Elliptic flow of electron fromheavy flavor decay by thePHENIX
Shingo Sakaifor PHENIX collaboration(Univ. of Tsukuba & JPSP)Outline
Physics motivation
 Method Result
 Compare with models
 Summarypage1Motivation
 flow & energy loss ?
 insight into theproperty of the medium Charm is produced in initial collisions via gluon fusionand propagates through medium=> good probe for studying property of the medium v2 and RAA measurement are useful analysis method Large energy loss has been observed. => talked by F. kajihara How about charm flow ?
=> indicate strongly coupling & quark level thermalization
 v2 & RAA are related to the diffusion coefficient D and η/sD ∝ η/(sT)page2

Charm via electron measurement
 Electron is one of the good probe of charm Electron sources photonic- photon conversion- Dalitz decay (π0,η,ω ---)
 non-photonic- Ke3 decay- primarily semi-leptonic decayof mesons containing c & b
 We have two independent method for photonic
electron subtraction.

page3

Photonic electron subtraction
Cocktail subtraction
photonic electrons are calculated
as cocktail of each sources.
[PRL 88, 192303 (2002) ]Converter subtraction
Photonic electrons are extracted
experimentally by special run withadditional converter(X = 0.4 + 1.7%)[PRL 94, 082301 (2005) ] 50 % of e come from non-γ @ high pT (>1.5 GeV/c)* Details about spectra analysis ; F. Kajihara’s talkpage4

Non-photonic electron v2 measurement
 Non photonic electron v2 is given as;eγ .e

non −γ .edNdNdN=+dΦdΦdΦγ .eeRvv(1+)−non −γ .e
22NPv2=RNP
v2e ; Inclusive electron v2=> Measure(1)(2)

RNP = (Non-γ e) / (γ e)=> Measurev2 γ.e ; Photonic electron v2⇒ Cocktail method (simulation) stat. advantage⇒ Converter method (experimentally)

page5

Electron ID @ PHENIX

counts Electron ID
 RICH ; electron ID
 EMC ; measure E request E/p matchingeID @ RICH

eAfter subtract
B.G.
B.G.

 Radiation length < 0.4 %((e/p)-1)/σpage6

Inclusive electron v2

 inclusive electron v2 measured w.r.t reaction plane converter --- increase photonic electron photonic & non-photonic e v2 is different

page7

Photonic e v2 determination
v2 (π0)R = N X->e/ NγepT<3 ; π (nucl-ex/0608033)
pT>3 ; π0 (PHENIX run4 prelim.)

decay
photonic e v2 (Cocktail) photonic electron v2=> cocktail of photonic e v2v2γ .e = ∑ R × v2decay
 good agreement
converter method(experimentally determined)page8Non-photonic electron v2

 Strong elliptic flow for non-photonic electron
 Main source is D meson -> indicate non-zero D v2
 Charm v2 also non-zero ?

page9Non-zero charm v2 ? (1) Apply recombination model Assume universal v2 (pT) for quark
universal v2 (pT) for quark

Shape is determinedwith measured identified
particle v2charm[PRC 68 044901
Zi-wei & Denes]

muq mcv ( pT ) = av (pT ) + bv 2 (pT ) → v2e
mDmD
D2q2a,b ; fitting parameters

 simultaneous fit to v2π, v2K and v2non-γe

page10b ; charmNon-zero charm v2 ? (2)χ2 minimum result
D->e2σ1σ4σa;u χ2 minimum ; a = 1, b = 0.96 (χ2/ndf = 21.85/27)
 Based on this recombination model, the data suggest
non-zero v2 of charm quark.

page11Compare with models(1) Charm quark thermal + flow [Phys.Lett. B595 202-208 ](2) large cross section ; ~10 mb [PRC72,024906](3) Resonance state of D & B in sQGP [PRC73,034913](4) pQCD [PRB637,362] --- fail=> Charm quark strongly coupled to the matterwork

page12Comparison with models; RAA & v2
Nucl-ex/0611018

 Two models describes strong
suppression and large v2
z Rapp and Van Hees
9 Elastic scattering-> small τ9 DHQ × 2πT ~ 4 - 6
z Moore and Teaney
9 DHQ × 2πT = 3~12
 These calculations suggest thatsmall τ and/or DHQ are required
to reproduce the data.

page13

Constraining η/s with PHENIX dataRapp and van Hees Phys.Rev.C71:034907,2005{

Simultaneously describe PHENIX
RAA(E) and v2(e) with diffusion
coefficient in range DHQ ×2πT ~4-6

Moore and Teaney Phys.Rev.C71:064904,2005{{Rapp & Hees private communication

Find DHQ/(η/(ε+p)) ~ 6 for Nf=3
Calculate perturbatively,
argue result also plausible
non-perturbatively

Combining{{{Recall ε+p = T sat μB=0

This then gives η/s ~(1.5-3)/4π
That is, within factor of 2 ofconjectured boundMoore & Teaney private communication

page14

Summary Non-photonic electron v2 mainly from charm decay wasmeasured @ √s = 200 GeV in Au+Au collisions atRHIC-PHENIX & non-zero v2 is observed The data suggest non-zero v2 of charm quark.
 Charm quark strongly coupled to the matter Model comparison suggests{ smallτ and/or DHQ are required{ η/s is very small, near quantum bound.

Thanks!

BackUp

Additional Remarks
What does DHQ/(η/(ε+p)) ~ 6 mean?
{Denominator:{

DHQ is diffusion length ~ heavy quark diffusion length λHQ

Numerator:
Note that viscosity η ~ n <p> λ{{{n = number density<p> = mean (thermal) momentum
λ = mean free path

“Enthalpy” ε + P ~ n <p>{Here P is pressureSo η/(ε+P) = (n <p> λ) / (n <p> ) ~ λNote this λ is for the medium, i.e., light quarks
Combining gives DHQ/(η/(ε+p)) ~ λHQ / λ
Not implausible this should be of order 6{Notes{{Above simple estimates in Boltzmann limit of well-defined(quasi)-particles, densities and mfp’s
The “transport coefficient” η/(ε+p) is preferred by theorists because it
remains well-defined in cases where Boltzmann limit does not apply(sQGP?)Outlook for heavy flavor v2 study @ PHENIX
 new reaction plane detector
 good resolution => reduce error from R.P.
 J/ψ v2 & high pT non-photonic electron v2
 silicon vertex detector
 direct measurement D meson v2[Silicon vertex detector][Reaction plane detector] Line on the figure ; D->e v2- v2,u (pT) = v2,c (pT)
- v2,D (pT)
= v2,u(1/6pT) + v2,c(5/6 pT)
 If charm & u has same v2, themaximum v2 = 0.1=> Non-photonic electron v2 issmaller than pi (pi0) v2

Converter method install “photon converter ”(brass ;X0 = 1.7 %) around beam pipe
 increase photonic electron yield Compare electron yield with &without converter experimentally separate
Non-converter ; Nnc = Nγ+Nnon-γ
Converter ; Nc = Rγ *Nγ+Nnon-γ

Cocktail method estimate background electronwith simulation
 sum up all background electrons Input π0 (dominant source)
use measured pT @ PHENIX
 other source
assume mt scale of pi clear enhancement of inclusiveelectron w.r.t photonic electron