# Presentation: 528017

##   PQCD Approach 

**      **
**  ****PQCD Approach **
**to Parton Propagation in Matter**

-                      Ivan Vitev

- Hard Probes 2006, Pacific Grove, CA

## Outline of the Talk

**  **

-    Final state interactions in the QGP:
-                 Radiative energy loss, universal features of jet quenching
-                 Modifications of di-jets, large angle correlations and flow

-    Final state interactions in cold nuclear matter:
-                 Coherent power corrections and nuclear shadowing
-                 Open charm production and modification in p+A reactions

-    Initial state interactions:
-                 Transverse momentum diffusion and Cronin effect
-                 Energy loss in cold nuclear matter and forward rapidity

**Acknowledgement****: thanks to the organizers for the invitation to give this talk**

**Acknowledgement****: thanks to my collaborators, P.Huovinen, T.Goldman, **
**                                       ****M.Gyulassy, M.B.Johnson, P.Levai, J.W.Qiu, X.N.Wang   **

## Predictive Power of PQCD

**  ****Factorization theorem:**
- 	      Scale of hadron wave function:
- 	      Scale of hard partonic collision:
- 	  **Factorization**
**           ** **Process-dependent:**
**             ****Process-independent:**
**  ****Predictive power:**
-                        Universality of:
-                   Infrared safety of:
**                         **

**J.Collins, D.Soper, G.Sterman, Nucl.Phys.B223  (1983)**

- pT (E) [GeV]

## In-Medium Modification of the PQCD Cross Sections

** ****The way to understand medium effects  on hadron cross sections in the framework of PQCD **
**is to ****follow the history of a parton**** from the IS nucleon wave function (PDF) to the FS hadron **
**wave function (FF) **

** ****Jet interactions in the medium result in ****kinematic modifications**** to the hard scattering cross **
**   ****section that are ****process dependent**

**d) Final state interactions in the QGP**
**     ****Jet quenching**

**e) Final state interactions in the QGP**
**     ****Large angle correlations, Di-Jet **
**     ****suppression, Deflection of jets by flow **

**a) Initial state interactions**
**     ****Elastic scattering and Cronin effect**

**c) Final state interactions**
**     ****Dynamical shadowing, Generalization**
**     ****to heavy quarks**

**Cold nuclear matter effects are present at times     **

**b) Initial state interactions**
**     ****Energy loss and forward Y suppression**

## Initial State Elastic Scatterings

- Initial State Elastic Scatterings

**Reaction Operator**** = all possible on-shell                cuts through a new ****Double Born**** interaction with the propagating system**

**The ****approximate**** solution is that of a ****2D**** diffusion**

**Unitarization of multiple scattering**

- =

**=**

**Initial condition****    **

**Solution****    **

**Mean number of scatterings****    **

**Elastic scattering cross section**

**Implemented in the PQCD approach as **
**     ****broadening**** of the initial state partons**

**a) Initial state elastic scattering**

## Cronin Effect

**Cronin Effect**

- Default

**Good description at mid rapidity **
**     **

**Wrong sign at forward rapidity **
**     **

**Data**

**I.V., Phys.Lett.B526 (2003)**

**Cronin effect: ****enhancement**** of cross sections**
**at intermediate transverse momenta relative**
**to the binary scaled p+p**

**A.Accardi, CERN yellow report, references therein**

## Cold Nuclear Matter Energy Loss 

**200 GeV (RHIC)**

-  **Shadowing parameterizations: (****not****) **

-  **Dynamical calculations of high twist **
**  ****shadowing: (****not****) **

-  **Energy loss: in combination with HTS **
**  ****(****yes****) **

**Initial state E-loss**

- To investigate**:**

**S.S.Adler et al., nucl-ex/0603017**

**        ****T.Alber et al., E.Phys.J.C 2 (1998) **

- Cold Nuclear Matter Energy Loss

**20 GeV (SPS)**

**I.V., T.Goldman, M.B.Johnson, J.W.Qiu, hep-ph/0605200**

**B.Kopeliovich, et al., Phys.Rev.C72 (2005) **** **

**J.Gunion and G.Bertsch, Phys.Rev.D25 (1982) **** **

**b) Initial state inelastic scattering**

## High Twist Shadowing in DIS 

- High Twist Shadowing in DIS** **

**J.W.Qiu, I.V., Phys.Rev.Lett. 93 (2004)**

- x = energy = mass

-  **Dynamical**** parton mass (QED analogy):**

**c) Final state coherent scattering**

## Heavy Quarks in p+p and p+A 

- Heavy Quarks in p+p and p+A** **

-  Anti-correlation between K and the
-    hardness of fragmentation r
-  Non-trivial hadron composition of c and b
-    triggered jets

**PDFs: CTEQ 6.1 LO, J.Pumplin et al., JHEP 207 (2002)  **

**FFs: Braaten et al., Phys.Rev.D51 (1995)**

**New possibility****: hadron composition**
**of heavy quark triggered jets**

## HTS for Light Hadrons and Open Charm 

- HTS for Light Hadrons and Open Charm** **

-  **Very ****similar dynamical shadowing**** **
**  ****for  light hadrons and heavy quarks**
-  **Insufficient**** to explain the forward **
**   ****rapidity data **
-  **Single**** and ****double**** inclusive cross **
**   ****sections are ****similarly**** suppressed**

**Single inclusive particles**

**Away-side correlations**

**J.W.Qiu, I.V., Phys.Lett.B632 (2006) **

**I.V., T.Goldman, M.B.Johnson, J.W.Qiu, hep-ph/0605200**

## Energy Loss and High Twist Shadowing 

- Energy Loss and High Twist Shadowing** **

-  **Main difference**** is ****much more p****T**** independent suppression**** as compared to high twist**
**  ****shadowing**

**Single inclusive particles**

**Double inclusive yields (away-side)**

**Same**

** **Very similar e-loss effects for  light hadron and heavy quark spectra
-  Single and double inclusive cross sections are similarly suppressed

**I.V., T.Goldman, M.B.Johnson, J.W.Qiu, hep-ph/0605200**

## Process Dependence of Power Corrections 

- Process Dependence of Power Corrections** **

-  **Power corrections are ****process dependent**** and ****not**** separable**** in PDFs and FFs**

-  The function F(xb) contains the small xb dependence

_**Enhancement**_** (                )**

_**Suppression**_** (                )**

**(For example DY)**

**(For example forward rapidity)**

-  **Similar process dependence in ****single spin asymmetries**

-           **S.Brodsky et al, Phys.Rev.D65 (2002) **

-           **S.Brodsky et al, Phys.Lett.B530 (2002) **

-  **Shadowing is ****dynamically generated**** in the hadronic collision**

## Radiative Energy Loss in the QGP

**M.Gyulassy, I.V., X.N.Wang , Phys.Rev.Lett.86 (2001)**

**M.Gyulassy,P.Levai,I.V., Nucl.Phys.B 594 (2001)**

**J.D.Bjorken, Phys.Rev.D 27 (1983)**

**Uncertainty relation**

**d) Final state radiative energy loss**

**Different problems require different solutions**

**Find a ****full solution**** to all orders**
**in the correlation between multiple**
**scattering centers**

## Prediction:

**Baseline:**

**Fractional energy loss:**

**I.V., Phys.Lett.B in press, hep-ph/0603010**

**Prediction:**

**Natural variables**

**Scalings:**

**Suppression:**

**Approximately universal behavior**

##  Small probability not to radiate

** **Small probability not to radiate
-  Small fractional energy loss at large ET

- 0-10%, 20-30% and 60-80% Au+Au,
- Cu+Cu and central Pb+Pb

**M.Gyulassy, P.Levai, I.V., Phys.Lett.B (2002)**

-  Scales in the QGP

**Initial parameters**

** **

- System Size Dependence of Jet Quenching ** **

**I.V., Phys.Lett.B in press, hep-ph/0603010**

** **Absolute scale comparisons can and  should be done at large pT
-  Similar pT dependence (flat) in Au+Au and Cu+Cu

** **In classes with the same            we find
-    numerically the same suppression

**For example central Cu+Cu and mid **
**central Au+Au**

** **Future tests of high energy nuclear
-    physics  at the LHC

** **

- Energy Loss and Di-Jets** **

- One way of incorporating energy loss:

- Satisfies the momentum sum rule

**A+A**

** “****Standard” quenching of leading**
**hadrons**

** ****Redistribution of the lost energy **
**in “soft” hadrons **

**RHIC**

**LHC**

**Away-side yields**

**Single inclusive particles**

**I.V., Phys.Lett.B630 (2005)**

**e) QGP effects on di-jet production**

## Radiation Distribution and Flow Effects

**Gluon number distribution ****without**** or ****with**** ****q****0 ****= 1 GeV**

** ****Mechanical analogy, Theoretical derivation**

** ****We ****cannot ****confirm the prescription **

**q****0**

**N.Armesto et al.,  Phys.Rev.C (2005)**

**Result: same energy loss and**
**shifted reference frame**

**Problem**

**Solution:  expand about**** **

**Show that                vanishes **

** ****Important for ****deflected jets****, to be seen in **
**  ****experiment **

## Conclusions

**  **

-    In-medim interactions can be understood
-        following the history of a jet in a hard scatter:

-    Coherent final state interactions:
-               Shadowing is dynamically generated and arises from the final state
-                 Shadowing for D mesons and light pions is similar

-    Initial state interactions:
-               Transvevrse momentum diffusion and Cronin effect
-                 Energy loss and rapidity asymmetry in p+A

-    Radiative energy loss in the QGP:
-               Predicted suppession for Cu+Cu vesus centrality and pT
-                 QGP suppression is consistent with perturbative interaction of jets
-                   in the medium

-    Modification of di-jets:
-                 Gluon feedback is important for di-hadrons at large  angle
-                 Flow leads to deflection of the jet+gluons, so be exp. determined

## II. Coherent Power Corrections

**II. Coherent Power Corrections**

- Data from: NMC

**Ivan Vitev,** **LANL**

**Deviation from A-scaling:**

**What remains for theory: **
**power corrections in DIS - suppression**

**FSI are always present:   **
**                     ****S.Brodsky et al.**

## Medium-Induced Bremsstrahlung

- 2

**p**

**p**

- Example of hard
- scattering

** ****Calculating the multiple scatterings in the plasma **

**Potential**

**M.Gyulassy, P.Levai, I.V., Nucl.Phys.B594 (2001)**

**Reaction operator: ****(Cross section level            ) **

**Medium**

- Advantage:  applicable for elastic, inelastic and coherent
-                         scattering
-                         controlled approach to coherent radiation (LPM)

## Transport Coefficients in Thermalized QGP 

- Transport Coefficients in Thermalized QGP** **

** ****Experimental: Bjorken expansion**

** ****Theoretical: Gluon dominated plasma**

** ****Energy density**

** ****Transport coefficients (not a good measure for expanding medium)**

** ****Define the average for Bjorken**

##  How do you build  from T =  400 MeV

** ****How**** do you build  from T =  400 MeV**

**LHC:   from T =  1 GeV**
** **

**B.Cole, QM 2005 proceedings**

**Strong coupling used as a ****parameter**
** ****Find  T = 370 MeV  (OK)**

**S.Turbide et al., Phs.Rev.C. (2005)**

**I.V., M.Gyulassy, Phys.Rev.Lett. (2002)**
**I.V. Phys.Lett.B in press**

** ****Find  dN****g****/dy = 1200  (OK)**

**G.Paic et al., Euro Phys.J C (2005)**
**K.Eskola et al., Phys.Rev.D (2005)**

** ****Find                              (****NOT**** OK)**

** ****These are not equivalent descriptions – the ****medium properties**** differ by more than**
**an ****order of magnitude****  (sometimes close to two)**

## The Source of the Problem

- Typical gluon energy

** ****Note that the region of P****T**** at RHIC is **
**  ****10-20 GeV and at the LHC 100-200 GeV **

**Problem**

**Problem**

**Problem**

**Negative ****gluon number and ****jet enhancement**** **
**from energy loss **

**Negative ****probability density**

**C.A.Salgado, U.Wiedeman, Phys.Rev.D (2003)**

**GLV**

** ****Symptomatic of problems**** in the underlying model of energy loss**

**A useful table**

**Realistic**

## Analytic Limits of Delta E

** **- transport coefficient
** **- effective gluon
-     rapidity density

**M.Gyulassy, I.V., X.N.Wang , Phys.Rev.Lett.86 (2001)**

** ****Controlled**** approach to coherence GLV**

**Includes the fluctuations of the gluon**
**momentum and energy**

** ****Average**** implementations in the large**
**number of scatterings limit**

**BDMPS, AMY**

** ****Calculate differential spectra in **

** ****Calculate the energy loss**

**Static: **

**BJ expansion: **
**BJ+2D**

**Different dynamics REQUIRES **
**different solutions**

## Energy Loss and High Twist Shadowing 

- Energy Loss and High Twist Shadowing** **

-  **Main difference**** is ****much more p****T**** independent suppression**** as compared to high twist**
**  ****shadowing**

**Single inclusive particles**

**Double inclusive yields (away-side)**

**Same**

** **Very similar e-loss effects for  light hadron and heavy quark spectra
-  Single and double inclusive cross sections are similarly suppressed

**I.V., T.Goldman, M.B.Johnson, J.W.Qiu, hep-ph/0605200**

## Future Directions of Jet Interaction Studies 

- Future Directions of Jet Interaction Studies** **

-  **Self ****consistency ****of the description of interactions in cold nuclear matter**

**I.V., in preparation**

-  **Regimes**** of initial state energy loss  **

**Is there a full Reaction Operator (GLV-like) expression via a ****formal **
**solution**** to ****recurrence relations?**** **

**Cronin effect**

**What is the energy loss for such momentum transfer from the medium?**