Azimuthal Correlations in p-p collisions Eleazar Cuautle∗ , Isabel Domínguez ∗ and Guy Pai´c∗
arXiv:hep-ph/0604257v1 27 Apr 2006
Instituto de Ciencias Nucleares, UNAM, A. P. 70543, 04510 Mexico City, Mexico.
Abstract. We report √ the analysis of experimental azimuthal correlations measured by STAR in p-p collisions at sNN = 200 GeV. We conclude that for a fit of data using Pythia event generator we need to include two values of kT .
INTRODUCTION Jets are produced by the hard scattering of two partons. Two scattered partons propagate nearly back-to-back in azimuth from the collision point and fragment into jet-like spray of final state particles (The schematic view is in Figure 1). These particles have a transverse momentum jT with respect to the parent partons, with component jT z projected onto the azimuthal plane. The magnitude of jT z measured at lower energies has been √ found to be sNN and pT independent. In collinear partonic collisions, the two partons emerge with the same magnitude of transverse momentum in opposite directions. However, the partons carry the “intrinsic” transverse momentum kT before the collision. This momentum affects the outgoing transverse momentum pT , resulting in a momentum imbalance (i.e. transverse momentum of one jet does not lie in the plane determined by the transverse momentum of the second jet and the beam axes) and consequently affects the back-to-back correlations of final high pT hadrons . The back-to-back azimuthal correlations of high pT hadrons is written as dN (1) Ntrigger d∆Φd∆η where ∆Φ and ∆η are, respectively, the azimuthal angle and pseudorapidity between a trigger and their associated particles. The azimuthal correlation function displays a twopeak structure, where the width of the near-side peak is denoted by σN and the width of the away-side peak is σA . The value of σN carries information on the fragmentation process only i.e. jT . For particles with average transverse momenta < pT,trigg > and < pT,associate > from the same jet, the width of the near-side correlation, σN , can be related to < jT z > as : C(∆Φ) =
< pT,trigger >< pT,associate > < jT z >= p σN (2) < pT,trigger >2 + < pT,associate >2 The width of the away-side peak σA contain the contribution of the intrinsic transverse momentum kT . It has been characterized by a Gaussian distribution 
Schematic view of a jet fragmentation, near-side jet (upper) and away-side jet (lower)
1 kT2 exp(− ) (3) 2πσ 2 2σ 2 The azimuthal correlations are used extensively in heavy ions collisions to understand the parton suppression mechanisms. We have concentrated in this work to the simplest case i.e. p-p to understand the size and details of the peaks in azimuthal correlations. g(kT ) =
KT CONTRIBUTION IN THE AZIMUTHAL CORRELATIONS Correlation function was calculated choosing < kT2 >=0, 1, 4 GeV 2 /c2 at 200 GeV in a mid-rapidity region (| η |< 0.7). Charged hadrons in 4 < pT,trigg < 6 GeV/c and in 2 GeV < pT,assoc < 4 GeV are defined to be trigger and associated particles respectively. In the actual calculation, we use PYTHIA 6.325  in AliRoot  to simulate each hard scattering where a Gaussian distribution is assuming for kT . The correlations functions were fitted by the sum of two Gaussians, one for the near-side component (around ∆Φ = 0 radians) and one for the away-side component (around ∆Φ = π radians) and a constant for the uncorrelated pairs. Figure 2 compares experimental data  with different < kT2 > simulations. In the four cases is observed that can not reproduce experimental data. In order to reproduce the experimental data, we characterize the intrinsic momentum by two Gaussians distributions
p-p sNN =200 GeV JETS (4,6) 4
=0 GeV 2 /c 2 =1 GeV 2 /c 2 =2 GeV 2 /c 2 PRL 91 072304 (STAR)
FIGURE 2. Azimuthal distributions for p+p collisions at simulations with different < kT2 >
g(kT 1 , kT 2 ) =
4 5 ∆φ(radians)
sNN = 200 GeV, experimental data  and
kT2 1 kT2 2 1 1 exp(− ) + exp(− ) 2πσ12 2σ12 2πσ22 2σ22
This distribution was adding in PYTHIA code and calculated the azimuthal correlations. The Figure 3 show the experimental data and the simulation. The simulation is in good agreement with the experimental data. The values of < kT 1 > and < kT 2 > are 0.558 ± 0.042 and < kT 2 > = 0.099 ± 0.050 respectively. In addition the magnitude of the partonic transverse momentum < jT z > was calculated. The values obtained of < jT z > = 0.397 ± 0.091 GeV/c are in agreement with the average value < jT z > = 0.324 ± 0.06 GeV/c obtained experimentally .
SUMMARY We report the√analysis of experimental azimuthal correlations measured by STAR in p-p collisions at sNN = 200 GeV. Comparisons between experimental data and simulation with different < kT2 > show that the < kT2 > characterized by a Gaussian distribution can not reproduce experimental data.
0.3 p-p sNN =200 GeV JETS(4,6) 4
PRL91 072304 (STAR)
2 Gaussian Distribution
4 5 ∆φ(radians)
FIGURE 3. Azimuthal distributions for p+p collisions, experimental data (line)  and simulations with two Gaussian distributions for the partons intrinsic momentum (circle)
Assuming two Gaussians distributions for kT the simulation is in agreement with the experimental data, as far as, we understand the use of two Gaussians. It has never been used before to explain the peaks observed in azimuthal correlations. In addition the magnitude of the partonic transverse momentum < jT z > was calculated. The values of < jT z > = 0.397 ± 0.091 GeV/c are in agreement with the average value < jT z > = 0.324 ± 0.06 GeV/c obtained experimentally.
ACKNOWLEDGMENTS The authors thanks A. Morsch for his valuable comments and suggestions. Support for this work has been received by PAPIT-UNAM under grant number IN107105.
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