ridges, jets and recombination in heavy-ion collisions

Ridges, Jets and Recombination in Heavy-ion

CollisionsRudolph C. Hwa

University of Oregon

Shandong University, Jinan, China

October, 2012

2

Outline• Introduction• Ridges• Minijets• Particle spectra and correlations• Azimuthal anisotropy• Large Hadron Collider• Conclusion

3

The conventional method to treat heavy-ion collisions is relativistic hydrodynamics---- which can be tuned to reproduce data.

There is no proof that it is the only way (necessary)---- can only demonstrate that it is a

possible way (sufficient).

We propose another possible way---- minijets and recombination.

An area of focus is about Ridgeswhich is an interesting phenomenon in its own right.

Yang Chunbin (Wuhan) Zhu Lilin (Sichuan) Charles Chiu (U. Texas)

4

Ridge

55

Collision geometry

azimuthal angle φ

φ

transverse momentum pT

pT

pseudorapidity

η =ln(cotθ / 2)

θ

6

η

p1p2

7

Ridgeology

η

J+R

ridge R Jet J

R

J

Correlation on the near side

Properties of Ridge YieldDependences on Npart, pT,trig, pT,assoc, trigger

Putschke, QM06STAR

trigger

8

Jet+Ridge () Jet ()Jetη)

Putschke, QM06

R

1. Dependence on Npart on pT,trig2.pt,assoc. > 2 GeVSTAR preliminary

Medium effect near surface

Ridges observed at any pT,trig

Ridge yield 0as Npart 0

depends on medium

Ridge is correlated to jet production. Surface bias of jet ridge is due to medium effect near the surface

participants

9

Ridge

Putschke, QM06

3. Dependence on pT,assoc

Yet Ridge is correlated to jet production; thermal does not mean no correlation.

Ridge is from thermal source enhanced by energy loss by semi-hard partons traversing the medium.

Ridge is exponential in pT,assoc slope independent of pT,trigExponential behavior

implies thermal source.

STAR

10

4. Dependence of jet and ridge yields on trigger s

20-60% top 5%jet part, near-side

ridge part, near-side

jet part, near-side

ridge part, near-side

STAR

3<pTtrig<4, 1.5<pT

assoc<2.0 GeV/c

Feng, QM08

In-plane

Out

-of-

plan

e

1

43

2

56s

Different s dependencies for different centralities --- important clues on the properties of correlation and geometry

11

Effect of Ridge on two-particle correlation without trigger

Ridges are present with or without triggers.

STAR, PRC 73, 064907 (2006)

Auto-correlation between p1 and p2

0.15<pt<2.0 GeV/c, |η|<1.3, at 130 GeV

12

From the data on ridge, we learn that1. Ridge is correlated to jets (detected or

undetected).2. Ridge is due to medium effect near the surface.3. Ridge is from the thermal source enhanced by

energy loss by semihard partons traversing the medium.

4. Geometry affects the ridge yield.On the basis of these phenomenological properties we build a theoretical treatment of the ridge.But first we outline the theoretical framework that describes the formation of hadrons from quarks.

13

Theoretical treatment

Fragmentation

kT > pT

Hadronization Cooper-Frye k1+k2=pT

lower ki higher density

TT TS SS

Usual domains in pT at RHIC

pQCDHydro

low high

ReCo

intermediate

2 6 pTGeV/c

14

Pion formation: qq distributionthermal

shower

soft component

soft semi-hard components

usual fragmentation(by means of recombination)

TSFqq =TT+TS+SS

Proton formation: uud distribution

Fuud =TTT +TTS +TSS +SSS

15

Once the shower parton distributions are known, they can be applied to heavy-ion collisions.The recombination of thermal partons with shower partons becomes conceptually unavoidable.

A AqD(z)

hfragmentation

In high pT jets it is necessary to determine the shower parton distributions.

S

16

hNow, a new component

Once the shower parton distributions are known, they can be applied to heavy-ion collisions.The recombination of thermal partons with shower partons becomes conceptually unavoidable.

In high pT jets it is necessary to determine the shower parton distributions.

17

thermal

fragmentation

soft

hard

TS Pion distribution (log scale)

Transverse momentum

TT

SS

18

production by TT, TS and SS recombination

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Hwa & CB Yang, PRC70, 024905 (2004)

thermal

fragmentation

TS

19

Now, back to Ridge.How do we relate ridge to TT, TS, SS recombination?

Recall what we have learned from the ridge data:1. Ridge is correlated to jets (detected or

undetected).2. Ridge is due to medium effect near the surface.3. Ridge is from the thermal source enhanced by

energy loss by semihard partons traversing the medium.

4. Geometry affects the ridge yield.

20

Medium effect near surface

SS

trigger

TT ridge (R)

η

associated particles

These wings are useful to identify the Ridge

At η0 it is mainly the distribution that is of interest.

Ridge is from enhanced thermal source caused by semi-hard scattering.

Recombination of partons in the ridge

ST

peak (J)

21

The medium expands during the successive soft emission process, and carries the enhanced thermal partons along the flow.

Hard parton directed at s , loses energy along the way, and enhances thermal partons in the vicinity of the path.

s

But parton direction s and flow direction are not necessarily the same.

s

Reinforcement of emission effect leads to a cone that forms the ridge around the flow direction .

If not, then the effect of soft emission is spread out over a range of surface area, thus the ridge formation is weakened.

Flow direction normal to the surface

Correlation between s and

C(x, y,φs)=ex −φs−x,))

2

2s 2

⎡⎣⎢

⎤⎦⎥

22

QuickTime™ and aTIFF (LZW) decompressor


CEM

s

Correlated emission model (CEM)

Chiu-Hwa, PRC 79, 034901 (09)

s ; 0.33

STAR

Feng QM08

3<pTtrig <4

1.5 <pTassoc

<2 GeV/c

23

Single-particle distribution at low pT (<2 GeV/c)

Region where hydro claims relevance --- requires rapid thermalization

0 = 0.6 fm/cSomething else happens even more rapidlySemi-hard scattering 1<kT<3 GeV/cCopiously produced, but not reliably calculated in pQCD t < 0.1 fm/c1. If they occur deep in the interior, they get absorbed and become a part of the bulk.2. If they occur near the surface, they can get out. --- and they are pervasive.

That was Ridge associated with a trigger

24

Base is the background, independent of

Ridge, dependent on , hadrons formed by TT reco

Correlated part of two-particle distribution on the near side ρ2

corr (1,2) = ρ2J (1,2) + ρ2

R (1,2)

trigger

assoc part

JET RIDGE

How is this untriggered ridge related to the triggered ridge on the near side of correlation measurement?

Ridge can be associated with a semihard parton without a trigger.

ρ1(pT ,φ,b) = B(pT ,b) + R(pT ,φ,b)

?

25

1

2

1

2Two events: parton 1 is undetected thermal partons 2 lead to detected hadrons with the same 2

R(φ2 )∝ dφ1∫ ρ2R φ1,φ2 )

Ridge is present whether or not 1 leads to a trigger.

Semihard partons drive the azimuthal asymmetry with a dependence that can be calculated from geometry. (next slide)

If events are selected by trigger (e.g. Putschke QM06, Feng QM08), the ridge yield is integrated over all associated particles 2.

Y R (φ1)∝ dφ2∫ ρ2R φ1,φ2 )

R(φ2 ) ρ2R (φ1,φ2 ) Y R (φ1)

untriggered ridge triggered ridge yield

26

Geometrical consideration for untriggered Ridge

QuickTime™ and a decompressorare needed to see this picture.QuickTime™ and a decompressorare needed to see this picture.

Ridge due to enhanced thermal partons near the surfaceR(pT,,b) S(,b)

nuclear density D(b)

For every hadron normal to the surface there is a limited line segment on the surface around 2 through which the semihard parton 1 can be emitted.

2 S(φ,b)= dl

aρc∫ = [w2 sin2a + η2

a−

a+

∫ cos2a]1/2da

=h E(α ,1− w2 / h2 )α −

α + a±=tan−1[

hwtan(φ ± σ )]

elliptical integral of the second kind

QuickTime™ and a decompressor


b normalized to RA

Top view: segment narrower at higher b

Side view: ellipse (larger b) flatter than circle (b=0) around =0.

Hwa-Zhu, PRC 81, 034904 (2010)

27



Asymmetry of S(,b)

=0

=/2

S(,b) converts the spatial elliptical anisotropy to momentum anisotropy --- key step in calculating v2 without free parameters.



=/2

=0

28

Momentum asymmetryConventional hydro approach

x

ypx

py

higher pressure gradient

Good support for hydro at pT<2 GeV/c

Inputs: initial conditions, EOS, viscosity, freeze-out T, etc.

Assumption: rapid thermalization

v2 = cos2φ =dφcos2φρφ)∫

dφρφ)∫

Elliptic flow

29

Minijet approachIf minijets are created within 1 fm from the surface, they get out before the medium is equilibrated.More in the x

direction than in the y directionTheir effects on hadronization

have azimuthal anisotropy

We can show agreement with v2 data in this approach also--- with no more parameters used than in hydro

and without assumption about rapid thermalization

asymmetry can be expanded in harmonics:ρ(pT ,φ,b) = ρ0 (pT ,b)[1+ 2v2 (pT ,b)cos(2φ) + ...]

30

Azimuthal anisotropy

=cos2φ S

Z −1(pT ) +1

factorizable

bpT

T0 is the only parameter to adjust to fit the v2 data

Hwa-Zhu (12)

T '=T0TT −T0

=e− pT /T − e− pT /T0

e− pT /T0= epT /T ' −1

ρh (pT ,φ,b) = Bh (pT ,b) + Rh (pT ,φ,b)

T0 to be determinedbase B

h (pT ,b)=NηT ,b)e−T /T0

ridge

Rh (pT ,φ,b)=Sφ,b)RηT ,b)

v2h (pT ,b)= cos2φ ρ

η =dφcos2φρηT ,φ,b)0

2

∫dφρηT ,φ,b)0

2

∫=

12

dφcos2φSφ,b)R ηT ,b)0

2

∫BηT ,b)+ R

ηT ,b)

Enhancement factor

Z(pT )=RηT ,b)BηT ,b)

31



STAR


are needed to see this picture.QuickTime™ and a

decompressorare needed to see this picture.

Npart dependence is independent of pTv2

h (pT ,b)=cos2φ S

Z−1T )+1

No free parameters used for Npart dependence

Agrees with <cos2>S for Npart>100

32




T0 = 0.245 GeV

One-parameter fit of pT dependence (Npart dependence already reproduced).

v2h (pT ,b)=

cos2φ S

Z−1T )+1Z(pT )=e

T /T '−1 T '=T0TT −T0

v2h (pT ,b)

hydrodynamical elliptic flowridge generated by minijets without hydro

T’ determines pT dependence of v2 as well as the ridge magnitude (T=T-T0)

33



R.Hwa - L. Zhu, Phys. Rev. C 86, 024901 (2012)

When TS recombination is also taken into account, we get better agreement with data

34

η dependence due to initial parton momenta

Nh (pT ,b)[e−T /T −e−T /T0 ]

Base Ridge =Nh (pT ,b)e

− pT /T Inclusive T=0.283 GeV

Nh (pT ,b)e−T /T0

v2 and ridge are intimately related

Base T0=0.245 GeV

enhancement of thermal partons by minijets

Ridge TR=0.32 GeV

pT dependence of Ridge



(inclusive)

Inclusive ridge

ρh (pT ,φ,b) = Bh (pT ,b) + Rh (pT ,φ,b)

S(φ,b)R ηT ,b)

ρ h (pT ,b) = Bh (pT ,b) + Rh (pT ,b)

35

ρh (pT ,φ,b) = Bh (pT ,b) + Rh (pT ,φ,b)B ridg

e Bridge

+ M h (pT ,φ,b)Minijet

dN

TS

TdTT ,x)=

1T2

dθθ∫i

∑ Fiθ,x)TS∂ θ, T )TS recombination

At pT>2GeV/c, we must further include SS recombination.



RHIC

36

Large Hadron Collider (LHC)

Using the same recombination model applied to Pb-Pb collisions at 2.76 TeV, we get T=0.38 GeV

and good fits of all identified particle spectra.

ALICE

38







R.H.-L.Zhu, PRC84,064914(2011)

39

We learn about the dependence of T and S on collision energy.





quarks pions

The pT range is too low for reliable pQCD, too high for hydrodynamics.Shower partons due to minijets are crucial in understanding the nature of hadronic spectra. TS and TTS recombination provides a smooth transition from low to high pT --- from exponential to power-law behavior.

40

ConclusionStudy of Ridge and Minijets gives us insight into the dynamical process of hadronization:

Ridge in TT reco with enhanced T due to minijetsAzimuthal anisotropy (v2) can be well reproduced without hydrodynamics.

As is increased from RHIC to LHC, S is significantly higher.

s

Spectra of all species of hadrons are well explained by TT, TTT, TS, TTS, TSS, SS, SSS recombination.

Minijets at LHC cannot be ignored --- even at low pT.

41

At LHC the Higgs boson may have been found.But in Pb-Pb collisions, nothing so spectacular has been discovered.

Most observables seem to be smooth extrapolations from RHIC in ways that have been foreseen.Can we think of anything that is really extraordinary? --- unachievable at lower energies

e.g., a strange nugget? solid evidence against something?

43

Backup slides

44

Hadron production by parton recombination

TT F(ki )=Cki ex−ki / T)dN

TdT=C

2

6ex−T / T)

TTTdN p

pT dpT

=NT2

m T

ex−T / T) same T for partons, , p

empirical evidence

At low pT thermal partons are most important

phase space factor in RF for proton formation

Pion p0dN

dT=

dk1k1∫

dk2k2

Fθθ k1, k2 )R k1, k2 , T )

Proton p0dN p

dpT

=dk1k1∫

dk2k2

dk3k3

Fuud k1, k2 , k3)Rk1, k2 , k3, T )

Recombination function

R k1, k2 , T )=k1k2T2dk1 +k2

T−1)

q and qbar momenta, k1, k2, add to give pion pT

45



p

PHENIX, PRC 69, 034909 (04)

dN p

pT dpT

=NT2

m T

ex−T / T)

Proton production from recombination

Slight dependence on centrality





Same T for , K, p --- in support of recombination.T=0.283

GeVHwa-Zhu, PRC 86, 024901 (2012)

46

q

b

Fi (q,φ,b)= dxPx∫ ,φ,b)Fiθ,x)geometrical factors due to medium

TS+SS recombination

G(k,q,x)=θdθ−ke−x )degradation

ρ1

TS+SS (pT ,φ,b) =dqq∫ Fi

i∑ (q,φ,b)H i (q, pT ) hadronization

dNihard

kdkdy y=0

=ik)

Fi (q,x)= dkki∫ k)G k,θ,x)

k probability of hard parton creation with momentum k

only adjustable parameter x =l(x0 , y0 ,φ,b)

xDi x)=

dx1x1∫

dx2x2

Siφx1),Si

φ'x2

1−x1)

⎧⎨⎩

⎫⎬⎭R x1, x2 , x)x =T / θ

TS∂ (q, pT )=

dθ2θ2∫ Si

φθ2θ) dθ1∫ Ce−θ1 /TR θ1,θ2 , T )

dN

TS

TdTT ,x)=

1T2

dθθ∫i

∑ Fiθ,x)TS∂ θ, T )

dN

SS

TdTT ,x)=

1T2

dθθ∫i

∑ Fiθ,x)SS∂ θ, T )

is calculable from geometry l (x0 , y0 ,φ,b)Path

length

47

Nuclear medium that hard parton traverses

x0,y0

k

Dynamical path length

x =l(x0 , y0 ,φ,b) to be determined

Geometrical considerations

Average dynamical path length

x (φ,b) = γ dx0dy0∫ l (x0 , y0 ,φ,b)Q(x0 , y0 ,b)

Q(x0 , y0 ,b)=

TAx0 , 0 ,−b / 2)TBx0 , 0 ,b / 2)d 2ρsTA

ρs+ρb / 2)TB

ρs−ρb / 2)∫

Probability of hard parton creation at x0,y0

Geometrical path length

l (x0 , y0 ,φ,b)= d[x),)]0

1 x0 ,0 ,φ,b)

∫D(x(t),y(t))density (Glauber)

48

Higher harmonicsConventional approach: fluctuations of initial configurationMinijet approach: hadronization of minijets themselves outside the medium --- plays the same role as fluctuations of initial state

J stays close to the semihard parton, whose angle is erratic; thus additional contribution to azimuthal anisotropy. pT dependence of TS component is known

Hwa-Yang PRC(04),(10)

dN

TS

TdT=2T2

d11

∫d22

T1)S2 ,x)R 1, 2 , T )

S

R J

T

A3(pT ,φ,b)=Jφ,b)A3T ,b)

A3(pT ,b)=dqq

Fi (q,x)Si2 / θ)i∑∫ QuickTime™ and a


49






a2=0.6, a3=1.6, a4=1.4

v3, v4 come only from cosnφ J

v2 arises mainly from cos2φ S

Hwa-Zhu

ridges, jets and recombination in heavy-ion collisions

Documents

ridge yield

assocyet ridge

sidestar3effect of ridge

shower partons

shower parton distributions

semihard partons

near side1

high pt jets