EPOS Klaus Werner with Tanguy Pierog, Karlsruhe, Germany Yuriy - - PowerPoint PPT Presentation

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 1

EPOS

Klaus Werner

with Tanguy Pierog, Karlsruhe, Germany Yuriy Karpenko, Nantes, France Benjamin Guiot, Valparaiso, Chile Gabriel Sophys, Nantes, France Maria Stefaniak, Nantes & Warsaw, Poland Mahbobeh Jafarpour, Nantes, France Johannès Jahan, Nantes, France

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 2

Contents

1 Introduction 4 2 Glauber and Gribov-Regge approach 32 3 Collectivity 60 4 Summary 84

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 3

Todays lecture: short version of a detailed lecture (266 pages) at the Joliot-Curie International School 2018 https://ejc2018.sciencesconf.org/data/pages/joliot.20.pdf Today only some selected (important) topics ...

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 4

—————————————————————

1

Introduction —————————————————————

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 5

EPOS is an event generator to treat consistently

e+e- annihilation (test string fragmentation) ep scattering (test parton evolution) pp, pA, AA collisions

at high energies

(collision finished before particle production starts)

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 6

Basic structure of EPOS (for modelling pp, pA, AA)

Primary interactions

Multiple scattering, instantaneously, in parallel (Parton Based Gribov-Regge Theory)

– in pA and AA: multiple NN scattering – but also in pp : Multiple parton scattering

(or for each NN scattering in pA, AA)

Secondary interactions

formation of “matter” which expands collectively, like a fluid, decays statistically

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 7

Some history of Gribov-Regge Theory (the heart of EPOS)

1960-1970: Gribov-Regge Theory of multiple scattering.

pp = multiple exchange of “Pomerons” (with amplitudes based on Regge poles)

1980-1990: pQCD processes

added into GRT scheme (Capella)

1990: M.Braun, V.A.Abramovskii, G.G.Leptoukh:

problem with energy conservation (not done consistently)

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 8

2001: H.J.Drescher, M.Hladik, S.Ostapchenko, T. Pierog,

and K. Werner, Phys. Rept. 350, p93: Marriage pQCD + GRT, with energy sharing (NEXUS)

x

+

2 2

x− x1

− +

x1

✎ ✍ ☞ ✌

∑ x±

i + x± remn = 1

Multiple scatterings (in parallel !!) in pp, pA, or AA

Single scattering = hard elementary scattering including IS + FS radiation

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 9

~ 2003 NEXUS split into

QGSJET (S. Ostapchenko)

– Triple Pomeron contributions and more, to all orders

EPOS (T. Pierog, KW)

– Saturation scale, secondary interactions – two versions, EPOSLHC and EPOS3, going to be “fused”, with a rigorous (selfconsistent) treatment of new key features (HF, saturation & factorization) => new public version (β version exists since few days ...)

Two of the key models used for airshower simulations

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 10

Secondary interactions:

Example: space-time evolution in pp leading to collective flow

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 11

pp @ 7TeV EPOS 3.119

x [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 y [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 50 100 150 200 250 300 350

= 0.10 fm/c) J 0 τ = 0.0 ,

s

η ] (

3

energy density [GeV/fm

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 12

pp @ 7TeV EPOS 3.119

x [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 y [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 10 20 30 40 50 60

= 0.29 fm/c) J 0 τ = 0.0 ,

s

η ] (

3

energy density [GeV/fm

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 13

pp @ 7TeV EPOS 3.119

x [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 y [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 5 10 15 20

= 0.48 fm/c) J 0 τ = 0.0 ,

s

η ] (

3

energy density [GeV/fm

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 14

pp @ 7TeV EPOS 3.119

x [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 y [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 1 2 3 4 5 6 7 8 9

= 0.68 fm/c) J 0 τ = 0.0 ,

s

η ] (

3

energy density [GeV/fm

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 15

pp @ 7TeV EPOS 3.119

x [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 y [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 1 2 3 4

= 0.87 fm/c) J 0 τ = 0.0 ,

s

η ] (

3

energy density [GeV/fm

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 16

pp @ 7TeV EPOS 3.119

x [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 y [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 0.5 1 1.5 2 2.5

= 1.06 fm/c) J 0 τ = 0.0 ,

s

η ] (

3

energy density [GeV/fm

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 17

pp @ 7TeV EPOS 3.119

x [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 y [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 0.2 0.4 0.6 0.8 1 1.2 1.4

= 1.25 fm/c) J 0 τ = 0.0 ,

s

η ] (

3

energy density [GeV/fm

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pp @ 7TeV EPOS 3.119

x [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 y [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

= 1.44 fm/c) J 0 τ = 0.0 ,

s

η ] (

3

energy density [GeV/fm

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pp @ 7TeV EPOS 3.119

x [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 y [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 0.1 0.2 0.3 0.4 0.5 0.6

= 1.63 fm/c) J 0 τ = 0.0 ,

s

η ] (

3

energy density [GeV/fm

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pp @ 7TeV EPOS 3.119

x [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 y [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

= 1.83 fm/c) J 0 τ = 0.0 ,

s

η ] (

3

energy density [GeV/fm

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 21

pp @ 7TeV EPOS 3.119

x [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 y [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 0.05 0.1 0.15 0.2 0.25 0.3 0.35

= 2.02 fm/c) J 0 τ = 0.0 ,

s

η ] (

3

energy density [GeV/fm

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 22

pp @ 7TeV EPOS 3.119

x [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 y [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 0.05 0.1 0.15 0.2 0.25

= 2.21 fm/c) J 0 τ = 0.0 ,

s

η ] (

3

energy density [GeV/fm

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 23

pp @ 7TeV EPOS 3.119

x [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 y [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 0.05 0.1 0.15 0.2

= 2.40 fm/c) J 0 τ = 0.0 ,

s

η ] (

3

energy density [GeV/fm

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 24

pp @ 7TeV EPOS 3.119

x [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 y [fm]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

= 2.59 fm/c) J 0 τ = 0.0 ,

s

η ] (

3

energy density [GeV/fm

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 25

Radial flow visible in particle distributions Particle spectra affected by radial flow

10

• 2

10

• 1

1 10 10 2 1 2 3 pt dn/dptdy _ π- K- p Λ hydrodynamics (solid) string decay (dotted)

=> mass ordering of pt, lambda/K increase

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pPb at 5TeV

CMS,EPJC 74 (2014) 2847, arXiv:1307.3442

0.5 1 1.5 2 2.5 3 3.5 4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 pt dn/dptdy K EPOS3.074 CMS 0.5 1 1.5 2 2.5 3 3.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 pt dn/dptdy p EPOS3.074 CMS

Strong variation of shape with multiplicity for kaon and even more for proton pt spectra (EPOS curves: flow changes shapes)

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Anisotropic radial flow visible in dihadron-correlations

R = 1 Ntrigg dn d∆φ∆η

Anisotropic flow due to initial azimuthal anisotropies

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Initial “elliptical” matter distribution: Preferred expansion along φ = 0 and φ = π ηs-invariance same form at any ηs

ηs = 1

2lnt+z t−z

φ

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 29

Particle distribution: Preferred directions φ = 0 and φ = π ∝ 1 + 2v2 cos(2φ)

0.05 0.1 0.15 0.2

• 1

1 2 3 4 φ f(φ) = dn / dφ

Dihadrons: preferred ∆φ = 0 and ∆φ = π (even for big ∆η)

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 30

Ridges (in dihadron correlation functions) seen in pPb (and even pp)

Central - peripheral (to remove jets) Phys. Lett. B 726 (2013) 164-177

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2

• 1

1 2 3 4 0.72 0.74 0.76 0.78

2.0-4.0 GeV/c

trigg T

p 1.0-2.0 GeV/c

assoc T

p

η ∆ φ ∆ R EPOS3.074

ALICE

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Heavy ion approach = primary (multiple) scattering + subsequent fluid evolution becomes interesting for pp and pA

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—————————————————————

2

Glauber and Gribov-Regge approach ————————————————————— concerning primary interactions

providing initial conditions for secondary interactions

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Glauber approach

Nucleus-nucleus collision A + B :

Sequence of independent binary

nucleon-nucleon collisions

Nucleons travel on straight-line trajectories The inelastic nucleon-nucleon cross-section σNN is in-

dependent of the number od NN collisions Monte Carlo version: Two nucleons collide if their trans- verse distance is less than √ σNN/π .

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 34

Analytical formulas for A + B scattering:

Be ρA and ρB the (normalized nuclear densities), and b = (bx, by) the

impact parameter x y b Define integral over nuclear density for each nucleus: TA/B(b′) =

• ρA/B(b′, z)dz,

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 35

and the “thickness function” TAB(b) =

• TA(b′)TB(b′ − b)d2b′

x y b b’ b’−b Probability of interaction (for ρA and ρB normalized to 1) P = TAB(b) σNN

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 36

Having AB possible pairs: probability of n interactions : Pn = AB n

• Pn(1 − P)AB−n

Probability of at least one interaction (given b):

AB

∑

n=1

Pn = 1 − P0 = 1 − (1 − P)AB And finally the AB cross section (called optical limit): σAB = 1 − (1 − P)AB d2b,

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 37

so the probability of an interaction is dσAB d2b = 1 − (1 − TAB(b) σNN)AB . Glauber MC formula (with σNN =

• f(b)d2b):

dσAB d2b = 1−

A

∏

i=1

d2bA

i TA(bA i ) B

∏

j=1

d2bB

j TB(bB j ) AB

∏

k=1

(1− f)

• .

In the MC version, one extracts Ncoll, Nparticip, and one usually employs a “wounded nucleon approach” Does this make sense?

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Theoretical justification? ... based on relativistic quantum mechanical scattering theory, compatible with QCD => Gribov-Regge approach

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Gribov-Regge approach and cut diagrams

details see https://ejc2018.sciencesconf.org/data/pages/joliot.20.pdf (266 page lecture for diploma and PhD students)

The scattering operator ˆ S is defined via

|ψ(t = +∞ = ˆ

S |ψ(t = −∞ Unitarity relation ˆ S† ˆ S = 1 gives (considering a discrete Hilbert space) 1 = i| ˆ S† ˆ S |i

= ∑

f

i| ˆ

S† | f f| ˆ S |i

= ∑

f

f| ˆ

S |i∗ f| ˆ S |i

= ∑

f

S∗

fiSfi

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 40

Using Sfi = δfi + i(2π)4δ(p f − pi)Tfi and the Schwarz re- flection principle (Tii(s∗, t) = Tii(s, t)∗) and disc T = Tii(s + iǫ, t) − Tii(s − iǫ, t)

• ne gets

1 i disc T = (2π)4δ(p f − pi)∑

f

• Tfi
• 2 = 2s σtot

Interpretation:

1 idisc T can be seen as a so-called “cut di-

agram”, with modified Feynman rules, the “intermediate particles” are on mass shell.

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Modified Feynman rules :

Draw a dashed line from top to bottom Use “normal” Feynman rules to the left Use the complex conjugate expressions to the right For lines crossing the cut: Replace propagators by mass

shell conditions 2πθ(p0)δ(p2 − m2)

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Cutting a diagram representing elastic scattering corresponds to inelastic scattering

2 =

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Cutting diagrams is useful in case of substructures:

=

Precisely the multiple scattering structure in EPOS (QCD is hidden in the colored squares)

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+ + +

Cut diagram = sum of products of cut/uncut subdiagrams => Gribov-Regge approach of multiple scattering

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What are the blocks, called Pomerons?

=

Pomeron = parton ladders cut Pomerons => open ladder => kinky string

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Gribov Regge for A+B scattering

In the GR framework, defining

• dTAB :=
• A

∏

i=1

d2bA

i TA(bA i ) B

∏

j=1

d2bB

j TB(bB j ),

we obtain (neglecting energy sharing): dσAB d2b =

• dTAB ∑

m1

... ∑

mAB

• ∑ mi=0

AB

∏

k=1

W(bk)mk mk! e−W(bk)) Relaxing the condition ∑ mi = 0 gives unity.

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 47

So σAB d2b = 1 −

• dTAB
• AB

∏

k=1

e−W(bk)

• Defining f = 1 − e−W(bk), i.e. the probability of an interac-

tion in pp, with σNN = f(b)d2b, we get the Gribov-Regge result σAB d2b = 1 −

• dTAB

AB

∏

k=1

(1 − f)

• which corresponds to “Glauber Monte Carlo”.

So everything OK?

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 48

Even if the cross section formulas in GR and GMC are the same, particle production is done in a fundamentally different fashion

In Glauber

– one has (usually) a hard component (∼ Ncoll) – and a soft one (∼ Npart, wounded nucleons)

In GR (EPOS)

– remnants contribute only at large rapidities, – otherwise everything is coming from

“cut Pomerons” associated to NN scatterings.

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Factorization

Factoriztion says that the pp inclusive cross section can be written as

∑

kl

• dxdx′dp2

⊥ fk(x, M2 F) fl(x′, M2 F)dσkl Born

dp2

⊥

(xx′s, p2

⊥),

with “parton distribution functions” obtained from DIS (ep scattering). Not obvious in the EPOS GR framework, but one can prove that in the basic approach factorization holds (Phys. Rept. 350 (2001) p93)

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Electron-proton scattering F2 vs x

1 2 Q2=1.5 Q2=2.5 Q2=3.5 Q2=5 Q2=6.5 1 2 Q2=8.5 Q2=12 Q2=15 Q2=20 Q2=25 1 2 Q2=35 Q2=45 Q2=60 Q2=90 Q2=120 1 2 Q2=150 Q2=200 Q2=250 Q2=350 Q2=500 1 2 10

• 4

10

• 1

x Q2=650 10

• 4

10

• 1

x Q2=800 10

• 4

10

• 1

x Q2=1200 10

• 4

10

• 1

x Q2=2000 10

• 4

10

• 1

x Q2=5000

We can compute F2 = ∑

k

e2

k x fk(x, Q2)

with x = xB = Q2 2pq in the EPOS frame- work

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 51

Compare with parton model calculation using CTEQ PDFs for pp at 7 TeV

10

• 10

10

• 9

10

• 8

10

• 7

10

• 6

10

• 5

10

• 4

10

• 3

50 100 150 200 250 300 parton pt (GeV/c) dnparton / dpt (c/GeV) line: CTEQ6.6M stars: EPOS

In EPOS we do not employ explicitely factorization!

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 52

Compare with data: jet production in pp at 7 TeV

10

• 8

10

• 7

10

• 6

10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

1 20 40 60 80 100 jet pt (GeV/c) d2n / dy dpt (c/GeV) pp at 7 TeV jets anti-kt preliminary EPOS3.076 ATLAS ALICE

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 53

Why does factorization work ? Easy to see in the GR picture without energy conservation, using simple assumptions. Consider multiple scattering amplitude iT = ∏ iTP cross section: sum over all cuts.

+ + +

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 54

For each cut Pom: 1 i discTP = 2ImTP ≡ G For each uncut one: iTP + {iTP}∗

= i (i ImTP) + {i (i ImTP)}∗ = −2ImTP ≡ −G

+ + +

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 55

Inclusive particle production cross section σincl: Assume that each cut Pomerons produces N particles, an uncut one nothing. Contribution to the inclusive cross section for n Pomerons (k refers to the cut Pomerons): σ(n)

incl ∝ n

∑

k=0

kN Gk (−G)n−k n k

• ∝

n

∑

k=0

(−1)n−k k ×

n k

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 56

∑n

k=0 (−1)n−k k ×

n k

• :

For n = 2 :

+0 × 1 − 1 × 2 + 2 × 1 = 0

No contribution ! For n = 3 :

−0 × 1 + 1 × 3 − 2 × 3 + 3 × 1 = 0

No contribution either !

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 57

Actually, for any n > 1 :

n

∑

k=0

(−1)n−k k ×

n k

• = 0

Almost all of the diagrams (i.e. n=2, n=3, ....) do not

contribute at all to the inclusive cross section

Enormous amount of cancellations (interference),

• nly n=1 contributes

AGK cancellations

(Abramovskii, Gribov and Kancheli cancellation (1973))

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 58

simple diagram even in case of multiple scattering corresponds to factorization:

σincl = f ⊗ σelem ⊗ f

The F2 discussed earlier: Half of this diagram

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 59

Since it is known that factorization works, the ansatz

σincl = f ⊗ σelem ⊗ f

may be used as starting point, with f taken from DIS (electron-proton).

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—————————————————————

3

Collectivity —————————————————————

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Pomerons => Parton ladders = color flux tubes = kinky strings

remnant remnant flux tube

(here no IS radiation, only hard process producing two gluons)

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which expand and break via the production of quark-antiquark pairs (Schwinger mechanism)

remnant remnant jet jet

String segment = hadron. Close to “kink”: jets

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 63

Consider heavy ion collisions

• r high energy & high multiplicity pp events:

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 64

again: single scattering => 2 color flux tubes

remnant remnant flux tube

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... two scatterings => 4 color flux tubes

remnant flux tube remnant

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... many scatterings (AA) => many color flux tubes

=> matter + escaping pieces (jets)

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 67

Core-corona procedure (for pp, pA, AA):

Pomeron => parton ladder => flux tube => string segments

✤ ✣ ✜ ✢

High pt segments escape => corona The others => core

(core = initial condition for hydro depending on the local string density)

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2

• 2
• 1

1 2 x (fm) y (fm) core- corona 5.7fm 5 Pomerons η = -1.00

pPb

10

• 4

10

• 3

10

• 2

10

• 1

1 10 10 2 10 3 2 4 6 pt dn/dptdy pPb 5TeV 20-40% pions x 100 protons corona core EPOS3.076

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 68

Hydrodynamic evolution of the core The evolution of the system for τ ≥ τ0 treated macroscopicly, solving the equations of relativistic hydrodynamics: Three equations concerning conserved currents:

∂νNν

q = 0

with

Nν

q = nq uν

and nq (q =u ,d, s) representing (net) quark densities, uν is the velocity four vector.

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 69

Four equations concerning energy-momentum conserva- tion:

∂νTµν = 0.

The energy-momentum tensor Tµν is

the flux of the µth component of the momentum vector across a surface with constant ν coordinate (using four-

vectors)

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 70

T00: Energy density dE/dx1dx2dx3 (x0 const) T01: Energy flux dE/dx0dx2dx3 (x1 const) Ti0: Momentum density Tij: Momentum flux

COST WS Lund University # February 2019 # Klaus Werner # Subatech, Nantes 71

The equation

∂νTµν = 0

is very general, no need for thermal equilibrium, no need for particles. The energy-momentum tensor is the conserved Noether current associated with space-time translations.

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∂νTµν represents 4 equations, so we should express T

in terms of 4 quantities (unknowns)

and/or find additional equations which means additional assumptions

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First approach: Ideal Fluid In the local rest frame of a fluid cell:

T00 = ε (energy density in LRF) T0i = 0 (no energy flow) T0i = 0 (no momenum in LRF) Tij = δijp (p = isotropic pressure)

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In arbitrary frame:

Tµν = (ε + p)uµuν − pgµν

+ Equation of state p = p(ε) of QGP from lQCD => 4 equations for 4 unknowns (ε, velocity)

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Beyond ideal (viscous hydro): The energy-momentum tensor may be expressed via a sys- tematic expansion in terms of gradients (of ln ε and u): Tµν = Tµν

(0) + Tµν (1) + Tµν (2) + ...,

with the “equilibrium term” Tµν

(0)

Mueller-Israel-Steward (MIS) approach (second order + shear stress tensor and bulk pressure dy- namical quantities, governed by relaxation equations)

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Freeze out happens at a hypersurface Σ (constant energy density). Cooper-Frye hadronization amounts to calculating E dn d3p =

• dΣµpµ f(up),

f is the Bose-Einstein or Fermi-Dirac distribution (in case of ideal hydro).

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How does hydro evolution affect results?

Mass dependent broadening of pt spectra (flow) Particular dihadron correlations Statistical particle production

(compared to string decay)

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Particle ratios to pions vs

dnch

dη (0)

• 10
• 3

10

• 2

10

• 1

10 10

2

10

3

<dnch/dη(0)> ratios to π ALICE data K K* p Λ Ξ Φ Ω Ξ* Ωx8 Ξx3 K*x2.3

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Proton to pion ratio (sofar GC)

10

• 2

10

• 1

1 10 10

2

10

3

<dnch/dη(0)> ratio to π ALICE (black) p EPOS 3.210 full co+co corona core

core hadronization: T = 164 MeV, µB = 0 statistical model fit (horizontal black line)

• A. Andronic et al.,

arXiv:1611.01347

T = 156.5 MeV, µB = 0.7 MeV thick lines = pp (7TeV) thin lines = pPb (5TeV) circles = pp (7TeV) squares = pPb (5TeV) stars = PbPb (2.76TeV)

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Omega to pion ratio (GC)

10

• 4

10

• 3

1 10 10

2

10

3

<dnch/dη(0)> ratio to π ALICE (black) Ω EPOS 3.210 full co+co corona core

thick lines = pp (7TeV) thin lines = pPb (5TeV) circles = pp (7TeV) squares = pPb (5TeV) stars = PbPb (2.76TeV)

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New trends on the foundations

• f hydrodynamics

A systematic way get the equations of relativistic hy-

drodynamics is via a formal gradient expansion of Tµν (in terms of gradients (of ln ε and u)

The hydrodynamic gradient expansion has

(maybe) a vanishing radius of convergence

There are tools to deal with that. Need to go beyond

perturbative expansions.

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In hydro toy models (Heller, Spalinski, PRL 115, 072501 (2015)) one can show that the hydrodynamical expansion (gradient expansion) is divergent, but numerically on gets an attractor well defined solutions even at small times, contrary to the pertur- bative expansion. => well defined solu- tions “far off equilib- rium” Same results via “re- summation”

Picture from Heller, M. Spalinski.

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What do these “resummation” results tell us?

Hydro may be applicable even far off equilibrium

(in particular relevant for small systems)

=> True solution : Hydrodynamic attractor

Accessible (in principle) via resummation

Frequently asked question:

“Why do small systems thermalize so quickly?” Maybe they simply don´t ...

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4

Summary

Multiple NN scattering in pA and AA: Essentially geometry

=> Glauber approach. Same cross section formula in Gribov- Regge, using Pomerons, but completely different particle pro- duction scheme

In the EPOS GR approach, multiple scattering naturally extends

to pp => multiple cut Pomerons => overlapping strings => mat- ter formation

Attractive option: Implementing hydrodynamic expansion (pro-

vides observed flow effects) + statistical hadronization