Summary of the context and overall objectives of the project

QCD predicted that, at extremely high energy densities, a new form of matter will be created. This form

of matter, called Quark Gluon Plasma (QGP), consists of interacting quarks, antiquarks and gluons, which

are no longer confined. It is believed that QGP existed a few µs after the Big-Bang, which marked the

beginning of the universe. Today, QGP is explored through Little Bangs in ultra-relativistic heavy ion

collisions at landmark experiments, such as RHIC at BNL and LHC at CERN.

It is by now widely accepted that QGP is discovered in RHIC and LHC experiments. However, it is now a

challenge to understand its properties. Regarding this, note that, according to the current paradigm, QGP

is considered to be a nearly perfect fluid. Its estimated sheer viscosity over entropy ratio (eta/s) is close

to the universal lower bound conjectured by string theory/gravity duality. Also, similar perfect fluid

behavior was observed for ultracold Fermi gases. This then brings surprising connections between systems

at extremely low and extremely high temperatures.

Though very interesting, the question is whether this picture of QGP as a nearly perfect fluid indeed

realistic? First, note that for other substances eta/s has a minimum near phase transition temperature

(Tc), and then increases, rather than remaining constant, with temperature. Moreover, it was shown by

several studies, including sophisticated viscous hydordynamics simulations, that bulk medium simulations

are insensitive to even a large increase in eta/s not far away from Tc. These all lead to the notion of the

perfect fluid being too perfect, that is the notion of the fluid with very low viscosity throughout QGP

evolution being unrealistic.

Since the perfect fluid picture of QGP comes from low momentum data and hydrodynamics models, the

question is how to provide a substantially different dataset and corresponding theoretical predictions,

which may point to an improved picture of QGP medium. The main idea of our research is that this

opportunity is provided by the data on the rare, high-momentum (high-pt) partons, through their

comparison with pQCD predictions. There is a wealth of precision high-pt data which are already available,

or will become available soon. These include the angular average suppression, which is a good probe of

high-pt parton interactions with QGP, and the angular differential suppression, which measures angular

asymmetry of parton energy loss, which is in turn a good probe of QGP evolution. From this then follows

a question if and how pQCD and high-pt data can be used for inferring the bulk medium properties (that

is for precision QGP tomography)?

Our main idea is that different QGP medium properties/parameters will lead to different temperature

profiles of the expanding QGP. For example, for different eta/s, QGP will differently expand and cool

down, thereby producing different temperature profiles. Through high-pt partons, we can directly probe

these different temperature profiles. That is, high-pt partons traversing QGP in different directions will

sense different temperature dependences and different path lengths. This will then lead to different

energy losses, and consequently different predictions for both light and heavy partons, and for a range of

high-pt observables. Comparing these predictions with experimental data will then allow inferring which

temperature profiles (and consequently which QGP properties) will be consistent with the high-pt data.

Importantly, the energy loss is larger for higher temperature (with strong temperature dependence).

Consequently, we expect to have larger sensitivity for inferring eta/s at higher T, which is in distinction to

low momentum data, which are the least sensitive at high T. Therefore high-pt theory and data will

provide a powerful new constraint for inferring QGP properties, which is the main idea behind the new

tomography tool DREENA that we develop within this project.

Work performed from the beginning of the project to the end of the period covered by the

report and main results achieved so far

To implement the idea outlined above, it is crucial to have a reliable high-pt parton energy loss model.

With this goal in mind, over the past several years, we developed the state-of-the-art dynamical energy

loss formalism, which has several unique features in the description of high-momentum parton medium

interactions. The formalism takes into account ﬁnite size, ﬁnite temperature QCD medium consisting of

dynamical (that is moving) partons, contrary to the widely used static scattering approximation and/or

medium models with vacuum-like propagators. ii) The calculations are based on the ﬁnite temperature

generalized Hard-Thermal-Loop approach, in which the infrared divergences are naturally regulated, so

we have no artificial cutoffs. iii) Both radiative and collisional energy losses are calculated under the same

theoretical framework, applicable to both light and heavy ﬂavor. iv) The formalism is generalized to the

case of ﬁnite magnetic mass and running coupling.

However, the model did not take into account the medium evolution, so the first task of our project was

to redevelop the formalism to include the medium evolution within the energy loss model. The

temperature profiles (which are direct outputs of the bulk medium simulations) are now a direct input in

our energy loss model, which is a major advantage for the execution of our project.

Additionally, to improve the prediction accuracy, we also relaxed the widely used soft-gluon

approximation within static energy loss model. We have surprisingly showed that, while relaxing the soft-

gluon approximation leads to significantly more complex analytical expressions compared to simpler soft-

gluon case, the numerical predictions were nearly indistinguishable between these two cases. These

results suggest that we can further use this approximation within our approach.

The redeveloped energy loss model was incorporated in a fully optimized numerical framework DREENA

(Dynamical Radiative and Elastic ENergy loss Approach), which is fully modular (i.e. it can incorporate any

temperature profile), and allows systematic comparison of experimental data and theoretical predictions,

obtained by the same formalism and the same parameter set and with no fitting parameters used in model

testing. In particular, the framework is able to efficiently and simultaneously generate predictions for:

 Different observables (e.g. both RAA and v2)

 Different collision systems (Pb+Pb, Au+Au, Xe+Xe, Cr+Cr, Ar+Ar, O+O)

 Different probes (light and heavy)

 Different collision energies and different centralities

During the first project period, this developed framework enabled us to:

 Propose a method (i.e. appropriate observable and appropriate systems) to differentiate between

different energy loss models in QGP.

 Analyze sensitivity of high-pt probes to initial and final QGP stages, which are crucial for

understanding QGP properties.

 Propose the observable to directly infer the shape of the QGP droplet from the data, which

presents the first application of high-pt data to infer the bulk QGP properties!

 Test sensitivity of high-pt observables to different temperature profiles, showing that

temperature profiles which lead to the same predictions in low-pt region, lead to notably different

predictions in high-pt region.

The above results, obtained during the first project period, strongly support our project idea that high-pt

probes are crucial for inferring the QGP properties.

Progress beyond the state of the art and expected potential impact (including the socio-

economic impact and the wider societal implications of the project so far)

During the first project period, our major achievement was development of the DREENA framework,

which combines full state-of-the-art high-pt dynamical energy loss with temperature profiles generated

from state of the art hydrodynamics or parton transport models. Two major advantages of DREENA

framework are that: i) it is based on a state of the art dynamical energy loss formalism, which has key

ingredients that are not available by other energy loss models, and which can explain a wide range of

experimental data (see above), ii) is fully modular, i.e. it can incorporate any temperature profile (which

is a direct output of the bulk medium simulations) as a (natural, i.e. direct) input in our energy loss model.

Development of such framework has been highly non-trivial, as our dynamical energy loss formalism is

complex, where all its ingredients are necessary for reliable description of high-pt parton medium

interactions; consequently we introduced no additional simplifications in developing DREENA framework.

Additionally the framework has been fully optimized, so that its computational speed is now several

orders of magnitude faster compared to the first demo version; this is crucial so that a large number of

computational predictions can be generated. In particular, in the upcoming project period, a very large

number of different temperature profiles will be tested to extract the bulk QGP properties.

In the upcoming project period, our DREENA framework will present a core of our new tomography tool,

which is schematically shown in the Figure below: We will start by varying the bulk medium parameters

in the range where they agree with the low momentum data. This will generate temperature profiles for

different input parameters, and those that agree with low momentum data will subsequently be used as

an input for the advanced dynamical energy loss model. We will then generate high-pt predictions for a

wide range of high-pt light and heavy observables, and comparing these predictions with high-pt data will

allow us selecting the QGP medium parameters that are in accordance with both low and high-pt data.

The selected parameter range will be further fine-tuned by repeating the procedure, where the new

parameters will now be varied on the finer scale.

This DREENA framework will help us in addressing several currently most pressing questions in the field:

 Is QGP a fluid or a gas-like system?

 Can QGP exist in small systems (or only in collisions of large ions)?

 Can a single theoretical approach explain a wealth of experimental data, for different probes,

experiments, collision energies, etc.?

In addition to these specific questions, the project will also lead to the following significant, more general

gains:

 Develop a novel tool to put massive data produced at LHC and RHIC experiments to optimal use,

particularly having in mind huge financial and time resources invested at these experiments.

 Possibly develop a more realistic picture of an exciting new form of matter

 Predictions will be ready at an optimal time for exploiting LHC and RHIC data, as our tomography

tool and its predictions will be ready for the down of the high precision era at RHIC and LHC.

The project will therefore allow better exploiting these two landmark science investments, and may

consequently allow addressing some of the most prominent questions on properties of this extreme form

of matter.