# VIP-2 —High-Sensitivity Tests on the Pauli Exclusion Principle for Electrons

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## Abstract

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## 1. Introduction

## 2. Experimental Method of VIP-2

- the VIP experiment used Charge Coupled Devices (CCDs) as X-ray detectors, which are characterized by a Full Width at Half Maximum (FWHM) of 320 eV at 8 keV. In order to improve the energy resolution at the anomalous transition energy 7746.73 eV (see Ref. [24]), the CCDs are replaced by Silicon Drift Detectors (SDDs) with a better energy resolution (190 eV FWHM at 8 keV) [28];
- the copper target is reshaped in order to increase the acceptance for the detection of the X-rays. The new target consists of two strips of copper (with a thickness of 50 μm, and a surface of 9 cm × 3 cm);
- the circulating DC current in the copper target is also increased, in order to enhance the pool of test electrons. To this end, a cooling pad (cooled down by a closed chiller circuit) is placed in between the two strips in order to avoid the temperature rise due to the heat dissipation in copper. This allows to increment the DC current from 40 A (in VIP) to 100 A;
- the timing resolution of the SDDs allows the implementation of a veto system which works as an active shielding, reducing the background originating from the high energy charged particles that are not shielded by the rocks of the Gran Sasso mountains. It is made of 32 plastic scintillators, each of size 250 mm × 38 mm × 40 mm, read from both sides by silicon photomultipliers.
- all the detectors and the front end preamplifier electronics are mounted inside the vacuum chamber which is kept at about 10
^{−6}mbar during operation; - the energy calibration and the measurement of the SDDs resolution is performed by means of a weakly radioactive Fe-55 source, with a 25 μm thick titanium foil attached on top, mounted together inside an aluminum holder. The fluorescence X-rays from titanium and manganese are used to calibrate the digitised channel into energy scale.

^{2}of effective surface. The experimental setup was further upgraded in April 2018, when the detector system was replaced with two new arrays each one with 2 × 8 SDDs, for a total of 32 SDDs. The SDDs are cooled down to about −90 °C. The target system is cooled down by a water cooling keeping them to a temperature of about 12 degrees. When the current of 100 A is turned on, the strips’ temperature increases of few degrees and this induces a temperature rise at the SDDs of the same amount, which does not significantly alter the SDDs’ performances. A schematic view of the VIP-2 apparatus is shown in Figure 2.

## 3. Data Analysis

## 4. Conclusions and Outlook

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

VIP | Violation of Pauli |

VIP-2 | Violation of Pauli-2 |

INFN | Istituto Nazionale di Fisica Nucleare |

PEP | Pauli Exclusion Principle |

SP | Symmetrization Postulate |

QFT | Quantum Field Theory |

SST | Spin Statistic Theorem |

MG | Messiah–Greenberg |

LNGS | Gran Sasso National Laboratory |

DC | Direct Current |

CCD | Charge Coupled Devices |

FWHM | Full Width at Half Maximum |

SDD | Silicon Drift Detector |

ROI | Region of Interest |

$pdf$ | probability distribution function |

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**Figure 1.**Schematic representation of a standard K${}_{\alpha}$ transition (

**left**) and a Pauli Exclusion Principle (PEP)-violating transition (

**right**).

**Figure 2.**Side views of the design of the core components of the VIP-2 setup, including the Silicon Drift Detectors (SDDs) as the X-ray detector, the scintillators as active shielding with silicon photomultiplier readout.

**Figure 3.**Energy calibrated spectra corresponding to about 42 days of data taking (during 2018) collected with current on (left), the spectrum collected with current off (right), which is normalized to the time of data taking with current on.

**Table 1.**Expectation values and standard deviations of all the parameters involved in the $pdf$ of ${\beta}^{2}/2$.

${\mathit{N}}_{\mathbf{int}}$ | ${\mathit{N}}_{\mathbf{new}}$ | $\mathit{\u03f5}$ |
---|---|---|

$(4.61\pm 0.09)\times {10}^{17}$ | $(2.25697\pm 0.00002)\times {10}^{27}$ | $(3.85\pm 0.05)\times {10}^{-2}$ |

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**MDPI and ACS Style**

Piscicchia, K.; Marton, J.; Bartalucci, S.; Bazzi, M.; Bertolucci, S.; Bragadireanu, M.; Cargnelli, M.; Clozza, A.; Del Grande, R.; De Paolis, L.;
et al. VIP-2 —High-Sensitivity Tests on the Pauli Exclusion Principle for Electrons. *Entropy* **2020**, *22*, 1195.
https://doi.org/10.3390/e22111195

**AMA Style**

Piscicchia K, Marton J, Bartalucci S, Bazzi M, Bertolucci S, Bragadireanu M, Cargnelli M, Clozza A, Del Grande R, De Paolis L,
et al. VIP-2 —High-Sensitivity Tests on the Pauli Exclusion Principle for Electrons. *Entropy*. 2020; 22(11):1195.
https://doi.org/10.3390/e22111195

**Chicago/Turabian Style**

Piscicchia, Kristian, Johann Marton, Sergio Bartalucci, Massimiliano Bazzi, Sergio Bertolucci, Mario Bragadireanu, Michael Cargnelli, Alberto Clozza, Raffaele Del Grande, Luca De Paolis,
and et al. 2020. "VIP-2 —High-Sensitivity Tests on the Pauli Exclusion Principle for Electrons" *Entropy* 22, no. 11: 1195.
https://doi.org/10.3390/e22111195