Extracting $\hat{q}$ in event-by-event hydrodynamics and the centrality/energy puzzle

In our analysis, we combine event-by-event hydrodynamics, within the EKRT formulation, with jet quenching -ASW Quenching Weights- to obtain high-$p_T$ $R_{\rm AA}$ for charged particles at RHIC and LHC energies for different centralities. By defining a $K$-factor that quantifies the departure of $\hat{q}$ from an ideal estimate, $K = \hat{q}/(2\epsilon^{3/4})$, we fit the single-inclusive experimental data for charged particles. This $K$-factor is larger at RHIC than at the LHC but, surprisingly, it is almost independent of the centrality of the collision.


Introduction
Study of suppression of high-p T particles in PbPb collisions at the LHC and AuAu collisions at RHIC.

Introduction Energy loss implementation
Hydrodynamic modelling of the medium Results Limitations and conclusions

Single inclusive cross section
The single inclusive cross section is described by Factorization scale Q 2 = (p T /z) 2 . Fragmentation scale as µ F = p T .
CTEQ6M + EPS09 (NLO). We absorb energy loss in a redefinition of the fragmentation functions: Energy loss implementation Hydrodynamic modelling of the medium Results Limitations and conclusions

Quenching Weights
The ASW Quenching Weights are given by

Independent gluon emission
Interference effects may break independent gluon emission.
Independent gluon emission is a good approximation for soft radiation.

Introduction
Energy loss implementation Hydrodynamic modelling of the medium Results

Limitations and conclusions
In dI (med) dω the medium properties appear in: σ(r)n(ξ).
In the multiple soft scattering approximation we use Perturbative tails neglected.

Introduction
Energy loss implementation Hydrodynamic modelling of the medium Results Limitations and conclusions

Nuclear modification factor
We use R AA experimental data: From Pb-Pb collisions at √ s NN = 2.76 TeV and Au-Au at √ s NN = 200 GeV. ALICE data on R AA for charged particles with p T > 5 GeV in different centrality classes and for |η| < 0.8, arXiv:1208.2711 [hep-ex].

Limitations
The definition ofq neglects the perturbative tails of the distributions.
The QW find support in the coherence analysis of the medium: if coherence is broken they could fail.
Finite energy corrections.
q energy or length independent.
Collisional energy loss is neglected.

Introduction
Energy loss implementation Hydrodynamic modelling of the medium Results Limitations and conclusions

Conclusions
We fit the single-inclusive experimental data at RHIC and LHC for different centralities.
The fitted value at RHIC confirms large corrections to the ideal case.
For the case of the LHC, the extracted value of K is close to unity.
K -factor is ∼ 2 − 3 times larger for RHIC than at the LHC.
Centrality dependences at RHIC and the LHC are rather flat.
The change in the value of K does not look to be simply due to the different local medium parameters. Multiple soft scattering approximation for a static medium The inclusive energy distribution of gluon radiation off an in-medium produced parton is given by , density of scattering centers. σ(r), strength of a single elastic scattering.

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The production weight is given by The average values of an observable and in particular of our fragmentations functions is computed as where N = 2π dx 0 dy 0 ω(x 0 , y 0 ).

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R AA at √ s NN =200 GeV for different centralities Energy density constant before thermalization. Free-streaming case. K depends mainly on the energy and it is almost independent of the centrality of the collision!! 16 / 16 K -factor vs. τ 0 forq constant before thermalization 2 4 6 8 10 12 τ 0 (GeV/fm 2 /c)

RHIC results
Nuclear modification factors R AA for single-inclusive and I AA for hadron-triggered fragmentation functions for different values of 2K = K /0.73, with K = 0.5, 1, 2, 3, ..., 20. The green line in the curve corresponding to the minimum of the common fit to R AA