Low p T Photons at RHIC Stefan Bathe UC Riverside Jet Physic, ECT*, 09/01/2006

Jet Physics, ECT*, 09/06Stefan Bathe 2 1. The Physics 2. Our Methods What we have learned…

Jet Physics, ECT*, 09/06Stefan Bathe 3 ● Expected photon sources ● Experimental result ● Comparison to theory 1. Physics

Jet Physics, ECT*, 09/06Stefan Bathe 4 ● Expected photon sources ● Experimental result ● Comparison to theory 1. Physics

Jet Physics, ECT*, 09/06Stefan Bathe 5 Soft Photons in Au+Au ● Photons don’t strongly interact with produced medium ● Carry information about early stage of collision ● QGP potentially detectable via thermal photon radiation

Jet Physics, ECT*, 09/06Stefan Bathe 6 Soft Photons in Au+Au Decay photons hard: thermal: ● Photons don’t strongly interact with produced medium ● Carry information about early stage of collision ● QGP potentially detectable via thermal photon radiation target region: ~ 1-3 GeV/c Schematic Photon Spectrum in Au+Au

Jet Physics, ECT*, 09/06Stefan Bathe 7 Photon Sources in A+A Photons in A+A Direct PhotonsDecay Photons Non-thermalthermalHard+thermal Initial hard scattering Pre-equili- brium photons QGPHadron gas pQCD or prompt photons Interaction of hard parton with QGP 1) and 2) Medium induced photon bremsstrahlung

Jet Physics, ECT*, 09/06Stefan Bathe 8 Beyond simple N coll Scaling: k T effects and jet-plasma interactions ● k T effect strongest where QGP photons expected ● Interaction of fast quarks with QGP (jet photons) significant photon source for p T < 6 GeV/c: and

Jet Physics, ECT*, 09/06Stefan Bathe 9 Only N coll scaling? ● What about fragmentation photons? fragmentation contribution (%) ● fragmentation contribution substantial in p+p ● parton energy loss in QGP reduces fragmentation contribution in Au+Au ● compensated by induced photon bremsstrahlung in QGP ● Effects cancel? Bremsstrahlung

Jet Physics, ECT*, 09/06Stefan Bathe 10 Only N coll scaling? fragmentation contribution (%) ● Effects cancel? Bremsstrahlung ● Possible observable consequence: v 2 for direct photons ● Alteration of fragmentation contribution ● Jet-plasma

Jet Physics, ECT*, 09/06Stefan Bathe 11 ● Expected photon sources ● Experimental result ● Comparison to theory 1. Physics

Jet Physics, ECT*, 09/06Stefan Bathe 12  direct ● very significant direct photon spectrum at 1-5 GeV/c

Jet Physics, ECT*, 09/06Stefan Bathe 13 The Spectrum Compare to NLO pQCD L.E.Gordon and W. Vogelsang Phys. Rev. D48, 3136 (1993) excess above pQCD

Jet Physics, ECT*, 09/06Stefan Bathe 14 The Spectrum Compare to thermal model 2+1 hydro T 0 ave =360 MeV(T 0 max =570 MeV)  0 =0.15 fm/c D. d’Enterria, D. Perresounko nucl-th/ Compare to NLO pQCD L.E.Gordon and W. Vogelsang Phys. Rev. D48, 3136 (1993) excess above pQCD data above thermal at high p T

Jet Physics, ECT*, 09/06Stefan Bathe 15 The Spectrum Compare to thermal + pQCD Compare to thermal model D. d’Enterria, D. Perresounko nucl-th/ Compare to NLO pQCD L.E.Gordon and W. Vogelsang Phys. Rev. D48, 3136 (1993) 2+1 hydro T 0 ave =360 MeV(T 0 max =570 MeV)  0 =0.15 fm/c excess above pQCD data above thermal at high p T data consistent with thermal + pQCD

Jet Physics, ECT*, 09/06Stefan Bathe 16 Similar description with other thermal models

Jet Physics, ECT*, 09/06Stefan Bathe 17 ● Data also described by jet-plasma interactions as most significant source for 2<pT<4 GeV/c Gale QM05

Jet Physics, ECT*, 09/06Stefan Bathe 18 ● Internal conversion ● External conversion ● Interferometry ● Cone/Tagging/ Statistical 2. Methods

Jet Physics, ECT*, 09/06Stefan Bathe 19 Why this is difficult Signal! Theoretical (or IRS) version Traditional experimental version Improved experimental version

Jet Physics, ECT*, 09/06Stefan Bathe 20 Limitation of Statistical Method ● No significant excess at low p T ● Thermal photons predicted to dominate photon spectrum at 1-3 GeV/c ● Direct measurement of photons in this energy region impaired by: ♦ Neutral hadron contamination ♦ Energy resolution in π 0 reconstruction

Jet Physics, ECT*, 09/06Stefan Bathe 21 ● Internal conversion ● External conversion ● Interferometry ● Cone/Tagging/ Statistical 2. Methods

Jet Physics, ECT*, 09/06Stefan Bathe 22 Opening up the phase space M inv pTpT direct photon analysis new dilepton analysis conventional dilepton analysis 0

Jet Physics, ECT*, 09/06Stefan Bathe 23 phase space factorform factor invariant mass of virtual photon invariant mass of Dalitz pair phase space factorform factor invariant mass of Dalitz pair invariant mass of virtual photon The Idea ● Start from Dalitz decay ● Calculate invariant mass distribution of Dalitz pairs ● Now direct photons ● Any source of real  produces virtual  with very low mass ● Rate and mass distribution given by same formula ♦ No phase space factor for m ee << p T photon 00   00  e+e+ e-e-  Compton q  g q q  g q e+e+ e-e-

Jet Physics, ECT*, 09/06Stefan Bathe 24 ● Calculate ratios of various M inv bins to lowest one: R data ● If no direct photons: ratios correspond to Dalitz decays ● If excess: direct photons In Practice ÷ ÷ ÷ MeV R data ● Material conversion pairs removed by analysis cut ● Combinatorics removed by mixed events

Jet Physics, ECT*, 09/06Stefan Bathe 25

Jet Physics, ECT*, 09/06Stefan Bathe 26   

Jet Physics, ECT*, 09/06Stefan Bathe 27    S/B=~1   

Jet Physics, ECT*, 09/06Stefan Bathe 28    S/B=~1    RR RR R direct calculated from Dalitz formula measured R data ÷

Jet Physics, ECT*, 09/06Stefan Bathe 29    S/B=~1    calculated from Dalitz formula measured R data ÷ RR RR R direct

Jet Physics, ECT*, 09/06Stefan Bathe 30    S/B=~1    calculated from Dalitz formula measured R data ÷ RR RR R direct measured with EMCal Here we are… ~25 % systematic error : ~20 % from measured  0 ratio ~10 % from  inclusive ~5 % acceptance

Jet Physics, ECT*, 09/06Stefan Bathe MeV 0-20 % R data

Jet Physics, ECT*, 09/06Stefan Bathe 32  * direct /  * inclusive Significant 10% excess of very-low-mass virtual direct photons 0-20 %

Jet Physics, ECT*, 09/06Stefan Bathe 33 Comparison to Conventional result ( + 1 )

Jet Physics, ECT*, 09/06Stefan Bathe 34 The Spectrum Compare to published Run2 result: PRL

Jet Physics, ECT*, 09/06Stefan Bathe 35 Advantages ● Decay photon background largely suppressed ● Good momentum resolution of tracking at low pT ● Yield ratio measurement: many uncertainties cancel

Jet Physics, ECT*, 09/06Stefan Bathe 36 Limitations ● Conversion probability low ♦ Statistics limited at high pT ● Theoretical uncertainties ♦ polarization Real direct photons only transversely polarized Virtual direct photons principally also longitudinally polarized Makes relating virtual to real photons uncertain However, in high Q 2 pQCD, longitudinal polarization suppressed in limit of zero quark mass Assumed same number of polarization states for both real and virtual  ♦ Possibly higher-order corrections of Kroll-Wada formula Valid to order of  QED in vacuum In environment of HI collision: high charge If all charges interact coherently with virtual photon, correction of O(Z 2  2 ) No calculation of effect available However, coherent interaction unlikely Correction assumed to be negligible for now

Jet Physics, ECT*, 09/06Stefan Bathe 37 ● Internal conversion ● External conversion ● Interferometry ● Cone/Tagging/ Statistical 2. Methods

Jet Physics, ECT*, 09/06Stefan Bathe 38 The idea: photon conversions ● Clean photon sample: e + e - pairs from beampipe conversion ● Why? ♦ clear photon identification ♦ Very good momentum resolution of charged tracks at low p T ● Procedure ♦ Identify conversion photons in the beampipe ♦ Tag  0 by pairing electron pairs from conversions with photons in EMCal ♦ Do the same in simulations ● Double Ratio: efficiencies and acceptance corrections cancel

Jet Physics, ECT*, 09/06Stefan Bathe 39 How external conversion compares ● to EMCal statistical measurement ♦ Clean photon sample ♦ Good resolution at low pT ♦ But: statistics limited (low conversion probability) ● to internal conversion ♦ No uncertainties as for Polarization for real vs. virtual photons Higher-order corrections for conversion rate (Kroll-Wada) ♦ But: no suppression of Dalitz background

Jet Physics, ECT*, 09/06Stefan Bathe 40 Double ratio: technique and advantages DATA SIMULATION DOUBLE RATIO f = conditional probability of having a photon in the acceptance, once you already have the e + e - pair in the acceptance a pair = e + e - pair acceptance  pair = e + e - pair efficiency   =  efficiency in simulations all efficiencies are 100% everything cancels out except for      minimal systematics

Jet Physics, ECT*, 09/06Stefan Bathe 41 The PHENIX experiment Beam Pipe West ArmEast Arm γ e+e+ e-e- e+e+ e-e- γ Collision Vertex e+e+ e-e- γ electrons: momentum reconstruction (1% resolution) particle ID: RICH (loose cuts because clean signature of conversion peak) same or opposite arms: different pT acceptance photons: EMCal (loose cuts  high efficiency ~ 98%) track reconstruction assumes vertex in the interaction point  conversion at radius r≠0: e+e- pairs ‘acquire’ an opening angle  they acquire an invariant mass m =  B dl ~ r > 0 if r=4 cm (beampipe) m =20 MeV

42 Invariant e + e - mass spectrum of Run 4 Au+Au: Dalitz decays beampipe conversions air conversions & combinatorial background Conversion pairs are created off-vertex Track reconstruction produces apparent opening angle Leads to apparent mass ~20MeV/c 2

43 Dalitz decays have a real opening angle due to the π 0 mass Conversion pairs have small intrinsic opening angle –magnetic field produces opening of the pair in azimuth direction –orientation perpendicular to the magnetic field Pair properties z y x e+e+ e-e- B Conversion pair z y x e+e+ e-e- B Dalitz decay MC Simulation all pairs dalitz decay beam pipe conversions MC Simulation all pairs dalitz decay beam pipe conversions

44 Beam pipe conversions How many of these conversion pairs come from: ? Let’s find photons in the EMCal and pair them… Invariant mass spectrum after applying pair cuts

45  0 signal extraction Real events Mixed event (normalized to area outside the signal) subtraction in p T bins

46 N γ incl (p T ) and N γ π 0 tag (p T ) all e + e - pairs e + e - pairs from π 0 all e + e - pairs e + e - pairs from π 0 dN/dp T [c/GeV]

Jet Physics, ECT*, 09/06Stefan Bathe 47 How external conversion compares ● to EMCal statistical measurement ♦ Clean photon sample ♦ Good resolution at low pT ♦ But: statistics limited (low conversion probability) ● to internal conversion ♦ No uncertainties as for Polarization for real vs. virtual photons Higher-order corrections for conversion rate (Kroll-Wada) ♦ But: no suppression of  0 background

Jet Physics, ECT*, 09/06Stefan Bathe 48 ● Internal conversion ● External conversion ● Interferometry ● Cone/Tagging/ Statistical 2. Methods

Jet Physics, ECT*, 09/06Stefan Bathe 49 A New Technique:  HBT D1 D2 pp d L R pp 1 2 h/R f pp 1 3/2 1+f 2 /2 The Hanbury- Brown-Twiss method of photon interferometry works from stars to nuclei!

Jet Physics, ECT*, 09/06Stefan Bathe 50 Direct Photon Measurement via  -HBT ● Two-photon correlations observed and attributed to Bose- Einstein correlations ● Direct photon yield extracted from correlation strength: WA98, Phys. Rev. Lett. 93 (022301), 2004 Background effects   decay photons 100 < k T < 200 MeV/c 200 < k T < 300 MeV/c genuine  correlations Central Pb+Pb at √s=17.2 GeV

Jet Physics, ECT*, 09/06Stefan Bathe 51 Background Effects which mimic Two-Photon Correlations ● Cluster splitting ● Photon conversion which are not identified by the CPV ● HBT correlations of charged pions misidentified as photons ● Residual photon correlations from   HBT correlations ● Collective flow  Very good understanding of detector effects necessary !

Jet Physics, ECT*, 09/06Stefan Bathe 52 Nucl-ex/ WA98, Aggarwal, et al  L min Dependence of  Correlation Strength  L min = Since Q inv ~ K T x  L min a cut on  L min has similar effect as restricting the fit to region above Q min. 100<K T <200 MeV/c 200<K T <300 MeV/c Stable fit results with  L min > 35cm cut or by restricting Q inv fit region. Similar result for R inv. Implies region free of background and detector effects.

Jet Physics, ECT*, 09/06Stefan Bathe 53 Dependence of  HBT Parameters on  PID Vary  shower identification criteria to vary non-  background fraction: 37% and 22%charged bkgd for 2 K T bins with All showers 16% and 4% with Narrow showers <2% with no CPV R inv ~ 5-6 fm Compare R inv (  - )= fm If correlation due to background, it should be strongly affected by PID cuts. Observe no dependence on PID cuts which indicates a true  correlation.

Jet Physics, ECT*, 09/06Stefan Bathe 54 Limitations of the Different Methods Subtraction method at low p T largely limited by uncertainty of   measurement:  Energy Scale  Reconstruction Efficiency  Peak Extraktion Low p T limitation of HBT method: Huge charged particle background (p T for MIP’s ~ 100 MeV) High p T limitation of HBT method: Hit distance cut of D > 20 cm (cluster splitting!) limits usable Q inv range

Jet Physics, ECT*, 09/06Stefan Bathe 55 ● Internal conversion ● External conversion ● Interferometry ● Cone/Tagging/ Statistical 2. Methods

Jet Physics, ECT*, 09/06Stefan Bathe 56 What is the Cone Method? calculate angle between decay photons depends on energy of photon and parent  0 calculate probability, P in, to find partner in cone of opening angle  12 only shape of  0 distribution has to be known, not normalization Calculate probability, P out, of photons w/o partner in cone Corresponds to P in extrapolate to P in =1 P out (P in =1) = fraction of direct photons P in P out 1 in

Jet Physics, ECT*, 09/06Stefan Bathe 57 Cone Method   P out  P in (  ) 1 1 P out Using shape of  0 spectrum, evaluate P in (  ) P out – (measured) proportion of photons without partners in cone P in – (pre-evaluated) number of photons with partner in cone 1 1 P in (  ) P out R R = # of direct photons # of inclusive photons  0 only:  0 and non-decay photons: Account corrections for final acceptance and bad modules, final resolution and probability to pick up fake partners…   11 22

Jet Physics, ECT*, 09/06Stefan Bathe 58 Cone method compared ● Subtraction method ♦ Subtraction of two close large numbers ♦ Requires large statistics ♦ Requires precision measurement with absolute normalization ♦  no information about angular distribution of decay partners used ● Tagging method ♦ Implicitly uses some information on angular distribution Calculating probability to find partner outside of detector ♦ No absolute normalization of  0 spectrum needed ● Cone method ♦ Explicitly accounts for angular distribution Measures distribution in available region Extrapolates to full solid angle ● Limitations of Cone Method ♦ Small PHENIX acceptance ♦ Measurement only for cone size with small probability to find partner ♦ Extrapolation to full probability ● corrections ♦ probability to pick up fake partners ♦ acceptance, bad modules, resolution ● Corrections make linear extrapolation more complicated ● No (big) advantage compared to tagging method 1 1 P in (  ) P out R