# Presentation: 712903

## Hard Scattering and QCD fundamentals at RHIC

- M. J. Tannenbaum
- Brookhaven National Laboratory
- Upton, NY 11973 USA

- 9th Workshop on Non-Perturbative QCD Paris, France                                       June 4-8, 2007

## BDMPS 1997-1998

- In 1998 at the QCD workshop in Paris, Rolf Baier asked me whether jets could be measured in Au+Au collisions because he had a prediction of a QCD medium-effect on colored partons in a hot-dense-medium with lots of unscreened color charge.
-  As the expected energy in a typical jet cone

- is  R2 x1/ 2 x dET/d= R2/2 x dET/d ~ 300 GeV for R=1 at sNN=200 GeV where the maximum Jet energy is 100 GeV, Jets can not be reconstructed in Au+Au central collisions at RHIC.
-  But hard-scattering can be well studied by single inclusive and 2-particle correlation measurements as it was discovered at the CERN ISR in the 1970’s
-  And it just so happened that the PHENIX detector was designed to trigger, measure and separate  and 0 out to pT> 25 GeV/c !

**Notes:**
I should make up a new slide saying that BDMPS predicted energy loss due to a coherent LPM effect of brems of a colored gluon on the unscreened color charges in the medium. de/dx propto L, so is coherent. This opened the way to use hard scattering as a probe of unscreened color charge density. Then mention that R. Baier asked me if we could find jets and jet phenomena at RHIC in 1998, since in RHI collisions.... Of courseI said we could do it with single and 2 particle correlation techniques we developed in the original high pT discovery at the CERN ISR

## Everything you want to know about JETS can be measured with 2-particle correlations--NOT 

- Everything you want to know about JETS can be measured with 2-particle correlations--NOT

- CCOR, A.L.S.Angelis, et al Phys.Lett. **97B**, 163 (1980)   PhysicaScripta **19**, 116 (1979)

- pTt > 7 GeV/c vs pT

- From RHIC97--QCD98

## Everything you want to know about JETS can be measured with 2-particle correlations--NOT

- CCOR, A.L.S.Angelis, et al Phys.Lett. **97B**, 163 (1980)   PhysicaScripta **19**, 116 (1979)

- pTt > 7 GeV/c vs pT

- From RHIC97--QCD98

## xE distribution measures fragmentation fn.-NOT

- xE distribution measures fragmentation fn.-NOT

- Dq(z)~e-6z

-  independent of pTt

- <ztrig>=0.85 measured

- See M. Jacob’s talk EPS 1979 Geneva

- From RHIC97--QCD98

- xE ~ pTa/pTt ~z/<ztrig>

## xE distribution measures fragmentation fn.-NOT

- xE distribution measures fragmentation fn.-NOT

- Dq(z)~e-6z

-  independent of pTt

- <ztrig>=0.85 measured

- See M. Jacob’s talk EPS 1979 Geneva

- From RHIC97--QCD98

- xE ~ pTa/pTt ~z/<ztrig>

## Where did I (and everybody in HEP) get this idea?---from Feynman, Field and Fox

- “There is a simple relationship
- between experiments done with single-particle triggers and those performed with jet triggers. The only difference in the opposite side correlation is due to the fact that the ‘quark’, from which a single-particle trigger came, always has a higher p than the trigger (by factor 1/ztrig). The away-side correlations for a single-particle trigger at p should be roughly the same as the away side correlations for a jet trigger at p (jet)= p (single particle)/ <ztrig>”.

- FFF Nucl.Phys. **B128**(1977) 1-65

## As measured at the ISR by Darriulat, etc.

- P. Darriulat, et al,  Nucl.Phys. **B107 **(1976) 429-456

## Inclusive invariant 0 spectrum is beautiful power law for pT3 GeV/c n=8.100.05

- PHENIX,          S.S.Adler, et al.,       nucl-ex/0611007     subm. PRC

## Suppression of 0 is arguably the major discovery at RHIC. Energy loss in medium?

- Suppression of 0 is arguably the major discovery at RHIC. Energy loss in medium?

**Au Au ********s****NN****=200 GeV-QM 2005**

- Non-identified h and 0 different pT<6GeV/c. Does either obey QCD?  xT scaling AuAu 200 cf 130 GeV showed 0 xT scaling  Energy loss scales. h do not xT scale: baryons not suppressed for 2 < pT < 6 GeV/c--This is called the baryon anomaly, still not understood.

- Original 0 discovery, PHENIX PRL **88 **(2002)022301; latest preprint nucl-ex/0611007

## The leading-particle effect a.k.a. trigger bias

-  Due to the steeply falling power-law spectrum of the scattered partons, the inclusive particle pT spectrum is dominated by fragments biased towards large z. This was unfortunately called trigger bias by M. Jacob and P. Landshoff, Phys. Rep. **48C**, 286 (1978) although it has nothing to do with a trigger.

- Fragment spectrum given *p*Tt is weighted to high *z*t by *z*tn-2

- ( <z>=1/b )

## Continuing as in PRD 74, 072002 (2006)

- Continuing as in PRD **74**, 072002 (2006)

- We can integrate over the trigger jet zt and find the inclusive pion cross section:

- Bjorken parent-child relation:  parton and particle invariant pT spectra have same power *n*

- Inclusive high pT particle has n-1 times larger <z> than unbiased fragmentation, <z>=1/b

## 2 particle Correlations

- (1)

- Appears to be sensitive to away jet Frag. Fn.

## PHENIX-compared measured xE distribution to numerical integral using LEP fragmentation functions-not sensitive!

-  independent of pTt

- xE ~ pTa/pTt ~z/<ztrig>

- <ztrig>=0.85 measured

- Dq (z)~e-6z

**ISR-CCOR 1979**

**LEP**

- PHENIX PRD** 74** (2006) 072002

**b****q****=8.2**

**b****g****=11.4**

## Amazingly, I got a neat analytical result

- Take:

- Using:

- Where (a,0)= (a)=(a-1) (a)

- (1)

- (2)

## The final result

- Where B/b<m>b is the mean charged multiplicity in the jet

## Why dependence on the Frag. Fn. vanishes

-  The only dependence on the fragmentation function is in the normalization constant B/b which equals <m>, the mean multiplicity in the away jet from the integral of the fragmentation function.
-  The dominant term in the xE distribution is the Hagedorn function  ...                      so that at fixed pTt the xE distribution is predominantly a function only of xE and thus exhibits xE scaling, as observed.
-  The reason that the xE distribution is not sensitive to the shape of the fragmentation function is that the integral over zt in (1, 2) for fixed pTt and pTa is actually an integral over jet transverse momentum  ..    . However since the trigger and away jets are always roughly equal and opposite in transverse momentum (in p+p), integrating over ...   simultaneously integrates over ...  . The integral is over zt, which appears in both trigger and away side fragmentation functions in (1).

## Oh yes--PHENIX o - h  correlation functionsp+p s=200 GeV: PRD 74, 072002 (2006)

- d+Au

- N   *j*T   jet fragmentation transverse momentum-measure directly
- F   *k*T  parton transverse momentum-more complicated.

## Results RMS kT in p+p @ 200 GeV

- Main contribution to the systematic errors comes from unknown ratio gluon/quark jet => D(z) slope =><m>

## A very interesting formula

- measured

- Ratio of jet transverse momenta

## Shape of xE distribution depends on         and n but not on b

- Shape of xE distribution depends on         and *n* but not on *b*

- 1.0
- 0.8
- 0.6
- 0.4
- 0.2

## Does the formula work?

-  PHENIX p+p   PRD **74**, 072002 (2006)

## It works for PHENIX p+p PRD 74, 072002 

## Away side correlations in Au+Au much wider than in p-p

- D

- Away side distribution much wider in A+A than p-p in correlation fn. C() Subtraction of v2 (flow?) effect J() causes a dip at 180o which gives 2 peaks at D~1 radian independent of system and centrality for Npart >100. This is also seen for (auto) correlations of low pT particles. Is this the medium reaction to the passage of a color-charged parton? Stay tuned, much more study needed.

-  PHENIX AuAu          PRL **98** (2007) 232302

## Formula works in Au+Au:  Away-side yield  vs pTa/pTt is steeper in Au+Au than p-p indicating energy loss

- h(3<pTt<4 GeV/c)--h

- The away side pTa/pTt  xE distribution triggered by a leading particle with pTt was thought to be equal to the fragmentation function but we found that it is NOT sensitive to the shape of the fragmentation function but only to the shape of the inclusive pTt spectrum  with power n (=8.1). Formula derived in PRD 74 (2006) 072002 works for pp and AA

## Direct  - h  correlations in p+p s=200 GeV    New PHENIX preliminary result

******0**

**Direct ******

- In order to understand whether away side xE distribution from a direct  is the (quark) fragmentation function must understand kT smearing for direct . Next step is to measure kT for direct 

## Direct 's in p-p s=200 GeV: Data vs. pQCD 

- Direct 's in p-p s=200 GeV: Data vs. pQCD

- Published results 3<pT<15 GeV/c

- PHENIX PRL **98** (2007) 012002

**p-p**

**p-p**

- Preliminary results for 5<pT<24 GeV/c

## Comparison with other data and pQCD

- Aurenche et al  Eur. Phys. JC**9** (1999)107

- PHENIX data clarifies longstanding data/theory puzzle

- Talk by Monique Werlen at RHIC&AGS users meeting 2005

## 2004--Direct Photons in Au+Au 200 GeV: follow TAB scaling from p-p for all centralities-no suppression

**2004--Direct Photons in Au+Au 200 GeV: follow T****AB**** scaling from p-p for all centralities-no suppression**

- Direct photons unaffected by QCD medium in Au+Au 
******0 ****suppression is medium effect**** **

- 1) Proves that initial state Au structure function is simply a superposition of p-p structure functions including g(x).

- PHENIX PRL**94** (2005) 232301

**Au+Au**

## Status of RAA in AuAu at sNN=200 GeV QM05

- Implies a strong medium effect (energy loss) since  not affected.
- Suppression is flat at high pT. Are data flatter than theory?

- Status of RAA in AuAu at sNN=200 GeV QM05

## The biggest result at QM2006??!

- QM2006-
- pp dir  reference is run 5 msmt
- If RAA= RAA the whole concept of energy loss changes: perhaps no effect for pT>20 GeV

- QM2005
- -I wanted to make a T-shirt
- pp dir  reference is pQCD

## For Au+Au min bias direct  RAA is simple

- For Au+Au min bias direct  RAA is simple

- Au+Au minimum bias

- Do the structure function ratios actually drop by ~20% from x=0.1 to x=0.2?

- Eskola,Kolhinen,Ruuskanen Nucl. Phys. B**535**(1998)351

## Central Collisions---no theory counterpart-yet

- Au+Au Central Collisions

- Nobody has seriously measured nor calculated structure function ratios as a function of centrality!!!

- Theorists, HELP!

- Very few attempts so far for structure function measurements or theory as a function of impact parameter:                                  E665, ZPC 65, 225 (1995)                 Li and Wang, PLB 527, 85 (2002)   Klein and Vogt PRL 91, 142301 (2003) Emel’yanov, et al. PRC 61, 044904 (2000) and references therein.

- Experimentalists: RHIC p+A, eRHIC

## QM2005-direct  in AuAu via internal conversion

- QM2005-direct  in AuAu via internal conversion

- Kroll Wada PR**98**(1955) 1355

- PHENIX NPA**774**(2006)403

- Eliminating the 0 background by going to 0.2<mee<0.3 GeV enables direct  signal to be measured for 1<pT <3 GeV/c in Au+Au. It is exponential, does that mean it is thermal. We must see whether p-p direct  is gaussian as pT 0 as in Drell-Yan or exponential like for 0

## QM2006-Direct e in Au+Au indicate a theoretical crisis

-  heavy quarks suppressed the same as light quarks, and they flow, but less.        This disfavors the energy loss by gluon bremsstrahlung in medium  hypothesis           but brings string theorists into the game.

- p-p beautiful agreement of e with *c b*  production PHENIX PRL**97**(2006)252002

**Au+Au **PHENIX   PRL **98 **(2007)172301

**Au+Au**

**p-p**

##  RAA 0 in AuAu sNN=200 GeV vs. Reaction Plane to probe details of the theory-learn something new!

**PHENIX nucl-ex/0611007**
**(submitted to Phys. Rev. C.)**

- Little/no energy loss for L< 2 fm

- L =  distance from edge to center of participants calculated in Glauber model

- RAA is absolute,  v2 is relative so no hint of this in v2 measurements. This result also suggests that v2 for pT>2GeV/c is due to anisotropic energy loss not flow.

- RAA() vs. centrality varies density of and distance through medium

## Comparison with theory including systematic error

**C. Loizides**
**hep-ph/0608133v2**

## Outline

-  correlations including photons
- kT
- xE, hatx_h
-  inclusive Gamma RAA--structure functions
-  gamma via internal conversion
-  RAA vs reaction plane
- fits to q-hat

## Normalization of Fragmentation Functions

- I assumed b is the same for 0 and all charged.  Then using B/b=b which normalizes total momentum to 1, I get the correct jet cross section. Obviously the total momentum for 0 is ~1/3 so B for pure 0 ~1/3 b2