On behalf of the VIP Collaboration On the Pauli Exclusion Principle search with VIP: some thoughts about data analyses Catalina Curceanu LNF-INFN On behalf of the VIP Collaboration FQT2015 Frascati, 23 – 25 September 2015

An experiment to test the Pauli Exclusion Principle (PEP) for electrons in a clean environment (LNGS) using atomic physics methods – the VIP experiment

Theories of Violation of Statistics O.W. Greenberg: AIP Conf.Proc.545:113-127,2004 “Possible external motivations for violation of statistics include: (a) violation of CPT, (b) violation of locality, (c) violation of Lorentz invariance, (d) extra space dimensions, (e) discrete space and/or time and (f) noncommutative spacetime. Of these (a) seems unlikely because the quon theory which obeys CPT allows violations, (b) seems likely because if locality is satisfied we can prove the spin-statistics connection and there will be no violations, (c), (d), (e) and (f) seem possible………….. Hopefully either violation will be found experimentally or our theoretical efforts will lead to understanding of why only bose and fermi statistics occur in Nature.”  

THE VIP COLLABORATION M. Bragadireanu, T. Ponta “Horia Holubei” National Institute of Physics and Nuclear Engineering - Bucharest, Romania   M. Laubenstein Laboratori Nazionali del Gran Sasso dell’INFN - Italy M. S. Bartalucci, S. Bertolucci, M. Catitti, C. Curceanu (Petrascu) , S. Di Matteo, C.Guaraldo, M. Iliescu, D. Pietreanu, D. L. Sirghi, F. Sirghi, L. Sperandio, O. Vazquez Doce Laboratori Nazionali di Frascati dell’INFN - Frascati, Italy   J.-P. Egger Univ. of Neuchâtel - Neuchâtel, Switzerland E. Milotti Univ. Degli Studi di Trieste and INFN Sezione di Trieste - Trieste, Italy   M. Cargnelli, T. Ishiwatari, J. Marton, E. Widmann, J. Zmeskal STEFAN MEYER Institute for Subatomic Physics - Vienna, Austria

Experimental method: n=2 n=2 n=1 n=1 2p –>1s transition violating Search for anomalous X-ray transitions when bringing “new” electrons n=2 n=1 n=2 n=1 2p –>1s transition violating Pauli principle Energy 7.7 keV Normal 2p –>1s transition Energy 8.04 keV Messiah Greenberg superselection rule

Experimental method: n=2 n=2 n=1 n=1 2p –>1s transition violating Search for anomalous X-ray transitions when bringing “new” electrons n=2 n=1 n=2 n=1 2p –>1s transition violating Pauli principle Energy 7.7 keV Normal 2p –>1s transition Energy 8.04 keV Messiah Greenberg superselection rule

The pre-VIP experiment limit: Ramberg and Snow (RS) Phys. Lett The pre-VIP experiment limit: Ramberg and Snow (RS) Phys. Lett. B238 (1990) 438 Search for anomalous electronic transitions in Cu induced by a circulating current (“new” external electrons, which interact with the valence electrons), namely transition from 2p to 1s already filled by 2 electrons

The parameter  Ignatiev & Kuzmin model creation and destruction operators connect 3 states - the vacuum state - the single occupancy state - the non-standard double occupancy state 0 1 2 through the following relations: The parameter  quantifies the degree of violation in the transition . It is very small and for   0 we can have the Fermi - Dirac statistic again. 1  2

this b can be simply related to the q parameter of the quon theory of Greenberg and Mohapatra quon algebra is a sort of weighted average between fermion and boson algebra: or also

The VIP experiment VIP is a much improved version of the previous (RS) experiment: sensitive, large-area, X-ray detectors: CCD di DEAR (non-triggerable…) clean, low-background experimental area (LNGS) large “electron reservoir”

The VIP setup

The VIP setup Cu Target

Test site and final location: Laboratori Nazionali del Gran Sasso, Istituto Nazionale di Fisica Nucleare LNGS

VIP setup at LNGS - 2006

Final setup at LNGS

VIP spectra at LNGS

VIP limit at LNGS (Foundation of Physics 41 (2011) 282) PEP violation Probability: We have thus improved the limit obtained by Ramberg & Snow by a factor  400 (Foundation of Physics 41 (2011) 282)

The (RS) analysis proceeds by assuming that conduction electrons behave like particles in a gas, and that capture can only proceed when electrons collide with atoms. This totally neglects the quantum nature of the conduction band, and there has been repeated criticism. Given the entangled wavefunction of the conduction electrons, and the indistinguishability of the electrons, how can “new” or “fresh” electrons exist? The question can be answered in the positive if electrons can be distinguished on the basis of a sort of “effective locality”, but how can this be?

A possible answer is provided by decoherence of electron wavefunctions in conductors

Experimentally, one finds that in real conductors there is a dependence on the environment that causes decoherence, and that this destroys the expected quantum interference of the electron paths inside conductors. This decoherence is usually parameterized by an exponential factor which multiplies the interference terms and gradually suppresses them as the system evolves in time. The conclusion is that after a time of the order of the decoherence time the electron wavefunctions are effectively decoupled and the environment acts on electrons by enforcing an effective locality.

Decoherence appears to be related to something really fundamental, it is not just thermal effects from P. Mohanti: "Of Decoherent Electrons and Disordered Conductors", Lecture Notes for NATO ASI, Norway ( 2001) Published in “Complexity from Microscopic to Macroscopic Scales: Coherence and Large Deviations”, NATO ASI, Edited by A. T. Skjeltorp and T. Vicsek (Kluwer, Dordrecht, 2001)

The experimental curves can be fitted with a simple phenomenological function P. Mohanti and R. A. Webb, PRB 55 (1997) R13452

When we extrapolate this behavior up to room temperature we find a decoherence time ≈ 80 ps With this decoherence time and the electron thermal speed we find a decoherence length of about 10 µm

Apart from solving the “fresh electron problem”, decoherence leads to an alternative analysis of experimental data slab of copper conductor z L the path of an electron defines a tube with radius equal to the decoherence length; electrons in this tube can entangle their wavefunction with the moving electron’s wavefunction tube volume number of atoms in the tube

During the walk from the entrance to the exit each electron would establish an entanglement with electrons up to the decoherence distance, as shown here vdrift

If this preliminary analysis is confirmed, it means that the “fresh electron problem” is solved the analysis gives a much better bound (about 104 improvement) the contribution of self-diffusion is negligible if do we detect anything, then there should be a well-defined dependence on temperature

VIP2

Drawbacks of VIP: Reused an already done setup (DEAR experiment) – limitations in many aspects: signal and background No timing (trigger) capabilities Limited energy (efficiency) range (30 microns) ....... VIP-upgrade: Use new detectors – triggerable SDD 300 microns – more efficient in a broader energy range Design a new setup – much more compact; higher acceptance (present one 2.8%) and lower background gain a factor of 100!

VIP physics  of interest!!! the only experiment checking PEP for elementary particle (electron) with a proper method (see VIP report) – superselection rule of Messiah - Greenberg Because we think we can improve the limit by 2 orders of magnitude (new detectors – triggerable, more compact geometry – bigger acceptance and smallr background) COST Action 1006 (EU program) Competitor experiment – S.R. Elliott et al. – Found. of Phys. -

SDD detectors (usati in SIDDHARTA)

Spin Statistics: (VIP) at LNGS VIP limit on the probability of PEP violation: VIP-2 (to be installed at LNGS in 2014) We have thus improved the previous limit by about 2 orders of magnitude In next 10-15 years: go to10-32 – 10-33 (-37 ?) “Hopefully either violation will be found experimentally or our theoretical efforts will lead to understanding of why only bose and fermi statistics occur in Nature” (Greenberg)