# Presentation: 659942

## Jet properties from di-hadron correlations in p+p collisions at  s =200 GeV

*Jan Rak**                         *collaboration
- Jyvaskyla University & HIP, Finland

- Presented by M. J. Tannenbaum

- Jan Rak

## Everything you want to know about jet-physics can be found using a 2-particle correlations

- , OK, almost everything...

- Analysis of PHENIXhigh pT  0 trigger associated charged hadron distributions in p+p data at s=200 GeV.
-  1 . 108 gamma3 triggered events (2x2 EMcal>1GeV/c)  analyzed.
- Jet kinematics from 2-particle correlation
- Trigger biases in 2-particle correlation - words of caution.
- Lorentz invariant 2D kT smearing.
- (In)Sensitivity of trigger associated distributions to the shape of the fragmentation function *D(z)*.
- Results on k2T evolution with trigger pTt.

- Jan Rak

## Modification of the fragmentation fcn

- pQCD nature of jet quenching should be accompanied by modification of partonic properties
*e.g. softening of the fragmentation function*
- Gyulassy, Vitev, Wang and Zhang
*nucl-th/0302077*

- Jan Rak

## Jet quenching at RHIC - do we see Induced Gluon Radiation ?

- Maybe but why there is
- Similar suppression pattern of high-pT electrons from semi-leptonic *D *and *B* mesons decays; PRL 91, 172302 (2003). Where is the ‘dead cone’ ? Is there unique  dNg/dy for light/heavy quarks quenching?
- No broadening of the associated correlation peak (nucl-ex/051000). According Ivan Vitev  (Phys. Lett. **B630**, 78 (2005)) there should be a significant broadening.
- induced gluon radiation should strongly violate the xT scaling in contrast to what is seen in the data - see *Brodsky, Pirner and Raufeisen*, hep-ph/0510315

- Detailed understanding of unmodified parton properties
- CRUCIAL

- Jan Rak

## Hard scattering – kT 

- Longitudinal

- transverse

- jet

- jet

- acoplanar in PL  PT space
- collinear   in PX  PY space

- Jan Rak

## Origin of kT

- Intrinsic *k*T “fermi motion”

- Soft QCD NLO radiation.

- As an example  - J/ production.

- pTJ/ =1.80.230.16 GeV/c
*Phys. Rev. Lett. 92, 051802, (2004).*

- Power law tail @ large value of pT,pair

- Gussian @ pT,pair0 Leading-Log resummation *Vogelsang,Sterman,Keusza Nucl Phys A721,591(2003)*

- Jan Rak

## ISR CCOR - s = 30-60 GeV

*A.L.S. Angelis, ... M.J. Tannenbaum Phys Lett 97B (1980)*

- k2T causes acoplanarity
- p2out transverse momentum component of the away-side particle measures accoplanarity

- kT is a 2D vector hence

*Feynman Field Fox Tannenbaum* assumed ‘hadron-parton duality’ (z=1) and xE is a two particle equivalent of z.
- Looks as a simple analysis, right?

- Note the rising trend

- Jan Rak

## Is it really that easy ?

- Shown at QM04 - fixed correlations pTtrigger=pTassoc

- Jan Rak

## Lesson I. “kT acoplanarity”

- pT,pair Lorentz boost preserves

- partonic

- hadronic

- Jet momenta imbalance due to  kT smearing

- Lab frame

- Hard scattering rest frame

- Jan Rak

## Lesson II

- There are ALWAYS two types of trigger biases  when correlating pTtriggerpTassoc

- Jan Rak

## o - h  correlation functionsp+p s=200 GeV

- d+Au

- Not corrected for acceptance

- Corrected for acceptance

- N

- A

- N   *j*T   jet fragmentation transverse momentum
- F   *k*T  parton transverse momentum
- YA   folding of D(z)  and  final state PDF.

- Jan Rak

## Lesson III

- Away side peak is not a Gaussian !

- It caused some confusion. Exctraction of pout from angular width of the away side peak - see e.g. P. Levai at.all hep-ph/0502238 does not converge.

- This distribution was fitted to the away-side peak; pout = free parameter.

- Jan Rak

## Fragmentation function

- In order to decompose the partonic variables on the left part of an eqution one has to know the fragmentation function *D(z)*

- Jan Rak

## Associated yield in p+p s=200 GeV

- Both distributions are almost identical. There is no difference between xE and pTa/pTt   (see *X.-N. Wang, Phys. Lett. ****B595****, 165 (2004)*)

- Jan Rak

## Slope variation

- In contrast to fragmentation function
- local slope varies with trigger pTt
- There are two reasons:
-  trigger bias: fixed momentum of the trigger particle does not fix jet momentum scale
-  kT smearing: imbalance between back-to-back parton momenta

- Jan Rak

## Parameterizations of effective D(z) and fQ(pT)

- Associated parton distribution  fa = kTft and the final formula for inclusive cross section:

- Fragmentation function parameterization

- Final state parton spectrum parameterization

**^**

- Jan Rak

## Trigger associated spectra are insensitive to D(z)

- LEP data

- Incomplete Gamma function when assumed power law for final state PDF and exp for D(z)=B exp-bz

- <m> is mean multiplicity of away jet, n is power of single inclusive: Sensitivity to D(z) parms. is lost

- PHENIX  hep-ex/0605039

- Jan Rak

## What did we learn from PYTHIA 

- If we assume the ppair momentum to be a random quantity with a Gaussian distribution, we can write the probability distribution for  “smeared” parton given a condition of detecting a trigger pTt and associated pTa particle as:

- Jan Rak

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

- ISR

- We gave up an effort to extract fragmentation function from di-hadron data, direct photon analysis under way - stay tuned ....
- For D(z) the LEP data were used.

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

- PHENIX

- Jan Rak

## Mean z and jet momenta imbalance

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

- Jan Rak

## pTt integrated k2T

- Jan Rak

## summary 

- As promised we learned everything what we want from di-hadron correlations except the Fragmentation function. However, there are facts not quite commonly understood:
- Away-side peak variance does not measure RMS of pout .
- Fixed trigger momentum doesn’t fix the jet momentum. The <z> variation propagates to the away side jet.
-  *k*T smearing – strong bias towards smaller parton momenta and *k*T pointing towards you.
- Gaussian 1D approximation for the kT smearing may be too rough even at relatively high pT region around 10 GeV/c.
- associated distribution in pTassoc, pTassoc/pTtrigg or in xE are convolutions of parton distribution function, product of two fragmentation function and kT and they are not  sensitive to the shape of the fragmentation only the mean multiplicity.
- Extracted k2T seems to follow general trend with s. The pTt dependence seems to be shallower than what has been observed at lower energies - this could be because of z variations were neglected.

- PHENIX  hep-ex/0605039

- Jan Rak