# Presentation: 668806

## Quenching of light hadrons at RHIC

**Kolkata, India**

**Pradip Roy**

**Quenching of light hadrons at RHIC**
**In**
**a collisional energy loss scenario**

**Saha Institute of Nuclear Physics**

## Motivation
Present status of collisional energy loss
Our formalism
Energy loss
Nuclear modification factor
Results
Discusson

**Present status of collisional energy loss**
**Our formalism**
**Energy loss**
**Nuclear modification factor**
**Results**
**Discusson**

- Plan

**Quark Matter 2008,  Feb 4-10**** ****Jaipur, India**

## Non-photonic electron data shows much larger suppression than expected

These data reflect the energy loss of heavy quarks

Mainly radiative loss has been discussed in the literature : dead cone effect => less energy loss => less suppression of the decay product coming from heavy quarks

Radiative energy loss seems to fail to describe the non-photonic single electron data (Wicks et. al, JPG 34, 2007)
Activities started  to re-visit the importance of collisional energy loss  for heavy as well as light quarks

**These data reflect the energy loss of heavy quarks**
**Mainly radiative loss has been discussed in the literature : dead cone effect => less energy loss => less suppression of the decay product coming from heavy quarks**
**Radiative energy loss seems to fail to describe the non-photonic single electron data (Wicks et. al, JPG 34, 2007)**
**Activities started  to re-visit the importance of collisional energy loss  for heavy as well as light quarks**
** **

- Motivation

**Quark Matter 2008, Feb 4-10**** ****Jaipur, India**

## Present status of collisional energy loss

**1. Peigne et al (JHEP 04, 2006)**
**Collisional energy loss is suppressed in comparison to infinite medium**
**2. Djordjevic (PRC 74, 2006)**
**For characteristic QCD medium scales finite size effects are negligible**
**3. Wang X.- N. (PLB650, 2007)**
**Interference between elastic amplitude and that of gluon radiation reduces the effective energy  elastic loss**
**4. Adil et. Al (PRC75 2007)**
**Similar results for collisional loss as 2**

**Quark Matter 2008,  Feb 4-10**** ****Jaipur, India**

## Contd.

**5. Dutt-Mazumder et. al (PRD 74 2005)**
**Below certain energy (Ec) collisional energy loss dominates (details will be shown)**
**6. Peshier et al. (EPJC 2007), Braun et al. (PRD75 2007)**
** ****running coupling constant**
**T~2T****c ****, dE/dx ~ 1.6 GeV/fm for a 100 GeV quark**
**Collisional energy loss is of the same order as radiative loss**
**            **

**Quark Matter 2008, Feb 4-10**** ****Jaipur, India**

## Infra-red divergent
Way out : Shielding of divergent by plasma effects
Sum of two diagrams separated by intermediate scale q*  (gT << q* << T)
(i) Soft scale (gT < q  < q*) : HTL propagator
(ii) Hard scale (q* < q <T) : bare propagator 
Cancellation of arbitrary scale q*

**Way out : Shielding of divergent by plasma effects**
**Sum of two diagrams separated by intermediate scale q*  (gT << q* << T)**
**(i) Soft scale (gT < q  < q*) : HTL propagator**
**(ii) Hard scale (q* < q <T) : bare propagator **
**Cancellation of arbitrary scale q***

**Bjorken **

-  Collisional energy loss

**Quark Matter 2008,  Feb 4-10**** ****Jaipur, India**

## Consider small angle qq scattering (t-channel )
Assume energy Ejet >> T

**Assume energy E****jet ****>> T**

**and**

**HTL gluon propagator**

**Bare gluon propagator**

**Hard + soft : independent of q***

- Energy loss contd.

**Quark Matter 2008,  Feb 4-10**** ****Jaipur, India**

## is of the order of 0.8 GeV/fm for a 20 GeV quark 

**is of the order of 0.8 GeV/fm for a 20 GeV quark **

**Factor of 2 -3 more than previously calculated**
_**Justifies not to neglect the collisional energy loss**_

**Dutt-Mazumder et al. PRD 74 2005**

**Quark Matter 2008,  Feb 4-10**** ****Jaipur, India**

## (PRD 74 2005)

**there might be domains where collisional loss could be comparable to radiative loss**

**Ec ~ 85 GeV : quarks**
**     ****~ 60 GeV : gluons**

***N(E) = *****10 **
******=1 GeV**
**L/******** = 4**

- Collisional vs. Radiative

**Quark Matter 2008,  Feb 4-10**** ****Jaipur, India**

## Transverse momentum distributions  hadrons : Nuclear modification factor

**p****T**** distribution :**

**Standard pQCD calculation : modification of the **
**FF **

**equal amount of energy loss for each parton**

**Essential to evaluate parton p****T**** spectra dynamically : FOKKER PLANCK **
**APPROACH**
** ****System of quarks, antiquarks, and gluons**
**Inject partons with given initial distributions**
**Study of time evolution as the system expands  and cools**

**Boltzmann Equation**
** ****Small angle scattering more frequent ~ O(g****2****T)**

**Collisional integral **
**reduces to appropriately**
**defined diffusion and**
**Drag coefficients**

**Quark Matter 2008, Feb 4-10**** ****Jaipur, India**

**(Roy et al. PRC 2006, Alam et al. NPA 2007)**

## Fokker-Planck Equation

**Solution by Green’s function technique:**

**All the jets are not produced**
** ****at the same space**
**time point**
**Path length traversed by these**
** ****partons before fragmentation **
**are not same **

**Temperature also varies along the trajectory of the partons**

**Jet produced at (r,********spends a time t****L**** or equivalently traverses a distance L ~ **** ****t****L ****and this is not a measurable quantity : time average**

**Finally,**

**Quark Matter 2008, Feb 4-10**** ****Jaipur, India**

**Nuclear modification factor**

**Fits the Phenix data quite well**
**Tendency to rise at high p****T **** : radiation starts to dominate**
**Detail calculation including both collisional and radiative losses should**
**be considered for quenching of high p****T**** hadrons**

**Quark Matter 2008, Feb 4-10**** ****Jaipur, India**

**R****AA**** is  sensitive to ****initial temperature**** ****velocity of sound**** ****initial thermalization time**

**Reasonable combination :**
**T****i**** =450 MeV, c****s****2****=0.2, and **
**t****i****=0.15 fm/c**

**Importance of coll. and rad. losses  :**
**the average energy of parton  <E> = p****T****h****/<z> **
***<E>******max****** ~ 26 GeV :****** ***_***maximum average energy to produce pions with p***__***T***__*** in the range of 1-13 GeV***_
**                                                                 **
**                                                     ****Quark Matter 2008, Feb 4-10**** ****Jaipur, India**

## Reviewed the current theoretical status  of collisional energy loss
Divergence is removed by plasma effects 
Included all possible diagrams for a given process
Domains  in energy: collisional loss dominates over radiative energy loss
 Nuclear modification factors for and  fragmentation of dynamically evolved parton distribution 
With parameters relevant for RHIC the data is well reproduced
Not surprising because for RHIC data quenching factor Q(pT) ~ 0.2 where collisional energy loss plays important role 

**Divergence is removed by plasma effects **
**Included all possible diagrams for a given process**
**Domains  in energy: collisional loss dominates over radiative energy loss**
** ****Nuclear modification factors for ****************and ******** fragmentation of dynamically evolved parton distribution **
**With parameters relevant for RHIC the data is well reproduced**
**Not surprising because for RHIC data quenching factor Q(p****T****) ~ 0.2 where collisional energy loss plays important role **

- Summary and Discussion

**Quark Matter 2008, Feb 4-10**** ****Jaipur, India**

## THANK YOU