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Ridges, Jets and Recombination in Heavy-ion Collisions. Rudolph C. Hwa University of Oregon. Shandong University, Jinan, China October, 2012. Outline. Introduction Ridges Minijets Particle spectra and correlations Azimuthal anisotropy Large Hadron Collider

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Ridges jets and recombination in heavy ion collisions

Ridges, Jets and Recombination in Heavy-ion Collisions

Rudolph C. Hwa

University of Oregon

Shandong University, Jinan, China

October, 2012


Outline

  • Introduction

  • Ridges

  • Minijets

  • Particle spectra and correlations

  • Azimuthal anisotropy

  • Large Hadron Collider

  • Conclusion


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

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

---- minijets and recombination.

An area of focus is about Ridges

which is an interesting phenomenon in its own right.



Collision geometry
Collision geometry

pseudorapidity

azimuthal angle

transverse momentum

5


p2

p1






ridge RJet J

trigger

J+R

R



J



STAR

Putschke, QM06

Properties of Ridge Yield

Dependences on Npart, pT,trig, pT,assoc, trigger 

Correlation on the near side

Ridgeology


on pT,trig

2.

participants

STAR preliminary

Putschke, QM06

pt,assoc. > 2 GeV

Jet+Ridge () Jet ()

Jet)

Ridges observed at any pT,trig

Ridge yield

0

R

as Npart

0

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

 depends on medium

Medium effect near surface

1. Dependence on Npart


Ridge

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

3.Dependence on pT,assoc

Ridge is exponential in pT,assoc slope independent of pT,trig

Putschke, QM06

STAR

Exponential behavior implies thermal source.

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


6

5

4

3

2

1

Out-of-plane

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

In-plane

Feng, QM08

4. Dependence of jet and      ridge yields on trigger s

STAR

jet part, near-side

ridge part, near-side

jet part, near-side

ridge part, near-side

20-60%

top 5%

s

3<pTtrig<4, 1.5<pTassoc<2.0 GeV/c


Effect of ridge on two particle correlation without trigger

Auto-correlationbetween p1 and p2

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

STAR, PRC 73, 064907 (2006)

Effect of Ridge on two-particle correlation without trigger

Ridges are present with or without triggers.


From the data on ridge, we learn that

Ridge is correlated to jets (detected or undetected).

Ridge is due to medium effect near the surface.

Ridge is from the thermal source enhanced by energy loss by semihard partons traversing the medium.

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.


Theoretical treatment

intermediate

ReCo

TT

TS

SS

Hadronization

Cooper-Frye

k1+k2=pT

lower ki higher density

Theoretical treatment

Usual domains in pT at RHIC

low

high

pT

2

6

Hydro

pQCD

GeV/c

Fragmentation kT > pT


Proton formation: uud distribution

usual fragmentation

soft component

soft semi-hard components

(by means of recombination)

Pion formation:

distribution

thermal

shower


h

fragmentation

S

D(z)

q

A

A

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

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.


h

Now, a new component

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

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.


soft

TT

TS

hard

SS

thermal

Pion distribution (log scale)

fragmentation

Transverse momentum


fragmentation

thermal

 production by TT, TS and SS recombination

Hwa & CB Yang, PRC70, 024905 (2004)


Recall what we have learned from the ridge data:

Ridge is correlated to jets (detected or undetected).

Ridge is due to medium effect near the surface.

Ridge is from the thermal source enhanced by energy loss by semihard partons traversing the medium.

Geometry affects the ridge yield.

Now, back to Ridge.

How do we relate ridge to TT, TS, SS recombination?


Recombination of partons in the ridge

associated particles

SS

trigger

ST

peak (J)

TT

ridge (R)

These wings are useful to identify the Ridge

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

Medium effect near surface

At 0 it is mainly the  distribution that is of interest.


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

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

Flow direction  normal to the surface

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

s

But parton directionsandflow direction are not necessarily the same.

s

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

Correlation betweens and


CEM

s

Correlated emission model (CEM)

Chiu-Hwa, PRC 79, 034901 (09)

STAR

Feng QM08

3<pTtrig <4

1.5 <pTassoc <2 GeV/c


Single particle distribution at low p t 2 gev c

Region where hydro claims relevance --- requires rapid thermalization

0 = 0.6 fm/c

Semi-hard scattering 1<kT<3 GeV/c

Copiously produced, but not reliably calculated in pQCD t < 0.1 fm/c

That was Ridge associated with a trigger

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

Something else happens even more rapidly

1. 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.


Base is the background, independent of thermalization

Ridge, dependent on , hadrons formed by TT reco

Correlated part of two-particle distribution on the near side

?

trigger

assoc part

JET

RIDGE

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

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


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

1

2

2

1

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

untriggered ridge

triggered ridge yield

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)


Geometrical consideration for untriggered ridge

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

2  

elliptical integral of the second kind

Ridge due to enhanced thermal partons near the surface

Top view: segment narrower at higher b

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

R(pT,,b)  S(,b)

b normalized to RA

nuclear density D(b)

Hwa-Zhu, PRC 81, 034904 (2010)

Geometrical consideration for untriggered Ridge


Asymmetry of s b

thermalization

Asymmetry of S(,b)

=0

=/2

=0

=/2

S(,b) converts the spatial elliptical anisotropy to momentum anisotropy --- key step in calculating v2without free parameters.


y thermalization

py

px

x

Elliptic flow

Momentum asymmetry

Conventional hydro approach

higher pressure gradient

Good support for hydro at pT<2 GeV/c

Assumption: rapid thermalization

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


More in the x direction than in the y direction thermalization

 asymmetry can be expanded in harmonics:

Minijet approach

If minijets are created within 1 fm from the surface, they get out before the medium is equilibrated.

Their 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


Azimuthal anisotropy

base thermalization

T0 to be determined

ridge

pT

Enhancement factor

factorizable

b

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

Hwa-Zhu (12)

Azimuthal anisotropy


STAR thermalization

Npart dependence is independent of pT

Agrees with <cos2>S for Npart>100

No free parameters used for Npart dependence


T thermalization0 = 0.245 GeV

hydrodynamical elliptic flow

ridge generated by minijets without hydro

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

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


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

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


p better agreement with dataT dependence of Ridge

Inclusive T=0.283 GeV

Base

Ridge

enhancement of thermal partons by minijets

(inclusive)

Base T0=0.245 GeV

Ridge TR=0.32 GeV

Inclusive ridge

v2 and ridgeare intimately related

 dependence due to initial parton momenta


B better agreement with dataridge

B

ridge

Minijet

TS recombination

RHIC

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


Large hadron collider lhc

ALICE better agreement with data

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.

Large Hadron Collider (LHC)


R.H.-L.Zhu, PRC better agreement with data84,064914(2011)


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

pions

quarks

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.


Conclusion

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

Conclusion

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

Ridge in TT reco with enhanced T due to minijets

Azimuthal anisotropy (v2) can be well reproduced without hydrodynamics.

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.


At LHC the Higgs boson may have been found. energy.

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?


The End energy.

Thank you


Backup slides
Backup slides energy.


Hadron production by parton recombination

Pion energy.

Recombination function

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

TT

Proton

same T for partons, , p

TTT

phase space factor in RF for proton formation

Hadron production by parton recombination

At low pT thermal partons are most important

empirical evidence


p energy.

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

T=0.283 GeV

Proton production from recombination

Hwa-Zhu, PRC 86, 024901 (2012)

PHENIX, PRC 69, 034909 (04)

Slight dependence on centrality


hadronization energy.

geometrical factors due to medium

q

probability of hard parton creation with momentum k

k

degradation

b

only adjustable parameter 

is calculable from geometry

Path length

TS+SS recombination


Nuclear medium that hard parton traverses energy.

Geometrical path length

k

D(x(t),y(t))

x0,y0

density (Glauber)

Dynamical path length

Average dynamical path length

 to be determined

Probability of hard parton creation at x0,y0

Geometrical considerations


Higher harmonics

R energy.

J

S

T

Hwa-Yang PRC(04),(10)

pT dependence of TS component is known

=

Higher harmonics

Conventional approach: fluctuations of initial configuration

Minijet 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.


v energy.2 arises mainly from

v3, v4 come only from

Hwa-Zhu

a2=0.6, a3=1.6, a4=1.4


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