## Principal Investigator and Collaborators

The principal investigator is Dr. Simone Biondini. The collaborators are from many different institutions in Europe and we would like to mention Dr. Jacopo Ghiglieri (University of Nantes), Dr. Vladyslav Shtabovenko (Karlsruhe Institute of Technology), Prof. Stefan Vogl (University of Freiburg), Gramos Qerimi, Prof. Nora Brambilla and Antonio Vairo (Technical University Munich), Dr. Tuomas Tenkanen (Nordita) and Dr. Philipp Schicho (University of Helsinki).

## The project in a nutshell

One of the major challenges in cosmology is to understand the matter content of our universe. According to General Relativity there are deep connections between what fills the universe and its geometry, its dynamical expansion and eventually its fate. Notably, visible ordinary matter appears to be only a small fraction of the matter in our universe, whereas the bulk comes in the form of non-luminous and non-baryonic particles, dubbed dark matter (DM). Complementary measurements of large scale structures, galaxy formation, gravitational lensing and of the cosmic microwave background (CMB) strongly suggest that more than 80% of the matter in the universe consists of DM.

If dark matter comes in the form of a particle, then its production happens in a **thermal collider,** namely the early universe plasma. Therefore the determination of the dark matter abundance comes as an interdisciplinary and challenging endeavour across particle physics and cosmology. The dark particles can experience their own hidden forces, which are partially or entirely secluded from the Standard Model (SM) sector. Furthermore, the existence of light force mediators with masses much smaller than that of the actual DM particles may affect the DM dynamics in many ways. A straightforward consequence is that DM may experience sizable self-interactions that depend on the relative velocity among dark particles and can provide a dynamical explanation for the scaling relations governing galactic halos and clusters of galaxies.

Another remarkable property of DM models with light mediators is the possibility to have bound states within the dark sector. Depending on the details of the model (i) both stable and unstable bounds state may form; (ii) the dark particles may exhibit a reach spectrum of bound states, that undergo various reactions in the thermal environment and (iii) can still give interesting signature in present day processes. Bound-state formation and dissociation rates can become important for an accurate determination of the present-day energy density. Indeed, whenever bound states are formed, and not effectively dissociated or melted away in the thermal plasma, they provide an additional process for the depletion of DM particles in the early universe.

The overall objective of the project is to develop and apply a novel approach for DM energy density computations in the framework of non-relativistic effective field theories (NREFTs), potential non-relativistic effective field theories (pNREFTs) and open quantum systems (OQSs). These tools allow for a systematic and rigorous treatment of the interplay between the several energy scales appearing in the system under study.

## Non-relativistic effective field theories

Dark matter particles in the early universe are an example of a multi-scale system. On the one hand, one finds three typical scales of a non-relativistic dynamics, which are assumed to be well separated, namely M >>Mv>>Mv^{2}, respectively the DM particle mass, its momentum and typical kinetic energy. In addition to these scales our system contains the mediator mass, which we assume to be much lighter than the DM mass, and thermal scales, most notably the temperature of the early universe plasma and thermal masses. In particular, we shall employ the framework of non-relativistic effective field theories NREFTs and potential non-relativistic effective field theories (pNREFTs), which are obtained by * integrating out* energy/momenta of order M and Mv respectively. In doing so we can construct suitable low-energy EFTs describing the degrees of freedom we are interested in. These are DM fermion pairs, either in bound or scattering states, and low-energetic vector or scalar mediators. Bound-state calculations can be then carried out in a very similar way to the ordinary quantum mechanics, with the important difference that higher order corrections to the potentials, and other observables, can be obtained in a systematic and model-independent way with

*calculations. A remarkable aspect of this approach is that the thermal scales can be taken into account within a quantum field theory at finite temperature. Physical processes like the thermal break-up of a bound state can be described, and rigorously derived, within our framework. Our approach is based on the renowned NREFTs of this sort that have been obtained for QED and QCD, and served as precious and handy tools for rigorous and systematic analyses of hydrogen atom, positronium, heavy quarkonia, heavy-light hadrons or muonic hydrogen.*

**matching**## Open quantum systems

In order to establish the fate of the dark matter pairs in a thermal medium, a detailed knowledge of the thermal rates is not sufficient though. Thermal cross sections and widths responsible for formation and dissociation processes should be consistently inserted into evolution equations for the number densities of scattering and bound states. To this end, we make use of the * open quantum systems *formalism. The picture is as follows: the heavy DM pairs, and single particles, are understood as an

*open system*, which interacts with an

*environment*, here the early universe plasma. As for the overall evolution of the system and environment is in general quite complicated, one can just retain the information of the system by

**the irrelevant degrees of freedom of the environment. As a result, the time evolution of the system is non-unitary and the interactions with the sourrounding medium typically induce dissipation and decoherence. This approach is highly interdisciplinary and connects with modern techniques of quantum infromation theory and quantum optics.**

*tracing out*## Project related publications (from the start of the Grant)

- ''Freeze-in produced dark matter in the ultra-relativistic regime'', S. Biondini and J. Ghiglieri, JCAP
**03**(2021) 075, arXiv:2012.09083 - ''Non-relativistic and potential non-relativistic effective field theories for scalar mediators'', S. Biondini and V. Shtabovenko, JHEP
**08**(2021) 114, arXiv:2106.06472 - "Bound-state formation, dissociation and decays of darkonium with potential non-relativistic Yukawa theory for scalar and pseudoscalar mediators", S. Biondini and V. Shtabovenko, JHEP
**03**(2022) 172, arXiv:2112.10145

## Outreach at conferences, workshops and seminar series

- PONT 2020, Old and New Thems in Cosmology, December 2020 (online conference)
- HECA seminars at the Research Nuclear Center and University of Warsaw, March 16th 2021 (online)
- Beyond the Standard Model 2021: from Theory to Experiment (online conference)
- Quarkonia meet Dark Matter, June 2021 (online workshop)
- Theory Seminar Series, Universita' di Camerino, July 2021
- Corfu 2021, Workshop on the Standard Model and Beyond

and stay tuned for the upcoming conferences where **new results** will be presented

- International Conference of High Energy Physics, ICHEP 2022
- Corfu 2022, Workshop on the Standard Model and Beyond