[PPT] - QCD phase diagram: overview of recent lattice results Gergely Endr PowerPoint Presentation

SLIDE 1

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

QCD phase diagram: overview of recent lattice results Gergely Endr˝

di

University of Regensburg Fairness 2013, 19th September, 2013

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 2

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

Outline

introduction

◮ QCD ◮ nonzero temperature / density / magnetic field ◮ lattice approach

lattice results about the phase diagram

◮ QCD at zero µ, zero B ◮ QCD at nonzero µ ◮ QCD at nonzero B

summary

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 3

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

QCD and quark-gluon plasma

elementary particle interactions:

gravitational, electromagnetic, weak, strong

Standard Model
strong sector: Quantum Chromodynamics
elementary particles: quarks (∼ electrons) and

gluons (∼ photons) but: they cannot be observed directly ⇒ confinement at low temperatures

asymptotic freedom [Gross, Politzer, Wilczek ’04]

⇒ heating or compressing the system leads to deconfinement: quark-gluon plasma is formed

transition between the two phases

characteristics: order (1st/2nd/crossover) critical temperature Tc

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 4

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

QCD phase diagram

why is the physics of the quark-gluon plasma interesting?

◮ large T: early Universe, cosmological models ◮ large ρ: neutron stars ◮ large T and/or ρ: heavy-ion collisions, experiment design QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 5

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

QCD phase diagram

why is the physics of the quark-gluon plasma interesting?

◮ large T: early Universe, cosmological models ◮ large ρ: neutron stars ◮ large T and/or ρ: heavy-ion collisions, experiment design QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 6

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

QCD phase diagram

why is the physics of the quark-gluon plasma interesting?

◮ large T: early Universe, cosmological models ◮ large ρ: neutron stars ◮ large T and/or ρ: heavy-ion collisions, experiment design QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 7

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

QCD phase diagram

why is the physics of the quark-gluon plasma interesting?

◮ large T: early Universe, cosmological models ◮ large ρ: neutron stars ◮ large T and/or ρ: heavy-ion collisions, experiment design QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 8

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

QCD phase diagram

why is the physics of the quark-gluon plasma interesting?

◮ large T: early Universe, cosmological models ◮ large ρ: neutron stars ◮ large T and/or ρ: heavy-ion collisions, experiment design

additional, relevant parameter:

◮ external magnetic field B QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 9

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

Example 1: neutron star

[Rea et al. ’13]

possible quark core at center with high density, low

temperature

magnetars: extreme strong magnetic fields

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 10

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

Typical magnetic fields

magnetic field of Earth

10−5 T

common magnet

10−3 T

strongest man-made field in lab

102 T

magnetar surface

1010 T

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 11

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

Typical magnetic fields

magnetic field of Earth

10−5 T

common magnet

10−3 T

strongest man-made field in lab

102 T

magnetar surface

1010 T Wikipedia: “At a distance halfway to the moon, a magnetar could strip information from the magnetic stripes of all credit cards on Earth.”

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 12

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

Example 2: heavy-ion collision

[STAR collaboration, ’10]

off-central collisions generate magnetic fields:

strength controlled by √s and impact parameter (centrality)

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 13

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

Example 2: heavy-ion collision

2 4 6 8 10 12 14 5 10 15 20 25 30

<(eB)

2>/m

4

b (fm) r=(0,0,0) r=(3 fm, 0, 0) r=(0, 3 fm, 0) r=(3 fm, 3 fm, 0)

[Bloczynski et al. ’12]

off-central collisions generate magnetic fields:

strength controlled by √s and impact parameter (centrality)

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 14

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

Typical magnetic fields

magnetic field of Earth

10−5 T

common magnet

10−3 T

strongest man-made field in lab

102 T

magnetar surface

1010 T

LHC Pb-Pb at 2.7 TeV, b = 10 fm [Skokov ’09]

1015 T

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 15

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

Typical magnetic fields

magnetic field of Earth

10−5 T

common magnet

10−3 T

strongest man-made field in lab

102 T

magnetar surface

1010 T

LHC Pb-Pb at 2.7 TeV, b = 10 fm [Skokov ’09]

1015 T

b = 12 fm b = 8 fm b = 4 fm τ(fm) eB (MeV2) 3 2.5 2 1.5 1 0.5 105 104 103 102 101 100

[Tuchin ’13]

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 16

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

Approaches to study QCD

various methods in various regimes:

◮ high T/µ/B: perturbation theory ◮ low T/µ/B: hadronic models ◮ transition region: non-perturbative methods, lattice gauge

theory [Wilson, ’74]

L = 1 4 FµνFµν+ ¯ ψ( / D+m)ψ, Dµ = ∂µ+igsAµ, Fµν = − i gs [Dµ, Dν]

discretize quark and gluon fields ψ and Aµ
n a 4D space-time lattice with spacing a
functional integral gives the partition function

Z =

DAµ D ¯

ψ Dψ exp

−
d4x L
QCD phase diagram

Gergely Endr˝

di

University of Regensburg

SLIDE 17

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

Approaches to study QCD

various methods in various regimes:

◮ high T/µ/B: perturbation theory ◮ low T/µ/B: hadronic models ◮ transition region: non-perturbative methods, lattice gauge

theory [Wilson, ’74]

L = 1 4 FµνFµν+ ¯ ψ( / D+m)ψ, Dµ = ∂µ+igsAµ, Fµν = − i gs [Dµ, Dν]

discretize quark and gluon fields ψ and Aµ
n a 4D space-time lattice with spacing a
functional integral gives the partition function

Z =

DAµ exp
−
d4x 1

4FµνFµν

· det

/ D + m

solve 109 dimensional integrals ⇒ Monte-Carlo methods

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 18

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

Lattice QCD

biggest challenges are to

◮ extrapolate a → 0 ‘continuum limit’

and keep physical size fixed: # of lattice points → ∞

◮ fix bare parameters of L: quark masses

tune m such that hadron masses at T = 0 are as in nature

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 19

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

Lattice QCD

biggest challenges are to

◮ extrapolate a → 0 ‘continuum limit’

and keep physical size fixed: # of lattice points → ∞

◮ fix bare parameters of L: quark masses

tune m such that hadron masses at T = 0 are as in nature

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 20

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

Lattice QCD

biggest challenges are to

◮ extrapolate a → 0 ‘continuum limit’

and keep physical size fixed: # of lattice points → ∞

◮ fix bare parameters of L: quark masses

tune m such that hadron masses at T = 0 are as in nature

check: different discretizations should give the same result

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 21

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

QCD phase diagram

how to map out the transition line?

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 22

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

Observables sensitive to transition

chiral condensate

→ chiral symmetry breaking ¯ ψf ψf = ∂ log Z ∂mf

chiral susceptibility

→ chiral symmetry breaking χf = ∂2 log Z ∂m2

f

Polyakov loop

→ deconfinement P = Tr exp

A4(x, t) dt
QCD phase diagram

Gergely Endr˝

di

University of Regensburg

SLIDE 23

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

Transition characteristics

chiral susceptibility

(∼ specific heat) χ = ∂2 log Z ∂m2

transition temperature: peak maximum
order of transition: volume-dependence of height h(V ) ∝ V α

1st (α = 1), 2nd (0 < α < 1) or crossover (α = 0)

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 24

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

Transition characteristics

chiral susceptibility

(∼ specific heat) χ = ∂2 log Z ∂m2

transition temperature: peak maximum
order of transition: volume-dependence of height h(V ) ∝ V α

1st (α = 1), 2nd (0 < α < 1) or crossover (α = 0)

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 25

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

Transition characteristics at µ = B = 0

no singular behavior as V → ∞

⇒ transition is analytic crossover

[Aoki, Endr˝

di, Fodor, Katz, Szab´
’06]
no unique definition for Tc

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 26

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

Transition characteristics at µ = B = 0

no singular behavior as V → ∞

⇒ transition is analytic crossover

[Aoki, Endr˝

di, Fodor, Katz, Szab´
’06]
no unique definition for Tc

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 27

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

Transition characteristics at µ = B = 0

no singular behavior as V → ∞

⇒ transition is analytic crossover

[Aoki, Endr˝

di, Fodor, Katz, Szab´
’06]
no unique definition for Tc
transition temperature with various fermion discretizations

¯ ψψ = ∂ log Z/∂m χ = ∂ ¯ ψψ/∂m

0.2 0.4 0.6 0.8 1 120 140 160 180 200 T [MeV]

∆l,s

fK scale asqtad: Nτ=8 Nτ=12 HISQ/tree: Nτ=6 Nτ=8 Nτ=12 Nτ=8, ml=0.037ms stout cont. 5 10 15 20 25 30 35 40 45 120 140 160 180 200 220 240 T [MeV] χR/T4 fK scale HISQ/tree: Nτ=6 Nτ=8 asqtad: Nτ=8 Nτ=12 stout: Nτ=8 Nτ=10

T

¯ ψψ c

≈ 150 MeV [Bors´

anyi et al. ’06 ’09 ’10, Bazavov et al. ’12]

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 28

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

QCD phase diagram

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 29

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

QCD at nonzero µ

grand canonical approach to QCD: control density by µ

⇒ need µ-dependence of observables

complex action problem: det[ /

D(µ) + m] ∈ C for µ > 0 standard Monte-Carlo methods fail Z =

DAµ exp
−
d4x 1

4FµνFµν

· det

/ D + m

possible ‘workarounds’:

◮ Taylor-expansion in µ: need only µ = 0 simulations ◮ reweighting of the µ = 0 ensemble ◮ analytic continuation from imaginary µ, where det ∈ R ◮ stochastic quantization, complex Langevin equation ◮ density of states, dual variables, canonical ensemble . . . QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 30

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

QCD at nonzero µ - sign problem

reweighting, imaginary µ, canonical ensemble compared on

small lattices [de Forcrand ’10]: different methods agree if µ/T 1

4.8 4.82 4.84 4.86 4.88 4.9 4.92 4.94 4.96 4.98 5 5.02 5.04 5.06 0.5 1 1.5 2 1.0 0.95 0.90 0.85 0.80 0.75 0.70 0.1 0.2 0.3 0.4 0.5 β T/Tc µ/T a µ

confined QGP

<sign> ~ 0.85(1) <sign> ~ 0.45(5) <sign> ~ 0.1(1) D’Elia, Lombardo 16

3

Azcoiti et al., 8

3

Fodor, Katz, 6

3

Our reweighting, 6

3

deForcrand, Kratochvila, 6

3

what about continuum limit, m = mphys?

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 31

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

Taylor-expansion in µ

dependence on µ (to leading order) is encoded in quark

number susceptibilities ⇔ fluctuations χf

2 = ∂2 log Z

∂µf ∂µf

µf =0
susceptibilities: the continuum limit at m = mphys is feasible

[Bors´ anyi et al. ’11]

0.2 0.4 0.6 0.8 1 150 200 250 300 350 400 χ2

u

T [MeV]

SB limit Nt=6 Nt=8 Nt=10 Nt=12 Nt=16 cont. HRG HTL

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 32

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

Taylor-expansion in µ

transition temperature via correlators with χu

2

Tc(µB) = Tc(0) ·

1 − κ · µ2

B/T 2 c (0)

+ O(µ4)
κ ≈ 0.006 [Endr˝
di et al. ’11],

(agreement with [Kaczmarek et al. ’11])

transition mildly weakens

→ no critical endpoint at small densities

compare to freezeout curve
extend range using higher order Taylor coefficients: up to

O(µ8), but yet to be extrapolated a → 0 [Datta et al. ’12]

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 33

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

QCD at nonzero B

magnetic field: external, uniform, time-independent

lattice: no dynamics for B, but ‘full simulation’, i.e. coupling both to quarks (direct) and gluons (indirect)

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 34

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

QCD at nonzero B

det[ /

D(B) + m] ∈ R ⇒ no complex action problem full phase diagram is accessible for lattice simulations!

prominent signal in chiral condensate:

‘magnetic catalysis’ at T = 0

magnetic catalysis turns to inverse catalysis around Tc if

quarks are light [Bali, Bruckmann, Endr˝

di et al. ’11, ’12]

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 35

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

QCD at nonzero B

det[ /

D(B) + m] ∈ R ⇒ no complex action problem full phase diagram is accessible for lattice simulations!

prominent signal in chiral condensate:

‘magnetic catalysis’ at T = 0

magnetic catalysis turns to inverse catalysis around Tc if

quarks are light [Bali, Bruckmann, Endr˝

di et al. ’11, ’12]

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 36

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

QCD at nonzero B

inverse catalysis related to indirect coupling to gluons,

through the Polyakov loop

P affected by B predominantly around Tc

[Bruckmann, Endr˝

di, Kov´

acs ’13]

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 37

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

Summary

the lattice regularization can be employed to deliver reliable

precision results about equilibrium QCD

challenges: continuum limit + physical quark masses
nonzero density: sign problem, circumvented through Taylor

expansion

nonzero magnetic fields: no sign problem

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 38

Introduction QCD at zero µ, zero B QCD at nonzero µ QCD at nonzero B Summary

3D phase diagram of QCD

QCD phase diagram Gergely Endr˝

di

University of Regensburg

SLIDE 39

Backup: complex Langevin

promising results up to high densities [Sexty ’13]
applicability at physical masses?
write det = r · eiϕ; sign problem ‘severe’ where
e2iϕ

∼ 0

0.2

0.2 0.4 0.6 0.8 1 1.2 2 4 6 8 10 12 14 16 µ/T 43*4 lattice beta=5.7 mass=0.05 NF=4 n/nsat average phase factor QCD phase diagram Gergely Endr˝

di

University of Regensburg