Heavy Ions Collisions and the search for the Quark-Gluon ... · PDF fileHeavy Ions Collisions and the search for the Quark-Gluon Plasma Carlos A. Salgado CERN, TH-Division ( @cern.ch,

Heavy Ions Collisions and the searchfor the Quark-Gluon Plasma

Carlos A. Salgado

CERN, TH-Division

([email protected], http://home.cern.ch/csalgado)

1. QCD matter. The final state in HIC.

2. The first stages and before. The initial state in HIC.

3. Signals for the QGP formation.

4. Experimental/Theoretical status.

RHIC

LHC

Islamabad, March 2004 HIC and the search for the QGP – p.1

Summary I+II

QCD vacuum:Confinement & chiral symmetry breaking

Theory −→ Different phases exist!

Order of the transition depends on quarks masses. For realisticmasses, most probably crossover at µB = 0.

Initial state effects

Multiple scattering and coherence effects necessary to describeheavy ion collisions

Large multiplicities in HIC

High densities created

Non-linear terms in the evolution equations appear.

Islamabad, March 2004 HIC and the search for the QGP – p.2

3. Signals of QGP formation

Islamabad, March 2004 HIC and the search for the QGP - 3. Signals. – p.3

3. Signals of QGP formation

Final state effects


High-energy heavy ion collisions

Before the collision: Lorentz-contracted nuclei



Before the collision: Lorentz-contracted nuclei



at t = 0 most of the energy in the central region

Initial stateIslamabad, March 2004 HIC and the search for the QGP - 3. Signals. – p.4


First ∼ 0.1 ÷ 0.3 fm. Quark gluon plasma formation



Expansion and hadronization


"Canonical" space-time picture

production and ther-malization

Transitions: lines of constant proper time τ .



QGPproduction and ther-malization




mixed phase??





hadron gas

mixed phase??





freeze-outhadron gas

mixed phase??




Characterization of the medium

The medium (or media?!), if formed, has a very short lifetime. In order tostudy its properties some (indirect) signals are proposed

Soft (bulk) signatures:

Strangeness enhancement

Flows

Particle composition

...






Flows


...

Hard probes (large Q2)

J/Ψ suppression

Jet quenching






Flows


...

Hard probes (large Q2)

J/Ψ suppression

Jet quenchingProduced at the early (τ ∼ 1/Q)stages


Soft probes



In order to produce strangeness,in a medium with broken chiralsymmetry one needs

mK+ +mK− ∼ 1GeV

In a medium in which chiral symmetry is restored, the energy is just thesum of the strange quark mass,

ms +ms ∼ 150÷ 400MeV



In order to produce strangeness,in a medium with broken chiralsymmetry one needs

mK+ +mK− ∼ 1GeV

In a medium in which chiral symmetry is restored, the energy is just thesum of the strange quark mass,

ms +ms ∼ 150÷ 400MeV

1

10

1 10 102

103

pT > 0, |y-ycm| < 0.5

< Nwound >

Par

ticle

/ ev

ent /

wou

nd. n

ucl.

rela

tive

to p

Be

Λ

Ξ-

pBe pPb PbPb

1

10

1 10 102

103

pT > 0, |y-ycm| < 0.5

< Nwound >

Par

ticle

/ ev

ent /

wou

nd. n

ucl.

rela

tive

to p

Be

Λ

Ξ +

Ω-+Ω +

pBe pPb PbPb

Strange baryons enhancement by NA57 (√s=17.3 GeV)


Statistical description of particle yields

Assuming an ideal gas of particles, the number densities are

ni = −TV

∂ lnZ

∂µi

gi

2π2

∫

∞

0

p2dp

exp[(Ei − µi)/T ]± 1

Only two independent parameters, µB and T (+some assumptions)

Rat

ios

10-2

10-1

1

=130 GeVNNs =200 GeVNNs

Braun-Munzinger et al., PLB 518 (2001) 41 D. Magestro (updated July 22, 2002)

STARPHENIXPHOBOSBRAHMS

Model prediction for = 29 MeVbµT = 177 MeV,

Model re-fit with all data = 41 MeVbµT = 176 MeV,

/pp Λ/Λ Ξ/Ξ Ω/Ω +π/-π +/K-K -π/-K -π/p -/h*0K-

/hφ -/hΛ -/hΞ *10-π/Ω /pp +/K-K -π/-K -π/p *50-/hΩ


Statistical description of particle yields

Assuming an ideal gas of particles, the number densities are

ni = −TV

∂ lnZ

∂µi

gi

2π2

∫

∞

0

p2dp

exp[(Ei − µi)/T ]± 1

However, it also works for e+e−...

Hadron mass (GeV)

nh

πππ

K

η

ρ0ω

K*

p

η, Φ

Λ

ΣΞ-

∆++

Σ*

Ξ*0 Ω

LEP

T=162.9±2.1 MeV

V=21.4±1.9 Fm3

γs=0.70±0.027

π0 π+ K+ K0 η ρ0 ω K*+K*0p η, Φ Λ Σ0 Σ+ ∆++Ξ- Σ* Ξ*0Ω

Num

ber

of s

t. de

v.

10-3

10-2

10-1

1

10

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

-4-2024

[Becattini 1995]


Collective flow

In a non-relativistic fluid, the fluid acceleration is given by Euler’s eq.

dβ

dt= −1

ρ∇P

[

dβ

dt= − c2

ε+ P∇P → relativistic

]

where, β is the fluid velocity, ρ the mass density and P the pressure.Pressure gradients produce collective flow.


Collective flow


dβ

dt= −1

ρ∇P

[

dβ

dt= − c2


]


Hydrodynamical models are fixed by

An equation of state −→ relation between P and ε.

Initial condition: fluid velocity and energy density.

freeze-out temperature.


Collective flow


dβ

dt= −1

ρ∇P

[

dβ

dt= − c2


]


Hydrodynamical models are fixed by

An equation of state −→ relation between P and ε.

Initial condition: fluid velocity and energy density.

freeze-out temperature.

Initial condition in a HIC has gradients of energy density. Thistranslates into gradients of the pressure and, by evolution, flow.

Relation between the initial distribution of energy and flow(s).


Elliptic flow

Gradients are more easily produced in asymmetric media: Changing thecentrality of the collision.

Reaction plane defined by theimpact parameter and thecollision axis.


Elliptic flow

Gradients are more easily produced in asymmetric media: Changing thecentrality of the collision.

Reaction plane defined by theimpact parameter and thecollision axis.

Doing the Fourier expansion ofthe number of particles in thereaction plane

dN

dφ∝ 1 + 2

∞∑

n=1

vn cos(nφ)

vn characterize the strength ofthe anisotropic flow.

v2 elliptic flow.


Elliptic flow

Elliptic flow has measured at RHIC (one of the main signals)

0

0.1

0.2

0.3

0 1 2 3 4

pbarK−π−

v 2

pT (GeV/c)0 1 2 3 4

pK+π+

pT (GeV/c)

0

0.1

0.2

0.3

0 1 2 3 4

p pbarK+ K−π+ π−

hydro πhydro Khydro p

v 2

pT (GeV/c)

0

0.05

0.1

0 0.5 1 1.5

p pbarK+ K−π+ π−

v 2/n

qu

ark

pT/nquark (GeV/c)

[STAR data]

Comparison with hydrodynamical calculations

The main interest of elliptic flow is that it is very difficult to generatewithout strong final state interactions/thermalization.


Hard Probes


J/Ψ suppression

A J/Ψ is a bound cc state.

We have seen that the potential between two quarks is screened inthe medium.

In this case, the cc pair is diluted in the medium and the production ofbound states is suppressed.


J/Ψ suppression

A J/Ψ is a bound cc state.

We have seen that the potential between two quarks is screened inthe medium.

In this case, the cc pair is diluted in the medium and the production ofbound states is suppressed.


J/Ψ suppression II

*p(450 GeV/c)-p,d (NA51)

208

16

p(200 GeV/c)-A (A=Cu,W,U) (NA38)

O(16x200 GeV/c)-Cu,U (NA38)

*

S(32x200 GeV/c)-U (NA38)

*Pb(208x158 GeV/c)-Pb (NA50)

32

p(450 GeV/c)-A (A=C,Al,Cu,W) (NA38)

10101 10101010652 3 4

B target

σ

projectile

µµB

(

J/

)/(

AB

) (n

b)

ψ

5

4

3

2

10.9

0.8

0.7

0.4

0.5

0.6

A

0.06 = 0.74K

R

0.01 = 0.92

* rescaled to 200 GeV/c

α

J/Ψ suppression measured atCERN (NA50).


J/Ψ suppression II

*p(450 GeV/c)-p,d (NA51)

208

16



*

S(32x200 GeV/c)-U (NA38)

*Pb(208x158 GeV/c)-Pb (NA50)

32


10101 10101010652 3 4

B target

σ

projectile

µµB

(

J/

)/(

AB

) (n

b)

ψ

5

4

3

2

10.9

0.8

0.7

0.4

0.5

0.6

A

0.06 = 0.74K

R

0.01 = 0.92


α


pA collisions→ nuclear absopt.(multiple scattering cc-A)


J/Ψ suppression II

*p(450 GeV/c)-p,d (NA51)

208

16



*

S(32x200 GeV/c)-U (NA38)

*Pb(208x158 GeV/c)-Pb (NA50)

32


10101 10101010652 3 4

B target

σ

projectile

µµB

(

J/

)/(

AB

) (n

b)

ψ

5

4

3

2

10.9

0.8

0.7

0.4

0.5

0.6

A

0.06 = 0.74K

R

0.01 = 0.92


α



OCu, OU, SU→ nuclearabsoption.


J/Ψ suppression II

*p(450 GeV/c)-p,d (NA51)

208

16



*

S(32x200 GeV/c)-U (NA38)

*Pb(208x158 GeV/c)-Pb (NA50)

32


10101 10101010652 3 4

B target

σ

projectile

µµB

(

J/

)/(

AB

) (n

b)

ψ

5

4

3

2

10.9

0.8

0.7

0.4

0.5

0.6

A

0.06 = 0.74K

R

0.01 = 0.92


α



OCu, OU, SU→ nuclearabsoption.

PbPb ”anomalous suppression”

hadronic or partonic origin?

Lattice results not yet determinant on whether J/Ψ dissociates at Tc orabove. Other cc states, as ψ′ or χc, could dissociate bellow Tc.


Jet quenching


Jet quenching

Suppose a particle entering amedium or created inside themedium


Jet quenching


The particle looses energy whiletraveling through the medium

by scattering with the medium

by radiation


Jet quenching




by radiation

At high energy, gluon radiationdominates: medium-induced gluonemission


Jet quenching




by radiation

At high energy, gluon radiationdominates: medium-induced gluonemission

A high-pt particle produced insidea medium will lose energy while es-caping it −→ spectrum suppressedat large pt.


High-pt production in pp: pQCD

QCD factorization formula:

dσhpp

dp2tdy∼∑

i,j

x1fpi (x1, Q

2)⊗ x2fpj (x2, Q

2)⊗ dσij→k

dt⊗Dk→h(z, µ2

F )

(Eskola and Honkanen: Nucl.Phys. A713 (2003) 167)


Space-time picture

Before the collision, initial state: nuclear PDF’s.


dσhAB

dp2tdy∼∑

i,j

x1fpi (x1, Q

2)⊗ x2fpj (x2, Q

2)⊗ dσij→k

dt⊗Dmed

k→h(z, µ2F )


Space-time picture

At t ∼ 0


dσhAB

dp2tdy∼∑

i,j

x1fpi (x1, Q

2)⊗ x2fpj (x2, Q

2)⊗ dσij→k

dt⊗Dmed

k→h(z, µ2F )


Space-time picture

Evolution.


dσhAB

dp2tdy∼∑

i,j

x1fpi (x1, Q

2)⊗ x2fpj (x2, Q

2)⊗ dσij→k

dt⊗Dmed

k→h(z, µ2F )


Effects of nuclear PDF.

Nuclear effects in PDF produce small changes in high–pt particleproduction at RHIC and LHC, at most 25 % .

0 5 10 15 200.7

0.8

0.9

1.0

1.1

1.2

1.3

AuAu/AuAu(ns)AuAu/pppAu/pAu(ns)pAu/ppRHIC, sqrt(s)=130 GeV

0 5 10 15 20 25qT (GeV)

AuAu/AuAu(ns)AuAu/pppAu/pAu(ns)pAu/ppRHIC, sqrt(s)=200 GeV

0 50 100 150 2000.7

0.8

0.9

1.0

1.1

1.2

1.3

PbPb/PbPb(ns), 5.5 TeVPbPb/pp, 5.5 TeVpPb/pPb(ns), 8.8 TeVpPb/pp, 8.8 TeVLHC

[Eskola and Honkanen]

Computed using EKS98 nPDF’s.


Matter affects evolution.

A quark or gluon (traveling in vacuum) with virtuality Q2 will radiategluons to become on-shell: DGLAP-like evolution.




Gluon radiation modified when the particle traverses a medium:medium-induced gluon radiation.




Gluon radiation modified when the particle traverses a medium:medium-induced gluon radiation.

Where to look?

Inclusive particle (suppression).

Jets: Jetshapes... −→ LHC


Medium–induced gluon radiation.

u,k)ω(

lyly

)1(E,p

. . .

. . .

. . .. . .. . .

,k)ω(

)1(E,p)2((1-x)E,p)2((1-x)E,p

For media of finite length

ωdItot

dωdk2⊥

=


Medium–induced gluon radiation.

u,k)ω(

lyly

)1(E,p

. . .

. . .

. . .. . .. . .

,k)ω(

)1(E,p)2((1-x)E,p)2((1-x)E,p

For media of finite length

ωdItot

dωdk2⊥

=

The medium induced gluon radiation

ωdI

dωdk2⊥

= ωdItot

dωdk2⊥

− ω dIvac

dωdk2⊥

Medium: L (length) and q (transport coefficient).


Double differential spectrum

High energy approximation −→ multiple scattering. The final result is

ωdI

dωdk⊥

=αs CR

(2π)2 ω22Re

∫

∞

ξ0

dyl

∫

∞

yl

dyl

∫

du e−ik⊥·u e−

12

∫

∞

yldξ n(ξ) σ(u)

× ∂

∂y· ∂∂u

∫ u=r(yl)

y=0=r(yl)

Dr exp

[

i

∫ yl

yl

dξω

2

(

r2 − n(ξ)σ (r)

i ω

)]

.




ωdI

dωdk⊥

=αs CR

(2π)2 ω22Re

∫

∞

ξ0

dyl

∫

∞

yl

dyl

∫


12

∫

∞

yldξ n(ξ) σ(u)

× ∂

∂y· ∂∂u

∫ u=r(yl)

y=0=r(yl)

Dr exp

[

i

∫ yl

yl

dξω

2

(

r2 − n(ξ)σ (r)

i ω

)]

.

Two approximations

Multiple soft scattering n(ξ)σ(r) = q(ξ)2 r2. The path integral reduces

to a harmonic oscillator of imaginary frequency.




ωdI

dωdk⊥

=αs CR

(2π)2 ω22Re

∫

∞

ξ0

dyl

∫

∞

yl

dyl

∫


12

∫

∞

yldξ n(ξ) σ(u)

× ∂

∂y· ∂∂u

∫ u=r(yl)

y=0=r(yl)

Dr exp

[

i

∫ yl

yl

dξω

2

(

r2 − n(ξ)σ (r)

i ω

)]

.

Two approximations

Multiple soft scattering n(ξ)σ(r) = q(ξ)2 r2. The path integral reduces

to a harmonic oscillator of imaginary frequency.

Single hard scattering First order in the opacity expansion parametern(ξ)σ(r).A Yukawa cross section is usually taken for the cross sectionσ(r)

Expansion in the number of scatterings


Coherent radiation

Two phases appear: quark and emitted gluon

ϕE =

⟨

k2⊥

2E∆z

⟩

ϕ =

⟨

k2⊥

2ω∆z

⟩

=⇒ lcoh ∼ω

k2⊥

High energy limit E →∞ so, the first one is neglected.


Coherent radiation


ϕE =

⟨

k2⊥

2E∆z

⟩

ϕ =

⟨

k2⊥

2ω∆z

⟩

=⇒ lcoh ∼ω

k2⊥

High energy limit E →∞ so, the first one is neglected.Medium −→ transport coefficient q ' µ2

λ , transverse momentum µ2 permean free path λ. So,

k2⊥∼ lcoh

λµ2 =⇒ k2

⊥∼ qL (for lcoh = L)


Coherent radiation


ϕE =

⟨

k2⊥

2E∆z

⟩

ϕ =

⟨

k2⊥

2ω∆z

⟩

=⇒ lcoh ∼ω

k2⊥

High energy limit E →∞ so, the first one is neglected.Medium −→ transport coefficient q ' µ2

λ , transverse momentum µ2 permean free path λ. So,

k2⊥∼ lcoh

λµ2 =⇒ k2

⊥∼ qL (for lcoh = L)

Let us define κ2 ≡ k2⊥

qL, ωc =

1

2qL2

So, the phase for ∆z = L −→ ϕ ∼ κ2 ωc

ω

gluon emitted when ϕ & 1⇐⇒ radiation suppressed for κ2 . ω/ωc

In cold nuclear matter: Q2sat = qL =⇒ κ2 =

k2⊥

Q2sat


Gluon energy distributions for quark jets

κ2 =k2⊥

qL, ωc =

1

2qL2

Plateau at small κ←→ coherencegluons =⇒ factor Nc/CF larger

ωdI

dω=

∫ ω

0

dk⊥ωdI

dωdk⊥

kinematical limitk⊥ ≤ ω =⇒ R = ωcL finite

Infrared safe.


Properties of the spectrum

For gluon emission, we have the restriction k⊥ ≤ ω.

Coherence, k2⊥

. qL. =⇒ spectrum suppressed for

ω2 . k2⊥∼ qL ⇐⇒

(

ω

ωc

)2

.2

R, R =

1

2qL3 .




Coherence, k2⊥


ω2 . k2⊥∼ qL ⇐⇒

(

ω

ωc

)2

.2

R, R =

1

2qL3 .

−→ Formation time effects suppress IR region.

Removing this limit (R→∞)

limR→∞

ωdI(ω)

dω=αsCR

πln

[

cosh2

√

ωc

2ω− sin2

√

ωc

2ω

]

.

[Baier, Dokshitzer, Mueller, Peigné, Schiff]




Coherence, k2⊥


ω2 . k2⊥∼ qL ⇐⇒

(

ω

ωc

)2

.2

R, R =

1

2qL3 .

−→ Formation time effects suppress IR region.

Removing this limit (R→∞)

limR→∞

ωdI(ω)

dω=αsCR

πln

[

cosh2

√

ωc

2ω− sin2

√

ωc

2ω

]

.

[Baier, Dokshitzer, Mueller, Peigné, Schiff]

The total energy loss:

limR→∞

ωdI(ω)

dω−−−→ω<ωc

√

ωc

ω⇐⇒ ∆E =

∫

dωωdI(ω)

dω∼ ωc ∼ qL2


Medium-modified fragmentation functions I

For large-pt the hadronization takes place outside the medium

Model: (Wang, Huang, Sarcevic, PRL 77 2537)

D(med)h/q (z,Q2) =

∫ 1

0

dε PE(ε)1

1− ε Dh/q(z

1− ε ,Q2) .

P (ε) probability that the hard parton loses a fraction of energy ε.

Independent gluon emission approx.: (BDMS, JHEP 0109:033)

PE(ε) =∞∑

n=0

1

n!

[

n∏

i=1

∫

dωidI(ωi)

dω

]

δ

(

ε−n∑

i=1

ωi

E

)

exp

[

−∫

dωdI

dω

]

.

P (ε) = p0δ(ε) + p(ε)

p0 ⇒ no E.loss

p(ε)⇒ sum for n ≥ 1.


Medium-modified FF II

Quenching weights for quarks.

Tabulated: http://home.cern.ch/csalgado

R =q

2L3 =

L2

R2A

dNg

dy

Suppression of ∼ 5 for pt ∼ 5÷7GeV =⇒ R∼ 2000.


Comparison with PHENIX data.

At RHIC, particles with pt . 10 GeV have been measured.

Ratio with proton-proton:

RAA =dNAA/dpt

NcolldNpp/dpt

RAA = 1⇒ no effect.

A factor of 5 suppression forcentral AuAu collisions.

Smallest values of pt are in thelimit of applicability of the calcu-lations.

Can be described with dNg/dy ∼ 1000÷ 2000.

Some estimates [X-N Wang]

ε|τ∼0.2fm/c ∼ 15GeV/fm3


Summary III

In order to characterize the created medium (indirect) signals arenecessary.

Soft: strangeness enhancement, particle ratios, flows

Hard: J/Ψ suppression, jet quenching

Hard probes specially interesting as

they are created at very short times ∼ 1/Q

can be described by perturbative QCD

All these effects have been measured in nucleus-nucleus collisions,however, they can also be produced by

Nuclear effects in the initial state (shadowing...)

Interaction with a confined medium (pion gas...)

Study proton-nucleus collisions as a control experiment.


Documents

Heavy Ions Collisions and the search for the Quark-Gluon ... · PDF fileHeavy Ions Collisions and the search for the Quark-Gluon Plasma Carlos A. Salgado CERN, TH-Division ( @cern.ch,