Upload
darrell-reed
View
213
Download
0
Embed Size (px)
Citation preview
Conical Flow induced by Quenched QCD Jets
Jorge Casalderrey-Solana,
Edward Shuryak and Derek Teaney, hep-ph/0411315
SUNY Stony Brook
Outline• Basic Ingredients: Hydrodynamics Thermalization of energy loss• Assumption: small perturbations due to
energy loss• Solution to the linearized problem: Conical shock waves• Possible experimental confirmation• Conclusions.
Hydrodynamics
• (local) Energy-momentum and baryon number conservation.
• At mid rapidity (neglecting nB)
• Ideal case (=0) provides a remarkable description of radial and elliptic flows at RHIC
• The viscosity at RHIC seems to be close to its minimal conjectured bound.
0 T
Jet Quenching and Energy Loss• High pt particles lose energy in the medium Radiative losses (main effect) Collision losses Ionization losses (bound states)
• From the hydrodynamical point of view, the different mechanisms may be only distinguished by the deposition process (what mode they excite)
• We study this modification through hydrodynamics.
• Similar ideas have been discussed by H. Stoeker (nucl-th/0406018)
fm
GeV
dx
dE2 Shuryak+Zahed,
hep-ph/0406100
Basic Assumptions• The deposited energy thermalizes at a scale:
• Minimal value >> point-like . s will be the only scale of the “source”
• Outside of the “source”, the modification of the properties of the medium is small
• Thus, linearized hydrodynamic description is valid:
3
4
pes
1)4( Ts 1)( jetP
0 T
depositedE <<depositedV
Summing the Spherical WavesParticle moving in the static medium with velocity v
00 vtx
0xxX
After the disturbance is thermalized
ijij TcT 002 00: T ii Tg 0:
Given the symmetries of the problem, we need to specify:
),(),( 0 XRtX
),(),(),( 0 XRgvXRgtXg ov
Adding all displacements we obtain the Mach cone
The different terms lead to different excitations of the medium
Two (linear) Hydro Modes
03
1
4
3 22
kgkgkkicg st
tl gkgg ˆ
0 lt ikg
Sound waves (propagating) Diffuson (not propagating)
),(4
3),( 2 tkgktkg
t tst
By defining the system decouples:
After Fourier transformed (space coordinates)0 gkit
022 lslt gkikcg
),(),( 0 ZRtX
vXRgtXg v
),(),( 0
),( XRgo
Excitations: Sound DiffusonYes
Yes
Yes
No
Yes
No
Flow Picture
0),( ZR 0),( XRgv
0),( XRgo
0),( ZR 0),( XRgv
0),( XRgoxv xv
Diffuson: Matter moving mainly along the jet direction
Sound motion along Mach direction.
<= RHIC
• Flow of the background medium modifies the shape and angle of the cone (Satarov et al.)
• c2s is not constant though system evolution:
csQGP= , cs= in the resonance gas and cs~0 in the mixed phase.
p/e() = EoS along fixed nB/s lines
Considerations about Expansion
•Distance traveled by sound is reduced Mach direction changes
2.031
33.0)(1
sf
avs cdc
(Hung,E. Shuryak hep-ph/9709264)
• = 1.23 rad =71o
Spectrum• Cooper-Fry with equal time freeze out
f
t
ffff
z
T
vp
T
T
T
E
T
E
T
up
ptz
dVedVepddp
dN
0
2
•At low pt~Tf
)cos(4
0
2
p
P
T
PE
T
EVe
pddp
dN dep
f
tdep
f
T
E
ptz
f
z
• Pt >>the spectrum is more sensitive to the “hottest points” (shock and regions close to the jet)
•If the jet energy is enough to punch through, fragmentation part on top of “thermal” spectrum
Two Particle Correlations
t
zppttz ddppdp
dN
Qc
0
1:)(
t
zppttz dppdp
dNQ
0:
•Normalized correlation function:
•The cone is also observed in the spectrum
3
1arccos
s=1/4T
Is such a sonic boom already observed?
M.Miller, QM04
Flow of matter normal to the Mach cone seems to be observed!
+/-1.23=1.91,4.37
(1/N
trig)d
N/d
()
STAR Preliminary
cGeVp
cGevpassocT
trigT
/42.0
/64
Conclusions
• We have used hydrodynamics to follow the energy deposited in the medium.
• Finite cs leads to the appearance of a Mach cone (conical flow correlated to the jet)
• Depending on the initial conditions,the direction of the cone is reflected in the final particle production.
Outlook
•Systematic study of initial conditions
•Role of non-linearities (mixing the modes)
•Precise effect of changing speed of sound as
well as the expanding media
• Realistic simulation of collision geometry
• Three particle correlations.
Problems that need to be addressed (on progress):
Swinging the back jetAssume a boost invariant medium and a yj-distribution for the backjet P(yj) (flat). Boosting by yj we assume a particle distribution:
**3
coscos cjpj pfPdypd
dNE
After boosting back to the lab frame
2
*2*
***
coscos
1cos
coscosc
c
jjc
yy
*
*
cos
coscosh
cjy
Now we integrate over yj:
2
*2*
3
coscos
1cos
1
cos
cos
cc
cTp pPf
pd
dNE
p*
*c
*c
Swinging the back jet (II)If we simply rotate the jet axis (Vitev):
22*2 tancottan
tan
cottan
2/322
2/122
22
*
cottan1
cottan
cossin
1
,
,sin
And use
sinsinsin
**
Pdd
dN
2*22 tantancos
1
cd
dNIntegrating over
*
z
y
x
I. Vitev hep-ph/0501255
However long tails may fill up the cone.
How to observe it?
• the direction of the flow is normal to the Mach cone, defined entirely by the ratio of the speed of sound to the speed of light
• Unlike the (QCD) radiation, the angle is not shrinking (1/ with the increase of the momentum of the jet but is the same for all jet momenta
• At high enough pt a punch through is expected, filling the cone