3/19/080 Analysis of the Direct photon associated spectra from RHIC to LHC DongJo Kim Rafael Diaz, Norbert Novitzky, Tuomo Kalliokoski Timo Alho, Sami Räsänen, Jan Rak Jyväskylä University & Helsinki Institute of Physics, Finland DongJo Kim, Tokaj 2008 High-pT Physics at LHC, Tokaj'08

Outline of the talk 1)Open Questions from RHIC a)R AA b)Modification of the Fragmentation in AA 2)Two particle correlation a)Kinematics b)What we learned from di-hadron correlation ? c)What we can obtain from gamma-hadron correlation? 3)Gamma-Hadron Correlation –Still various Contributions to be Understood ? a)Soft QCD radiations b)  -jet momentum imbalance due to the k T smearing 4)Conclusion and Open Issues 3/19/081DongJo Kim, Tokaj 2008

3/19/082 On the mission from RHIC to LHC Great success of RHIC gave us a perfect liquid sQGP test bench for string theory (AdS/CFT) but also an opportunity to ask why: Light and heavy quarks suppression looks so similar: Quarks and gluons suppression looks similar: Direct photon suppression at high p T looks similar: Two particle correlations - more detailed view into a nature of parton interactions with QCD medium. Access to parton intrinsic momentum k T -> soft pQCD radiation, jet shape parameters j T -> induced radiation, fragmentation function -> energy loss. o Di-hadron correlations and conditional yields o Direct photons-hadron correlations in  s=200 GeV and 14 TeV DongJo Kim, Tokaj 2008

3/19/083 PHENIX Charm, PRL. 98, (2007) Medium tomography: T. Renk, K. Eskola hep-ph/ Nuclear Modification Factor for various particles PHENIX M. G. Mustafa, Phys.Rev.C72:014905,2005

More intuitive exercises…. 3/19/084 can’t get error on best fit from  2 /d.o.f curves, need  2. N standard deviation errors on fit parameters are given by  2 =  2 min + N 2, so depending on d.o.f can’t really tell from  2 /d.o.f whether I AA gives better constraint than R AA However  2 min /d.o.f=2.8 for I AA fit seems too large to be acceptable. (?) Zhang,Owens,Wang, PRL (2007) NLO pQCD + KKP FF + expanding medium  2 (I AA )  2 (R AA ) Single Di-hadron y (fm) x (fm) T.Renk, K.Eskola, PRC 75, (2007) DongJo Kim, Tokaj 2008 I AA better than R AA at RHIC and LHC R AA similar situation between RHIC and LHC I AA looks better probe in LHC I AA better than R AA at RHIC and LHC R AA similar situation between RHIC and LHC I AA looks better probe in LHC

I AA is better than R AA Gamma-h will be better 3/19/085 6< p T trig < 10 GeV STAR Preliminary  Inconsistent with Parton Quenching Model calculation (1) C. Loizides, Eur. Phys. J. C 49, (2007)  Modified fragmentation model better (2) H. Zhang, J.F. Owens, E. Wang, X.N. Wang – Phys. Rev. Lett. 98: (2007)  Di-Hadron correlation is more sensitive for jet tomography than R AA (2)(3) Gamma-h will be better but current results with very wide bins, not much different at this moment (3) K.Eskola, T.Renk, Phys.Rev.C75:054910,2007 DongJo Kim, Tokaj 2008 Phys.Rev.C75:054910,2007 (1) (2) (3)

3/19/086 More Exclusive observ. - modification of D(z) Wang, X.N., Nucl. Phys. A, 702 (1) 2002  = ln( E Jet / p hadron ) p T hadron ~2 GeV for E jet =100 GeV Borghini and Wiedemann, hep-ph/ MLLA: parton splitting+coherence  angle-ordered parton cascade. Theoretically controlled, experimentally verified approach Medium effects introduced at parton splitting pp-data also interesting DongJo Kim, Tokaj 2008

3/19/087 How can one measure D(z) Assumption: Leading particle fixes the energy scale of the trigger & assoc. jet => leading particle - trigger p Tt xEzxEz p out kTkT away-side fragments - associated particles p Ta is the jet fragmentation variable: z t and z a is a simplified Fragmentation Function, b~ 8-11 at RHIC DongJo Kim, Tokaj 2008

3/19/088 Azimuthal correlation function in  s=200 GeV d+Au Phys.Rev.D74:072002,2006 NN AA  N   j T  jet fragmentation transverse momentum  F   k T  parton transverse momentum Y A  folding of D(z) and final state parton dist. p + p  jet + jet  DongJo Kim, Tokaj 2008

3/19/089 Two-particle correlations in p+p Fragmentation function D(z) and Intrinsic momentum k T Fragmentation function D(z) and Intrinsic momentum k T DongJo Kim, Tokaj 2008

3/19/0810 Correl. fcn width - k T and acoplanarity Lorentz boost => p T,pair || k T,t || k T,a colinearity partonic hadronic Lab frame Hard scattering rest frame DongJo Kim, Tokaj 2008

3/19/0811 LEP data yield Trigger associated spectra are insensitive to D(z) b q =8.2 b g =11.4 DongJo Kim, Tokaj 2008 – Quark FF --- Gluon FF – DELPHI, Eur. Phys. J. C13,543, (1996) --- OPAL Z.Phys. C 69, 543 (1996)

3/19/0812 Unavoidable z-bias in di-hadron correlations z-bias; steeply falling/rising D(z) & PDF(1/z)  z trig   z assoc  Varying p Tassoc with p Ttrigger kept fixed leads to variation of both trigger and associated jet energies. Fixed trigger particle momentum does not fix does not fix the jet energy! Angelis et al (CCOR): Nucl.Phys. B209 (1982) Angelis et al (CCOR): Nucl.Phys. B209 (1982) DongJo Kim, Tokaj 2008

3/19/0813  k 2 T  and  z t  in 200 GeV from  0 -h CF Phys.Rev.D74:072002,2006 For D(z) the LEP date were used. Main contribution to the systematic errors comes from unknown ratio gluon/quark jet => D(z) slope. Base line measurement for the k T broadening - collisional energy loss. Direct width comparison is biased. Still, we would like to extract FF from our own data -> direct photon-h correl. DongJo Kim, Tokaj 2008

3/19/0814 D(z) from gamma tagged correlation D(z) from gamma tagged correlation leading particle - trigger p Tt xEzxEz p out kTkT away-side fragments - associated particles p Ta h-h: Leading particle does not fix Energy scale. Direct gamma - trigger p Tt xEzxEz p out kTkT away-side fragments - associated particles p Ta  -h: direct gamma does fix Energy scale if no k T DongJo Kim, Tokaj 2008 D(z t )  (z t )

3/19/0815 Soft + hard QCD radiation k T phenomenology Back-to-back balanced Soft QCD radiation Hard NLO radiation Compton photo-production DongJo Kim, Tokaj 2008

3/19/0816 00 Direct  PHENIX  s=200 GeV  0 and dir-  assoc. distributions Run GeV Statistical Subtraction Method Arbitrary Normalization Exponential slopes still vary with trigger  p T . If dN/dx E  dN/dz then the local slope should be p T  independent. FF slope DongJo Kim, Tokaj 2008

3/19/08DongJo Kim, Tokaj PYTHIA  -h simulations at RHIC 1) Initial State Radiation/Final State Radiation OFF,  2 =0 GeV/c x E slope is constant 2) IR/FR ON,  2 = 3 GeV/c x E slope is raising! Also PYTHIA shows the same trend, though, not as large as in the data, not so trivial even with Direct photons 1) 2)

3/19/0818 Pythia Initial/Final st. radiation & k T Initial/Fina state radiation OFF,  k 2 T  =0 GeV/c Initial/Fina state radiation ON,  k 2 T  =5 GeV/c DongJo Kim, Tokaj ) Initial State Radiation/Final State Radiation OFF,  2 =0 GeV/c x E slope is constant 2) IR/FR ON,  2 = 5 GeV/c x E slope is raising! Also PYTHIA shows the same trend, though, not as large as in the data, not so trivial even with Direct photons 1) Initial State Radiation/Final State Radiation OFF,  2 =0 GeV/c x E slope is constant 2) IR/FR ON,  2 = 5 GeV/c x E slope is raising! Also PYTHIA shows the same trend, though, not as large as in the data, not so trivial even with Direct photons

3/19/0819 PYTHIA  -h simulation p T,pair -  correlation  1) IR/FR k T ON  -h: p T,pair correlated with trigger photon jet balance destroyed by k T. h-h: jet balance destroyed by k T and  z T  2) IR Only Not in the case of “Initial State Radiation”. It is due to the collinearity of initial quark with photon DongJo Kim, Tokaj ) IR/FR k T ON2) IR Only

3/19/0820  -h correlation and k T bias Question: Can one extract the Fragmentation Function from  -h associated distribution despite the k T bias?  Solve for net-pair momentum DongJo Kim, Tokaj 2008

3/19/0821  -h correlation and k T bias And assuming 2D Gaussian distribution for p T,pair => A conditional probability for detecting photon p Tt and assoc p Ta given parton momentum p T in CMS of hard scattering as: DongJo Kim, Tokaj 2008

3/19/0822  -mometum distribution due to the k T smearing  Lorentz Invariant Gaussian k T smearing -> non-Gaussian distributions even at high-p T. Good agreement between simul. And formulae. DongJo Kim, Tokaj 2008

3/19/08DongJo Kim, Tokaj What about LHC ? PHENIX measured  p T  pair =3.36  0.09  0.43GeV/c extrapolation to LHC  k 2 T  ~ 6.1 GeV/c

3/19/0824 Folding with a Fragmentation function Assoc x E distrib for various slopes of D(z)  exp(-k*z) DongJo Kim, Tokaj 2008  Deviation from dashed lines (the true slopes of D(z)) at low p T due to the k T bias.  Unlike the di-hadron correlation it asymptotically converges to the correct value.  Knowing that we could unfold the k T or correct for the bias.

Comparisons to Pythia and PHENIX 3/19/0825  -h DongJo Kim, Tokaj 2008 Pythia

26 points are p+p 14 TeV PYTHIA xE distribution, dashed line KKP FF parameterization Nucl. Phys., 2001, B597, Comparison to KKP PYTHIA  - gluon jet (Annihilation) 17 %  - u quark jet (Compton) 66 % PYTHIA  - gluon jet (Annihilation) 17 %  - u quark jet (Compton) 66 % 3/19/08DongJo Kim, Tokaj 2008

3/19/0827 Summary and Open issues Inclusive and two-particle correlation measurement in the high-p T sector at RHIC opened a new window into a QGP physics. LHC will be an ideal laboratory - larger xsection and center-of-mass energy available for hard-probes production. As a next goal after “day one” physics: di-hadron and direct photon-h correlations - base line measurement for nuclear modification study: k T and initial/final state QCD radiation, resummation vs NLO j T near-side jet shape modifications fragmentation function - can be measured using jets - not from the first data. Despite our expectation FF is not accessible in di-hadron correlations. FF can be extracted from direct photons correlation only at relatively high trigger- photon momenta. k T -bias still present - pushes the minimum photon-trigger p T above 10 GeV/c at RHIC and 30 GeV/c at LHC. fragmentation photon contribution ? We are at the beginning of hard-probes exploration in heavy ion environment - LHC (supported by RHIC) will be fun ! DongJo Kim, Tokaj 2008

3/19/0828 Direct photons won’t be easy at LHC Decay photons energy and asymmetry distributions are in the ideal situation (no detector response) flat. 0 E  E  Below threshold hits “Direct” photons from  0 E cut /E   E  =10 GeV, however,  /  ratio is also of that order -> Subtraction method we started recently the full PHOS simulation project -> DongJo Kim, Tokaj 2008

3/19/08DongJo Kim, Tokaj PID FF studies MLLA + LPHD Sapeta, Wiedeman hep-ph/

30 x E slopes 3/19/08DongJo Kim, Tokaj 2008

Hard Process: Uncertainty from FF Wide z range –Due to interplay of steep jet pT distribution and steep fragmentation function. –z = 0.1 – 0.8 Missing knowledge of gluon fragmentation at larger z. –Measurement from LEPII is not still enough for larger z. 3 jets events or global analysis. –NLO FF parameters fit failed to describe the entire kinematic range (= scale violation) 31 EPJC37(2004)25 Wide z distribution 3/19/08DongJo Kim, Tokaj 2008

Model Highlight GLVPQMModification of D(z) Realistic geometry Bjorken expanding medium Radiative energy loss – gluon brehmsstralung to all orders in opacity Calculate a priori (w/o en loss) the average path length to the edge – use it to calculate partonic energy loss qhat = product of parton-medium cross- section * color-charge density BDMPS quenching weights – only coherent radiative energy loss via gluon bremsstrahlung Realistic geometry Static Avg qhat -> time- dependent density = scheme dependent\ No initial state multiple scattering No modified nuclear parton distribution function Longitudinally expanding medium Hard spheres PDFs factorized into nucleon ones and HIJING parameterization of the impact parameter dependent nuclear modification factor radiative gluon energy loss – incorporated in effective medium modified FF 3/19/0832DongJo Kim, Tokaj 2008

h-h correlations - jet functions unchanged near-side peak in the final jet functions when moving away from Reaction plane. Away side is clearly modified. Cone angle (radians) p T (GeV/c) 3/19/0833DongJo Kim, Tokaj 2008

3/19/0834 Assoc. yield - “Averaged” LO approach Assumption ( Phys.Rev.D74:072002,2006 for details) : Invariant mass of mass-less partons in hard scattering CMS and in LAB is the same -> non-Gaussian k T -smearing. DongJo Kim, Tokaj 2008

3/19/0835 Final state parton dist and FF from data of pQCD? Effective FS parton distribution: Effective Fragmentation function:  0 invariant cross section provides a constrain: DongJo Kim, Tokaj 2008

3/19/08DongJo Kim, Tokaj kT effect Outgoing partons carries transverse momentum k T. momentum imbalance (partons pt are not equal ) due to k Tx component acoplanarity (the transverse momentum of one jet doesn’t lie in the plane determined by the transverse momentum of the second jet and the beam axes) due to k Ty component R. P. Feynman, R. D Field, and G. C. Fox, Phys Rev D J. Rak and M. Tannenbaum hep-ex/ v1 Intrinsic : Fermi motion of the confined partons inside the proton. NLO : Hard gluon radiation Soft : Initial and Final state radiation, resummation techniques (hep-ph/ ).

Direct Photon is isolated in p+p PHENIX PRL 98 (2007) Seems to imply N frag ≈ 66% of N dir Only  from (Only ~50% of inclusive photons included ) Which gives you “ N frag ≈ 33% of N dir “ QM08 PHENIX 3/19/0837DongJo Kim, Tokaj 2008 √s = 200GeV

Fragmentation photons are isolated ? 3/19/08DongJo Kim, Tokaj √s = 14 TeV Pythia Isolation done on the pure PYTHIA particles |  | < 0.7, R=0.4, p T th = 1 GeV/c Isolation Cut efficiency for direct and frag photons Gustavo Conesa Balbastre

Quark, Gluon Energy Loss QM08 3/19/0839 Baryon & meson NMF STAR Preliminary Mark Thomas Heinz Sapeta, Wiedeman hep-ph/ DongJo Kim, Tokaj 2008