heavy flavor flow from electron measurements at rhic shingo sakai (univ. of california, los angeles)
TRANSCRIPT
Heavy flavor flow from electron measurements at RHIC
Shingo Sakai
(Univ. of California, Los Angeles)
Outline
Introduction Non-photonic e v2 measurement
Non-photonic e v2
D meson v2
Charm v2
Outlook (B decay)
Elliptic flow
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)))
λ >> R ; Isotropic
λ << R ; anisotropic
Y
X
Y
X
Elliptic flow @ RHIC
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
Hydro;Phys. Rev. C 67 (03) 044903v2; Phys.Rev.Lett.91 182301 (2003) PHENIX
5 2006/5/20
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
Charm study @ RHIC
Electron measurement photonic
- photon conversion
- Dalitz decay (π0,η,ω ---) nonphotonic
- Ke3 decay
- primarily semileptonic decay
of mesons containing c & b
D meson measurement => reconstructed from π,K
Charm quark yield
Phys.Rev.Lett.94:082301,2005(PHENIX)
QM06, F. Kajihara
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 , K, p
AuAu Central strangeness hadron
Brast-wave fit to D-meson and single electron and muon from D-meson decay spectra
non-zero collective velocity
further information of charm flow obtain v2 measurement SQM06, Y. Yifei
STAR
Non-photonic electron v2 measurement
Non-photonic electron v2 is given as;
v2 γ.e ; Photonic electron v2
Cocktail method (simulation) stat. advantage Converter method (experimentally)
v2e ; Inclusive electron v2
=> Measure RNP = (Non-γ e) / (γ e)=> Measure
NP
eeNPenon
enonee
R
vvRv
d
dN
d
dN
d
dN
.22.
2
..
)1(
(1)
(2)
Photonic e v2 determination
decaye vRv 2.2
compare inclusive e v2
with/without converter (converter only increase photonic component)
photonic electron v2
=> cocktail of photonic e v2
R = N X->e/ Nγe
photonic e v2 (Cocktail)
decay
v2 (π0)
pT<3 ; π (nucl-ex/0608033)pT>3 ; π0 (PHENIX run4 prelim.)
Non-photonic electron v2
non-zero non-photonic electron v2 was observed below 3 GeV/c
Non-photonic electron v2
Phys. Rev. Lett. 98, 172301 (2007)
dN/d() = N (1 + 2v2cos(2(φ)))
12
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
Non-photonic electron v2 seems like get large with impact parameter
0-20% 20-40% 40-60%
Non-photonic electron v2 (centrality dep.)
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
0-20% 20-40% 40-60%
1
14
D meson v2
charm →D meson → non-photonic e non-photonic electron v2
reflect D meson v2 ?
pT<1.0 GeV/c, smeared by the large mass difference
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
Line ; D mesonCircle ; electron
Electron pT(GeV/c)
<co
s(φ
e -
φD)>
simulation
simulation
Phys.Lett.B597
D v2 estimation
π(PHENIX prelim.) p (PHENIX prelim.) k (PHENIX prelim.) D from scaling(kET=mT-m0) + ・・・ φ
MC simulation (PYTHIA) e v2
Assumptions
non-photonic electron decay from D meson
D meson v2 ; D v2 = a*f(pT)
f(pT) ; D meson v2 shape assume various shapea ; free parameter (pT independent)
f(pT)
compared with measured v2 and find “a” range (Χ2 test)
16
Fitting result
fitting result χ2 / ndf vs. a ndf = 13
χ2 /
nd
f
Pion shape Kaon shape Proton shape
φshape scale shape
χ2 /
nd
f
1
1
a[%]
a[%]
17
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 v2(pT<3 GeV/c)
Charm flow ?
RAA for non-photonic electron ;
A large suppression of high pT electron yield
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)
[PLB623]
Estimation of charm quark v2
(1) Apply coalescence model(2) Assume universal pT dependence of v2 for quark
e
T
q
T
q
T
D
cq
T
D
uq
T
D
vpbvpav
pm
mbvp
m
mavpv
222
222
)6
5()
6
1(~
)()()(
[PRC 68 044901 Zi-wei & Denes]
Quark v2
(3)Quarks which have same velocity coales
charm
u
Dv
v
mu + mc = mD
mu = 0.3 & mc = 1.5 (effective mass) a,b --- fitting parameter simultaneous fit to non-γ e v2 , v2
K, v2p
v2,u = a ×v2,q
v2,c = b ×v2,q
Fitting result (1)
χ2 minimum result
The best fitting (Χ2 minimum) a = 1, b = 0.96 (χ2/ndf = 21.85/27)
v2,u = a ×v2,q
v2,c = b ×v2,q
Kaonv2
k = 2(av2,u(2pT,u))
protonv2
p = 3(av2,u(3pT,u)) Non-photonic
Fitting result (1)
χ2 minimum result
the coalescence model well represent low pT v2 shape saturate point and value
Fitting result (2)
χ2 minimum ; a = 1, b = 0.96 (χ2/ndf = 21.85/27) Quark coalescence model indicate non-zero charm v2
a ; u quark
0.96
1
v2,u = a ×v2,q
v2,c = b ×v2,q
23
Charm quark v2
In the assumptions(1)Charm quark v2 is non-zero(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
[PRC72,024906] [PRC73,034913
]
[Phys.Lett. B595 202-208 ]
models support a non-zero charm v2
25
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 andsuppression for nonphotonicwould indicate early time thermaliation of charm
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
RUN4RUN7
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 /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 ×2T ~4-6
Moore and Teaney Phys.Rev.C71:064904,2005 Find DHQ/(/(+p)) ~ 6 for Nf=3 Calculate perturbatively,
argue result also plausible non-perturbatively
Combining Recall +p = T s at B=0 This then gives /s ~(1.5-3)/4 That is, within factor of 2 of
conjectured bound
Rapp & Hees private communication
Moore & Teaney private communication
Additional Remarks What does DHQ/(/(+p)) ~ 6 mean?
Denominator: DHQ is diffusion length ~ heavy quark diffusion length HQ
Numerator: Note that viscosity ~ n <p>
n = number density <p> = mean (thermal) momentum = mean free path
“Enthalpy” + P ~ n <p> Here P is pressure
So /(+P) = (n <p> / (n <p> ) ~ Note this is for the medium, i.e., light quarks
Combining gives DHQ/(/(+p)) ~ HQ / 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” /(+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 usingNon-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
v2non-γ(non-photonic) & v2γ(photonic) is “experimentally” determined !
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)
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)