  The VIP2 (VIolation of the Pauli Exclusion Principle) experiment at the Gran
Sasso underground laboratory (LNGS) is searching for possible violations of
standard quantum mechanics predictions in atoms at very high sensitivity. We
investigate atomic transitions with precision X-ray spectroscopy in order to
test the Pauli Exclusion Principle (PEP) and therefore the related
spin-statistics theorem. We will present our experimental method for the search
for "anomalous" (i.e. Pauli-forbidden) X-ray transitions in copper atoms,
produced by "new" electrons, which could have tiny probability to undergo
Pauli-forbidden transition to the ground state already occupied by two
electrons. We will describe the VIP2 experimental setup, which is taking data
at LNGS presently. The goal of VIP2 is to test the PEP for electrons with
unprecedented accuracy, down to a limit in the probability that PEP is violated
at the level of 10$^{-31}$. We will present current experimental results and
discuss implications of a possible violation.
