[PPT] - Chiral phase transition of (2 + 1)-flavor QCD QCD phase diagram PowerPoint Presentation

SLIDE 1

Chiral phase transition of (2 + 1)-flavor QCD QCD phase diagram MEOS Lattice Setup NO evidence for the 1st

rder phase

transition Extract T 0

c

Summary and

utlook

Backup

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Chiral phase transition of (2 + 1)-flavor QCD

Sheng-Tai Li for HotQCD collaboration

Institute of Particle Physics Central China Normal University July 26, 2018

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SLIDE 2

Chiral phase transition of (2 + 1)-flavor QCD QCD phase diagram MEOS Lattice Setup NO evidence for the 1st

rder phase

transition Extract T 0

c

Summary and

utlook

Backup

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Chiral crossover transition of QCD in the real world

3p/T4

/T4 3s/4T3 4 8 12 16 130 170 210 250 290 330 370 T [MeV]

HRG non-int. limit Tc 150 152 154 156 158 160 162 164 166 c

n

t i n u u m N

=

1 6 N

=

1 2 N

=

8 N

=

6

HotQCD preliminary

Tc(µB=0) [MeV] 1/N

2

disc sub sub µB

2 sub

µB

2 disc

156.5 ± 1.5 MeV

PRD 90, 094503 (2014)

P. Steinbrecher, 1807.05607
The transition from Hadronic phase to Quark Gluon Plasma

phase at µB = 0 is a crossover but NOT a PHASE transition

(Y. Aoki .et al, Nature 443 (2006) 675-678 and A. Bazavov et al., Phys.Rev.D85(2012) 054503 and the ref therein)

Latest results Tpc(µB = 0) = 156.5 ± 1.5 MeV (“QCD

crossover at zero and non-zero baryon densities” by P. Steinbrecher, Wed. 16:10-16:30)

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SLIDE 3

Chiral phase transition of (2 + 1)-flavor QCD QCD phase diagram MEOS Lattice Setup NO evidence for the 1st

rder phase

transition Extract T 0

c

Summary and

utlook

Backup

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QCD chiral phase transition

cross over

1st

rder
rder

1st mphy

s

physical point Nf = 3 2nd order Z2 2nd order Z2

ms

mu,d = ml PURE GAUGE

Nf = 2

∞ ∞

Nf = 1

2nd order O(4)

mc

H = ml mphy

s

The real PHASE transition in the chiral limit ?
The order and universality class of the phase transition ?
Influence of the criticality in the chiral limit to the

thermodynamics at the physical point ?

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SLIDE 4

Chiral phase transition of (2 + 1)-flavor QCD QCD phase diagram MEOS Lattice Setup NO evidence for the 1st

rder phase

transition Extract T 0

c

Summary and

utlook

Backup

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Two different scenarios at µB ̸= 0

cross over 1st

rder
rder

1st mphy

s

physical point Nf = 3 2nd order Z2 2nd order Z2

ms mu,d = ml PURE GAUGE

Nf = 2

∞ ∞

Nf = 1 2nd order O(4) mc

H = ml mphy

s

− mc mphy

s

cross over 1st

rder
rder

1st mphy

s

physical point Nf = 3 2nd order Z2 2nd order Z2

ms mu,d = ml PURE GAUGE

Nf = 2

∞ ∞

Nf = 1 2nd order O(4) mc

H = ml mphy

s

1 st

rder

critical point cross over

µ

mphy

s

< mtri

s

T

2 nd

rder

tri-critical point 1 st

rder

µ

mphy

s

> mtri

s

T

ml = 0 ml = 0

B B

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SLIDE 5

Chiral phase transition of (2 + 1)-flavor QCD QCD phase diagram MEOS Lattice Setup NO evidence for the 1st

rder phase

transition Extract T 0

c

Summary and

utlook

Backup

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Magnetic Equation of State (MEOS)

Behaviour of QCD continuous phase transition can be described by the MEOS M(t, h) = h1/δfG(z) + freg = ms f 4

K

[⟨ ¯ ψψ ⟩

l − 2ml

ms ⟨ ¯ ψψ ⟩

s

] χM(t, h) = ∂M ∂H = H−1h1/δfχ(z) + ∂freg ∂H = m2

s

f 4

K

χsubtot where, freg = a1(T)H + a3(T)H3 + ... (1)

Scaling variables

z = t/h1/βδ, t = 1 t0 T − T 0

c

T 0

c

, h = H h0 = 1 h0 ml ms (2)

I. scaling variables, h: external field, t: reduced temperature,
II. β and δ are universal critical exponents.
III. t0, h0, T 0

c are unique parameters from QCD, T 0 c is the chiral phase transition

tempearture and it is a fundamental quantity of QCD

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SLIDE 6

Chiral phase transition of (2 + 1)-flavor QCD QCD phase diagram MEOS Lattice Setup NO evidence for the 1st

rder phase

transition Extract T 0

c

Summary and

utlook

Backup

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Scaling functions & universal critical exponents

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

4
2

2 4 z=t/h1/ βδ fχ Z(2) O(2) O(4) 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

4
2

2 4 z=t/h1/ βδ fG Z(2) O(2) O(4)

mtri

s > mphy s

→ Z(2) at ml = mc

mtri

s < mphy s

→ O(4) at ml = 0

Staggered→ O(2)

Model β δ Z(2) 0.3258 4.805 O(4) 0.380 4.824 O(2) 0.349 4.780

Difficulities:

I. Critical exponents of O(2), Z(2), O(4) are similar
II. Regular contribution from free energy maybe complicated.

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SLIDE 7

Chiral phase transition of (2 + 1)-flavor QCD QCD phase diagram MEOS Lattice Setup NO evidence for the 1st

rder phase

transition Extract T 0

c

Summary and

utlook

Backup

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A novel way to determine T 0

c

HχM M = fχ(z) fG(z) = ⎧ ⎪ ⎨ ⎪ ⎩ z → −∞ 1/δ z = 0 1 z → +∞

1

T −

60%(H) = T 0 c

1 +

z−

60%

z0 H1/βδ

⎪

⎩ → ∞

0.2 0.4 0.6 0.8 1

0.4
0.2

0.2 0.4 (T-Tc

0)/Tc

fχ/fG O(2) z0=0 H=1/20 H=1/40 H=1/80 1/δ 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

2
1

1 2 3 z=t/h1/βδ fχ(z) O(4) O(2) 60% of peak z=0 1/δ zp 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

2
1

1 2 3 z=t/h1/βδ fχ(z) O(4) O(2) Z(2) 60% of peak z=0 1/δ zp

O(2) z0 = 1

The crossing point gives T 0

c at H → 0

At z−

60%, T − 60% ≈ T 0 c

Model zp z−

60%

Z(2) 2.0 0.1 O(4) 1.37

0.01

O(2) 1.56

0.009

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SLIDE 8

Chiral phase transition of (2 + 1)-flavor QCD QCD phase diagram MEOS Lattice Setup NO evidence for the 1st

rder phase

transition Extract T 0

c

Summary and

utlook

Backup

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Lattice Setup

cross over

1st

rder
rder

1st mphy

s

physical point Nf = 3 2nd order Z2 2nd order Z2

ms

mu,d = ml PURE GAUGE

Nf = 2

∞ ∞

Nf = 1

2nd order O(4)

mc

H = ml mphy

s

The strange quark mass is

fixed at its physical value

4-5 values of quark masses

are chosen for Nτ = 6, 8 ,12 to approach the chiral limit

55 MeV⩽ mπ ⩽ 160MeV
mphy

l

= mphy

s

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(HISQ/tree) action Nτ mphy

s

/ml window mπ window Nσ/Nτ window 6 [20, 80] [80, 160] MeV [4, 6.7] 8 [20, 160] [55, 160] MeV [4, 7] 12 [20, 80] [80, 160] MeV [4, 5]

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SLIDE 9

Chiral phase transition of (2 + 1)-flavor QCD QCD phase diagram MEOS Lattice Setup NO evidence for the 1st

rder phase

transition Extract T 0

c

Summary and

utlook

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SLIDE 10

Chiral phase transition of (2 + 1)-flavor QCD QCD phase diagram MEOS Lattice Setup NO evidence for the 1st

rder phase

transition Extract T 0

c

Summary and

utlook

Backup

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Binder cumulant of chiral order parameter

1 2 3 4 5 6 7 135 140 145 150 155 160 165 170 175 T[MeV] Bψ

ψ

Nτ=6

Binder cumulant of < ψ

ψ >

mπ=80MeV mπ=90MeV mπ=110MeV mπ=140MeV mπ=160MeV 1 2 3 4 5 6 7 8 135 140 145 150 155 160 165 170 175 T[MeV] Bψ

ψ

Nτ=8

Binder cumulant of < ψ

ψ >

mπ=55MeV, V=563x8 mπ=80MeV, V=563x8 1 2 3 4 5 6 7 8 135 140 145 150 155 160 165 170 175 T[MeV] Bψ

ψ

Nτ=12

Binder cumulant of < ψ

ψ >

mπ=110MeV, V=603x12 mπ=80MeV, V=603x12

Model B ¯

ψψ

Z(2) 1.604(2) O(2) 1.242(2) O(4) 1.092(3) 1 st 1 crossover 3

B ¯

ψψ ≈ 3 suggests that the transition is crossover in the pion

mass window 55 MeV ⩽ mπ ⩽ 160 MeV

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SLIDE 11

Chiral phase transition of (2 + 1)-flavor QCD QCD phase diagram MEOS Lattice Setup NO evidence for the 1st

rder phase

transition Extract T 0

c

Summary and

utlook

Backup

50 100 150 200 250 300 350 400 135 140 145 150 155 160 165 170 175 180 T[MeV] χM=ms

2χsubtot/fk4

Nτ=6

mπ=160MeV 141 142 143 144 145 146 147 148 149 1/160 1/80 1/60 1/40 ml/ms Tc

0 [MeV]

from 60% peak,Nτ=6 from 60% peak,Nτ=8 HotQCD preliminary

Current estimation from 60% peak of χM: T 0

c is around

147(2) MeV for Nτ=6, and 142(2) MeV for Nτ = 8 MeV.

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SLIDE 12

Chiral phase transition of (2 + 1)-flavor QCD QCD phase diagram MEOS Lattice Setup NO evidence for the 1st

rder phase

transition Extract T 0

c

Summary and

utlook

Backup

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Sanity check for T 0

c

0.15 0.2 0.25 0.3 0.35 140 141 142 143 144 145 146 147 148

T[MeV] χMH/M

Nτ=8

mπ=55MeV mπ=80MeV mπ=110MeV O(2), 1/δ

140 140.5 141 141.5 142 142.5 143 143.5 144 0.005 0.01 0.015 0.02 0.025 0.03

ml/ms Tc crossing point by 1/δ and χMH/M

Current estimation from χMH/M = 1/δ, H → 0 shows the chiral phase transition temperature T 0

c ≈ 144 MeV for Nτ = 8.

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SLIDE 13

Chiral phase transition of (2 + 1)-flavor QCD QCD phase diagram MEOS Lattice Setup NO evidence for the 1st

rder phase

transition Extract T 0

c

Summary and

utlook

Backup

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Sanity check for T 0

c

20 22 24 26 28 30 32 34 144 145 146 147 148 149 150 151 152 153

T[MeV] (M/H-χM)/H1/δ - 1

Nτ=6

mπ=80MeV mπ=90MeV

15 20 25 30 35 40 45 140 141 142 143 144 145 146 147 148

T[MeV] (M/H-χM)/H1/δ - 1

Nτ=8

mπ=55MeV mπ=80MeV

Crossing point by two lightest quarks gives an estimate of T 0

c .

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SLIDE 14

Chiral phase transition of (2 + 1)-flavor QCD QCD phase diagram MEOS Lattice Setup NO evidence for the 1st

rder phase

transition Extract T 0

c

Summary and

utlook

Backup

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Towards the continuum limit

120 125 130 135 140 145 150 155 160 165 1/1621/122 1/82 1/62 1/Nτ

2

Tc

0 [MeV]

from peak, mπ=140MeV mπ=110MeV mπ=90MeV mπ=80MeV mπ=55MeV from 60% peak mπ=80MeV from 60% peak mπ=110MeV

HotQCD preliminary

ms/ml T 0

c towards continuum limit[MeV]

40 136(3) 80 137(3)

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SLIDE 15

Chiral phase transition of (2 + 1)-flavor QCD QCD phase diagram MEOS Lattice Setup NO evidence for the 1st

rder phase

transition Extract T 0

c

Summary and

utlook

Backup

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The order of the chiral phase transition

M χM = ml − mc ms fG(z) fχ(z) (3)

0.00 0.02 0.04 0.06 0.08 0.10 1 / 1 6 1 / 8 1 / 6 1 / 4 1 / 2 7 1 / 2 55 80 90 110 140 160 M/χM H

t

Q C D p r e l i m i n a r y

solid : Nτ=6

pen : Nτ=8

half-filled : Nτ=12 @χmax

M

1 / 1 6 1 / 8 1 / 6 1 / 4 1 / 2 7 1 / 2 0.00 0.05 0.10 0.15 0.20 0.25 0.30 55 80 90 110 140 160 M/χM ml/ms mπ [MeV] H

t

Q C D p r e l i m i n a r y

colored : O(N) black solid : Z(2)@Hc=1/120 black dashed : Z(2)@Hc=1/240 @0.6⋅χmax

M

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SLIDE 16

Chiral phase transition of (2 + 1)-flavor QCD QCD phase diagram MEOS Lattice Setup NO evidence for the 1st

rder phase

transition Extract T 0

c

Summary and

utlook

Backup

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Summary and outlook

✓ We have performed simulations on Nτ = 6, 8, 12 lattice using the HISQ action with five different values of light quark masses towards the chiral limit ✓ No first order phase transition is observed in our current pion mass window (55MeV < mπ < 160MeV) ✓ Our scaling analyses suggest that mphy

s

> mtri

s

✓ The chiral phase transition temperature T 0

c = 138(5) MeV

at a → 0, V → ∞, m → 0.

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SLIDE 17

Chiral phase transition of (2 + 1)-flavor QCD QCD phase diagram MEOS Lattice Setup NO evidence for the 1st

rder phase

transition Extract T 0

c

Summary and

utlook

Backup

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Volume dependence of chiral observables

200 250 300 350 400 450 140 145 150 155 160 165 T[MeV] χM=ms

2χsubtot/fk4

mπ=80 MeV Nτ=8

200 250 300 350 400 450 140 145 150 155 160 165 T[MeV] χM=ms

2χsubtot/fk4

mπ=80 MeV Nτ=8

Nσ=32 200 250 300 350 400 450 140 145 150 155 160 165 T[MeV] χM=ms

2χsubtot/fk4

mπ=80 MeV Nτ=8

200 250 300 350 400 450 140 145 150 155 160 165 T[MeV] χM=ms

2χsubtot/fk4

mπ=80 MeV Nτ=8

Nσ=40 200 250 300 350 400 450 140 145 150 155 160 165 T[MeV] χM=ms

2χsubtot/fk4

mπ=80 MeV Nτ=8

200 250 300 350 400 450 140 145 150 155 160 165 T[MeV] χM=ms

2χsubtot/fk4

mπ=80 MeV Nτ=8

Nσ=56

0.2 0.4 0.6 0.8 1 130 135 140 145 150 155 160 165 170 175 180 T[MeV] χMH/M mπ=80MeV, Nσ=32 mπ=80MeV, Nσ=40 mπ=80MeV, Nσ=56

5 10 15 20 135 140 145 150 155 160 165 170 T[MeV] M mπ=80MeV,Nσ=32 5 10 15 20 135 140 145 150 155 160 165 170 T[MeV] M mπ=80MeV,Nσ=40 5 10 15 20 135 140 145 150 155 160 165 170 T[MeV] M mπ=80MeV,Nσ=56 0.2 0.4 0.6 0.8 1 0.005 0.01 0.015 0.02 Nτ

3/Nσ 3

HχM/M T=Tpc

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SLIDE 18

Chiral phase transition of (2 + 1)-flavor QCD QCD phase diagram MEOS Lattice Setup NO evidence for the 1st

rder phase

transition Extract T 0

c

Summary and

utlook

Backup

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Volume correction to T −

60%

0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 141 142 143 144 145 146 147 148 149 150 T[MeV] χMH/M

Nτ=6

mπ=80MeV, Nσ=32 mπ=80MeV, Nσ=48 0.2 0.4 0.6 0.8 1 130 135 140 145 150 155 160 165 170 175 180 T[MeV] χMH/M

Nτ=12

mπ=80MeV, Nσ=48 mπ=80MeV, Nσ=60

120 125 130 135 140 123/963123/723 123/603 123/483 Nτ

3/Nσ 3

T-

60%

Nτ=12 mπ=80 MeV

T=T-

60%

T −

60% ≈ 138(2)MeV 145 146 147 148 149 150 123/963123/723 123/603 123/483 Nτ 3/Nσ 3 Tpc T=Tpc

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