Search

The SIDDHARTA-2 experiment installed at the DA$\mathrm{\Phi}$NE collider of INFN-LNF performed, for the first time, measurements of high-n transitions in intermediate mass kaonic atoms during the data taking campaigns of 2021 and 2022. Kaonic carbon, oxygen, nitrogen and aluminium transitions, which occur in the setup materials, were measured by using the kaons stopped in the gaseous helium target cell with aluminium frames and Kapton walls, and are reported in this paper. These new kaonic atoms measurements add valuable input to the kaonic atoms transitions data base, which is used as a reference for theories and models of the low-energy strong interaction between antikaon and nuclei. Moreover, these results pave the way for future dedicated kaonic atoms measurements through the whole periodic table and to a new era for the antikaon-nuclei studies at low energy., Comment: 8 pages, 7 figures

In the last decade, heavy-ion based experiments (HypHI, STAR and ALICEi ) announced surprisingly short lifetime for 3 ΛH mesonic weak decay (MWD), which is difficult to interpret given the fact that 3 ΛH is a very loosely bound system. It will be very interesting to study this issue with a different experimental approach. We propose a direct measurement for 3 ΛH hypernucleus MWD lifetime with ∼10% precision as J-PARC E73 experiment; 4 ΛH hypernucleus lifetime will also be measured as a feasibility test for our experimental approach. In this proceeding, we will introduce the experimental method and the current status of E73 experiment.

We have measured the 3d→2p transition x rays of kaonic ^{3}He and ^{4}He atoms using superconducting transition-edge-sensor microcalorimeters with an energy resolution better than 6 eV (FWHM). We determined the energies to be 6224.5±0.4(stat)±0.2(syst) eV and 6463.7±0.3(stat)±0.1(syst) eV, and widths to be 2.5±1.0(stat)±0.4(syst) eV and 1.0±0.6(stat)±0.3(stat) eV, for kaonic ^{3}He and ^{4}He, respectively. These values are nearly 10 times more precise than in previous measurements. Our results exclude the large strong-interaction shifts and widths that are suggested by a coupled-channel approach and agree with calculations based on optical-potential models.

The SIDDHARTINO experiment at the DAΦNE collider of INFN-LNF, the pilot run for the SIDDHARTA-2 experiment which aims to perform the measurement of kaonic deuterium transitions to the fundamental level, has successfully been concluded in July 2021. The paper reports the main results of this run, including the optimization of various components of the apparatus, among which the degrader needed to maximize the fraction of kaons stopped inside the target, through measurements of kaonic helium transitions to the 2p level. The obtained shift and width values are ε 2p = E exp − E e.m = 0.2 ± 2.5(stat) ± 2.0(syst) eV and Γ2p = 8 ± 10 eV (stat), respectively. This new measurement of the shift, in particular, represents the most precise one for a gaseous target and is expected to contribute to a better understanding of the kaon–nuclei interaction at low energy. The results obtained in this pilot run, combined with the foreseen additional veto systems and projected for the total 48 SDD arrays of the SIDDHARTA-2 final setup, represent a solid starting point for the successful measurement of the kaonic deuterium 2p → 1s transition, main goal of the experiment.

Kaonic atoms are a unique tool to explore quantum chromodynamics in the strangeness sector at low energy, with implications reaching neutron stars and dark matter. Precision X-ray spectroscopy can fully unlock the at-threshold isospin dependent antikaon-nucleon scattering lengths, via the atomic transitions to the fundamental level. While the SIDDHARTA experiment at the INFN-LNF DA$\Phi$NE collider successfully measured kaonic hydrogen, its successor SIDDHARTA-2 is starting now its data taking campaign aiming to finally fully disentangle the isoscalar and isovector scattering lengths via the measurement of kaonic deuterium. An overview of the first experimental results from a preparatory run for the SIDDAHARTA-2 experiment is presented., Comment: 13 pages, 7 figures, to be sumbitted to Phys. Scr. - Focus on New Frontiers in Physics - Selected Papers from ICNFP 2021

The nuclear E2 resonance effect occurs when an atomic de-excitation energy is closely matched by a nuclear excitation energy. It produces an attenuation of some of the atomic X-ray lines in the resonant isotope target. Investigating the nuclear E2 resonance effect in kaonic atoms, important information about kaon-nucleus strong interaction can be provided. The only K − − 42 98 Mo nuclear resonance effect was measured by G. L. Goldfrey, G- K. Lum and C. E. Wiegand at Lawrence Berkeley Laboratory, in 1975. The nuclear E2 resonance effect was observed in 25 hours of data taking, not enough to provide a conclusive result. In four kaonic Molybdenum isotopes ( 42 94 Mo , 42 96 Mo , 42 98 Mo and 42 100 Mo ), the nuclear E2 resonance effect is expected at the same transition, with similar energy values. The KAMEO (Kaonic Atoms Measuring nuclear resonance Effects Observables) experiment plans to study the E2 nuclear resonance effect in kaonic Molybdenum isotopes at the DAΦNE e+e− collider, during the SIDDHARTA-2 experiment. The experimental strategy consists of exposing four solid strip targets, each enriched with one Molybdenum isotope, to negatively charged kaons, using a germanium detector for X-ray transition measurements. A further exposure of a non-resonant 42 92 Mo isotope solid strip target will be used as reference for standard non-resonant transitions.

The SIDDHARTA-2 collaboration is aiming to perform the challenging measurement of kaonic deuterium X-ray transitions to the ground state. This will allow to extract the isospin-dependent antikaon-nucleon scattering lengths, providing input to the theory of Quantum Chromodynamics (QCD) in the non-perturbative regime with strangeness. This work describes the SIDDHARTA-2 experimental apparatus and presents the results obtained during the commissioning phase realized with kaonic helium measurements. In particular, the first observation of the kaonic helium transitions to the 3s level (M-lines), reported in this work, represents a new source of information to study the kaonic helium cascade process and demonstrates the potential of the SIDDHARTA-2 apparatus, in the view of the ambitious kaonic deuterium measurement.

The SIDDHARTA-2 experiment at the DAΦNE collider aims to perform the first kaonic deuterium x-ray transitions to the fundamental level measurement, with a systematic error at the level of a few eV. To achieve this challenging goal the experimental apparatus is equipped with 384 Silicon Drift Detectors (SDDs) distributed around its cryogenic gaseous target. The SDDs developed by the SIDDHARTA-2 collaboration are suitable for high precision kaonic atoms spectroscopy, thanks to their high energy and time resolutions combined with their radiation hardness. The energy response of each detector must be calibrated and monitored to keep the systematic error, due to processes such as gain fluctuations, at the level of 2–3 eV. This paper presents the SIDDHARTA-2 calibration method which was optimized during the preliminary phase of the experiment in the real background conditions of the DAΦNE collider, which is a fundamental tool to guarantee the high precision spectroscopic performances of the system over long periods of data taking, as that required for the kaonic deuterium measurement.

The VIP-2 experiment performs a high sensitivity test of the Pauli Exclusion Principle for electrons, and is operated in the ultra-low cosmic background environment of the Gran Sasso Underground Laboratories of INFN. The experimental technique consists in testing the symmetry state of an open, continuously supplied, system of fermions; thus representing the only spin-statistics test which strictly fulfills the Messiah-Greenberg superselection rule. In April 2019, VIP-2 started the ongoing data taking campaign in its final layout, with the goal to improve the previous VIP result of at least two orders of magnitude. Before April 2019, VIP-2 collected, in a partial configuration of the external shielding complex, two sets of data in 2018–2019 for a total duration of about 208 days. We present in this work the results of the analyses of the first two data sets collected by VIP-2, which already improve the VIP result by one order of magnitude. The results are also interpreted in the framework of a diffusion random walk model, which provides a significantly enhanced description of the electrons-atoms close encounters process, and hence a boost on the estimated limit on the Pauli Exclusion Principle violation probability.

The current work presents the optimization of large area silicon drift detectors developed by the SIDDHARTA-2 collaboration for high precision x-ray measurements of light exotic atom transitions. Two different radiation sources were employed in the study: an x-ray tube, for investigating the energy resolution and the charge collection efficiency of the device in the range 4000 eV–13 000 eV, and a β − 90Sr radioactive source for measuring the timing response, thus qualifying the charge drift parameters inside the semiconductor. The study reports the spectroscopic response optimization, together with the tuning of the electron dynamics for the given Silicon technology, by adjusting the applied electric field and the working temperature, which allow a good control of the device’s performances for high precision, timed x-ray spectroscopy applications.

High precision light kaonic atoms X-ray spectroscopy is a unique tool for performing experiments equivalent to scattering at vanishing relative energies, to determine the antikaon–nucleus interaction at threshold without the need of extrapolation to zero energy. The SIDDHARTA-2 collaboration is going to perform the first measurement of kaonic deuterium transitions to the fundamental level, which is mandatory to extract the isospin dependent antikaon–nucleon scattering lengths. The SIDDHARTA-2 experiment is presently installed on the DA $$\Phi $$ NE collider of INFN-LNF. The preliminary results obtained during the machine commissioning phase in preparation for the kaonic deuterium data taking campaign, together with future perspectives for extreme precision kaonic atoms studies at DA $$\Phi $$ NE are presented.

The SIDDHARTA-2 collaboration developed an innovative large area Silicon Drift Detectors technology to perform high precision spectroscopy for the investigation of the K¯ N strong interaction in the low-energy regime, in the strangeness sector. The SIDDHARTA-2 devices take advantage of special geometry to maximize the experimental geometrical acceptance together with a dedicated Front End electronics able to provide energy resolution of 163 1 eV at 170 K for the Fe Kα line and a linear response better than 10-3, both preserved along the whole DAQ analog-digital chain in a colliding beams challenging environment. In this work the SIDDHARTA-2 Silicon Drift Detectors spectroscopic characterization and the preliminary results obtained at the DAΦNE collider of Istituto Nazionale di Fisica Nucleare - Laboratori Nazionali di Frascati are presented.

The collapse models were proposed more than 30 years ago to save the poor Schrodinger’s cat from its zombie-fate. In these models the standard Schrodinger equation is modified with the introduction of non-linear and stochastic terms, naturally collapsing the wave function in space. Ghirardi was pioneering these models, which predict deviations from the standard Quantum Mechanics. One of these predictions is the emission of a “spontaneous radiation”, which we explored to set the most stringent limits on the collapse models parameters in a broad range. This allowed us paraphrasing the title of his famous book, to sneak a look at Ghirardi’s cards.

The standard scheme of several tests of the Pauli Exclusion Principle in bulk matter — both in the experiment and in the subsequent data analysis — has long been based on the seminal paper by E. Ramberg, G.A. Snow [Phys. Lett. B 238, 438 (1990)]. The ideas exposed in that paper are so simple and immediate that they have long gone unchallenged. However, while some of the underlying approximations are still valid, other parts of the article must be reconsidered. Here, we discuss some new concepts thatare related to the motion of the electrons in the test metal (the “target” of the experiment) and which have been recently studied in the framework of the VIP-2 Collaboration.

The VIP experiment performed an accurate investigation of the Pauli Exclusion Principle for electrons. The apparatus was installed in the Gran Sasso Laboratories of the National Institute of Nuclear Physic in Italy, an underground environment with an extremely low cosmic background. The aim of the experiment was to test the Pauli Exclusion Principle for electrons in a copper target circulated by a Direct Current (DC) current, searching for X-rays emission due to an atomic transition forbidden by Pauli exclusion principle, from the L shell to the K shell of copper when the K shell is already occupied by two electrons. VIP set an upper limit on the Pauli exclusion principle violation probability 1/2β 2 –29. The goal of the upgraded VIP-2 experiment, presently in data taking at Gran Sasso Laboratories, is to improve this limit by two orders of magnitude. The VIP-2 experimental apparatus, in which the Silicon Drift Detectors have the key role of X-ray detectors, and preliminary results are presented.

X-ray spectroscopy of kaonic atoms provides a versatile tool to study the strong interaction at low energies via a direct observation of its influence on the ground state of kaonic hydrogen atoms. The SIDDHARTA experiment provided precise results on the energy shift and width of the kaonic hydrogen 1s state induced by the strong interaction. To enable the extraction of the antikaon-nucleon scattering lengths a0 and a1, SIDDHARTA-2 aims to determine the energy shift and width in kaonic deuterium with precisions of 30 eV and 75 eV, respectively. This measurement is aggravated by the low kaonic deuterium X-ray yield and a high background environment and will only be possible by implementing a severe upgrade on the SIDDHARTA apparatus.

The VIP Collaboration is performing high precision tests of the Pauli Exclusion Principle for electrons in the extremely low cosmic background environment of the Underground Gran Sasso Laboratories of INFN (Italy). The experimental technique consists in introducing a DC current in a copper conductor, searching for Kα PEP-forbidden atomic transitions when the K shell is already occupied by two electrons. VIP set an upper limit on the PEP-violation probability (½) x β^2 < 4.7 × 10^−29. The aim of the upgraded VIP-2 experiment is to improve this result at least by two orders of magnitude. The improved experimental setup and the results of a preliminary data analysis, corresponding to the the first run of the VIP-2 data taking (2016–2017), will be presented.

Light kaonic atoms spectroscopy offers the unique opportunity to perform experiments equivalent to scattering at vanishing relative energies. This allows the determination of the antikaon-nucleus interaction at threshold, without the need of extrapolation to zero energy, as in the case of scattering experiments. In this framework, the SIDDHARTA-2 collaboration aims to perform the first measurement of kaonic deuterium transition to the fundamental level, which is mandatory to extract the isospin dependent antikaon—nucleon scattering lengths. The experiment will be carried out at the DA(formula presented)NE collider of LNF-INFN in 2019–2020.

The VIP-2 (VIolation of the Pauli Exclusion Principle) experiment conducted at the Gran Sasso underground laboratory (LNGS) of INFN is searching for possible tiny violations of standard quantum mechanics in copper atoms with extremely high sensitivity. We investigate atomic transitions with precision X-ray spectroscopy in order to test the Pauli Exclusion Principle (PEP) and therefore the spin-statistics theorem. We present the experimental method for the search for "anomalous" (i.e. Pauli-forbidden) X-ray transitions in copper atoms, produced by "new" electrons, which could have a tiny probability to undergo a Pauli-forbidden transition to the 1s ground state already occupied by two electrons. We describe the VIP-2 experimental setup and its recent optimisations. Presently VIP-2 is taking data at LNGS. The goal of VIP-2 is to test PEP for electrons with unprecedented accuracy, down to a limit in the probability that PEP is violated at the level of 10-31 (and using a more elaborate analysis even 10-40). We present current experimental results.

The VIP collaboration is performing high precision tests of the Pauli Exclusion Principle for electrons in the extremely low cosmic background environment of the Underground Gran Sasso Laboratories of INFN (Italy). The experimental technique consists in introducing a DC current in a copper conductor, searching for the X-rays emission due to a PEP-forbidden atomic transition from the L shell to the K shell of copper when the K shell is already occupied by two electrons. VIP set un upper limit on the PEP violation probability 1 2 β 2 < 4.7 × 10 − 29 , the aim of the upgraded VIP-2 experiment is to improve this result by two orders of magnitude at least. The experimental setup and the results of preliminary data analyses will be presented.

We present the first observation of K- and \phi absorption within nuclear matter by means of \pi- -induced reactions on C and W targets at an incident beam momentum of 1.7 GeV/c studied with HADES at SIS18/GSI. The double ratio (K-/K+)W / (K-/K+)C is found to be 0.319 \pm 0.009(stat)+0.014-0.012 (syst) indicating a larger absorption of K- in heavier targets as compared to lighter ones. The measured \phi/K- ratios in \pi-+C and \pi^- +W reactions within the HADES acceptance are found to be equal to $0.55 \pm 0.03(stat)+0.06-0.07$ (syst) and to $0.63 \pm 0.05(stat)-0.11+0.11$ (syst), respectively. The similar ratios measured in the two different reactions demonstrate for the first time experimentally that the dynamics of the \phi meson in nuclear medium is strongly coupled to the K- dynamics. The large difference in the \phi production off C and W nuclei is discussed in terms of a strong \phiN in-medium coupling., Comment: 6 pages, 3 figures

The determination of low-energy cross sections and branching ratios of the K$^-$ multi-nucleon absorption processes in $\Lambda$p and $\Sigma^0$p final states performed by the AMADEUS collaboration is presented. Low momentum K$^-$ ($p_\mathrm{K} \simeq$ 127 MeV/c) produced at the DA$\Phi$NE collider are impinged on a Carbon target within the KLOE detector and the two and three nucleon absorption processes are disentangled by comparing the experimental data to phenomenological calculations. The $\Lambda$p spectra are interpreted in terms of K$^-$ multi-nucleon absorption processes; the possible contribution of a K$^-$pp bound state is demonstrated to overlap with the two nucleon capture process, its absolute yield thus resulting indistinguishable.

The precision of the charged kaon mass is an order of magnitude worse than the precision of the charged pion mass mainly due to two inconsistent measurements. We plan to improve this precision by determining the charged kaon mass with the requested accuracy in the measurements of X-ray transitions in kaonic atoms of selected solid targets with the HPGe detector at DAΦNE in Laboratori Nazionali di Frascati, Italy. The measurements will be performed in parallel with SIDDHARTA-2 measurements of X-ray transitions in gaseous targets. The status of the preparation of the measurements will be presented.

The investigations of light kaonic atoms offer the unique opportunity to perform experiments equivalent to scattering at vanishing relative energies, being their atomic binding energies in the keV range. This allows the determination of the hadron-nucleus interaction at threshold without the need of an extrapolation to zero relative energy. The energy shift and broadening of the lowest-lying states of such atoms, induced by the kaon-nucleus strong interaction, can be determined with high precision from atomic X-ray spectroscopy. The lightest atomic systems, kaonic hydrogen and kaonic deuterium, deliver the isospin-dependent kaon-nucleon scattering lengths. The most precise kaonic hydrogen measurement to date, together with an exploratory measurement of kaonic deuterium, were carried out by the SIDDHARTA collaboration at the DAΦNE electron-positron collider of LNF-INFN. The measurement of kaonic deuterium will be realized in the near future by SIDDHARTA-2, a major upgrade of SIDDHARTA. A correlated study of the kaon-nuclei interaction at momenta below 130 MeV/c is carried out by the AMADEUS collaboration, using the KLOE detector and dedicated targets inserted near the collider interaction point. In this paper an overview of the main results obtained by SIDDHARTA together with the future plans, the SIDDHARTA-2 experiment and with the preliminary results of the study of charged antikaons interacting with nuclei by the AMADEUS collaboration, are shown. (Less)

Collapse models consist in dynamical reformulations of the standard quantum mechanics aiming to solve the measurement problem. The standard Schrödinger dynamics is modified with the introduction of nonlinear and stochastic terms, which induce the wave function collapse in space. Collapse models predict slight deviations from the standard quantum mechanics predictions, in particular the emission of a “spontaneous radiation”, which we explored to set the most stringent limits on the collapse models parameters in a broad range. To this end, the X-ray emission data collected by the IGEX collaboration are analyzed and compared with the spectrum of the spontaneous photon emission process predicted by the theories. The results of the data analyses, and the ongoing experimental efforts will be presented.

Light kaonic atoms studies provide the unique opportunity to perform experiments equivalent to scattering at threshold, being their atomic binding energies in the keV range. High precision atomic X-rays spectroscopy ensures that the energy shift and broadening of the lowest-lying states of the kaonic atoms, induced by the strong interaction between the kaon and nucleus, can be detected. Kaonic hydrogen and kaonic deuterium are the lightest atomic systems and their study deliver the isospin-dependent kaon-nucleon scattering lengths. The SIDDHARTA collaboration was able to perform the most precise kaonic hydrogen measurement to date, together with an exploratory measurement of kaonic deuterium. The measurement of the kaonic deuterium will be realized in the near future by a major upgrade of SIDDHARTA: SIDDHARTA-2. In this paper an overview of the main results obtained by SIDDHARTA together with the future plans are presented.

The main steps for the analysis of the Λp correlated production in low-energy K− captures on Carbon nuclei, performed by the AMADEUS collaboration, are presented. The goal is to perform the first comprehensive study of the K− absorption on two, three and four nucleons, exploiting the lowmomentum K−s (pK ~ 127 MeV/c) produced at the DAΦNE collider, and to measure the low-energy cross sections and branching ratios of the K− multinucleon absorption processes in both the Λp and Σ0p channels. An integrated luminosity of 1.74 fb−1 collected during the KLOE 2004/2005 data campaign is analysed by reconstructing the Λp final state.

The DAΦNE electron-positron collider of the Laboratori Nazionali di Frascati of INFN is a worldwide unique low-energy kaon source, which is being used to produce and to study kaonic atoms by the SIDDHARTA collaboration. The X-ray measurements of kaonic atoms play an important role for understanding the low-energy QCD in the strangeness sector. Significant achievements have been obtained by the SIDDHARTA experiment, among which: the most precise kaonic hydrogen measurement of the 1s level shift and width induced by the presence of the strong interaction; an upper limit of the X-ray yield for kaonic deuterium K-series; the accurate measurement of the 2p level shift and width of kaonic helium-4 and kaonic helium-3; yields of various light kaonic atoms transitions. Using the experience gained with SIDDHARTA experiment, the first kaonic deuterium measurement is in preparation in the framework of the SIDDHARTA-2 experiment, with the goal to determine the antikaon-nucleon isospin dependent scattering lengths, which is possible only by combining the K−p and the upcoming K−d results. An overview of the experimental results of SIDDHARTA and an outlook to SIDDHARTA-2 experiments are given in this paper. (Less)

The interaction of antikaons (K−) with nucleons and nuclei in the low-energy regime represents a very active research field in hadron physics. A unique and rather direct experimental access to the antikaon-nucleon scattering lengths is provided by precision X-ray spectroscopy of transitions in low-lying states in the lightest kaonic atoms (i.e. kaonic hydrogen and deuterium). In the SIDDHARTA experiment at the electron-positron collider DAFNE of LNFINFN we measured the most precise values of the strong interaction observables in conic hydrogen. The strong interaction on the 1s ground state of the electromagnetically bound K-p atom causes an energy shift and broadening of the 1s state. SIDDHARTA will extend the spectroscopy to kaonic deuterium to get access to the antikaon-neutron interaction and thus the isospin dependent scattering lengths. At J-PARC a kaon beam is used in a complementary experiment with a different setup for spectroscopy of kaonic deuterium atoms. The talk will give an overview of the of the upcoming experiments SIDDHARTA and the complementary experiment at J-PARC.Furthermore, the implications of the experiments for the theory of low-energy strong interaction with strangeness will be discussed.

The structure of the Λ(1405) hyperon is an important and long-standing issue related to the K-nucleus interaction. The J-PARC E31 experiment has been performed to investigate the Λ(1405) spectrum shape. Because it is hard to form the Λ(1405) directly by a KN scattering in free space, E31 uses the d(K-, n) reaction with an incident kaon momentum of 1 GeV/c. We will identify three final states - ς-π+, ς+π-, ς0π0-so that the isospin structure of hyperon resonance states produced can be decomposed. The first physics run of the E31 experiment was performed in 2016. To enhance the statistics of the data set, we have performed the second physics run in the beginning of 2018. During the second run of E31, around 3.9×1010 kaons impacted on the deuteron target.

The ongoing data analyses by the AMADEUS/KLOE-2 Collaboration on the 2004–2005 KLOE data revive studies of the K ‾ nuclear absorption at low energies. The aim is to study K ‾ interactions at subthreshold energies and to search for signals of K ‾ meson nuclear states. In this paper the spectrum of the K − He 4 → Λ π − He 3 reaction is discussed. One – calculable – mode of decay involves P-wave intermediate Σ ( 1385 ) resonance. Another mode involves S-wave K N → Λ π amplitude which may be extracted from the experimental results. Comparison of these two allows a check of subthreshold extrapolations of multichannel K ‾ N S-wave interaction models. Given the established significance of the P wave interaction in the K ‾ N system presented here, the obtained spectra will serve for the AMADEUS/KLOE-2 data analysis, in order to properly extract the subthreshold non-resonant transition amplitude.

The work presented in this paper aimed to obtain new, more stringent, limits on the parameters of the Continuous Spontaneous Localization collapse model. The result is accomplished by performing a Bayesian analysis of the X-ray emission data collected by the IGEX collaboration, compared with the spontaneous photon emission which is predicted by collapse models. The most stringent limits on the collapse rate $\lambda$ and the correlation length $r_C$ of the CSL model are obtained , with respect to any other method, over a broad range of the parameters space.

The VIolation of Pauli exclusion principle -2 experiment, or VIP-2 experiment, at the Laboratori Nazionali del Gran Sasso searches for X-rays from copper atomic transitions that are prohibited by the Pauli exclusion principle. Candidate direct violation events come from the transition of a 2p electron to the ground state that is already occupied by two electrons. From the first data taking campaign in 2016 of VIP-2 experiment, we determined a best upper limit of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3.4~\times ~10^{-29}$$\end{document}3.4×10-29 for the probability that such a violation exists. Significant improvement in the control of the experimental systematics was also achieved, although not explicitly reflected in the improved upper limit. By introducing a simultaneous spectral fit of the signal and background data in the analysis, we succeeded in taking into account systematic errors that could not be evaluated previously in this type of measurements.

The VIolation of Pauli (VIP) experiment (and its upgraded version, VIP-2) uses the Ramberg and Snow (RS) method (Phys. Lett. B 1990, 238, 438) to search for violations of the Pauli exclusion principle in the Gran Sasso underground laboratory. The RS method consists of feeding a copper conductor with a high direct current, so that the large number of newly-injected conduction electrons can interact with the copper atoms and possibly cascade electromagnetically to an already occupied atomic ground state if their wavefunction has the wrong symmetry with respect to the atomic electrons, emitting characteristic X-rays as they do so. In their original data analysis, RS considered a very simple path for each electron, which is sure to return a bound, albeit a very weak one, because it ignores the meandering random walks of the electrons as they move from the entrance to the exit of the copper sample. These complex walks bring the electrons close to many more atoms than in the RS calculation. Here, we consider the full description of these walks and show that this leads to a nontrivial and nonlinear X-ray emission rate. Finally, we obtain an improved bound, which sets much tighter constraints on the violation of the Pauli exclusion principle for electrons.