# Presentation: 658673

## From di-hadron correlations to intrinsic transverse momentum

-  George Fai, Péter Lévai, Gábor Papp
- Kent State University / CRIP / ELTE

- ٭ Supported in part by U.S. DOE DE-FG02-86ER-40251, NSF INT-0435701

**IN PROTON-PROTON COLLISIONS****٭**

## Motivation

**Motivation**

** ****Data available on di-hadron correlations in**
**     ****proton-proton collisions at 200 GeV**

** ****Proton-proton result as baseline for dAu, AuAu, etc.**

** ****LO pQCD reasonable for single particle spectra –**

**START FROM INITIAL PARTONS**

**History:**
**           ****R.P. Feynman, R.D. Field, and G.C. Fox, Nucl. Phys. B 128 (1977)1**
**             ****A.L.S. Angelis et al. (CCOR), Phys. Lett. B 97 (1980) 163**
**             ****.**
**             ****.**
**           ****M.J. Tannenbaum, J. Phys. Conf. Ser. 27 (2005) 1**

- Hard Probes 2

- June 14, 2006

**Notes:**
Several ways to address; if we want generalization to dAu, AuAu, can not avoid starting from partons to calculate 

## Dan Magestro at Hard Probes 2004

**Dan Magestro at Hard Probes 2004**

- STAR preliminary

_**4 < p**__**T**__**(trig) < 6 GeV**_

_**3 < p**__**T**__**(trig) < 4 GeV**_

_**6 < p**__**T**__**(trig) < 12 GeV**_

**2 < p****T****(assoc) < p****T****(trig)**

- || < 0.7

- || < 0.7

**Near **
**side**

- Hard Probes 2

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##  J. Adams et al. (STAR), Phys. Rev. Lett. 91 (2003) 072304 

**C. Adler ****  ****et al. ****(****STAR****), Phys. Rev. Lett. 90 (2003) 082302 **
**J. Adams et al. (STAR), Phys. Rev. Lett. 93 (2004) 252301,**

** ****J. Adams et al. (STAR), Phys. Rev. Lett. 91 (2003) 072304 **

**plus**

**plus....**

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## PHENIX, hep-ex/0605039

**PHENIX, hep-ex/0605039**

**Neutral pion – charged hadron correlations**

**1.4 < p****T****assoc**** ****< 5.0 GeV/c**

**3.0 < p****T****trig**** ****< 10.0 GeV/c**

**2.5 – 3.0**

**3.0 – 3.5**

**3.5 – 4.5 **

**4.5 – 5.5**

**5.5 –6.5**

**6.5 – 8.0**

**p****T****trig**

**1.0 – 2.0**

**2.0 – 3.0**

**3.0 – 4.0**

**4.0 – 5.0**

**p****T****assoc**

- Hard Probes 2

- June 14, 2006

## PHENIX, hep-ex/0605039

**PHENIX, hep-ex/0605039**

**1.4 < p****T****assoc**** ****< 5.0 GeV/c**

**3.0 < p****T****trig**** ****< 10.0 GeV/c**

**Neutral pion – charged hadron correlations**

- Hard Probes 2

- June 14, 2006

## Leon Gaillard at Hot Quarks 2006:

**Leon Gaillard at Hot Quarks 2006:**

- Azimuthal correlations tell half the story...

- ~

- d+Au

- Hard Probes 2

- June 14, 2006

## Near and away-side π0--h± correlations in pp collisions

**1. Hard 2********2 parton-parton collision ******** back-to-back jets  **

**2. Transverse momentum ‘imbalance’ (K****T****) at jet level**
**    ****(intrinsic, gluon radiation, etc.) **

**3. Fragmentation**

**Model:**

**A. Hadrons carry a fraction of parton transverse momentum**

**B. Hadrons acquire a random fragmentation transverse **
**     ****momentum component**

**4. Azimuthal difference  ****ΔΦ**** between final hadrons**
**    ****is measured**

- Hard Probes 2

- June 14, 2006

## A. Single jet, near-side correlation

**p****T0**

**initial parton**
**transverse**
**momentum**

**p*****T1**

**p*****T2**

**p****T1**

**p****T2**

**j****T1**

**j****T2**

**Fragmentation**

**Measured**

**ΔΦ**

**p*****T1 ****= z****1 ****p****T0 **

**p*****T2 ****= z****2 ****p****T0**

**Gaussian for ****j****T1 ****and ****j****T2**** ****with given width and random angles  **

- Hard Probes 2

- June 14, 2006

## B. Back-to-back jets, away-side correlation

**p****T0**

**-p****T0**

**K****T**

**p****T2****'**

**=p****T1****'**

**p****T1*******

**p****T2*******

**j****T1**

**j****T2**

**p****T1**

**p****T2**

**Transverse momentum `imbalance’ (intrinsic, radiation, etc.) **

**Measured**

**ΔΦ**

**Gaussian for ****K****T**** with given width and random angle **

**followed by fragmentation**

- Hard Probes 2

- June 14, 2006

## B. Back-to-back jets, away-side correlationOption II

**p****T0**

**-p****T0**

**K****T**

**p****T1*******

**p****T2*******

**j****T1**

**j****T2**

**p****T1**

**p****T2**

**Transverse momentum `imbalance’ (intrinsic, radiation, etc.) **

**Measured**

**ΔΦ**

**+ simult. fragmentation**

**Expected to lead to smaller K****T**** **

**USE OPTION I HERE**

- Hard Probes 2

- June 14, 2006

## A few key formulae

**Composition of `intrinsic’ K****T**

**Near side**

**Away side**

- Hard Probes 2

- June 14, 2006

## PHENIX, hep-ex/0605039

**PHENIX, hep-ex/0605039**

**3.0 < p****T****trig**** ****< 10.0 GeV/c**

**1.0 – 2.0**

**2.0 – 3.0**

**3.0 – 4.0**

**4.0 – 5.0**

**p****T****assoc**

**present calculation**

**Quantitative reproduction of dN/d(****ΔΦ****) based on **
**widths of K****T**** and j****T**** distributions (no pedestal)**

- Hard Probes 2

- June 14, 2006

## PHENIX, hep-ex/0605039 data

**PHENIX, hep-ex/0605039 data**

**near-side width**

**away-side width**

- Hard Probes 2

- June 14, 2006

**Best values of Gaussian fragmentation widths to **
**reproduce above data on near-side width in given**
**p****Tt**** windows as function of p****Ta**** in the model**** **

- Hard Probes 2

- June 14, 2006

- Hard Probes 2

- June 14, 2006

**width of**
**`intrinsic’**
**tr. mom.**
**distrib. in**
**proton**

- Hard Probes 2

- June 14, 2006

**width of**
**`intrinsic’**
**tr. mom.**
**distrib. in**
**proton**

- Hard Probes 2

- June 14, 2006

## `Intrinsic’ transverse momentum width

**`Intrinsic’ transverse momentum width**

- Hard Probes 2

- June 14, 2006

## `Intrinsic’ transverse momentum width

- Hard Probes 2

- June 14, 2006

## `Intrinsic’ transverse momentum width

**`Intrinsic’ transverse momentum width**

- Hard Probes 2

- June 14, 2006

## `Intrinsic’ transverse momentum width

**`Intrinsic’ transverse momentum width**

- Hard Probes 2

- June 14, 2006

## `Intrinsic’ transverse momentum width

**`Intrinsic’ transverse momentum width**

- Hard Probes 2

- June 14, 2006

## `Intrinsic’ parton transverse momentumis not  a simple Gaussian

**D. Boer and W. Vogelsang,**
**Phys. Rev. D69 (2004) 094025 **

**J. Qiu and I. Vitev,**
**Phys. Lett. B570 (2003) 161 **

**J. Jia, APS/DNP Meeting,  Oct 30, 2004 **

**B. Cole, Users Meeting, June 20, 2005**

**pp**

- PHENIX ** **preliminary

**radiative tails**

- STAR

**pp**

- Hard Probes 2

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## Conclusions

**Developed constructive method for ****building in**** **
**     ****`intrinsic’ K****T**** and fragmentation  **

**2. Flexibility to treat any K****T**** distribution**

**3. Results tested against PHENIX data on pp at 200 GeV**

**4. Can generalize to pA and AA**

**6. To do: consider ****Δη**** dimension **

**5. Can be useful in jet quenching calculations**

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## Backup slides

- Hard Probes 2

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## `Intrinsic’ transverse momentum width

**`Intrinsic’ transverse momentum width**

**Final result from**
**PHENIX hep-ex/0605039**
**for the width of the **
**`intrinsic’ transverse **
**momentum distribution **

**< k****T****2 >  = 2.68 ± 0.04 GeV/c**

**1⁄2**

- Hard Probes 2

- June 14, 2006

## Jet basics

**R****cone****=0.7 rad**

**pQCD**

**fragmentation**

**parton**

**parton**

**Transverse energy deposition **
**in two variables:**

**hadrons**

**hard process**

**Focus on azimuthal angle correlations**

- Hard Probes 2

- June 14, 2006

##  kT at RHIC from p+p data

-  ***k******T****** *****at RHIC from p+p data**

- J. Rak, Wed.

- PHENIX preliminary

- J. Rak, DNP03

- di-hadron

- Statistical Errors Only

**near-side**

**away-side**

- 

**B. Jacak, Hard Probes 2004**

- Hard Probes 2

- June 14, 2006

## Jets in various collisions

**F. Wang, RBRC Workshop, March 10, 2005 **

- “We can do it but with some care...”

- Hard Probes 2

- June 14, 2006

## Di-hadron correlations in pp at 200 GeV

**dN/d******

****

**0****o**

**180****o**

** ****STAR: p-p jet event **

- Analyze jets by measuring **** between high-pT hadrons

**Di-hadron correlations in pp at 200 GeV**

**B. Cole, RHIC & AGS Users Meeting, June 20, 2005**

**Rich content already in p + p collisions: **
**                                         ****widths of the near and away side peaks**

- Hard Probes 2

- June 14, 2006

## CCOR ztrig measurement

- Angelis et al (CCOR):
- Nucl.Phys. B209
- (1982)

- Hard Probes 2

- June 14, 2006

## Charged particle density at the Tevatron 

**Charged particle density at the Tevatron**** **

-       ****** ****dependence of the charged particle density****, dNchg/d********d********, for p****T**** > 0.5 GeV/c and |********| < 1 relative to jet#1 (rotated to 270****o****)  for ****“leading jet”**** events 30 < E****T****(jet#1) < 70 GeV. **

**      ****dNchg/d********d********, for charged particles in the range p****T**** > 0.5 GeV/c and |********| < 1 for ****“min-bias”**** collisions.**

**R. Field,**
**ISMD’04**

**p+pbar**
**2 TeV**

- Hard Probes 2

- June 14, 2006

## Starting point: transverse momentum conservation

**Starting point: transverse momentum conservation**

**for  a ****2**** ******** 2 partonic process**

**Gaussian for magnitude of k****T**

**Calculate **

- Hard Probes 2

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## Jet-jet correlation scenarios

**Strongly correlated**

**Partially correlated**

**due to scattering, gluon radiation, or any **
**combination of collisions and 2******** n processes**

**2**** ******** 2**

- Hard Probes 2

- June 14, 2006

## Degree of randomization

**Randomization prescriptions:**

**uniform in [****Φ****2 ****– ****δΦ****, ****Φ****2 ****+ ****δΦ****]**

**Gauss:**

**α**** = 4[< (p****T2 ****sin****ΔΦ****)2 > - 2****σ****k****2] / p****T1****2**
**β**** = 4[< (p****T2**** cos****ΔΦ****)2 > - 2****σ****k****2] / p****T1****2**

- Hard Probes 2

- June 14, 2006

## To extract width from hadron correlations

**Need to take fragmentation into account**

**Near side**

**Away side**

- Hard Probes 2

- June 14, 2006

## Guy Paic et. al., hep-ph/0604257

**Using PYTHIA, STAR data **
**can not be fitted with a **
**single Gaussian intrinsic k****T**

- Hard Probes 2

- June 14, 2006