛t✐♦♥s✿ ❚❡♠♣❡r❛t✉r❡ ❞❡✜♥✐t✐♦♥ T =

1 aNt ✱

a ✲ ❧❛tt✐❝❡ s♣❛❝✐♥❣ β = 6/g2 Nf = 2 ◗❈❉ ✕ mu = md✱ ms = ∞✱ ✳✳✳ Nf = 2 + 1 ◗❈❉ ✕ mu = md✱ ms > mu✱ mc = ∞✱ ✳✳✳

❱✳ ❇♦r♥②❛❦♦✈ ✭■❍❊P✮ ❋✐♥✐t❡ t❡♠♣❡r❛t✉r❡ ▲◗❈❉ ✶✹✳✵✻✳✶✵ ✹ ✴ ✶✼

■♥tr♦❞✉❝t✐♦♥

Pr❡s❡♥t s✐t✉❛t✐♦♥ ✐s r❛t❤❡r ❝♦♥tr♦✈❡rs✐❛❧ ✕ ❘❇❈✴❇✐❡❧❡❢❡❧❞ ❝♦❧❧❛❜♦r❛t✐♦♥✱ ✐♠♣r♦✈❡❞ st❛❣❣❡r❡❞ ❢❡r♠✐♦♥s✱ Nf = 2 + 1✱ Nt ✉♣ t♦ ✽ Tc✭❞❡❝♦♥❢✮= Tc✭❈❙❇✮❂✶✾✻✭✸✮ ▼❡❱ ✕ ❲✉♣♣❡rt❛❧ ❣r♦✉♣✱ ✐♠♣r♦✈❡❞ st❛❣❣❡r❡❞ ❢❡r♠✐♦♥s✱ Nf = 2 + 1✱ Nt ✉♣ t♦ ✶✻ Tc✭❞❡❝♦♥❢✮❂✶✺✶✭✻✮▼❡❱✱ Tc✭❈❙❇✮❂✶✼✻✭✼✮ ▼❡❱ ✕ ❲❍❖❚✲◗❈❉ ❝♦❧❧❛❜♦r❛t✐♦♥✱ ✐♠♣r♦✈❡❞ ❲✐❧s♦♥ ❢❡r♠✐♦♥s✱ Nf = 2✱ Nt = 6 Tc✭❞❡❝♦♥❢✮❂✶✺✵ t♦ ✶✽✵ ▼❡❱✱ ✕ ❉■❑ ❛♥❞ ◗❈❉❙❋ ❝♦❧❧❛❜♦r❛t✐♦♥s✱ ✐♠♣r♦✈❡❞ ❲✐❧s♦♥ ❢❡r♠✐♦♥s✱ Nf = 2✱ Nt ✉♣ t♦ ✶✷ Tc✭❞❡❝♦♥❢✮❂Tc✭❈❙❇✮❂✶✼✹✭✸✮✭✻✮ ▼❡❱ ✕ Pr❡❧✐♠✐♥❛r② r❡s✉❧ts✿ t♠❢❚ ❝♦❧❧❛❜♦r❛t✐♦♥✱ t✇✐st❡❞ ♠❛ss ❢❡r♠✐♦♥ ❛❝t✐♦♥✱ Nf = 2 ▼✉♥st❡r ❯♥✐✈❡rs✐t② ❣r♦✉♣✱ ■♠♣r♦✈❡❞ ❲✐❧s♦♥ ❢❡r♠✐♦♥s✱ Nf = 2

❱✳ ❇♦r♥②❛❦♦✈ ✭■❍❊P✮ ❋✐♥✐t❡ t❡♠♣❡r❛t✉r❡ ▲◗❈❉ ✶✹✳✵✻✳✶✵ ✺ ✴ ✶✼

■♥tr♦❞✉❝t✐♦♥

• F

C D A G H

• rder

first order region

B

m ms

ud

first

E

crossover region

physical point?

❱✳ ❇♦r♥②❛❦♦✈ ✭■❍❊P✮ ❋✐♥✐t❡ t❡♠♣❡r❛t✉r❡ ▲◗❈❉ ✶✹✳✵✻✳✶✵ ✻ ✴ ✶✼

■♥tr♦❞✉❝t✐♦♥

❖r❞❡r ♦❢ tr❛♥s✐t✐♦♥ ✐♥ t❤❡ ❧✐♠✐t ♦❢ ♠❛ss❧❡ss q✉❛r❦s P✐s❛rs❦✐✱ ❲✐❧❝③❡❦✱ ✶✾✽✹ Nf = 2 ✕ s❡❝♦♥❞ ♦r❞❡r ✐♥ ✸❞ O(4) ❝❧❛ss ♦❢ ✉♥✐✈❡rs❛❧✐t② Nf = 3 ✕ ✜rst ♦r❞❡r O(4) s❝❛❧✐♥❣ ✇❛s ♦❜s❡r✈❡❞ ❢♦r ❲✐❧s♦♥ ✭■✇❛s❛❦✐ ❡t ❛❧✱ ✶✾✾✼✮ ❛♥❞ ✐♠♣r♦✈❡❞ ❲✐❧s♦♥ ✭❆❧✐ ❑❤❛♥ ❡t ❛❧✱ ✷✵✵✶✮ ♦♥❧② r❡❝❡♥t❧② ❢♦r ✐♠♣r♦✈❡❞ st❛❣❣❡r❡❞ ❢❡r♠✐♦♥s ✭❊❥✐r✐ ❡t ❛❧✱ ✷✵✵✾✮ t❤❡r❡ ❛r❡ ❝❧❛✐♠s ❛❜♦✉t s✐❣♥❛❧s ♦❢ ✶st ♦r❞❡r tr❛♥s✐t✐♦♥ ✭❈♦ss✉ ❡t ❛❧✱ ✷✵✵✼✮

❱✳ ❇♦r♥②❛❦♦✈ ✭■❍❊P✮ ❋✐♥✐t❡ t❡♠♣❡r❛t✉r❡ ▲◗❈❉ ✶✹✳✵✻✳✶✵ ✼ ✴ ✶✼

❙✐♠✉❧❛t✐♦♥ ❞❡t❛✐❧s ❛♥❞ r❡s✉❧ts

❙✐♠✉❧❛t✐♦♥ ❞❡t❛✐❧s ❛♥❞ r❡s✉❧ts

✕ Nf = 2 ❧❛tt✐❝❡ ◗❈❉ ✕ ❲✐❧s♦♥ ❣❛✉❣❡ ✜❡❧❞ ❛❝t✐♦♥ ✕ ■♠♣r♦✈❡❞ ❲✐❧s♦♥ ❢❡r♠✐♦♥✐❝ ❛❝t✐♦♥ SF = S(0)

F

− i 2κ g cswa5

s

¯ ψ(s)σµνFµν(s)ψ(s) ✕ Nt × N3

s = 8 × 163, 10 × 243, 12 × 243, 12 × 323, 14 × 403

✕ 0.6 < r0mπ < 2.9 ✕ r0mπ ❛♥❞ r0/a ♦❜t❛✐♥❡❞ ❜② ✐♥t❡r♣♦❧❛t✐♦♥✴❡①tr❛♣♦❧❛t✐♦♥ ♦❢ r❡s✉❧ts ❜② ◗❈❉❙❋✲❯❑◗❈❉

❱✳ ❇♦r♥②❛❦♦✈ ✭■❍❊P✮ ❋✐♥✐t❡ t❡♠♣❡r❛t✉r❡ ▲◗❈❉ ✶✹✳✵✻✳✶✵ ✽ ✴ ✶✼

❙✐♠✉❧❛t✐♦♥ ❞❡t❛✐❧s ❛♥❞ r❡s✉❧ts

◆❡✇ ✇❛② t♦ ❝♦♠♣✉t❡ ❝❤✐r❛❧ ❝♦♥❞❡♥s❛t❡ s✉s❝❡♣t✐❜✐❧✐t②✲ ▼❛①✇❡❧❧ r❡❧❛t✐♦♥ 1 V ∂ ∂ β ln Z

• ˆ

m

= −6 P + 2 ∂ ˆ mc ∂ β ˆ σ − 2 ∂ cSW ∂ β ˆ δ , ✭✶✮ 1 V ∂ ∂ ˆ m ln Z

• β

= 2 ˆ σ , ✭✷✮ 1 V ∂ 2 ∂ β ∂ ˆ m ln Z = 2 ∂ ˆ σ ∂ β

• ˆ

m

= −6 ∂ P ∂ ˆ m

• β

+ 2 ∂ ˆ mc ∂ β ∂ ˆ σ ∂ ˆ m

• β

− 2 ∂ cSW ∂ β ∂ ˆ δ ∂ ˆ m

• β

✭✸✮

❱✳ ❇♦r♥②❛❦♦✈ ✭■❍❊P✮ ❋✐♥✐t❡ t❡♠♣❡r❛t✉r❡ ▲◗❈❉ ✶✹✳✵✻✳✶✵ ✾ ✴ ✶✼

❙✐♠✉❧❛t✐♦♥ ❞❡t❛✐❧s ❛♥❞ r❡s✉❧ts

❝❤✐r❛❧ ❝♦♥❞❡♥s❛t❡ s✉s❝❡♣t✐❜✐❧✐t② χσ = 1 µ ∂P ∂ ˆ m , ✇❤❡r❡ µ−1 = 3 ∂ ˆ mc ∂ β + ∂ ˆ m ∂ β

• ˆ

σ

−1

❱✳ ❇♦r♥②❛❦♦✈ ✭■❍❊P✮ ❋✐♥✐t❡ t❡♠♣❡r❛t✉r❡ ▲◗❈❉ ✶✹✳✵✻✳✶✵ ✶✵ ✴ ✶✼

❙✐♠✉❧❛t✐♦♥ ❞❡t❛✐❧s ❛♥❞ r❡s✉❧ts

1638 40314

❱✳ ❇♦r♥②❛❦♦✈ ✭■❍❊P✮ ❋✐♥✐t❡ t❡♠♣❡r❛t✉r❡ ▲◗❈❉ ✶✹✳✵✻✳✶✵ ✶✶ ✴ ✶✼

❙✐♠✉❧❛t✐♦♥ ❞❡t❛✐❧s ❛♥❞ r❡s✉❧ts

P♦❧②❛❦♦✈ ❧♦♦♣ L = 1 N3

s

• x

Re L( x) , L( x) = 1 3 Tr

Nt

• x4=1

U4(x) . ✭✹✮ ❛♥❞ ✐ts s✉s❝❡♣t✐❜✐❧✐t② χL ≡ N3

s L2c , L2c =

• L2 − L2

✭✺✮ ❈♦rr❡❧❛t♦r Lσc = Lσ − L σ , ✭✻✮

❱✳ ❇♦r♥②❛❦♦✈ ✭■❍❊P✮ ❋✐♥✐t❡ t❡♠♣❡r❛t✉r❡ ▲◗❈❉ ✶✹✳✵✻✳✶✵ ✶✷ ✴ ✶✼

❙✐♠✉❧❛t✐♦♥ ❞❡t❛✐❧s ❛♥❞ r❡s✉❧ts

r0 mTc

π

β V r0 Tc(m) χL χσ Lσc ✺✳✷✺ 243 8 ✵✳✼✸✺✭✸✮ ✸✳✶✽✭✹✮ ✸✳✶✼✭✹✮ ✸✳✸✸✭✼✮ ✺✳✷✵ 163 8 ✵✳✻✽✷✭✼✮ ✷✳✼✸✭✻✮ ✷✳✼✽✭✻✮ ✷✳✽✶✭✼✮ ✺✳✷✵ 243 10 ✵✳✺✹✺✭✻✮ ✶✳✺✾✭✽✮ ✶✳✺✾✭✶✻✮ ✶✳✺✺✭✶✹✮ ✺✳✷✾ 243 12 ✵✳✺✶✼✭✷✮ ✶✳✹✾✭✽✮ ✶✳✹✵✭✾✮ ✶✳✸✭✶✮ ✺✳✷✺ 323 12 ✵✳✹✾✵✭✷✮ ✶✳✵✵✭✶✶✮ ✶✳✵✺✭✽✮ ✶✳✵✺✭✼✮ ✺✳✷✺ 403 14 ✵✳✹✷✵✭✷✮ ✵✳✺✾✭✻✮

❱✳ ❇♦r♥②❛❦♦✈ ✭■❍❊P✮ ❋✐♥✐t❡ t❡♠♣❡r❛t✉r❡ ▲◗❈❉ ✶✹✳✵✻✳✶✵ ✶✸ ✴ ✶✼

❙✐♠✉❧❛t✐♦♥ ❞❡t❛✐❧s ❛♥❞ r❡s✉❧ts ❱✳ ❇♦r♥②❛❦♦✈ ✭■❍❊P✮ ❋✐♥✐t❡ t❡♠♣❡r❛t✉r❡ ▲◗❈❉ ✶✹✳✵✻✳✶✵ ✶✹ ✴ ✶✼

❙✐♠✉❧❛t✐♦♥ ❞❡t❛✐❧s ❛♥❞ r❡s✉❧ts

r0Tc(r0mπ) = r0Tc(0) + cm · (r0mπ)d ✭✼✮ ✇✐t❤ d =✶✳✵✼ ♣r❡❞✐❝t❡❞ ❜② O(4) s❝❛❧✐♥❣

❱✳ ❇♦r♥②❛❦♦✈ ✭■❍❊P✮ ❋✐♥✐t❡ t❡♠♣❡r❛t✉r❡ ▲◗❈❉ ✶✹✳✵✻✳✶✵ ✶✺ ✴ ✶✼

❙✐♠✉❧❛t✐♦♥ ❞❡t❛✐❧s ❛♥❞ r❡s✉❧ts

❛t t❤❡ ♣❤②s✐❝❛❧ ♣✐♦♥ ♠❛ss r0 Tc = 0.408(5) − → Tc = 172(3)(6) ▼❡❱ r0❂✵✳✹✻✼ ❢♠

❱✳ ❇♦r♥②❛❦♦✈ ✭■❍❊P✮ ❋✐♥✐t❡ t❡♠♣❡r❛t✉r❡ ▲◗❈❉ ✶✹✳✵✻✳✶✵ ✶✻ ✴ ✶✼

❈♦♥❝❧✉s✐♦♥s ❛♥❞ ♦✉t❧♦♦❦

❈♦♥❝❧✉s✐♦♥s ❛♥❞ ♦✉t❧♦♦❦

✕ ◆❡✇ ♠❡t❤♦❞ t♦ ❝♦♠♣✉t❡ χσ ❤❛s ❜❡❡♥ ✉s❡❞ ✕ ◆✉♠❡r✐❝❛❧ ✈❛❧✉❡ ❢♦r Tc ❛t t❤❡ ♣❤②s✐❝❛❧ ♣♦✐♥t ✐s ✐♥ ❛❣r❡❡♠❡♥t ✇✐t❤ st❛❣❣❡r❡❞ ❢❡r♠✐♦♥s r❡s✉❧t ❢♦r Tc(deconf) ✕ P❡❛❦s ✐♥ χσ, χL, Lσc ❝♦✐♥s✐❞❡✱ ✐♠♣❧②✐♥❣ Tc(deconf) = Tc(CSB) ✕ ❆❣r❡❡♠❡♥t ✇✐t❤ O(4) s❝❛❧✐♥❣ ✐♥ Tc(m) ✕ ❉✐r❡❝t ❝♦♠♣✉t❛t✐♦♥ ♦❢ χσ ✐s ❞❡s✐r❛❜❧❡ ✕ 2 + 1 ◗❈❉ s✐♠✉❧❛t✐♦♥s ❛r❡ ♣❧❛♥♥❡❞

❱✳ ❇♦r♥②❛❦♦✈ ✭■❍❊P✮ ❋✐♥✐t❡ t❡♠♣❡r❛t✉r❡ ▲◗❈❉ ✶✹✳✵✻✳✶✵ ✶✼ ✴ ✶✼