Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
Directed flow of heavy flavor dragged by a hot tiltedfireball and pushed by electromagnetic field
Sandeep ChatterjeeWith: Piotr BozekAGH-UST, Krakow
based on:Phys. Rev. Lett. 120, 192301 (2018) (arXiv: 1712.01189);
arXiv: 1804.04893
WPCF, Krakow, 24 May, 2018
, 1/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
EM field in the initial state
x(a) reaction plane
projectile spectators
participant zone
target spectators
projectile (η>0)target (η<0)
z
fig. from 1306.4145
• B = −B y , B decreases as the spectators recede. Fornon-zero conductivity σ of the medium, this gives rise to aclock-wise E in the above reaction plane
• A positive charge at η > 0 experiences B force along x whileE force along −x , the net force resulting in a directed flow v1
, 2/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
v1 split between positive and negative chargedparticles due to EM field
-3 -2 -1 1 2 3Y
-0.00004
-0.00002
0.00002
0.00004
v1
Gursoy, Kharzeev, Rajagopal 2014
, 3/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
1000 times stronger effect on HQ
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2y
-0.04
-0.02
0
0.02
0.04
v1
(y
)
D[cq] , t=tf.o.
D [cq], t=tf.o.
D [cq], t=2 fm/c.
D [cq], t=5 fm/c
Das, Plumari, SC, Alam, Scardina, Greco 2016•
v avg1 =
1
2
(v1
(D0)
+ v1
(D0))
vdiff1 = v1
(D0)− v1
(D0)
v avg1 = 0, vdiff
1 6= 0;, 4/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
Effect of bulk v1 on HQ ?
η-6 -4 -2 0 2 4 6
(%
)1
v
-3
-2
-1
0
1
2
3
PHOBOS: 6 - 40%
0 - 5%
: 0 - 5%⟩ t
p⟨ / ⟩ x
p⟨
5 - 40%40 - 80%
-1 -0.5 0 0.5 1
-0.4
-0.2
0
0.2
0.4
fig. from PRL 101 252301 (2008)
, 5/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
entropy deposition in non-central collision
r1r2
-6 -4 -2 0 2 4 6
-4
-2
0
2
4
x
y
r1 < r2 → ρ (r1) > ρ (r2)
, 6/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
entropy deposition in non-central collision
-4 -2 0 2 4
-6
-4
-2
0
2
4
6
Η
x
, 7/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
entropy deposition from participant sources
Tilted bulk: Brodsky et. al. 1977; Adil, Gyulassy 2005; Bialas,Czyz 2005
x(a) reaction plane
projectile spectators
participant zone
target spectators
projectile (η>0)target (η<0)
z
-3 -2 -1 0 1 2 3
-2
-1
0
1
2
Η
x
from 1306.4145 Bulk profile
, 8/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
Initial condition for a tilted fireball
s(τ0, x , y , η||
)= s0
[αNcoll + (1− α)
(N+
part f+(η||)
+
N−part f−(η||))]
f(η||)
f(η||)
= exp
−θ (|η||| − η0||
) (|η||| − η0||
)2
2σ2
f+(η||)
=
0, η|| < −ηTηT +η||
2ηT, −ηT ≤ η|| ≤ ηT
1, η|| > ηT
with f−(η||)
= f+(−η||
)(rapidity-odd component)
Bozek, Wyskiel 2010
, 9/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
Tilted bulk → directed fluid velocity
-4 -2 0 2 4
-4
-2
0
2
4
Η
x
, 10/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
Tilted bulk → directed fluid velocity
Tilted bulk: Brodsky et. al. 1977; Adil, Gyulassy 2005; Bialas,Czyz 2005
x(a) reaction plane
projectile spectators
participant zone
target spectators
projectile (η>0)target (η<0)
z
-3 -2 -1 0 1 2 3
-2
-1
0
1
2
Η
x
from 1306.4145 Bulk directed flow
, 11/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
Tilted bulk → directed fluid velocity → chargedparticle v1
Bozek, Wyskiel 2010
• Tilted IC captures the charged particle v1
• small v1
, 12/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
entropy depositing sources: participant vs binarycollision sources
HQ from hard processes → FB-symmetricRapidity-even HQ dragged by Rapidity-odd bulk
x(a) reaction plane
projectile spectators
participant zone
target spectators
projectile (η>0)target (η<0)
z
-4 -2 0 2 4
-2
-1
0
1
2
Η
x
from 1306.4145 Bulk vs heavy flavor
, 13/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
Heavy Quark Tomography
charm, anti-charm stronger probes of the tilt than the light flavor
-4 -2 0 2 4
-4
-2
0
2
4
Η
x
, 14/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
entropy depositing sources: participant vs binarycollision sources
x(a) reaction plane
projectile spectators
participant zone
target spectators
projectile (η>0)target (η<0)
z
-4 -2 0 2 4
-2
-1
0
1
2
Η
x
from 1306.4145 v1(HQ) > v1(Bulk)
, 15/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
to quantify the heavy flavor v1
need to calibrate
• the tilt of the bulk: constrained by charged particle v1, Bozek,Wyskiel 2010
• drag between the bulk and heavy flavor: constrained by heavyflavor RAA and v2 at mid-rapidity, we use an ansatzγ = γ0T
(Tm
)x
, 16/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
Calibrating the drag on HQs
0 1 2 3 40
0.5
1
1.5
2T/m = 0.2Tγ
= 0.2Tγ
STAR
(a)
(GeV)T
p
AA
R
0 1 2 3 40
0.05
0.1
0.15
0.2
0.25
T/m = 0.2Tγ = 0.2Tγ
STAR
(b)
(GeV)T
p
2v
1 1.5 2 2.55−
0
5
10
15
20 T/m = 0.2Tγ = 0.2Tγ
(c)
LQCD QPM Bayesian DpQCD
cT/T
T sDπ2
SC, Bozek PRL,120, 192301 (2017)
, 17/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
HQ v1 O(10) larger !
predicted to be 5 - 20 times larger than charged particle v1 slope !
0 2 4 60
2
4
6
8
charged particles STAR
DD, T∝γ 1.5
T∝γ
Tη
%=0η
ηd1
dv
-
TiltLarge Small
2− 0 210−
5−
0
5
10(a) :DD,
∝γ T 1.5TTiltlargesmall
Charged Particle: STAR Hydro
η
(%
)1v
SC, Bozek PRL,120, 192301 (2017)
, 18/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
fresh from QM 2018: largest measured directedflow
, 19/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
comparison to data
largest measured v1: order of magnitude larger than that ofcharged particle
0 2 4 60
5
10
15
charged particles
STAR QM2018
DD, T∝γ 1.5
T∝γ
Tη
%=0η
ηd1
dv
-TiltLarge Small
SC, Bozek PRL,120, 192301 (2017)
, 20/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
comparison to data
largest measured v1: order of magnitude larger than that ofcharged particle
0 2 4 60
5
10
15
charged particles
STAR QM2018
DD, T∝γ 1.5
T∝γ
Tη
%=0η
ηd1
dv
-
TiltLarge Small
0 1 26−
4−
2−
0
2
4
6(b)
DD,
charged particles STAR Hydro
(GeV)T
p)
(%)
T(p 1v
NOTE: data with pT > 1.5 GeV, similar cut in model will result inlarger v1
SC, Bozek PRL,120, 192301 (2017)
, 21/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
HQ acquires non-zero 〈pX 〉 - a clear signal of theinitial shift between HQ and bulk
0.95
0.65
0.35
hard processes
thermalized matter
ΗÈÈ = - 2
-6 -3 0 3 6
-6
-3
0
3
6
x HfmL
yHfmL
2− 0 2
6−
4−
2−
0
2
4 DD, %1v > %
T>/<p
x<p
charged particles
STAR Hydro
η
〈px〉 ∼ 40 MeV at η = 1
SC, Bozek PRL,120, 192301 (2017)
, 22/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
Beam energy dependence
210 310
1−10
1
(b)
charged particles
Data Hydro
DD, T∝ γ 1.5 T∝ γ
GeVNNs
%=0ηavg
ηd1
dv
-
SC, Bozek 1804.04893
, 23/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
Ratio of HQ to bulk v1
210 310
5
10
15
T∝ γ 1.5 T∝ γ
(GeV)NNs
=0ηηd1Bu
lkd
v /
=0ηavg
ηd1H
Qd
v
SC, Bozek 1804.04893
, 24/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
HQ v1 with Tilt+EM field
1− 0 13−
2−
1−
0
1
2
3 = 200 GeVNNsAu+Au,
1.5 T∝ γ = 0.4 fm0τ
-1 = 0.035 fmσ
D
D
η
(%
)1v
• v avg1 6= 0, vdiff
1 6= 0
SC, Bozek 1804.04893
, 25/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
Dependence on conductivity and initializationtime
10 20 30
0
0.2
0.4
0.6
0.8 = 200 GeVNNsAu+Au,
(a)
(fm)0τ
0.2 0.6
)-1 (fmσ310
%=0ηdif
f
ηd1
dv
-
0.2 0.4 0.6
3
3.2
3.4
3.6
3.8
4
(b)
= 200 GeVNNsAu+Au,
)-1 (fmσ310 35 11
(fm)0τ%
=0ηavg
ηd1
dv
-
SC, Bozek 1804.04893
, 26/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
Beam energy dependence
210 3100
0.2
0.4
0.6
0.8
1
(a)
T∝ γ 1.5 T∝ γ
(GeV)NNs
%=0ηdif
f
ηd1
dv
-
SC, Bozek 1804.04893
, 27/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
fresh from QM 2018: hint of split in v1 of D0
and D0
, 28/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
Summarising
• Heavy flavor directed flow as a probe of 2 initial state physicswas discussed: longitudinal profile of matter distribution andthe electromagnetic field and medium conductivity
• Order of magnitude larger directed flow was predicted forheavy flavor compared to bulk. Split due to EM field issmaller compared to the average directed flow due to tiltedbulk, resulting in same sign flow of both D0 and D0
• Comparison to STAR QM2018 data suggests preference forlarge tilt (effect of pT cut is expected to allow for smaller tilt)
• Ratio of HQ to bulk v1 is predicted to be larger at LHC thanat RHIC- stronger drag due to higher temperature
• HQ v1 adds to the existing list of HQ RAA and v2 to provideinformation on the drag coefficient between the bulk matterand HQ
, 29/30
Directed flow:Electromagnetic origin
Directed flow:Geometric origin
Directed flow:electromagnetic +geometric
Summary
Backup
BACKUP: what causes the large v1: T or uµ ?
2− 0 20.04−
0.02−
0
0.02
0.04
both none T µ u
η
1v
• FB asymmtery of which hydro field causes the large HQ v1 ?• By selectively choosing profiles with broken boost invarinace,
we find the HQ v1 is mainly caused by the FB asymmetricdrag by the flow field uµ
, 30/30
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