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We study the transitions between the different color states of a static quark-antiquark pair, singlet and octet, in a thermal medium. This is done non-perturbatively exploiting the infinite mass limit of QCD. This study is interesting because it can be used for future developments within the framework of Effective Field Theories (EFTs) and because it can be combined with other techniques, like lattice QCD or AdS/CFT, to gain non-perturbative information about the evolution of quarkonium in a medium. We also study the obtained expressions in the large Nc limit. This allows us to learn lessons that are useful to simplify phenomenological models of quarkonium in a plasma.

This is a discussion about open quantum systems and its application to the study of hard probes. It reviews some of the things that were said in the corresponding round table. Views are only my own.

We study exclusive quarkonium production in the dipole picture at next-to-leading order (NLO) accuracy, using the non-relativistic expansion for the quarkonium wavefunction. The quarkonium light cone wave functions needed in the dipole picture have typically been available only at tree level, either in phenomenological models or in the nonrelativistic limit. Here, we discuss the compatibility of the dipole approach and the non-relativistic expansion and compute NLO relativistic corrections to the quarkonium light-cone wave function in light-cone gauge.

The medium that forms in a heavy-ion collision modifies the properties of jets traversing it. These modifications give substantial information about the nature of the medium and, therefore, they are one of the main focuses of the heavy-ion program at LHC. The influence of the medium into highly energetic partons depends on correlators of Wilson lines, which have been studied in perturbation theory and in several phenomenological models. Here, we focus on the antenna configuration, the study of the evolution of the large energy partons resulting from a collinear splitting inside of the medium. In the eikonal limit, the interaction of each daughter parton with the medium can be parametrized by a light-like Wilson line in a given direction. We consider the case in which the angle between these two directions θ is small but such that Lθ is of the order of the medium resolution scale, where L is the size of the medium. We find that finite angle effects give sub-leading corrections to jet broadening. The physical effect in the antenna configuration is to make the decoherence effect larger when finite angle corrections are taken into account.

The evolution of hard probes in a medium is a complex multiscale problem that significantly benefits from the use of Effective Field Theories (EFTs). Within the EFT framework, we aim to define a series of EFTs in a way that addresses each energy scale individually in separate steps. However, studying hard probes in a medium presents challenges. This is because an EFT is typically constructed by formulating the most general Lagrangian compatible with the problem's symmetries. Nevertheless, medium effects may not always be encoded adequately in an effective action. In this paper, we construct an EFT that is valid for studying the evolution of a heavy quark in a QCD plasma containing few other heavy quarks, where degrees of freedom with an energy of the order of the temperature scale are integrated out. Through this example, we explicitly demonstrate how to handle the doubling of degrees that arise in non-equilibrium field theory. As a result, we derive a Fokker–Planck equation using only symmetry and power counting arguments. The methods introduced in this paper will pave the way for future developments in the study of quarkonium suppression. [ABSTRACT FROM AUTHOR]

The aim of the present study was to determine humoral and T-cell responses after four doses of mRNA-1273 vaccine in solid organ transplant (SOT) recipients, and to study predictors of immunogenicity, including the role of previous SARS-CoV-2 infection in immunity. Secondarily, safety was also assessed. Liver, heart, and kidney transplant recipients eligible for SARS-CoV-2 vaccination from three different institutions in Barcelona, Spain were included. IgM/IgG antibodies and T cell ELISpot against the S protein four weeks after receiving four consecutive booster doses of the vaccine were analyzed. One hundred and forty-three SOT recipients were included (41% liver, 38% heart, and 21% kidney). The median time from transplantation to vaccination was 6.6 years (SD 7.4). In total, 93% of the patients developed SARS-CoV-2 IgM/IgG antibodies and 94% S-ELISpot positivity. In total, 97% of recipients developed either humoral or cellular response (100% of liver recipients, 95% of heart recipients, and 88% of kidney recipients). Hypogammaglobulinemia was associated with the absence of SARS-CoV-2 IgG/IgM antibodies and S-ELISpot reactivity after vaccination, whereas past symptomatic SARS-CoV-2 infection was associated with SARS-CoV-2 IgG/IgM antibodies and S-ELISpot reactivity. Local and systemic side effects were generally mild or moderate, and no recipients experienced the development of de novo DSA or graft dysfunction following vaccination. [ABSTRACT FROM AUTHOR]

There are many interesting problems in heavy-ion collisions and in cosmology that involve the interaction of a heavy particle with a medium. An example is the dissociation of heavy quarkonium seen in heavy-ion collisions. This was believed to be due to the screening of chromoelectric fields that prevents the heavy quarks from binding, however in the last years several perturbative and lattice computations have pointed out to the possibility that dissociation is due to the finite lifetime of a quarkonium state inside the medium. Regarding cosmology, the study of the behavior of heavy Majorana neutrinos in a hot medium is important to understand if this model can explain the origin of dark matter and the baryon asymmetry. A very convenient way of studying these problems is with the use of non-relativistic effective field theories (EFTs), this allows to make the computations in a more systematic way by defining a more suitable power counting and making it more difficult to miss necessary resummations. In this proceedings I will review the most important results obtained by applying the EFT formalism to the study of quarkonium suppression and Majorana neutrinos, I will also discuss how combining an EFT called potential non-relativistic QCD (pNRQCD) with concepts coming from the field of open quantum systems it is possible to understand how the population of the different quarkonium states evolve with time inside a thermal medium.

We discuss the evolution of an energetic jet which propagates through a dense quark-gluon plasma and radiates gluons due to its interactions with the medium. Within perturbative QCD, this evolution can be described as a stochastic branching process, that we have managed to solve exactly. We present exact, analytic, results for the gluon spectrum (the average gluon distribution) and for the higher n-point functions, which describe correlations and fluctuations. Using these results, we construct the event-by-event picture of the gluon distribution produced via medium-induced gluon branching. In contrast to what happens in a usual QCD cascade in vacuum, the medium-induced branchings are quasi-democratic, with offspring gluons carrying sizable fractions of the energy of their parent parton. We find large fluctuations in the energy loss and in the multiplicity of soft gluons. The multiplicity distribution is predicted to exhibit KNO (Koba-Nielsen-Olesen) scaling. These predictions can be tested in Pb+Pb collisions at the LHC, via event-by-event measurements of the di-jet asymmetry. Based on [1, 2].

The dynamics by which polymeric protein filaments divide in the presence of negligible growth, for example due to the depletion of free monomeric precursors, can be described by the universal mathematical equations of 'pure fragmentation'. The rates of fragmentation reactions reflect the stability of the protein filaments towards breakage, which is of importance in biology and biomedicine for instance in governing the creation of amyloid seeds and the propagation of prions. Here, we devised from mathematical theory inversion formulae to recover the division rates and division kernel information from time dependent experimental measurements of filament size distribution. The numerical approach to systematically analyze the behaviour of pure fragmentation trajectories was also developed. We illustrate how these formulae can be used, provide some insights on their robustness, and show how they inform the design of experiments to measure fibril fragmentation dynamics. These advances are made possible by our central theoretical result on how the length distribution profile of the solution to the pure fragmentation equation aligns with a steady distribution profile for large times. Author summary: Amyloid fibrils are fibrillar protein structures involved in many neurodegenerative illnesses, such as Parkinson's disease or Alzheimer's disease. To propagate in disease, these misfolded protein aggregates must grow and divide to proliferate. Therefore, the intrinsic characteristics of their division, including the division rate and the pattern of division in terms of whether the fibrils are likely to break in the middle or at the edges, impact the disease aetiology. Here, we discovered mathematical formulae that can be used to directly extract the fibril division characteristics from recent experiments data obtained from time-dependent fibril length distribution measurements. We explain how these formulae can be used, and prove the robustness of the division rate formula where small errors in the measurement leads to small errors in the division rate. We also demonstrate that the mathematical formula is not robust enough to precisely decipher the pattern of division in the data, and suggest instead new future experimental design with short time measurements in experiments starting with fibril suspensions where all fibrils have similar size, which would be suitable to provide an improved estimates. [ABSTRACT FROM AUTHOR]

Abstract Heavy quarkonium related observables are very useful to obtain information about the medium created in relativistic heavy ion collisions. In recent years the theoretical description of quarkonium in a medium has moved towards a more dynamical picture in which decay and recombination processes are very important. In this talk we will discuss the equations that describe the evolution of the heavy quark reduced density matrix in different approximations, highlighting the color dynamics that is absent in the Abelian case, and we will study their semi-classical limit. This will allow us to obtain stochastic equations (similar to Langevin or Boltzmann equations) that can be useful to obtain phenomenological predictions. We will observe that the region of validity of the Langevin-like or Boltzmann-like equations in QCD is much smaller than the corresponding QED case. The reason for this can be understood by studying how differently the free energy evolves in these two theories, and this observation will allow us to propose an equation with a small computational cost that captures many of the essential features of quarkonium evolution in a QCD plasma. These results are based on [J.-P. Blaizot, M. A. Escobedo, Quantum and classical dynamics of heavy quarks in a quark-gluon plasma, JHEP 06 (2018) 034. arXiv:1711.10812 , doi: 10.1007/JHEP06(2018)034 ; J.-P. Blaizot, M. A. Escobedo, The approach to equilibrium of a quarkonium in a quark-gluon plasma. arXiv:1803.07996 ]. [ABSTRACT FROM AUTHOR]

We study the gluon distribution produced via successive medium-induced branchings by an energetic jet propagating through a weakly-coupled quark-gluon plasma. We show that under suitable approximations, the jet evolution is a Markovian stochastic process, which is exactly solvable. For this process, we construct exact analytic solutions for all the n-point correlation functions describing the gluon distribution in the space of energy [M. A. Escobedo, E. Iancu, Event-by-event fluctuations in the medium-induced jet evolution, JHEP 05 (2016) 008. arXiv: arXiv:1601.03629 , doi: http://dx.doi.org/10.1007/JHEP05(2016)008 , M. A. Escobedo, E. Iancu, Multi-particle correlations and KNO scaling in the medium-induced jet evolution, JHEP 12 (2016) 104. arXiv: arXiv:1609.06104 , doi: http://dx.doi.org/10.1007/JHEP12(2016)104 ]. Using these results, we study the event-by-event distribution of the energy lost by the jet at large angles and of the multiplicities of the soft particles which carry this energy. We find that the event-by-event fluctuations are huge: the standard deviation in the energy loss is parametrically as large as its mean value [M. A. Escobedo, E. Iancu, Event-by-event fluctuations in the medium-induced jet evolution, JHEP 05 (2016) 008. arXiv: arXiv:1601.03629 , doi: http://dx.doi.org/10.1007/JHEP05(2016)008 ]. This has important consequences for the phenomenology of di-jet asymmetry in Pb+Pb collisions at the LHC: it implies that the fluctuations in the branching process can contribute to the measured asymmetry on an equal footing with the geometry of the di-jet event (i.e. as the difference between the in-medium path lengths of the two jets). We compute the higher moments of the multiplicity distribution and identify a remarkable regularity known as Koba-Nielsen-Olesen (KNO) scaling [M. A. Escobedo, E. Iancu, Multi-particle correlations and KNO scaling in the medium-induced jet evolution, JHEP 12 (2016) 104. arXiv: arXiv:1609.06104 , doi: http://dx.doi.org/10.1007/JHEP12(2016)104 ]]. These predictions could be tested via event-by-event measurements of the di-jet asymmetry. [ABSTRACT FROM AUTHOR]

In this article we consider the Stokes problem with Navier-type boundary conditions on a domain $${\Omega}$$ , not necessarily simply connected. Since, under these conditions, the Stokes problem has a non trivial kernel, we also study the solutions lying in the orthogonal of that kernel. We prove the analyticity of several semigroups generated by the Stokes operator considered in different functional spaces. We obtain strong, weak and very weak solutions for the time dependent Stokes problem with the Navier-type boundary condition under different hypotheses on the initial data u and external force f. Then, we study the fractional and pure imaginary powers of several operators related with our Stokes operators. Using the fractional powers, we prove maximal regularity results for the homogeneous Stokes problem. On the other hand, using the boundedness of the pure imaginary powers, we deduce maximal $${L^{p}-L^{q}}$$ regularity for the inhomogeneous Stokes problem. [ABSTRACT FROM AUTHOR]

Fragmentation and growth-fragmentation equations is a family of problems with varied and wide applications. This paper is devoted to the description of the long-time asymptotics of two critical cases of these equations, when the division rate is constant and the growth rate is linear or zero. The study of these cases may be reduced to the study of the following fragmentation equation: ... Using the Mellin transform of the equation, we determine the long-time behavior of the solutions. Our results show in particular the strong dependence of this asymptotic behavior with respect to the initial data. [ABSTRACT FROM AUTHOR]