Effects of Fluctuations and Effects of Fluctuations and Inhomogeneities on Jet Quenching in Inhomogeneities on Jet Quenching in

High Energy Nuclear CollisionsHigh Energy Nuclear CollisionsEnrique Ramirez-Homs

University of Texas at El PasoAdvisor: Dr. Rainer Fries

Texas A&M UniversityCyclotron Institute REU 2009

● Heavy ion collisions● Quark gluon plasma● Jet production● Jet quenching● Fluctuations● Fragmentation● Observables

− Elliptic flow and nuclear modification factor

Heavy Ion Collisions

● RHIC - = 200 GeV

● quark-gluon plasma – color degrees of freedom● formation time .5 fm● εC ≈ 1 GeV/fm3

● TC ≈ 170 MeV (1012 K).

NNs

Nucleus-nucleus collisions

● Glauber model of multiple collisions for protons and neutrons used[1]

● Relates impact parameter to Npart and Ncoll

● Geometrical model based on assumption of constant cross section for each collision,

− σinel ≡ inelastic cross section, − TAB(b) ≡ thickness function, i.e. integral of

nuclear densities over longitudinal dir.[1] R. J. Glauber and G. Matthiae. (1970).

)(bTN ABinelcoll σ=

Jet quenching

● Hard scattering considered dominant process of particle production pT ≥ 2 GeV

● GLV formulation for radiative energy loss[2],

● Modest reduction in fragmenting parton energy -> significant decrease in hadron yield at pT ≥ 3 GeV

[2] M. Gyulassy, P. Levai and I.Vitev. (2000).

CCRR ≡≡ color factorcolor factorL L ≡≡ distance traveleddistance traveled≡ transport coefficient

µµ ≡≡ momentum transfermomentum transferμα EqLC sR logˆ =E 2Δ q̂

Jet quenching

● The medium determines energy loss amount via transport coefficient,

● Implemented to energy loss formulation,

● Parameter found to be .08 to make fit of pTspectrum and determine overall normalization

43432

ˆ partg

Nq ∝∝= ελμ λg ≡ mean free path

ε ≡ local energy density Npart ≡ participant nucleons density

ENLconstdLdE

npart log***.)( 4/3=

Fluctuations

● Fluctuations for the number of participants in the medium calculated through normal distribution with finite spatial size, λ, in each coordinate and standard deviation, σ, at points within the interaction zone.

● Fluctuations implemented as checkerboard.− At any point in interaction zone, fluctuation at

distance < λ used to avoid washing out any possible effect

Fluctuations

Bilinear interpolation of random fluctuations in the interactionBilinear interpolation of random fluctuations in the interaction zone for three zone for three impact parameters.impact parameters.Step size of one fermi and fluctuation size Step size of one fermi and fluctuation size σσ=0.1 used.=0.1 used.

Hadronization

● Due to color confinement, separated quarks go through hadron fragmentation

● New quark/anti-quark pairs appear before ever separating further.

● Individual quarks lose energy and tight cones of color-neutral particles created.

● Fragmentation function[3], Dπo(z,Q2)− probability for πo to carry a fraction z = pπo/p

of outgoing parton momentum.

[3] Bernd A. Kniehl, G. Kramer, B. Potter. (2000).

Hadronization

● New hadron spectra can then be calculated,

● Q2 ≡ factorization scale − introduced to account for collinear

singularities in structure and fragmentation functions

● dN/(2πpdp) ≡ hard scattering cross section.

pdpdNQzD

zdz

dppdN

z

o

oo

o

πππ

ππ

π

2),(

2

12

2min

∫=

Putting things together…

● Parton production ->jet quenching ->fragmentation -> …

Calculated Calculated ππoo spectra with and without energy loss.spectra with and without energy loss.

TT dppdN

oπ

● Rather than looking and the spectra, two observables, v2 and RAA, are introduced.

Elliptic flow

● Dense nuclear overlap at beginning of heavy ion collision resembles ellipsoid due to incomplete overlap of two colliding nuclei.

● Spatial anisotropy converted into momentum anisotropy with any strong scattering.

YY

ZZ

XX

PPyy

PPxx PPzz

Elliptic flow

● Azimuthal anisotropy of spectra in transverse plane can be characterized in terms of the second Fourier coefficient,

● Elliptic flow, v2, measures eccentricity in momentum space

)2cos21(2 2 ψπψ

vdpp

dNdppd

dN

TTTT

+=

)2cos(2 ψ=v

Nuclear modification factor

● RAA, useful tool to probe jet suppression, either in the initial or final state.

● Ratio of number of particles produced in Au+Au collisions to the number of particle produced in p+p collisions, scaled by the average number of collisions.

T

pp

coll

T

AA

AA

dpdNN

dpdN

R =

Everything together…

● Parton production -> jet quenching -> fluctuations -> probe -> fragmentation -> probe -> …

● Fluctuations in RAA measured but did not show any dependence, as expected.

● With large fluctuations of energy density, found observable effects larger for v2 than for RAA growing from central to peripheral collisions.

RRAAAA for pions without fluctuations (solid), 5 random fluctuation evfor pions without fluctuations (solid), 5 random fluctuation events of ents of σσ = 2 = 2 (red(red--dash), and the average of 20 events (red) compared with PHENIX ddash), and the average of 20 events (red) compared with PHENIX data [4] ata [4] at different centrality bins corresponding to their average impaat different centrality bins corresponding to their average impact parameter.ct parameter.

Plot of the elliptical flow without fluctuations and the averagePlot of the elliptical flow without fluctuations and the average of 20 fluctuation events.of 20 fluctuation events.

Changing jet quenching method

● Rather than using GLV formulation for energy loss, decided to use linear dependence of distance traveled.

4/3**.)( npartNLconstdLdE = 2/1*.)( npartNconstdLdE =

Original v2 (solid) compared to change in jet quenching (dashed)Original v2 (solid) compared to change in jet quenching (dashed)

Single forward jet conclusions

● RAA reproduced centrality scaling; little effect from fluctuations

● v2: effects from fluctuations larger than for RAA but smaller than 10%

● Observed suppression link to centrality but not as expected, which will lead into further investigation.

Back-to-back jet production

Parton spectra for back jets coming from initial pParton spectra for back jets coming from initial pTT=10 GeV at two observation angles=10 GeV at two observation angles

Future work

a) Poisson statistics for Npartor event generator (NEXUS,EPOS)

a) Detailed study of fluctuations

Reference and Acknowledgement

[1] R. J. Glauber and G. Matthiae, Nucl. Phys. B 21 (1970) 135[2] M. Gyulassy, P. Levai and I.Vitev. Phys. Rev. Lett. 85, 5535 5538 (2000).[3] Bernd A. Kniehl, G. Kramer, B. Potter. Nucl.Phys.B582:514-536 (2000).[4] PHENIX Collaboration, A. Adare, et al. Phys. Rev. Lett. 101, 232301 (2008).

● Dr. Rainer Fries● Dr. Ricardo Rodriguez● Dr. Sherry Yennello

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