## Periodic Reporting for period 4 - NEO-NAT (Understanding the mass scales in nature)

Reporting period: 2020-09-01 to 2021-11-30

After the emergence of the Standard Model of the Fundamental Interactions, theorists started to investigate its features. Its most puzzling aspect is the existence of two vastly separate mass scales: the electro-weak scale (set by the Higgs mass, that controls the mass of all other elementary Standard Model particles) and the gravitational Planck scale (the mass above which any elementary particle is a black hole, according to General Relativity and Quantum Mechanics). This difference by 19 orders of magnitude is what allows the existence of objects made of many particles.

The puzzle is that, according to the usual naturalness argument, in the Standard Model (SM) the squared Higgs mass receives huge (quadratically divergent) quantum corrections, that tend to ruin the separation between the scales. Then, theorists invented concrete proposals of new physics that protects the Higgs mass from such corrections - technicolor, extra dimensions, supersymmetry - with the latter possibility being widely considered as the most plausible. Such arguments lead most theorists to think that the electro-weak scale is the scale of supersymmetry breaking.

The experimental results of the first run of the Large Hadron Collider lead to the discovery of the Higgs boson but have not confirmed such dominant theoretical paradigm about the naturalness of the electro-weak scale, according to which the Higgs boson should have been accompanied by supersymmetric particles or by some other new physics able of protecting the Higgs boson mass from quadratically divergent quantum corrections. The lack of supersymmetry and of any other new physics that makes the weak scale `natural' is now considered as a serious issue. Crisis in physics can lead to progress. It is maybe not exaggerated to see a parallel between the present negative results from LHC and the negative results of the Michelson-Morley experiment, that in 1887 shacked the strong belief in the aether theory, opening a crisis later resolved by relativity.

The main generic goal of this project is exploring and developing non-conventional theoretical ideas about the origin of mass scales, in particular about the origin of the electro-weak scale, which is presently being explored by LHC experiments.

The puzzle is that, according to the usual naturalness argument, in the Standard Model (SM) the squared Higgs mass receives huge (quadratically divergent) quantum corrections, that tend to ruin the separation between the scales. Then, theorists invented concrete proposals of new physics that protects the Higgs mass from such corrections - technicolor, extra dimensions, supersymmetry - with the latter possibility being widely considered as the most plausible. Such arguments lead most theorists to think that the electro-weak scale is the scale of supersymmetry breaking.

The experimental results of the first run of the Large Hadron Collider lead to the discovery of the Higgs boson but have not confirmed such dominant theoretical paradigm about the naturalness of the electro-weak scale, according to which the Higgs boson should have been accompanied by supersymmetric particles or by some other new physics able of protecting the Higgs boson mass from quadratically divergent quantum corrections. The lack of supersymmetry and of any other new physics that makes the weak scale `natural' is now considered as a serious issue. Crisis in physics can lead to progress. It is maybe not exaggerated to see a parallel between the present negative results from LHC and the negative results of the Michelson-Morley experiment, that in 1887 shacked the strong belief in the aether theory, opening a crisis later resolved by relativity.

The main generic goal of this project is exploring and developing non-conventional theoretical ideas about the origin of mass scales, in particular about the origin of the electro-weak scale, which is presently being explored by LHC experiments.

Work has been done on all tasks of the project.

Among the most interesting results, in the paper "Fundamental partial compositeness" we proposed the first realistic fundamental theory where the Higgs can be a composite particle. In the paper "Agravity up to infinite energy" we showed that dimension-less gravity can be valid up to infinite energy. This theory employs negative-norm quantum states, and can make sense if they can have a physical interpretation. We started exploring such issue in the paper "Quantum mechanics of 4-derivative theories". We proposed models where Dark Matter is a composite particle, showing that it could be a bound state of ordinary strong interactions. We explored issues related to the possible vacuum instability of the Higgs potential.

Furthermore we explored experimental anomalies that could become new discoveries or fade away, such as violation of lepton universality in flavour physics.

Among the most interesting results, in the paper "Fundamental partial compositeness" we proposed the first realistic fundamental theory where the Higgs can be a composite particle. In the paper "Agravity up to infinite energy" we showed that dimension-less gravity can be valid up to infinite energy. This theory employs negative-norm quantum states, and can make sense if they can have a physical interpretation. We started exploring such issue in the paper "Quantum mechanics of 4-derivative theories". We proposed models where Dark Matter is a composite particle, showing that it could be a bound state of ordinary strong interactions. We explored issues related to the possible vacuum instability of the Higgs potential.

Furthermore we explored experimental anomalies that could become new discoveries or fade away, such as violation of lepton universality in flavour physics.

The works mentioned above go beyond the state of the art. The general goal of the project is exploring new ideas for understanding why there are vastly different mass scales in nature.

This is a basic issue in physics, so its potential impact would be the one typical of physics: in the past century, physics understood that matter is made of a few particles (the ones that happen to be stable), and discovered a few extra particles. Understanding matter had a huge socio-economic impact; extra particles so far only had an indirect impact.

Furthermore, this is applied to the study of dark matter, which constitutes a bigger fraction of the universe total mass than normal matter, and presumably it is some extra unknown stable particle. Understanding what Dark Matter is might again have a direct socio-economic impact, depending on what the answer will turn out to be.

This is a basic issue in physics, so its potential impact would be the one typical of physics: in the past century, physics understood that matter is made of a few particles (the ones that happen to be stable), and discovered a few extra particles. Understanding matter had a huge socio-economic impact; extra particles so far only had an indirect impact.

Furthermore, this is applied to the study of dark matter, which constitutes a bigger fraction of the universe total mass than normal matter, and presumably it is some extra unknown stable particle. Understanding what Dark Matter is might again have a direct socio-economic impact, depending on what the answer will turn out to be.