# Presentation: 630035

## Color charge dependence of energy loss at RHIC

-  Introduction
-          What are color factors in QCD ?
-            What should be the  effect of color charge on Eloss ?
-            What are the experimental observables to see this effect ?
-  Search for color charge effect at RHIC
-  Physics possibilities regarding the observations at RHIC
-  Future measurements
-  Summary

- Outline

-                Bedanga Mohanty
-         (for the STAR Collaboration)
- Lawrence Berkeley National Laboratory

## Introduction  

- Introduction

-  Quantum chromodynamics (QCD) is  the theory
-     of color charge (strong interactions)
-  Many quantities can be calculated in
-     perturbative QCD with a free parameter,
-     the strong coupling strength
-  Another key ingredient of QCD is the underlying
-     gauge group
-  QCD is a gauge theory with SU(3) as underlying
-     gauge group. This can be tested by measurement
-     of color factors

- The running of QCD coupling

- Jet cross section

- What are color factors ?

- RHIC

- S. Bethke, Nucl. Phys. Proc.
-                   Suppl 121 (2003)  74

## Introduction - Color factors

-   Consider a Lie group of dimension Nc.
-   For SU(Nc), the color factors are
-             CA = Nc, CF = (Nc2-1)/2Nc and TF = 1/2
-             A and F represent adjoint and fundamental representations
-  Technically they are the eigen values of the Casimir operator
-     of the gauge group
-  For QCD : Nc = 3, CA = 3, CF = 4/3
-    Quarks are represented by Dirac fields in the fundamental rep of SU(3)
-    Gluons lie in the adjoint rep of SU(3); 8 generators so 8 gluons

- What is the physical picture for the color factors ?

## Physical picture - Color factors

-    Color factors are related to fundamental couplings of the theory :
-    CF - determines coupling strength of a gluon to a quark,
-    CA - related to the gluon self coupling (fundamental property of QCD
-               arising due to non-Abelian nature of the theory)
-     TF - strength of splitting of a gluon into a quark pair

- Can we experimentally determine color factors ?

- QCD : For SU(3) :
-  Nc = 3
-  CA = 3, CF = 4/3

## Experimental determination of Color factors

-   All of the three basic vertices are present in
-      four jet production in e+e- collisions
- Since each diagram involves spin-1 or spin-1/2
-     particles in different configurations. So  each
-     graph results in a different angular distributions
-    in the  final states.
-  The observed jet angular distributions are then
-     fitted to theoretical predictions with CA, CF, TF as
-    free parameters.

- What are the experimental results ?

## Results on Color factors and QCD gauge group

-  For SU(Nc), the color factors are
-       CA = Nc,
-       CF = (Nc2-1)/2Nc
-         and TF = 1/2
- For SU(3) :  Nc = 3
-       CA = 3, CF = 4/3

**What this has to do with**
**E****loss**** at RHIC ?**

-   Results from L3, OPAL and ALEPH experiments

- s(Mz) = 0.119  0.006  0.022
- CA = 2.93  0.14  0.49
- CF = 1.35  0.07  0.22

-    SU(3) is the gauge group for QCD

- ALEPH : Z. Phys. C 76 (1997) 1

- OPAL: Eur. J. Phys. C 20 (2001) 601

- L3 : Note 1805 (1995)

## The color factors and Eloss in heavy ion collisions

- The color factors and Eloss in heavy ion collisions

-   One of the mechanism of parton energy loss is through medium induced gluon radiation
-  Average energy loss in most models ~ BDMPS or GLV

- Color factor: 4/3 for quarks and 3 for gluons

- Medium transport coefficient --- gluon density and momenta

- Strong force coupling constant

- Path length

- BDMPS : Nucl. Phys. B 483 (1997) 291
- GLV     : PRL 85 (2000) 5535

## Experimental observables sensitive to color charge effect

-  Energy loss : High pT region has to be probed
- Look for difference in Nuclear Modification Factors (RAA or RCP) between  particles dominantly coming from gluon jets and quark jets
- Question is :
- How to know which particles are produced dominantly from gluon jets and which are produced from quark jets ?

- It is not very clear if this ~2 difference will remain after hadronization of the partons. However model calculation shows this effect should be observable.
- But most model calculations do not use the current knowledge of fragmentation function from RHIC data!

## NLO pQCD calculations and RHIC data 

- NLO pQCD calculations and RHIC data

- K0s

- , p,K and production
- at high pT well explained by NLO pQCD calculations with AKK fragmentation function.
- AKK FF uses recent light flavor separated e+e- data from OPAL Collaboration.
- First time baryon production reasonably well described by NLO pQCD

- Expt : PLB 637 (2006) 161, nucl-ex/0607033
- Theory : S. Albino et al., Nucl. Phys. B 597 (2001) 337

## Experimental Observable - I 

- Experimental Observable - I

- Gluon jet contribution factor increases as we go from , K,p and
- If
- and
- Then
-       at high pT  for same beam energy, collision species and collision centrality the NMF for
-                    RCP( ) >  RCP (p)
-      and
-                    RCP (K) > RCP ()

## Experimental Results at RHIC - I 

- Experimental Results at RHIC - I

- Observation at high pT :
- RCP( ) ~  RCP (p)     and
- Comparison of  RCP (K) and RCP () need
-    more statistics and higher pT range
- No difference observed in RCP which is suppose to reflect Eloss

- Does it mean  similar Eloss of  partons ?

## Experimental Observable - II 

- Experimental Observable - II

- In Au+Au collisions there is a dense medium where gluons loose more energy than quarks. Anti-protons are mostly coming from gluon jets.
- and
- In p+p and d+Au collisions no such dense medium -
- Then  at high pT  for same beam energy,
-       pbar/  (Au+Au) <  pbar/ (p+p or d+Au)
-       /K0s (Au+Au) < /K0s (p+p or d+Au)
-  And
-           pbar/p (Au+Au) < pbar/p (p+p or d+Au)
-           bar/ (Au+Au) < bar/ (p+p or d+Au)

- STAR : PRL 91 (2003) 172302
-              PRL 91 (2003) 072304

## Experimental Results at RHIC - II 

- Experimental Results at RHIC - II

- Observation at high pT :
-   p/ (Au+Au) ~ p/ (d+Au)
-   Ratios way above jet quenching calculations
-   For the  /K0s (Au+Au)  and /K0s (p+p)
-      we need more statistics to conclude

- p,: PRL 97   (2006) 152301
- ,K    : nucl-ex/0601042
- Theory : Fries et al, PRC 68 (2003) 044902

## Experimental Results at RHIC - II 

- Experimental Results at RHIC - II

- Observation at high pT :
-  pbar/p (Au+Au) >~ pbar/p (d+Au)
-  pbar/p (Au+Au) > models with Eloss

- We do not observe the naively expected lower ratios for Au+Au collisions due to difference in Eloss of quarks and gluons

- AuAu : PRL 97   (2006) 152301
- dAu    : PLB 637 (2006) 161
- Theory : X. N. Wang - PRC 70 (2004) 031901

## Experimental Observable - III 

- Experimental Observable - III

- Probing quark dominated jet production at
-    lower energy to gluon dominated jet production
-    at higher energy
- Then beam energy dependence of high pT nuclear
-    modification factor can in principle probe the color
-    charge effect.

- Proton - parton distribution function

**x****T**** = 2p****T****/√s****NN**
- At pT = 10 GeV
- 62.4 GeV : xT ~ 0.32
- 200 GeV  : xT ~ 0.1

## Experimental Results at RHIC - III 

- Experimental Results at RHIC - III

- Observations at high pT :
-  In general RCP at 62.4 higher than 200 GeV
-  Values approach each other at highest pT
- RAA shape different beyond pT= 4 GeV/c

- Need for higher pT measurements  Au+Au collisions at RHIC

- Given the errors in current measurements,
- may be not worth comparing to models

- Complicated dependence
- initial jet spectra
- dNg/dy
-  color effect on
-     parton Eloss

- Wang et al., PRC 71 (2005) 014903

## So why we do not observe the color charge effect 

- So why we do not observe the color charge effect

- Is it because of other mechanism of energy loss (e.g collisional)
-    can smear the effect ?
- Is it because we have a gluon dominated initial conditions in heavy
-    ion collisions at RHIC ?
- Is it because we still need to understand - how quarks and
-    gluons interact with the medium formed. Is there a possibility of
-    conversions between quark and gluon jets in the medium ?
- Is it because in realistic calculations, to start with the differences are
-    not very large ?
- Are color factors and S inter-dependent ?

## Physics possibilities : different Eloss mechanism

- Physics possibilities : different Eloss mechanism

- Can  collisional process of energy loss
- lead to non observation of the effect

- PEHNIX : QM2006

- Non-photonic electrons

## Physics possibilities : mostly gluons at initial stage 

- Physics possibilities : mostly gluons at initial stage

- Is it all gluon jets in RHIC ?

- Fragmentation of gluon, a baryon-meson splitting Fragmentation from quark, a mass splitting

- STAR: nucl-ex/607033

## Physics possibilities : quark and gluon jet conversions

- Mechanism to reduce the effect of color charge dependence of Eloss in QGP is to allow for conversions between q- and g- jets via both inelastic (qqbar -- gg) and elastic (gq(qbar) -- q(qbar)g) scatterings with thermal partons in the QGP

- The conversion rate depends on collisional widths. For a chemically equilibrated QGP,  the conversion rate for quark jet is larger than gluon jet. Increasing the final abundance of gluon jets and hence compensating for their larger Eloss in the QGP.

- NMF for partons

## Physics possibilities : lower difference to start with

- Calculations by I. Vitev (PLB 639 (2006) 38), suggests only in the limit Ejet tending to infinity,
- i.e E/E tending to zero does the energy loss of quarks and gluons approach the naïve ratio Eg/Eq ~ CA/CF ~ 9/4. For large fractional energy loss this ratio is determined by the E<<E constraint.

## Physics possibilities : s and C interdependent

- Physics possibilities : s and C interdependent

- PRD 57 (1998) 5793 :
- In the experimental analysis of color factor
- extraction from 4-jet events use of NLO predictions
- introduces an S dependence, that shifts the color factor ratios by 1 + 2 S in the direction of TR/CF

**With LO calculation**

**With NLO calculation**

- Does this influence the conclusions ?

- RHIC

- Color Factor
- measurements

## Outlook - Heavy flavor sector 

- Outlook - Heavy flavor sector

- One possibility to look at color charge dependence is look at ratio of heavy to light NMF ratio.

- Few aspects have to be disentangled to
- Get the color charge effect :
- Mass effect - heavier the particle less is the Eloss. Solved by going to higher pT
- Partonic pT spectra, heavy quarks have less steeper spectra. For same Eloss, steeper spectra, lower RAA
-  Fragmentation of parton, heavy quarks have harder FF. For same parton Eloss, steeper FF, lower RAA

- Theory : Armesto at al., PRD 71 (2005) 054027

## Outlook - Strangeness sector 

- Outlook - Strangeness sector

- -meson can be used to study the color charge dependence.
- At RHIC energies, production is not dominantly from kaon coalescence,
- So they may  reflect s-quark energy loss.

- Similar to ratios of NMF heavy-to-light ,
- the -meson to light hadron (from
-  gluon jets) NMF ratio can also be sensitive
-  to color charge dependence of Eloss in
-  heavy ion collisions

- STAR : PLB 612 (2005) 181

## Summary 

- Summary

- QCD with SU(3) as gauge group tells us, gluons are expected to loose more energy due to their strong coupling with the medium in heavy ion collisions compared to quarks. This effect is not washed out by collisional process of Eloss

- Observations

- Conclusion and Possible interpretation

- Similar RCP for protons and pions at high pT
-   and K0s RCP approach each other at high pT
-  Similar particle ratios (,p,pbar) at high pT for Au+Au and d+Au (p+p) collisions
- Jet quenching not able to reproduce high pT ratios
- Energy dependence of NMF for pions  is different at higher pT
- R(D/ h) and R(/h) may provide a clear picture, or look at particle
-                    ratios in a jet

- Similar  Eloss for partons or gluon dominated matter at RHIC or need to understand quark and gluon jet interactions in medium
- Need for higher pT reach at RHIC. Higher statistics data needed
- Energy dependence is complicated by  initial jet spectra, gluon density. Models suggest differences larger at higher energies due to color effect
-  Color factor and S , E/E     dependence?
-  Use of better FF is needed in theory

- Thanks

## Outlook - Energy dependence of NMF RHIC &LHC 

- Outlook - Energy dependence of NMF RHIC &LHC

- Look for energy dependence of RAA at a fixed high pT (6 GeV/c). The big difference between similar Eloss for quarks and gluons  and QCD type (color charge effect) Eloss only appears at higher energy as effect of initial gluon density and slope of initial jet spectra gets lesser

- Similar Eloss for quarks and gluons

- QCD type (color charge effect) Eloss

- Probing quark dominated jet production at lower energy  to gluon dominated jet production at higher energy

- Theory :
- Wang et al., PRC 58 (1998) 2321
- Wang et al., PRC 71 (2005) 014903

## Physical picture - Color factors

-    Color factors are related to fundamental couplings of the theory :
-    CF - determines coupling strength of a gluon to a quark,
-    CA - related to the gluon self coupling (fundamental property of QCD
-               arising due to non-Abelian nature of the theory)
-     TF - strength of splitting of a gluon into a quark pair

- Can we experimentally determine color factors ?

-  For SU(Nc), the color factors are
-       CA = Nc,
-       CF = (Nc2-1)/2Nc
-         and TF = 1/2
- For SU(3) :  Nc = 3
-       CA = 3, CF = 4/3