Initial Conditions Fluctuations and the Ridge
Philipe de Almeida MotaTakeshi Kodama (Ph.D. Advisor)
Instituto de F́ısica – UFRJ, Rio de Janeiro, Brasil
June 9, 2010
Ph. Mota, [email protected] (UFRJ) June 9, 2010 1 / 24
motivation
study the effects of initial condition fluctuation to the observables,specially azimuthal correlations throught the shadow effect [Hama’s talk]
Ph. Mota, [email protected] (UFRJ) June 9, 2010 2 / 24
lternative approach to Mach cone
medium modified by fast parton
supersonic parton generates shock waves in the medium which propagatethrought the medium and give rise to the correlation observedpros: possible extraction of in medium propertiescons: idealized, many dynamical effects act against the simple Mach conepicture
Ph. Mota, [email protected] (UFRJ) June 9, 2010 3 / 24
shadow effect
smooth initial condition plusgaussian tube
Ph. Mota, [email protected] (UFRJ) June 9, 2010 4 / 24
shadow effect
single particle distribution two particle correlation
dip at the tube position andshoulders around it
features dip at away side
Ph. Mota, [email protected] (UFRJ) June 9, 2010 5 / 24
smooth + 1 tube
single particledistribution
temperature profile t=7 fm
medium blocked by tube expansion which is much more explosive
Ph. Mota, [email protected] (UFRJ) June 9, 2010 6 / 24
smooth + 1 tube
3 particle correlation 2 particle correlation
dN123
d∆φ12∆φ13=∫
dφdN1
dφ(φ)
dN2
dφ(φ+ ∆φ12)
dN3
dφ(φ+ ∆φ13)
Ph. Mota, [email protected] (UFRJ) June 9, 2010 7 / 24
smooth + fluctuation
3 tubes, average over different events
average of correlation correlation of averages
C(∆φ) =∫
dφ⟨f1(φ)f2(φ+ ∆φ)
⟩−⟨f1(φ)
⟩⟨f2(φ+ ∆φ)
⟩Ph. Mota, [email protected] (UFRJ) June 9, 2010 8 / 24
smooth + fluctuation
3 particle correlation 3 particle cumulant
Ph. Mota, [email protected] (UFRJ) June 9, 2010 9 / 24
dependence on distance
2 particle cumulant particle spectra
strongly affects the cumulant but does not changes the spectrum
Ph. Mota, [email protected] (UFRJ) June 9, 2010 10 / 24
peripheral collisions
temperature profile temperature profile
Ph. Mota, [email protected] (UFRJ) June 9, 2010 11 / 24
fluctuating initial conditions
applying hydro to an e-by-e basis one has to face the possibility ofnon-homogenous IC
it is interesting to study if the effect is not washed out by thedynamics (Mach cone)
Ph. Mota, [email protected] (UFRJ) June 9, 2010 13 / 24
Random Tubes Model
energy density profile
ε(x⊥; b) =N(b)∑
i
εtube(x⊥ −Ri⊥)
spatial probability
P(R⊥; b) ∝ εWN(R⊥; b)
tube energy density
εtube(x⊥) = εtube0 exp
( x2⊥
2(σtube)2
)
number of tubes
N(b) =N(0)
EWN(0)EWN(b)
tube energy density at origin
εtube0 =
12π(σtube)2
EWN(b)N(b)
model parameters σ and N0
Ph. Mota, [email protected] (UFRJ) June 9, 2010 14 / 24
random tubes
σtube = 0.7 fm N b=0 = 200 σtube = 0.35 fm N b=0 = 200
both for b = 0.4STAR (arXiv:0809.3769): 0–20%−→ b < 6.6 fm
Ph. Mota, [email protected] (UFRJ) June 9, 2010 15 / 24
azimuthal distribution (.4–1×2–3)
Ph. Mota, [email protected] (UFRJ) June 9, 2010 16 / 24
azimuthal distribution (.4–1×2–3)
Ph. Mota, [email protected] (UFRJ) June 9, 2010 17 / 24
elliptic flow
Ph. Mota, [email protected] (UFRJ) June 9, 2010 18 / 24
elliptic flow
Ph. Mota, [email protected] (UFRJ) June 9, 2010 19 / 24
spectrum
Ph. Mota, [email protected] (UFRJ) June 9, 2010 20 / 24
spectrum
Ph. Mota, [email protected] (UFRJ) June 9, 2010 21 / 24
conclusions
shadow effect survives throuth 2-particle correlations
fluctuations should exist at RHIC
simple and robust description for the ridge
understanding of the physical role of the parameters
position of the minimum may be related to EoS throught (c2s)
Ph. Mota, [email protected] (UFRJ) June 9, 2010 22 / 24
perspectives
compare results with other approaches
understand the microscopic origin of the tubes
aplication to p+p at LHC
study c2s dependence
perform v3 subtraction
let σtube fluctuate
longitudinal dynamics
Ph. Mota, [email protected] (UFRJ) June 9, 2010 23 / 24