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Testing the Pauli Exclusion Principle for electrons at LNGS

High-precision experiments have been done to test the Pauli exclusion principle (PEP) for electrons by searching for anomalous $K$-series X-rays from a Cu target supplied with electric current. With the highest sensitivity, the VIP (VIolation of Pauli Exclusion Principle) experiment set an upper limit at the level of $10^{-29}$ for the probability that an external electron captured by a Cu atom can make the transition from the 2$p$ state to a 1$s$ state already occupied by two electrons. In a follow-up experiment at Gran Sasso, we aim to increase the sensitivity by two orders of magnitude. We show proofs that the proposed improvement factor is realistic based on the results from recent performance tests of the detectors we did at Laboratori Nazionali di Frascati (LNF).