## Periodic Reporting for period 1 - ENCORE (Exploring Neutrinos: Cosmology, Oscillations, REactors)

Berichtszeitraum: 2018-04-01 bis 2020-03-31

The so-called Standard Model (SM) of particle physics is the theory that describes how fundamental forces act on all of the matter particles. It has successfully explained almost all experimental results, such as those from the LHC accelerator, but it does not provide answers to other phenomena such as the existence of dark matter or neutrino oscillations. The most elusive of all known elementary particles, neutrinos come in three types or flavors (electron, muon and tau). Experimental results have provided evidence that neutrinos change (or oscillate) flavor during their propagation, which implies that neutrinos are massive, a fact that is not explained in the SM.

After fifty years of experimental results, most neutrino properties are well measured. There are, however, some that we still ignore, such as their absolute mass scale, how their masses are ordered or whether additional neutrino states exist beyond the standard three (they would be insensitive to weak interactions or “sterile”). Knowledge of these quantities is necessary for a better understanding of particle physics, and they may indicate us the direction where to best look for new physics beyond the SM.

The ongoing experimental efforts need a theoretical input in order to fully exploit the observations, and the measurements from different probes provide maximal information only when combined together. The global objective of the Proposal was to provide theoretical results which could help to better understand neutrino physics, focusing on three aspects: cosmology, oscillations and nuclear reactors.

The objectives of the Action can be divided in two categories: new theoretical calculations and phenomenological analyses of experimental data.

Concerning neutrino cosmology, we performed improved calculations of both full active-sterile neutrino oscillations in the early Universe and the local overdensity of relic neutrinos near the Earth. We also compared the reactor antineutrino spectrum with new estimates from running experiments and found new global analyses of neutrino data that lead to updated constraints on the oscillation parameters and mass properties, including the ordering and the absolute scale of neutrino masses, for the cases of three and four neutrinos. Our results also include the first application in a cosmological context of a statistics method meant to derive prior-free results in the context of Bayesian analyses.

To summarize, the Action helped to fill some missing pieces of information and to increase our knowledge of neutrinos and their properties.

After fifty years of experimental results, most neutrino properties are well measured. There are, however, some that we still ignore, such as their absolute mass scale, how their masses are ordered or whether additional neutrino states exist beyond the standard three (they would be insensitive to weak interactions or “sterile”). Knowledge of these quantities is necessary for a better understanding of particle physics, and they may indicate us the direction where to best look for new physics beyond the SM.

The ongoing experimental efforts need a theoretical input in order to fully exploit the observations, and the measurements from different probes provide maximal information only when combined together. The global objective of the Proposal was to provide theoretical results which could help to better understand neutrino physics, focusing on three aspects: cosmology, oscillations and nuclear reactors.

The objectives of the Action can be divided in two categories: new theoretical calculations and phenomenological analyses of experimental data.

Concerning neutrino cosmology, we performed improved calculations of both full active-sterile neutrino oscillations in the early Universe and the local overdensity of relic neutrinos near the Earth. We also compared the reactor antineutrino spectrum with new estimates from running experiments and found new global analyses of neutrino data that lead to updated constraints on the oscillation parameters and mass properties, including the ordering and the absolute scale of neutrino masses, for the cases of three and four neutrinos. Our results also include the first application in a cosmological context of a statistics method meant to derive prior-free results in the context of Bayesian analyses.

To summarize, the Action helped to fill some missing pieces of information and to increase our knowledge of neutrinos and their properties.

During the Action, the fellow worked on the planned topics: neutrino physics in the early Universe, in the local astrophysical environment, bounds on neutrino masses and mass ordering, and reactor neutrinos. In total, the Action results have been published in 9 peer-reviewed articles (one of them still under review).

All the objectives proposed in the context of neutrino cosmology have been fully achieved. The first multi-momentum calculation of neutrino oscillations in the early Universe in the context of a 3 active plus one sterile (3+1) sterile neutrino model has been published in [JCAP 07 (2019) 014], while its application in a global fit of 3+1 sterile neutrino constraints [preprint arxiv:2003.02289] is currently under review. The Researcher also worked on a new calculation of the propagation of relic neutrinos in the local astrophysical environment, published in [JCAP 01 (2020) 015].

Concerning neutrino oscillations, an updated analysis of the neutrino mass ordering constraints appeared as a Topical Review in [Frontiers in Astronomy and Space Sciences 5 (2018) 36]. An article related to the mass ordering quest in the DUNE experiment was published in [PRD 100 (2019) 093004]. Techniques of Bayesian statistics have been implemented in two works, published in [PRD 99 (2019) 021301(R)] and [EPJC 80 (2020) 552], aiming at improving the robustness of the results on the neutrino masses.

Finally, an analysis of the reactor antineutrino flux and its implication in the search for light sterile neutrinos was performed in [PLB 782 (2018) 13-21].

The scientific results obtained have been disseminated through several talks at international meetings (17), conference proceedings (6) and seminars (6).

The research gained benefits from the secondment at RWTH University (Aachen, Germany,2/2/2019-30/4/2019) and the short stays (Turin University; MPP Institute, Munich; Stockholm University; Naples University), which increased the collaboration opportunities of the Fellow and allowed multi-disciplinary studies.

As part of the outreach activities, an article was published in the blog of the hosting institute, the IFIC. Training of the Researcher has been performed through actively participating in the fund management, mentoring of Master (2 students) and PhD (1 student) students, and the organization of a PhD school (ISAPP 2020 Valencia, postponed due to the CoVid-19 outbreak) and a workshop (The quest of new physics, December 2018, Valencia).

All the objectives proposed in the context of neutrino cosmology have been fully achieved. The first multi-momentum calculation of neutrino oscillations in the early Universe in the context of a 3 active plus one sterile (3+1) sterile neutrino model has been published in [JCAP 07 (2019) 014], while its application in a global fit of 3+1 sterile neutrino constraints [preprint arxiv:2003.02289] is currently under review. The Researcher also worked on a new calculation of the propagation of relic neutrinos in the local astrophysical environment, published in [JCAP 01 (2020) 015].

Concerning neutrino oscillations, an updated analysis of the neutrino mass ordering constraints appeared as a Topical Review in [Frontiers in Astronomy and Space Sciences 5 (2018) 36]. An article related to the mass ordering quest in the DUNE experiment was published in [PRD 100 (2019) 093004]. Techniques of Bayesian statistics have been implemented in two works, published in [PRD 99 (2019) 021301(R)] and [EPJC 80 (2020) 552], aiming at improving the robustness of the results on the neutrino masses.

Finally, an analysis of the reactor antineutrino flux and its implication in the search for light sterile neutrinos was performed in [PLB 782 (2018) 13-21].

The scientific results obtained have been disseminated through several talks at international meetings (17), conference proceedings (6) and seminars (6).

The research gained benefits from the secondment at RWTH University (Aachen, Germany,2/2/2019-30/4/2019) and the short stays (Turin University; MPP Institute, Munich; Stockholm University; Naples University), which increased the collaboration opportunities of the Fellow and allowed multi-disciplinary studies.

As part of the outreach activities, an article was published in the blog of the hosting institute, the IFIC. Training of the Researcher has been performed through actively participating in the fund management, mentoring of Master (2 students) and PhD (1 student) students, and the organization of a PhD school (ISAPP 2020 Valencia, postponed due to the CoVid-19 outbreak) and a workshop (The quest of new physics, December 2018, Valencia).

Concerning neutrino cosmology, we wanted to improve the calculation of active-sterile neutrino oscillations in the early Universe. Before this Action, literature offered several studies of multi-momentum calculation with up to 2 active plus 1 sterile neutrinos, or an average-momentum calculation with 3+1 neutrinos. We implemented a series of numerical optimizations and coding improvements to obtain the first multi-momentum 3+1 neutrinos calculation, which sets the new state of the art.

We also wanted to ameliorate the local number density calculation of relic neutrinos in the local astrophysical environment. Such neutrinos, released in the very early Universe, traveled undisturbed until when they started to become non-relativistic. The last calculation of the effect of gravitational clustering of relic neutrinos was performed in a spherically symmetric environment composed of our galaxy alone. By using a method called back-tracking, which allowed to relax the assumption of spherical symmetry and to evaluate the effect of the gravitational potential of the Virgo cluster and of the Andromeda galaxy, we obtained a more precise calculation of the relic neutrino local number density, extremely important for computing the event rate at direct detection experiments, such as PTOLEMY, in preparation.

In the context of neutrino properties, we employed techniques of Bayesian statistics to propose a new bound on the absolute neutrino mass scale from cosmology. Our method allows to account for the possible effect of changing the free parameters in the analysis when computing a bound. The method was already known, but it was never applied to analyse cosmological data. We have also extended this method to eliminate from the final results the dependence of the obtained bounds on the prior which is assumed on the considered parameter. Such method is particularly useful when one cannot decide if it is best to use a logarithmic or linear prior on the absolute scale of neutrino masses, or which parameter range to use when scanning the parameter space.

Concerning the neutrino mass ordering, we updated existing constraints with the most recent terrestrial and cosmological data in order to reinforce the preference in favor of the normal mass ordering. We proposed a new observation to be performed at the future neutrino experiment DUNE, which could improve its sensitivity.

We also wanted to ameliorate the local number density calculation of relic neutrinos in the local astrophysical environment. Such neutrinos, released in the very early Universe, traveled undisturbed until when they started to become non-relativistic. The last calculation of the effect of gravitational clustering of relic neutrinos was performed in a spherically symmetric environment composed of our galaxy alone. By using a method called back-tracking, which allowed to relax the assumption of spherical symmetry and to evaluate the effect of the gravitational potential of the Virgo cluster and of the Andromeda galaxy, we obtained a more precise calculation of the relic neutrino local number density, extremely important for computing the event rate at direct detection experiments, such as PTOLEMY, in preparation.

In the context of neutrino properties, we employed techniques of Bayesian statistics to propose a new bound on the absolute neutrino mass scale from cosmology. Our method allows to account for the possible effect of changing the free parameters in the analysis when computing a bound. The method was already known, but it was never applied to analyse cosmological data. We have also extended this method to eliminate from the final results the dependence of the obtained bounds on the prior which is assumed on the considered parameter. Such method is particularly useful when one cannot decide if it is best to use a logarithmic or linear prior on the absolute scale of neutrino masses, or which parameter range to use when scanning the parameter space.

Concerning the neutrino mass ordering, we updated existing constraints with the most recent terrestrial and cosmological data in order to reinforce the preference in favor of the normal mass ordering. We proposed a new observation to be performed at the future neutrino experiment DUNE, which could improve its sensitivity.