Open Charm at LHCMarlene Nahrgang
Duke University
July 8th, Dubna,Strangeness in Quark Matter
2015
1 / 34
Probes of the quark-gluon plasma• Study of properties of strongly interacting many-body systems via ultra-relativistic
heavy-ion collisions.
• Probes should not thermalize with the medium, e.g. dileptons, high-pT jets,...
• The mass of heavy quarks (HQ) sets another scale: mc , mb
• HQ vacuum shower terminates much earlier: E/Q2H with QH =
√Q2
0 + m2Q .
• Number of thermally excited HQ is negligibly small.
• Contributions from gluon-splitting are negligible for charm quarks at currentpT -range.
• HQ as leading parton is always tagged.
2 / 34
Quark-gluon plasma and its properties
jet quenching
observable: nuclear modification factor
RAA(pT ) =1
Ncoll
dNAA/dpT
dNpp/dpT
sensitive to jet quenching parameter q
collective flow
observable: Fourier coefficients of
d2NdpT dy
∝ ∑n
vn cos(nφ)
sensitive to viscosity η/s
3 / 34
Formation of QGP, which evolves fluid dynamically as a nearly perfect fluid.
Quark-gluon plasma and its properties
jet quenching
Jet Collab. PRC90 (2014)
observable: nuclear modification factor
RAA(pT ) =1
Ncoll
dNAA/dpT
dNpp/dpT
sensitive to jet quenching parameter q
collective flow
0
0.1
0.2
0.3
0.4
0.5
0 0.5 1 1.5 2 2.5 3 3.5 4
v2
pT [GeV]
LHC 2.76 TeV
ALICE h+/-
30-40%
ideal, avg
η/s=0.08, avg
ideal, e-b-e
η/s=0.08, e-b-e
η/s=0.16 , e-b-e
B. Schenke et al. PLB702 (2011)
observable: Fourier coefficients of
d2NdpT dy
∝ ∑n
vn cos(nφ)
sensitive to viscosity η/s
4 / 34
Formation of QGP, which evolves fluid dynamically as a nearly perfect fluid.
Quark-gluon plasma and its properties
jet quenching
Jet Collab. PRC90 (2014)
observable: nuclear modification factor
RAA(pT ) =1
Ncoll
dNAA/dpT
dNpp/dpT
sensitive to jet quenching parameter q
collective flow
0
0.1
0.2
0.3
0.4
0.5
0 0.5 1 1.5 2 2.5 3 3.5 4
v2
pT [GeV]
LHC 2.76 TeV
ALICE h+/-
30-40%
ideal, avg
η/s=0.08, avg
ideal, e-b-e
η/s=0.08, e-b-e
η/s=0.16 , e-b-e
B. Schenke et al. PLB702 (2011)
observable: Fourier coefficients of
d2NdpT dy
∝ ∑n
vn cos(nφ)
sensitive to viscosity η/s
5 / 34
Formation of QGP, which evolves fluid dynamically as a nearly perfect fluid.
Learn from the success in the light hadron sector for heavy-flavor studies!
What to expect from heavy-quark observables?
PHENIX, PRC84 (2011)
at low pT ∼ mQ
• Very different from light partons.
• Nonperturbative!
• Partial thermalization with the lightpartons in the QGP?
• Diffusion D mainly via collisionalprocesses?
• Hadronization viacoalescence/recombination?
• Initial shadowing and cold nuclearmatter effects?
at high pT >> mQ
• Similar to light partons.
• Perturbative regime...
• Rare processes, probe the opacity ofthe matter.
• Energy loss dE/dx via collisional andradiative processes?
• Coherent energy loss→jet-quenching parameter q?
• Hadronization via (medium-modified)fragmentation?
6 / 34
Modeling of heavy-quark dynamics in the QGP
103
104
105
106
107
108
0 5 10 15 20 25 30
dσ
/dp
t (p
b/G
eV
)pt [GeV]
pp Õ D+ + X
LHC 7 TeV
|y| < 0.5CTEQ6.6
FONLL [f(c Õ D+) = 0.238]
POWHEG-PY
POWHEG-HW
MC@NLO
0
0.5
1
1.5
2
2.5
0 5 10 15 20 25 30
ratio
to
FO
NL
L
pt [GeV]
W. Ke et al., Duke, in prep.
• LO pQCD, e.g. FONLL→ inclusive spectra, no azimuthal QQ correlationsM. Cacciari et al. PRL95 (2005), JHEP 1210 (2012)
• NLO pQCD matrix elements plus parton shower, e.g. POWHEG or MC@NLO⇒exclusive spectra, like QQ correlations S. Frixione et al. JHEP 0206 (2002), JHEP 0308 (2003)
• Consistent initialization of HF and LF sectors!
• Cold nuclear matter effects, i.e. shadowing, pT broadening aka Cronin effect, etc.K. J. Eskola, H. Paukkunen and C. A. Salgado, JHEP 0904 (2009)
7 / 34
production interaction with the medium hadronization
Remember talk by C.Y. Wong Tue 15h40!
Modeling of heavy-quark dynamics in the QGP
103
104
105
106
107
108
0 5 10 15 20 25 30
dσ
/dp
t (p
b/G
eV
)pt [GeV]
pp Õ D+ + X
LHC 7 TeV
|y| < 0.5CTEQ6.6
FONLL [f(c Õ D+) = 0.238]
POWHEG-PY
POWHEG-HW
MC@NLO
0
0.5
1
1.5
2
2.5
0 5 10 15 20 25 30
ratio
to
FO
NL
L
pt [GeV]
W. Ke et al., Duke, in prep.
• LO pQCD, e.g. FONLL→ inclusive spectra, no azimuthal QQ correlationsM. Cacciari et al. PRL95 (2005), JHEP 1210 (2012)
• NLO pQCD matrix elements plus parton shower, e.g. POWHEG or MC@NLO⇒exclusive spectra, like QQ correlations S. Frixione et al. JHEP 0206 (2002), JHEP 0308 (2003)
• Consistent initialization of HF and LF sectors!
• Cold nuclear matter effects, i.e. shadowing, pT broadening aka Cronin effect, etc.K. J. Eskola, H. Paukkunen and C. A. Salgado, JHEP 0904 (2009)
8 / 34
production interaction with the medium hadronization
Remember talk by C.Y. Wong Tue 15h40!
∆φ DD distributions in pp collisions need to be betterunderstood!
Modeling of heavy-quark dynamics in the QGP
J. D. Bjorken (1982); E. Braaten et al, PRD 44 (1991), PRD 44 (1991); A. Peshier, PRL 97 (2006); S. Peigne et al., PRD 77 (2008) 114017;
M. Gyulassy et al, NPB 420 (1994); BDMPS PLB 345 (1995); NPB 483 (1997); ibid. 484 (1997); B. G. Zakharov, JETP Lett. 63 (1996) 952;
ibid. 64 (1996) 781; ibid. 65 (1997) 615; ibid. 73 (2001) 49; ibid. 78 (2003) 759; M. Gyulassy et al, PRL 85 (2000); NPB 571 (2000) 197;
ibid. 594 (2001); Y. L. Dokshitzer et al., PLB 519 (2001); P. B. Arnold et al., JHEP 0011 (2000), 0305 (2003); N. Armesto et al., PRD
69(2004); PRCC 72 (2005); B.-W. Zhang et al., PRL 93 (2004); NPA783 (2007); S. Wicks et al., NPA783 (2007); W. Horowitz et al., PLB666
(2008); P. Chesler et al. JHEP1310 (2013); B. Kampfer et al., PLB 477 (2000); M. Djordjevic et al., PRC 68 (2003); PLB560 (2003); NPA733
(2004); PRC 77 (2008); PLB734 (2014); M. Bluhm et al. PRL 107 (2011); O. Fochler et al. PRD88 (2013); J. Aichelin et al. PRD89 (2014),
A. Majumder 1506.08648
9 / 34
production interaction with the medium hadronization
Remember talk by B. Blagojevic Tue 17h40!
Modeling of heavy-quark dynamics in the QGP
S. Cao et al. arxiv:1505.01413Gossiaux et al. PRC 78 (2008)
• Coalescence/Recombination – predominantly at small pT . Parameter-dependent!e.g. C. B. Dover et al., PRC 44 (1991)
• Fragmentation – predominantly at large pT . Medium-modification?e.g. M. Cacciari et al., PRL 95 (2005)
• After hadronization: final hadronic interactions of D mesons.L. Tolos et al., PRD88 (2013); J. Torres-Rincon et al., PRD89 (2014)
10 / 34
production interaction with the medium hadronization
See talk J. Torres-Rincon Thu 17h40!
Set the stage: Transport equations & coefficients
Boltzmann equation for HQ phase-space distribution
ddt
fQ(t ,~x ,~p) = C[fQ ] with C[fQ ] =∫
d~k [w(~p +~k ,~k)fQ(~p +~k)︸ ︷︷ ︸gain term
−w(~p,~k)fQ(~p)︸ ︷︷ ︸loss term
]
expanding C for small momentum transfer k p (in the medium k ∼ O(gT )) andkeeping lowest 2 terms⇒ Fokker-Planck equation
∂
∂tfQ(t ,~p) =
∂
∂pi
(Ai (~p)fQ(t ,~p) +
∂
∂pj
[Bij (~p)fQ(t ,~p)
])friction (drag) momentum diffusion
Recast to Langevin equation (probably good for bottom, but for charm?)
ddt~p = −ηD(p)~p +~ξ with 〈ξ i (t)ξ j (t ′)〉 = κδij δ(t − t ′)
Transport coefficients connected by fluctuation-dissipation theorem (Einstein relation):
ηD =κ
2mQT, Ds =
TmQηD
spatial diffusion
D. Walton et al., PRL84 (2000); G. Moore et al., PRC71 (2005)
11 / 34
Boltzmann vs Langevin dynamics
• Under which conditions should Brownian motion be a valid approximation forrelativistic particles?
• Calculations of transport coefficients from the underlying theory do notnecessarily fulfil FDT.
• Langevin leads to Gaussian momentum distribution, Boltzmann very different.
Langevin Boltzmann
0 2 4 6 8 10 12 14
p [GeV]
0
100
200
300
400
500
dN/dp
t=0 fm
t=2 fm
t=4 fm
t=6 fm
Charm
2 4 6 8 10 12 14p [GeV]
100
200
300
400
500
dN
/dp
t=0 fmt=2 fmt=4 fmt=6 fm
Charm
S. Das et al, PRC90 (2014)
12 / 34
Remember talk by S. Das Tue 16h20!
Boltzmann equation assumes independent scatterings (dilute medium) - isthis a correct assumption?
Diffusion coefficient from lattice QCD
Lattice QCD at finite T is performed in Euclidean space⇒ notoriously difficult tocalculate dynamical quantities.
Transport coefficients calculated from correlation function of conserved currents
via slope of spectral function ρE at ω = 0 (Kubo formula)
momentum diffusion:
κ
T 3 = limω→0
2T ρE (ω)
ω
spatial diffusion: Ds = 2T 2
κ
1 1.5 2 2.5 3
T/T
0
4
8
12
16
2π
T D
Ding et al. (2012)
Banerjee et al. (2012)
Kaczmarek (2014)
s
c
13 / 34
No reliable input from lattice QCD calculations yet...
Collisional (elastic) energy loss
LO Feynmann diagrams for perturbative heavy quark scattering off a light parton
Q Q
gg
Q Q
gg q q
Q Q
g
g
• t-channel IR singularity, regulated by the Debye screening mass mD
• HTL energy loss: resummed propagator for |t | t∗, bare propagator |t | t∗
• Relevant separation of scales g2T 2 T 2 probably not fullfilled at RHIC/LHC.
• One-gluon exchange model: reducedIR regulator λm2
D in the hardpropagator
• Running coupling αeff(t) andself-consistentm2
D = (1 + 6nf )4παs(m2D)T
2
A. Peshier, hep-ph/0601119, PRL 97 (2006); P. B. Gossiaux et al. PRC78 (2008), NPA 830 (2009)
14 / 34
Radiative energy loss
q
p2
p1
p4
p3
k
q
p2
p1
p4
p3
k
q
p2
p1
k
p4
p3
q
p2
p1
k
p4
p3
q
q − k
p2
p1
p4
k
p3
• Extention of Gunion-Bertsch approximation beyond mid-rapidity and to finitemass mQ (heavy quarks!) ⇒ distribution of induced gluon radiation (E loss
rad ∝ E L):
Pg(x , ~k⊥, ~q⊥,mQ) =3αs
π21− x
x
~k⊥~k⊥
2+ x2m2
Q
−~k⊥ − ~q⊥
( ~k⊥ − ~q⊥)2 + x2m2Q
2
J. Gunion, PRD25 (1982); O. Fochler et al. PRD88 (2013); J. Aichelin et al. PRD89 (2014)
τform
lmfp
• coherent (LPM) emission if τform =√
ωq > lmfp
• E lossrad ∝
√E L, if τform > L then E loss
rad ∝ L2
• Dynamical realization challengingK. Zapp et al. PRL103 (2009), JHEP 1107 (2011)
• Dead cone effect: Dokshitzer et al., PLB 519 (2001)
dσrad
θdθ∝
θ2(θ2 + M2
Q/E2Q
)• When the hard scattering assumption is relaxed,
emission at low k⊥ is significantly less suppressed.J. Aichelin et al. PRD89 (2014)
15 / 34
Non-perturbative approaches
Resonance scattering:
• Basic assumption: for T . 3Tc two-bodyinteractions→ potential V (t)
• Spatial diffusion coefficient comparable toquenched lQCD.
• smooth transition to hadronic medium withminimum close to Tc
H. v. Hees, PRC73 (2006); H. v. Hees, PRL100 (2008); R. Rapp arxiv:0903.1096
Strong coupling:
• In AdS/CFT a heavy quark is represented by a string connected to a D7 brane.
• Leading-order drag coefficients were excluded by comparison to data.
• Momentum-kicks are multiplicative and grow with the HQ velocity→ importanttoward higher pT !
• At larger momenta HQ in strong-coupling reach a speed limit→ expected to workin an intermediate pT regime! W. Horowitz, PRD (2015)
16 / 34
See talk by W. Horowitz, Fr 16h!
From theoretical input to dynamical modeling
τform
lmfp
)c (GeV/T
p0 2 4 6 8 10 12 14 16
AA
R
0
0.2
0.4
0.6
0.8
1
1.2
WHDG rad+collPOWLANGCao, Qin, BassMC@sHQ+EPOS, Coll+Rad(LPM)BAMPSTAMU elasticUrQMD
|<0.5y average, |*+
, D+
, D0
ALICE D
= 2.76 TeVNNsPbPb,
Centrality 020%
• Simple approximations are prone to fail in some kinematic region, mostly atintermediate pT .
• Due to uncertainties all models when compared to data contain (implicit orexplicit) parameter tuning.
• Proper modeling of the QGP evolution is important! Should be well tested in thelight hadron sector!
• Does the equation of state match the representation of the mediumquasiparticles?
• Effects of viscosity, initial state fluctations, preequilibirum dynamics?
17 / 34
How to get access to fundamental QGP properties from theory to datacomparison?
D meson RAA and v2 in AA at LHCpu
rely
elas
ticsc
atte
rings
(GeV/c)T
p0 2 4 6 8 10 12 14 16 18 20
AA
R
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
= 2.76 TeVNNsPbPb at
Centrality: 0-20%
ALICE D mesons (|y|<0.5)TAMUPOWLANG (HTL) vac.frag.POWLANG (HTL)MC@sHQ+EPOS2BAMPS el.UrQMD
(GeV/c)T
p0 2 4 6 8 10 12 14 16 18 20
2v
0.1−
0
0.1
0.2
0.3
0.4
0.5
0.6
= 2.76 TeVNNsPbPb at
Centrality: 30-50%
ALICE D mesons (|y|<0.5)TAMUPOWLANG (HTL) vac.frag.POWLANG (HTL)MC@sHQ+EPOS2BAMPS el.UrQMD
(GeV/c)T
p0 2 4 6 8 10 12 14 16 18 20
AA
R
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
= 2.76 TeVNNsPbPb at
Centrality: 0-20%
ALICE D mesons (|y|<0.5)
WHDG
MC@sHQ+EPOS2+rad.+LPM
BAMPS rad.+el.
Vitev et al.
Djordjevic et al.
Duke
(GeV/c)T
p0 2 4 6 8 10 12 14 16 18 20
2v
0.1−
0
0.1
0.2
0.3
0.4
0.5
0.6
= 2.76 TeVNNsPbPb at
Centrality: 30-50%
ALICE D mesons (|y|<0.5)
WHDG
MC@sHQ+EPOS2+rad.+LPM
BAMPS rad.+el.
Duke
elas
ticsc
atte
rings
+ra
diat
ion
SaporeGravis Network, arXiv:1506.03981
• The simultaneous description of RAA and v2 is challenging.
18 / 34
D meson RAA and v2 in AA at LHCpu
rely
elas
ticsc
atte
rings
(GeV/c)T
p0 2 4 6 8 10 12 14 16 18 20
AA
R
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
= 2.76 TeVNNsPbPb at
Centrality: 0-20%
ALICE D mesons (|y|<0.5)TAMUPOWLANG (HTL) vac.frag.POWLANG (HTL)MC@sHQ+EPOS2BAMPS el.UrQMD
(GeV/c)T
p0 2 4 6 8 10 12 14 16 18 20
2v
0.1−
0
0.1
0.2
0.3
0.4
0.5
0.6
= 2.76 TeVNNsPbPb at
Centrality: 30-50%
ALICE D mesons (|y|<0.5)TAMUPOWLANG (HTL) vac.frag.POWLANG (HTL)MC@sHQ+EPOS2BAMPS el.UrQMD
(GeV/c)T
p0 2 4 6 8 10 12 14 16 18 20
AA
R
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
= 2.76 TeVNNsPbPb at
Centrality: 0-20%
ALICE D mesons (|y|<0.5)
WHDG
MC@sHQ+EPOS2+rad.+LPM
BAMPS rad.+el.
Vitev et al.
Djordjevic et al.
Duke
(GeV/c)T
p0 2 4 6 8 10 12 14 16 18 20
2v
0.1−
0
0.1
0.2
0.3
0.4
0.5
0.6
= 2.76 TeVNNsPbPb at
Centrality: 30-50%
ALICE D mesons (|y|<0.5)
WHDG
MC@sHQ+EPOS2+rad.+LPM
BAMPS rad.+el.
Duke
elas
ticsc
atte
rings
+ra
diat
ion
SaporeGravis Network, arXiv:1506.03981
• The simultaneous description of RAA and v2 is challenging.
19 / 34
(Too?) many models reproduce the RAA and/or the v2 well.
D meson RAA and v2 - miscellaneous
plot by S. Das, Catania
• Enhancement of strangeness in theQGP can lead to an enhancement ofDs mesons by coalescence.
• RAA robust, but v2 changessignificantly:
• affected by interaction details,Langevin vs Boltzmann, coalescence,hadronic final interactions...
0 5 10 15 200.0
0.5
1.0
1.5
2.0
Pb + Pb, sNN= 2.76 TeV, 0-7.5% ALICE (prel.), average D meson ALICE (prel.), Ds meson
D meson at Tkin Ds meson at Tc
RA
A
pT (GeV)
H. Min et al. PLB735 (2014)
20 / 34
Charm production (and diffusion?) in pPb collisions
• 3 + 1d fluid dynamical evolution + Langevin dynamics, initial shadowing.
• Centrality dependence of RpPb expected due to energy loss.(Note, that experimentally QpPb !)
• Indications that v2 of D mesons decouples from medium flow - unlike in AAcollisions - and decreases with centrality.
• Can HF measurements in pPb help answering the question of initial vs final stateeffects?
Y. Xu et al, Duke University, in preparation
21 / 34
Beyond traditional observables...
• Observables with high discriminating power between different interactionmechanisms: e.g. azimuthal correlations of QQ pairs.
〈p⊥〉 from MC@sHQ+EPOS2:
T = 400 MeV
0
1
2
3
4
5
6
7
8
9
0 5 10 15 20 25
d〈p
2 ⊥〉/dt[G
eV2/fm
]
pini|| [GeV]
coll, K = 1.5rad, K = 1.8
coll+rad, K = 0.8
DD correlation plot from Duke model
-π/2 0 π/2 π 3π/2∆φ
0.150
0.155
0.160
0.165
0.170
0.175
1/N
dN
/d∆
φ
col.+rad. D(2πT)=5.0col. only D(2πT)=1.5
rad. only D(2πT)=3.0
col. only without flow
Au-Au @ 200 GeV 0-10%
D-Dbar correlation
PYTHIA initialization
pT, trig
> 2 GeV
(a)
MN et al. PRC90 (2014) Cao et al., arxiv:1505.01869
• Difficulties: already the cc proton-proton baseline is not well understoodtheoretically and experimental feasibility...
22 / 34
For possible e(HF)-h or D-h correlations models need to couple HF-LF sectorsconsistently!
Beyond traditional observables...
• Most models give a τrelax for charm quarks much longer than the evolution of theQGP, but v2(HF) ∼ v2(LF).
• Higher-order Fourier coefficients were important for understanding chargedhadron flow.
• What about heavy-flavor v3, v4, ...?
0
0.05
0.1
0.15
0 2 4 6
vn
pT [GeV]
LHC, 20−30%
D mesons
v2
v3
v4
v5 0.01
0.1
1
0 10 20 30 40 50
vn/ε
n
centrality [%]
v2/ε2
light charged hadronsD mesonsB mesons
0 10 20 30 40 50 60
centrality [%]
v3/ε3
• Expectation: v3 and higher-order coefficients show the incomplete coupling ofHQ to the medium.
MN et al. PRC91 (2015)
23 / 34
Looking forward to experimental data for v3 from LHC and RHIC!
Summary
• HQ probe partial thermalization at low pT and energy loss athigh pT in the QGP.
• Many effects important at intermediate pT : onset of coherentgluon emission, gluon thermal mass, finite path length,nonperturbative scatterings,...
• Transport coefficients/scattering cross sections in Langevin orBoltzmann transport.
• Coupling to a dynamical evolution of the QGP (should be welltested in the light hadron sector!)
• RAA and v2 are described well by (too?) many models.
• Learn from the success in the the light-flavor sector!
• Study further observables, like QQ correlations andhigher-order flow coefficients, for veri/falsi-fication of models!
• Need to identify most dominant features of HQ-mediuminteraction: connect data to fundamental properties of QCD!
Thanks to J. Aichelin, S. Bass, S. Cao, P.B. Gossiaux, K. Werner, Y. Xu for fruitfulcollaborations and discussions!
24 / 34
Don’t miss plenary talks (theory) by M. Djordjevic, A. Beraudo, this session,E. Bratkovskaya Thu 12h30!
backup
25 / 34
Modeling of heavy-quark dynamics in the QGP
• Model the QGP: a locally thermalized medium provides the scattering partners.
• Input from a fluid dynamical description of the bulk QGP medium: temperaturesand fluid velocities.
• Use a fluid dynamical description which describes well the bulk observables!
smooth initial conditions
-8 -6 -4 -2 0 2 4 6 8
-8
-6
-4
-2
0
2
4
6
8
0
5
10
15
20
25
30
35
40
45
energ
y d
ensity in G
eV
/fm
3
fluctuating initial conditions
-8 -6 -4 -2 0 2 4 6 8
-8
-6
-4
-2
0
2
4
6
8
0
5
10
15
20
25
30
35
40
45
energ
y d
ensity in G
eV
/fm
3
0 5 1 0 1 50 . 00 . 20 . 40 . 60 . 81 . 01 . 21 . 4
y = 0
D - m e s o n s
0 - 2 0 %
A L I C E , 0 - 2 0 % E v e n t - b y - e v e n t : r a d + c o l l ( K = 0 . 8 ) c o l l ( K = 1 . 5 ) A v e r a g e d : r a d + c o l l ( K = 0 . 8 ) c o l l ( K = 1 . 5 )
R AA
p T [ G e V ]
plot by V. Ozvenchuk, Nantes
MN, J. Aichelin, P. B. Gossiaux, K. Werner NPA932 (2014)
26 / 34
production interaction with the medium hadronization
medium description coupling medium - HF sector
“Partonic wind” effect
X. Zhu, N. Xu and P. Zhuang, PRL 100 (2008)
• Due to the radial flow of the matterlow-pT cc-pairs are pushed into thesame direction.
• Initial correlations at ∆φ ∼ π arewashed out but additional correlationsat small opening angles appear.
• This happens only in the purelycollisional interaction mechanism!
• No “partonic wind” effect observed incollisional+radiative(+LPM)interaction mechanism!
~p iniT,Q
~p iniT,Q
~p finT,Q
~p finT,Q
~p finT,cm
flow
cc, 0− 20%
LHC 1 < pT/GeV < 4
dN
cc/d∆φ
∆φ
0
0.05
0.1
0.15
0.2
0.25
0 1 2 3 4 5 6
coll, K = 1.5coll+rad, K = 0.8
MN et al. PRC90 (2014)
27 / 34
QGP: initial state and bulk flow (2)
0
0.1
0.2
0.3
0.4
0.5
0.6
εn
LHC
ε2 ε3
0
0.1
0.2
0.3
0.4
0.5
0−10 10−20 20−30 30−40 40−50 50−60
εn
centrality [%]
RHIC
average temperature and overlap area
0.2
0.3
0.4
0.5
0.6
0−10 10−20 20−30 30−40 40−50 50−60
<T
ini>
[G
eV
]
centrality [%]
LHC
0
50
100
150
200
250
0−10 10−20 20−30 30−40 40−50 50−60
<A
ini>
[fm
2]
centrality [%]
LHC
centrality dependence:
+ increase of initial eccentricities
+ decrease of interaction rate and medium size
⇒ expectation: heavy-flavor flow shows a weakerdependence on centrality, especially for v3
MN et al. PRC91 (2015)
28 / 34
D meson v2 and v3 at LHC and RHIC
0
0.1
0.2
0.3
2 4 6 8 10 12
vn
pT [GeV]
0−10%
v2v3
2 4 6 8 10 12
pT [GeV]
10−30%
coll, K=1.5
coll+rad, K=0.8
2 4 6 8 10 12
pT [GeV]
30−50%
v2 ALICE D
0
0.1
0.2
0 1 2 3 4 5
vn
pT [GeV]
0−10%
v2v3
1 2 3 4 5
pT [GeV]
10−20%
coll, K=1.8
coll+rad, K=1.0
1 2 3 4 5
pT [GeV]
RHIC D
20−40%
• At small pT : relative enhancement of flow in purely collisional scenario overcollisional+radiative(+LPM) larger for v3 than for v2
MN et al. PRC91 (2015)
29 / 34
Charm flow: hadronization and energy loss
collisional+radiative(+LPM), K = 0.8
0
0.1
0.2
0 2 4 6 8 10
vn
pT [GeV]
LHC, 30−50%
D mesons
charm quarks
v2
v3
0
0.1
0.2
0 2 4 6 8 10
vn
pT [GeV]
LHC, 30−50%
charm quarks
w bulk flow
w/o bulk flow
v2
v3
• Contribution to the flow from hadronization.
• For low pT the charm flow is predominantly due to the flow of the bulk.
MN et al. PRC91 (2015)
30 / 34
Radiative energy loss
I Incoherent radiation:Gunion-Bertsch spectrumextended to finite quark mass.J. Aichelin et al., PRD89 (2014), arXiv:1307.5270
I Inclusion of an effectivesuppression of the spectra in thecoherent radiation regime (LPMeffect)
I Influence of gluon damping (not inthis talk)M. Bluhm et al., PRL 107 (2011), arXiv:1204.2469
T=250 MeV, E=20GeV
c-quark
GB
LPM
1.000.50 5.000.10 10.000.05Ω@GeVD
0.2
0.4
0.6
0.8
1.0
1.2
1.4
d I
dzdΩ
T=250 MeV, E=20GeV
b-quark
GB
LPM
1.000.50 5.000.10 10.000.05Ω@GeVD
0.2
0.4
0.6
0.8
1.0
1.2
1.4
d I
dzdΩ
31 / 34
pQCD Boltzmann transport• pQCD-inspired Boltzmann transport in 3 + 1d ideal fluid dynamics (EPOS) or in
partonic transport (BAMPS).
MN et al. (Nantes) - MC@sHQ+EPOS2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 5 10 15 20 25 30
RA
A
pT [GeV]
ALICE D, 0−7.5%
dashed lines are with EPS09 shadowing
coll, K=1.5
coll+rad, K=0.8
0
0.05
0.1
0.15
0.2
0.25
0.3
0 2 4 6 8 10 12 14
v2
pT [GeV]
ALICE D, 30−50%
coll, K=1.5
coll+rad, K=0.8
Uphoff et al. (BAMPS)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 5 10 15 20 25 30 35
D m
eson R
AA
pT [GeV]
Pb+Pb, √s = 2.76 TeV
b = 3.6 fm, |y| < 0.5
running αs
κ=1.0, XLPM=1.0 κ=0.2, XLPM=0.2
only 2→2, κ=0.2, K=3.50-7.5% (ALICE)
0
0.1
0.2
0.3
0.4
0.5
0 2 4 6 8 10 12 14 16
D m
eson v
2
pT [GeV]
Pb+Pb√s = 2.76 TeV
b = 9.7 fm
|y| < 0.5
running αs
κ=1.0, XLPM=1.0κ=0.2, XLPM=0.2
only 2→2, κ=0.2, K=3.530-50% (ALICE)
• Rather good description of the RAA and the v2.
• Slight preference for purely collisional energy loss in MC@sHQ+EPOS2.
MN et al. PRC 89 (2014); K. Werner et al. PRC 85 (2012); J. Uphoff et al. arxiv:1408.2964 (2014)
32 / 34
Importance of recombination - RHIC
• Recombination needs to be included in order to describe the RAA at lower pT .
Cao et al. arxiv:1505.01413
33 / 34
Non-perturbative resonance scattering
• Basic assumption: two-body interactions→ potential V (t) with t ' −~q 2 (c, bquarks; T . 3Tc )
• T -matrix follows from Lippmann-Schwingerequation: T = V +
∫d3kV G2 T → HQ transport
coefficients, e.g. AQ(~p) ∼ |T |2
• Medium-modified HQ potential from lQCDfree/internal energy:
I Stronger interaction from internal energybased V
I Enhanced ∆Eloss than in pQCD due toresonant HQ-meson and di-quark states inscattering channels
• Spatial diffusion coefficient Ds = 2πT 2/mQAQ :I comparable to quenched lQCDI smooth transition to hadronic medium with
minimum close to Tc
H. v. Hees, PRC73 (2006); H. v. Hees, PRL100 (2008); R. Rapp arxiv:0903.1096
34 / 34
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