-- do hadrons, consisting of u,d,s, allow for this we will see: no
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Transcript of -- do hadrons, consisting of u,d,s, allow for this we will see: no
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-- do hadrons, consisting of u,d,s, allow for this
we will see: no
-- what’s about heavy mesons (c,b)
tomography of a plasma possible
Collaborators:
P.-B. Gossiaux , R. Bierkandt, K. Werner
Subatech/ Nantes/ France
Nuclear Winter Workshop, Big Sky, Febr 09
How can we look into the interior of a QGP?
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Centrality Dependence of Hadron Multiplicities
can be described by a very simple model (confirmed by EPOS)
No (if stat. Model applied) or one free parameter
Calculation of the Cu+Cu results without any further input
arXiv:0810.4465
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strange non-strange
works for non strange and strange hadrons at 200 AGeV
Cu+Cu: completely predicted from Au+Au and pp
Theory = lines
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at 62 AGeV
and even et SPS
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….. and even if one looks into the details:
For all measured hadrons the core/corona ratio is strongly correlated with ratio of peripheral to central HI collisionsTheory reproduces the experimental results quantitativelyEror bars are not small enough to improve the simple model
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This model explains STRANGENESS ENHANCEMENTespecially that the enhancement at SPS is larger than at RHIC
Strangeness enhancement in HI is in reality
Strangeness suppression in pp
string
Strangeness suppr in pp
PRD 65, 057501 (2002)
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- Central Mi /N part same in Cu+Cu and Au+Au (pure core)- very peripheral same in Cu+Cu and Au+Au (pp) increase with N part stronger in Cu+Cu
- all particle species follow the same law
Φ is nothing special (the strangeness content is not considered in this model) Strangeness enhancement is in reality strangeness suppression in pp (core follows stat model predictions which differ not very much) - works for very peripheral reactions (Ncore =25). The formation of a possible new state is not size dependent
Particle yield is determined at freeze out by phase space (with γS = 1 (a lower γS models corona contributions)
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Rescattering later -> neither yield nor spectra sensitive to state of matter before freeze out
Light hadrons insensitive to phase of matter prior to freeze out (v2 or other collective variables?)
Production: hard process described by perturbative QCD initial dσ/dpT is known (pp) comparison of final and initial spectrum: gives direct information on the interaction of heavy Q with the plasma if heavy quarks are not in thermal equilibrium with the plasma : tomography possible
Why are heavy quarks (mesons) better?
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Individual heavy quarks follow Brownian motion: we can describe the time evolution of their distribution by a
Fokker – Planck equation:
fBfAtf
pp
K
Input reduced to Drift (A) and Diffusion (B) coefficient.
Much less complex than a parton cascade which has to follow the light particles and their thermalization as well.
Can be combined with adequate models for the dynamics of light quarks and gluons (here hydrodynamics of Heinz and Kolb)
Interaction of heavy quarks with the QGP
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drift and diffusion coefficient
:take the elementary cross sections for charm scattering (Qq and Qg) and calculate the coefficients (g = thermal distribution of the collision partners)
|M|2 = lowest order QCD with (αs( 2πT) , m_D)
and then introduce an to study the physics.
Diffusion (BL , BT) coefficient Bνμ ~ << (pν - pν
f )(pμ -
pμf )> >
taken from the Einstein relation A = p/mT BL
A (drift) describes the deceleration of the c-quark B (diffusion) describes the thermalisation
Strategy:
overall K factor
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p +p(pQCD)
c and b carry direct informationon the QGP
QGP expansion: Heinz & Kolb’s hydrodynamics
K=1 drift coeff from pQCD
This may allow for studying plasma properties usingpt distribution, v2 transfer, back to back correlations etc
Interaction of c and b with the QGP
K< 40: plasma does not thermalize the c or b:
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RAA or energy loss is determined by the elementary elastic scattering cross sections. q channel:
Neither α(t) =g2/4 nor κmD2= are well determined
α(t) =is taken as constant [0.2 < α < 0.6] or α(2πT)
mDself2 (T) = (1+nf/6) 4πas( mDself
2) xT2 (Peshier hep-ph/0607275)
But which κ is appropriate?κ =1 and α =.3: large K-factors are necessary to describe data
Is there a way to get a handle on α and κ ?
Weak points of the existing approaches
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Loops are formed
If t is small (<<T) : Born has to be replaced by a hard thermal loop (HTL) approach like in QED:(Braaten and Thoma PRD44 (91) 1298,2625)
For t>T Born approximation is ok
QED: the energy loss
( = E-E’)
Energy loss indep. of the artificial scale t* which separates the 2 regimes.
B) Debye mass
mD regulates the long range
behaviour of the interaction
PRC78 014904, 0901.0946
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This concept we extend to QCD
HTL in QCD cross sections is too complicated for simulations
Idea: - Use HTL (t<t*) and Born (t>t*) amplitude to calculate dE/dx make sure that result does not depend on t*
- determine which gives the same energy loss as if one uses a cross section of the form
In reality a bit more complicated: with Born matching region of t*
outside the range of validity of HTL (<T) -> add to Born a constant ’
Constant coupling constant -> Analytical formula -> arXiv: 0802.2525Running -> numerically
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2 1 1 2Q2GeV20.2
0.4
0.6
0.8
1
1.2
eff
nf3
nf2
SL TL
• Effective s(Q2) (Dokshitzer 95, Brodsky 02)
Observable = T-L effective coupling * Process dependent fct
“Universality constrain” (Dokshitzer 02) helps reducing uncertainties:
IR safe. The detailed form very close to Q2 =0 is not important does not contribute to the energy loss
Large values for intermediate momentum-
transfer
Additional inputs (from lattice) could be helpful
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Describes e+e- data
A) Running coupling constant
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Large enhancement of cross sections at small t
Little change at large t
Largest energy transfor from u-channel gluons
The matching gives 0.2 mD for running S for theDebye mass and 0.15 mD not running!
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The expaning plasma
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. c-quark transverse-space distribution according to Glauber
• c-quark transverse momentum distribution as in d-Au (STAR)… seems very similar to p-p (FONLL) Cronin effect included.
• c-quark rapidity distribution according to R.Vogt (Int.J.Mod.Phys. E12 (2003) 211-270).
• QGP evolution: 4D / Need local quantities such as T(x,t) taken from hydrodynamical evolution (Heinz & Kolb)
•D meson produced via coalescence mechanism. (at the transition temperature we pick a u/d quark with the a thermal distribution) but other scenarios possible.
Au + Au @ 200 AGeV
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minimum bias
NewK=1,5-2
Central and minimum bias events described by the same parameters.The new approach reducesthe K- factor
K=12 -> K=1,5-2
No radiative energy loss yet(complicated: Gauge+LPM)
pT > 2 bottom dominated!!more difficult to stop,compatible with experiment
Difference between b and c becomes smallerin minimum bias events
RAA
b
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NewK=1,5-2
v2 of heavy mesons depends on where fragmentation/ coalescence takes place
end of mixed phase beginning of mixed phase
minimum bias out of plane distribution v2
Centrality dependence of integrated yield
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6-8 fm
4-6 fm
2-4 fm0-2 fm
The stopping dependsstrongly on the positionwhere the Q’s are created
The spectra at large pT
are insensitive to theQ’s produced in the centerof the plasma No info about plasma center
At high momenta the spectrumis dominated by c and b produced close to the surface
Conclusion:Singles tell little about the center of the reactions
centrality dependence of RAA for c quarks
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Strong correlation betweencentrality of the production and the final momentum difference of Q and Qbar
A ) Decreasing relative energy loss with increasing pt
B) Small ΔpT same path length from center
Pairs with small ΔpT can be usedto test the theoryto explore the center of thereaction
c cbar pairs are more sensitive to the center
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p(Q) p(Qbar)
Due to geometry:The final momentumdifference is smallerfor centrally producedpairs
pairs
Singles: RAA flat at large pt
Pairs : RAA increases with pt
Less relative energy lossTypical pQCD effectNot present in AdS/CFT
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Conclusions
• Experimental data point towards a significant (although not complete) thermalization of c and b quarks in QGP tomography of the plasma possible
• Using a running coupling constant, determined by experiment, and an infrared regulator which approximates hard thermal loop pQCD calculations come close to the experimental RAA and v2.
• Radiative energy loss has to be developed
• Ads/CFT prediction differ: Experiment will decide
• pQCD calculations make several predictions which can be checked experimentaly
• Very interesing physics program with heavy quarks after the upgrate of RHIC and with LHC
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Horowitz et Gyulassy 0804.4330Gubser PRD76, 126003
Wicks et al. NPA783 493 nucl-th/0701088Fixed coupling coll+radiative
pQCD dσ/dt: only mass dependentin the subdominant u-channel
AdS/CFT versus pQCD
AdS/CFT: final dpT/dt = -c T2/MQ pT
AdS/CFT:Anti de Sitter/conformal field theory
RHIC centralRCB = RAA charm/RAAbottom
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Cacciari et al. hep-ph/0502203 and priv. communication
and at LHC?
For large pT: distribution of b and c identical
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LHC will sort out theories as soon as RCB is measured
pQCD: RCB =1 for high pt:neither initial distrnor σ depends on the mass
AdS/CFT massdependence remains
But: what is the limitof the model?? Forvery large pt pQCDshould be the righttheory
LHC central
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Conclusions
• Experimental data point towards a significant (although not complete) thermalization of c and b quarks in QGP tomography of the plasma possible
• Using a running coupling constant, determined by experiment, and an infrared regulator which approximates hard thermal loop pQCD calculations come close to the experimental RAA and v2.
• Radiative energy loss has to be developed
• Ads/CFT prediction differ: Experiment will decide
• pQCD calculations make several predictions which can be checked experimentaly
• Very interesing physics program with heavy quarks after the upgrate of RHIC and with LHC
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0.05 0.1 0.15 0.2 0.25 0.3
0.1
0.2
0.3
0.4
dEdxGeVfm
s2Tt mD2T
T0.25GeV
p20GeVcs0.2
mD0.45GeV
THEN: Optimal choice of in our OBE model:
(T) 0.15 mD2(T)
with mD2 = 4s(2T)(1+3/6)xT2
s(2)
Model C: optimal 2
… factor 2 increase w.r.t. mod B (not enough to
explain RAA)T(MeV) \p(GeV/c) 10 20
200 0.36 (0.18)
0.49
(0.27)
400 0.70 (0.35)
0.98
(0.54)
dx
cdEcoll
)(Convergence with “pQCD” at high T
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Surprisingly we expect for LHC about the same v2 as at RHICdespite of the fact that in detail the scenario is rather different
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31(provided g2T2<< |t*| << T2
)
Braaten-Thoma:
HTL: collective
modes +
Large |t|: close coll.
Bare propagator
...3/
*ln
3
2
D
2D
m
tm
dx
dEsoft ...
*ln
3
2 2
D
t
ETm
dx
dEhard
SUM:
3/ln
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D
2D
mETm
dxdE
Low |t|: large distances
Indep. of |t*| !
(Peshier – Peigné) HTL: convergent kinetic
(matching 2 regions)
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E: optimal , running s,eff
C: optimal , s(2T)
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Transport coefficientsDrag coefficient Diff. coefficient
Long. fluctuations
Running s and Van Hees &Rapp: roughly same trend
mod C – mod E - AdS/CFT Evolution ? Not so clear
Caution: One way of implementing running s
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HTL+semihard, neededto have the transitionin the range of validityof HTLdE/dx does not dependon t*
The resulting values areconsiderably smaller than those used up to now.
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Goal: find observables which are sensitive to the interaction of heavy quarks with the plasma -> agreement of predictions provide circumstantial evidence that the plasma is correctly described
prob
Pt initial [GeV]
Pt final [GeV]
Q with small pt initial gain momentum (thermalization)
with large pt inital loose momentum Distribution very broad
Tomography of the plasma
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Where are we?
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Teaney & MooreK=12
NewK=1.5-2
b
c
central
The new approach reducesthe K- factor
K=12 -> K=1,5-2
No radiative energy loss yet(Hallman )
pT > 2 bottom dominated!!more difficult to stop,compatible with experiment
central events
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Where can we improve?
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Moore and Teaney:Hydro with EOS which gives the largest v2 possibledoes not agree with data. Drift Coefficient needed forRAA corresp. to K=12
Van Hees & RappCharmed resonances exists in the plasma Dynamics = expanding fireball:
K12
RAA=(dσ/dpT)AA /(( dσ/dpT )pp Nbinary)
v2 = < cos2φ> ..
RAA and v2 need different values of K:Only exotic hadronization mechanisms may explain
thelarge v2
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Averaged of inital positions and of the expanding plasma
pT final (>5GeV) = pT ini – 0.08 pT ini – 5 GeV dominant at large pT
Functional form expected from the underlying microscopic energy loss but numerical value depends on the details of the expansion
momentum loss of c in the plasma
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There is a double challenge: description of the expanding plasma ANDdescription of interaction of the heavy quarks with this plasma
Model of van Hees and Rapp:v2 seems to depend on howthe expanding plasma isdescribed
if we use their drift coefficientin our (Heinz-Kolb) hydro approach (which describes the v_2 of the other mesons)
we get 50% less v_2
Preliminary andpresently under investigation
But if one looks into the details ….