Strongest constraint on the parastatistical Quon model with the VIP-2 measurements

The spin-statistics theorem leads to Pauli’s Exclusion Principle (PEP), the basis of the stability of matter and many other phenomena relevant to physics, astrophysics, cosmology, and even biology. Possible violations of the PEP (PEPV) have been searched for since its inception; they may come from various Beyond Standard Model descriptions, including Non-Commutative Quantum Gravity models and extensions of the Quantum Field Theory, which must follow the Messiah-Greenberg Super-Selection (MGSS) rule and lead to the Quon description of the spin-statistic symmetries: the parastatstics. Efforts to search for a PEPV are not new; however, they have typically measured those cases without respecting MGSS. VIP (VIolation of the Pauli exclusion principle) first and its successor VIP-2, both sited in the “Gran Sasso underground laboratory,” aimed to set the most stringent limit for the non-Paulian transition following the MGSS rule. After two years of data with VIP-2 and better modeling of the electron-atom interaction, we present the most stringent upper limit of the probability of PEP violation for this case ( $$\beta ^{2}/2<2.47\times 10^{-43}$$ ), thus completing the state-of-the-art of all possible PEPV cases, and the consequent constraint to the Quon description: $$1+q < 4.94 \times 10^{-43}$$ .