Transcript Charm quark v2 from non-γ electron v2 (for QM2006)

Heavy flavor flow from electron
measurements at RHIC
Shingo Sakai
(Univ. of California, Los Angeles)
Outline
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Introduction
Non-photonic e v2 measurement
Non-photonic e v2
D meson v2
Charm v2
Outlook (B decay)
Elliptic flow
λ >> R ; Isotropic
Y
 In non-central collisions, the initial shape is anisotropic
 The emission pattern is influenced by mean free path
 Mean free path λ = (nσ) -1
λ>> R ; isotropic
λ<< R ; anisotropic
RHIC ; n ~ 4 [1/fm3], σππ = 20mb
λ ～ 10-1 fm << R(Au) ～ 6 fm
 hydro model；
medium is equilibrium, pressure gradient is
larger x than y, and the collective flow is
developed in x.
 second harmonic of the azimuthal distribution
=> “elliptic flow”
dN/d() = N (1 + 2v2cos(2(φ)))
X
λ << R ; anisotropic
Y
X
Elliptic flow @ RHIC
Hydro;Phys. Rev. C 67 (03) 044903
v2; Phys.Rev.Lett.91 182301 (2003) PHENIX
 In low pT (pT<1.5 GeV/c),
v2 increases with pT, and
show mass dependence
v2(π)>v2(K)>v2(p)
=> hydro model well represents
identified particle v2
 assume early time
thermalization
τ0 = 0.6 fm/c
v2 already developed in partonic phase ?
 identified hadrons v2 after
scaling pT and v2
number of quarks
 v2 after scaling fall on
same curve
 v2 already formed in the
partonic phase for hadrons
made of light quarks (u,d,s)
 charm flow
=> re-scattering is so intense
=> quark level thermalization 5
2006/5/20
Charm study @ RHIC
 D meson measurement
=> reconstructed from π,K
 Electron measurement
 photonic
- photon conversion
- Dalitz decay (π0,η,ω ---)
 nonphotonic
- Ke3 decay
- primarily semileptonic decay
of mesons containing c & b
Charm quark yield
QM06, F. Kajihara
Phys.Rev.Lett.94:082301,2005
(PHENIX)
 Non-suppressed charm yield at low pT
=> they are initially produced and survived until the end
Non-photonic electron v2 @ low pT does not come from energy loss
=> would reflect collective flow
* energy loss also generate non-zero v2

Radial flow of charm meson
AuAu Central
charm hadron
AuAu Central
strangeness hadron
Brast-wave fit to D-meson and
single electron and muon from
D-meson decay spectra
STAR
AuAu Central
, K, p
 non-zero collective velocity
 further information of charm
flow obtain v2 measurement
SQM06, Y. Yifei
Non-photonic electron v2 measurement
 Non-photonic electron v2 is given as;
e
 .e
non  .e
dN
dN
dN


d
d
d
e
 .e
(
1

R
)
v

v
NP
2
2
v2non  .e 
RNP
v2e ; Inclusive electron v2
=> Measure
(1)
(2)
RNP = (Non-γ e) / (γ e)
=> Measure
v2 γ.e ; Photonic electron v2
 Cocktail method (simulation) stat. advantage
 Converter method (experimentally)
Photonic e v2 determination
v2 (π0)
R = N X->e/ Nγe
pT<3 ; π (nucl-ex/0608033)
pT>3 ; π0 (PHENIX run4 prelim.)
decay
photonic e v2 (Cocktail)
 photonic electron v2
=> cocktail of photonic e v2
v2 .e   R  v2decay
 compare inclusive e v2
with/without converter
(converter only increase
photonic component)
Non-photonic electron v2
dN/d() = N (1 + 2v2cos(2(φ)))
Phys. Rev. Lett. 98, 172301 (2007)
Non-photonic electron v2
 non-zero non-photonic electron v2 was observed
below 3 GeV/c
Non-photonic electron v2 (centrality dep.)
 Hydro -> driving force of v2 is pressure gradient (ΔP)
 ΔP get large with impact parameter (centrality)
=> v2 get large with centrality
0-20%
20-40%
40-60%
 Non-photonic electron v2 seems like get large with impact parameter
12
Non-photonic electron v2 (centrality dep.)
1
0-20%
20-40%
40-60%
 Non-photonic electron v2 seems like get large with impact parameter
 RAA =1 @ peripheral collisions but non-zero v2
 non-photonic e v2 => result of collective flow
 charm →D meson
→ non-photonic e
 non-photonic electron v2
reflect D meson v2 ?
<cos(φe - φD)>
D meson v2
simulation
pT<1.0 GeV/c, smeared
by the large mass difference
Electron pT(GeV/c)
pT > 1.0 GeV/c, decay
electrons have same
angle of the parents
 “non-zero” non-photonic e v2
=> indicate non-zero D meson v2
Phys.Lett.B597
Line ; D meson
Circle ; electron
simulation
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D v2 estimation
 Assumptions
 non-photonic electron
decay from D meson
 π(PHENIX prelim.)
 p (PHENIX prelim.)
f(pT)
 k (PHENIX prelim.)
 D from scaling(kET=mT-m0)
 + ・・・ φ
 D meson v2 ; D v2 = a*f(pT)
 f(pT) ; D meson v2 shape
assume various shape
a ; free parameter
(pT independent)
MC simulation (PYTHIA)
e v2
 compared with measured v2
and find “a” range (Χ2 test)
χ2 / ndf
Fitting result
1
Pion shape
Kaon shape
Proton shape
χ2 / ndf
a[%]
1
 fitting result
χ2 / ndf vs. a
ndf = 13
φshape
scale shape
16
a[%]
Expected D meson v2
 D meson v2 expected from non-photonic e v2
 D meson v2 ; Max 0.09±0.03
 D v2 is smaller than pion v172(pT<3 GeV/c)
Charm flow ?
 RAA for non-photonic electron；
 A large suppression of
high pT electron yield
[PLB623]
 model predict initial parton
density > 3500
=> high parton dense matter
 charm mean free path
n > 7 fm-3
σ = 3 mb (pQCD)
=> λcharm < 0.5 fm
shorter than R(Au) ~ 6 fm
=> would expect charm v2
nucl-ex/0611018 (PRL)
Estimation of charm quark v2
(1) Apply coalescence model (3)Quarks which have same
velocity coales
(2) Assume universal pT
dependence of v2 for quark
charm
Quark v2
D
v
v2,u = a ×v2,q
v2,c = b ×v2,q
u
v
[PRC 68 044901
Zi-wei & Denes]
v2D ( pT )  av2q (
mu
m
pT )  bv2q ( c pT )
mD
mD
1
5
~ av2q ( pT )  bv2q ( pT )  v2e
6
6
 mu + mc = mD
 mu = 0.3 & mc = 1.5
(effective mass)
 a,b --- fitting parameter
 simultaneous fit to
non-γ e v2 , v2K, v2p
Fitting result (1)
χ2 minimum result
Non-photonic
Kaon
v2k = 2(av2,u(2pT,u))
 The best fitting (Χ2 minimum)
 a = 1, b = 0.96 (χ2/ndf = 21.85/27)
proton
v2p = 3(av2,u(3pT,u))
v2,u = a ×v2,q
v2,c = b ×v2,q
Fitting result (1)
χ2 minimum result
 the coalescence model well represent
 low pT v2 shape
 saturate point and value
Fitting result (2)
v2,u = a ×v2,q
v2,c = b ×v2,q
0.96
1
a ; u quark
 χ2 minimum ; a = 1, b = 0.96 (χ2/ndf = 21.85/27)
 Quark coalescence model indicate non-zero charm v2
Charm quark v2
In the assumptions
(1)Charm quark v2 is non-zero
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(2)Charm quark v2 is same
as light quarks
Compare with models
(1) Charm quark thermal + flow
(2) large cross section ; ~10 mb
(3) Elastic scattering in QGP
[Phys.Lett. B595 202-208 ]
[PRC72,024906]
[PRC73,034913]
 models support a non-zero charm v2
Charm thermalization ?
 Theoretical calculation
[PRC73 034913]
 assume D & B resonance
in sQGP
=> accelerate c & b thermalization
time
=> comparable to τQGP~ 5 fm/c
Strong elliptic flow and
suppression for nonphotonic
would indicate early time
thermaliation of charm
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Bottom quark contribution
 Three independent methods
provide B/D @ pp
e-h azm. correlation (STAR)
 e-D0 azm. correlation (STAR)
 e-h invariant mass (PHENIX)

Bottom quark contribution
 Three independent methods
provide B/D @ pp
e-h azm. correlation (STAR)
 e-D0 azm. correlation (STAR)
 e-h invariant mass (PHENIX)

=> consistent
 Bottom contribution is significant
B/D = 1 above 5 GeV/c

pQCD (FONLL) calculation well
represent B/D ratio as a function
of pT
pp 200 GeV
Bottom quark contribution
RUN4
RUN7
min.bias
 B/D = 1.0 (pT>5.0) @ pp but unclear @ AuAu
 but their contribution would large at high pT @ AuAu
 nonphotonic electron decay from B keeps parent direction
above 3 GeV/c
 high pT nonphotonic electon v2 would provide B v2 information
 SVT will install in STAR & PHNIX
Summary
 Non-photonic electron v2 mainly from charm decay was
measured @ s = 200 GeV in Au+Au collisions at RHIC
& non-zero v2 is observed
 Non-photonic electron v2 is consistent with hydro
behavior
 Measured non-photonic electron indicate non-zero D
meson v2
 Based on a quark coalescence model, the data suggest
non-zero v2 of charm quark.
BackUp
Comparison with models; RAA & v2
Nucl-ex/0611018
 Two models describes strong
suppression and large v2
 Rapp and Van Hees
 Elastic scattering
-> small τ
 DHQ × 2πT ~ 4 - 6
 Moore and Teaney
 DHQ × 2πT = 3~12
 These calculations suggest that
small τ and/or DHQ are required
to reproduce the data.
Constraining h/s with PHENIX data
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Rapp and van Hees Phys.Rev.C71:034907,2005
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Simultaneously describe PHENIX
RAA(E) and v2(e) with diffusion
coefficient in range DHQ ×2T ~4-6
Moore and Teaney Phys.Rev.C71:064904,2005


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Rapp & Hees private communication
Find DHQ/(h/(e+p)) ~ 6 for Nf=3
Calculate perturbatively,
argue result also plausible
non-perturbatively
Combining

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
Recall e+p = T s
at mB=0
This then gives h/s ~(1.5-3)/4
That is, within factor of 2 of
conjectured bound
Moore & Teaney private communication
Additional Remarks

What does DHQ/(h/(e+p)) ~ 6 mean?

Denominator:


DHQ is diffusion length ~ heavy quark diffusion length lHQ
Numerator:

Note that viscosity h ~ n <p> l




n = number density
<p> = mean (thermal) momentum
l = mean free path
“Enthalpy” e + P ~ n <p>

Here P is pressure
So h/(e+P) = (n <p> l) / (n <p> ) ~ l

Note this l is for the medium, i.e., light quarks
Combining gives DHQ/(h/(e+p)) ~ lHQ / l

Not implausible this should be of order 6
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Notes
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Above simple estimates in Boltzmann limit of well-defined
(quasi)-particles, densities and mfp’s
The “transport coefficient” h/(e+p) is preferred by theorists because it
remains well-defined in cases where Boltzmann limit does not apply
(sQGP?)
qc & gc cross section
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 = R *Nγ+Nnon-γ
Cocktail method
 estimate background electron
with simulation
 sum up all background electrons
 Input
 π0 (dominant source)
use measured pT @ PHENIX
 other source
assume mt scale of pi
 clear enhancement of inclusive
electron w.r.t photonic electron
Converter method
Separate non-photonic & photonic e v2 by using
Non-converter run & converter run
Non-converter ; Nnc = Nγ+Nnon-γ
Converter ; Nc = R *Nγ+Nnon-γ
(1+RNP)v2nc = v2γ + RNPv2non-γ
(R +RNP) v2c = R v2γ + RNPv2non-γ
R --- ratio of electrons with & without converter (measured)
RNP --- non-photonic/photonic ratio (measured)
v2nc --- inclusive e v2 measured with non-converter run (measured)
v2c --- inclusive e v2 measured with converter run (measured)
v2non-γ(non-photonic) & v2γ(photonic) is
“experimentally” determined !
Outlook for heavy flavor v2 study @ RHIC
 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]
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 with
additional converter
(X = 0.4 + 1.7%)
[PRL 94, 082301 (2005) ]
 50 % of e come from non-γ @ high pT (>1.5 GeV/c)