# Presentation: 849647

## Why the xE distribution triggered by a 0 does not measure the fragmentation function

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

- Quark Matter 2006 Shanghai, PRC November 15-20, 2006 corrected 2/8/7

## 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--HP04

## xE distribution measures fragmentation fn.-NOT

- xE distribution measures fragmentation fn.-NOT

- xE ~ z/<ztrig>

- Dq(z)~e-6z

-  independent of pTt

- <ztrig>=0.85 measured

- See M. Jacob’s talk EPS 1979 Geneva

- From RHIC97--HP04

## 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=8.10.1

## Formula for xE distribution                from PRD 74, 072002 (2006)

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

- (1)

## How we found the problem in PHENIX

- Following FFF and CCOR PLB**97**(1980)163-168 we were trying to measure the net transverse momentum of the di-jet (2 x <kT>)

-  jT is parton fragmentation transverse momentum
-  kT is transverse momentum of a parton in a proton (2 protons)
-  xE=-pTpTt/|pTt|2 represents away jet fragmentation z
-  pout is component of away pT perpendicular to trigger pTt

- We needed <zt> to solve for kT. Tried to get it from xE dist.

## Fit xE distributions to form of D(z) used by LEP measurements by integrating Eq (1) numerically  

- Fit xE distributions to form of D(z) used by LEP measurements by integrating Eq (1) numerically

- D(z)=exp(-10z)

- D(z)=exp(-20z)

- After many convergence difficulties, two vastly different fragmentations  functions triedNo effect on calculated xE distributions---Mike, can you check this analytically?!

## Amazingly, I could; and got a neat 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).

## DiscussionApplication

## 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 

## Now Apply Eq. To (STAR) Au+Au data

- STAR, J. Adams, Fuqiang Wang, et al  PRL **95**, 152301 (2005)

- 4 < pTt < 6 GeV/c <pTt>=4.56 GeV/c

- pp,  AuAu sNN=200 GeV

## It works for STAR p+p and:

-   a) * means data normalized w.r.  to hep-ex/0605039

- b)

## STAR Au+Au--Clear effect with centrality

| p+p | data*0.6 | fit*1.16 |        =1.0 |
| --- | --- | --- | --- |
| AuAu40-80 | data*0.6 | fit*2.03 |         =0.75 |
| AuAu00-05 | data*0.6 | fit*4.64 |        =0.48
 |

- STAR, J. Adams, Fuqiang Wang, et al  PRL **95**, 152301 (2005)

-  Away jet     /trigger jet    decreases with increasing centrality
-  consistent with increase of energy loss with distance traversed in  medium

## New STAR data AuAu: nucl-ex/0604018

- 8 < pTt < 15 GeV/c  <pTt>=9.38 GeV/c

- Thanks to Dan Magestro for table of data points

- STAR, J. Adams, D. Magestro, et al  PRL **97**, 162301 (2006)

## STAR(nucl-ex/0604018)  differs from     STAR (PRL95) in normalization and SHAPE

## Normalize 064018 to PRL95 by eye

## Normalized data with PRL95 curve

## STAR 0604018 AuAu central flatter than PHENIX 0605039 p+p for xE>0.5!

- Can still fit, but curves too flat xh>1, but still decreases with increasing centrality

- Norm (data) Norm fit     hatx_h
- Data*0.6      Fit*0.580   1.300
- Data*0.6      Fit*0.406   1.200
- Data*0.6      Fit*0.348   0.850

## PHENIX d+Au results

-  Beautiful p+p and dAu results with pTt in STAR punchthrough range.

- PHENIX, PRC 73, 054903 (2006)

## PHENIX d+Au PRC73

-  STAR 0604018 AuAu0-5 flatter than all published p+p and d+Au data ????

## Conclusions