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Pauli exclusion principle (PEP) · Pauli exclusion principle (PEP) violation The exclusion principle was postulated by Pauli

Jun 23, 2020



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  • Pauli exclusion principle (PEP) violationThe exclusion principle was postulated by Pauli in 1925 to explain atomic spectra

    and regularities of the Periodic Table of the elements.

    In modern Quantum Field Theory the PEP is related to the spin statistics and

    automatically arises from the anti-commutation property of the fermion creation

    and destruction operators

    Although all the well known successes of the PEP in explaining phenomena the

    exact validity of the PEP is still an open question

    Despite the fact that the foundation of PEP lies deep in the structure of Quantum

    Field Theory a simple and easy explanation is still missing

    General principles of quantum theory do not require that all the particles must be

    either fermions or bosons, but also generalized statistics could be considered

    Similar arguments have inspired many experimental tests of the PEP validity with

    improved sensitivities since the first pioneering experiments in 1948


    In particular, four classes of experiments have been considered so far:

    1. searches for PEP-forbidden electronic states

    2. searches for PEP-forbidden nuclear states

    3. searches for PEP-forbidden electronic transitions

    4. searches for PEP-forbidden nuclear transitions

  • Since 1948 many experimental tests of CNC processes have been performed

    The first test was the search for possible PEP-forbidden (PEPf) electronic states

    The best sensitivities obtained for 4 classes of experiments for PEPf states are:

    Experimental tests for PEP violation

    Experiment Result Ref.

    searches for PEPf

    electronic states in atoms

    [12C']/[12C] < 2.5∙10-12

    [Be']/[Be] < 9∙10-12A.S. Barabash et al., JETPL 68 (1998) 112

    D. Javorsek II et al., PRL 85 (2000) 2701

    searches for PEPf nuclear

    states[5He']/[4He] < 2∙10-15 E. Nolte et al., J. Phys. G 17 (1991) S355

    searches for PEPf

    electronic transitions

    δ2< 4.7∙10-29

    δ2< 1.1∙10-46

    δ2 < 1.3∙10-47

    C. Curceanu et al., JP:Con.Se. 306(2011)012036

    H. Ejiri et al., NPB(Proc.Sup.) 28A (1992) 219

    R. Bernabei et al., EPJC 62 (2009) 327

    searches for PEPf nuclear


    δ2 < 3-4∙10-55

    δ2< 4.1∙10-60R. Bernabei et al., EPJC 62 (2009) 327

    G. Bellini et al., PRC 81 (2010) 034317

    It is worth noting that in 1980 Amado & Primakoff [PRC 22(1908)1338] criticized the

    possibility of testing the Pauli principle by looking for PEP-forbidden transitions.

    However their arguments can be evaded either as demonstrated in PRL

    68(1992)1826 or PRD39(1989)2032 (for example extra dimensions could lead to

    apparent PEP violations)

    Thus experimental tests of PEPf transitions can also investigate the deep structure

    of matter and/or of space-time

  • Charge Non-Conserving (CNC) processes

    Electric Charge Conservation (CC) is a fundamental law in QED

    This law is correlated with gauge invariance and photon mass (Weinbergtheorem)

    The possibility that CC may be broken in future unified theories and the relative implications have been discussed in last years since the first experimental test in 1959

    At present no self-consistent theories have been developed, but in some modern theories (for example extra-dimensions) these processes can bepossible

    In 1978 Zeldovich, Voloshin and Okun considered problems due to a

    phenomenological description of CNC processes; they demonstrated that

    CNC can not be due to a spontaneus breaking if photon mass is zero

    CNC processes are possible if photon mass is not zero

  • Since 1959 many experimental tests fot CNC processes have been done

    The first test was the search for electron decay, but other possible processes have been considered

    The best sensitivities obtained for some CNC precesses are:

    Experimental tests for CNC processes

    Process τ (yr) Ref.

    CNC-β decay (71Ga) >1.4∙1027 M. Torres et al. MPLA 19 (2004) 639

    p→anything >4∙1023 V.I. Tretyak & Yu.G. Zdesenko PLB 505 (2001) 59

    p→invisibile >2.1∙1029 S. N. Ahmed et al. PRL 92 (2004) 102004

    n→invisibile >5.8∙1029 T. Araki et al. PRL 96 (2006) 101802

    pp→invisibile >5.0∙1025 H.O. Back et al. Phys. Lett. B 563 (2003) 23

    nn→invisibile >1.4∙1030 T. Araki et al. PRL 96 (2006) 101802

    nnp→invisibile >1.4∙1022 R.Bernabei et al., EPJA 27,s01(2006)35

    npp→invisibile >2.7∙1022 R.Bernabei et al., EPJA 27,s01(2006)35

    ppp→invisibile >3.6∙1022 R.Bernabei et al., EPJA 27,s01(2006)35

    e-→invisible >2.4∙1024 P.Belli et al. PLB 460(1999)236

    e-→νeγ >4.6∙1026 H. O. Back et al. PLB 525(2002)29

    CNC-Elect. Capt. (129Xe) >3.7∙1024 P.Belli et al. PLB 465(1999)315

    [S.N.Gninenko, arXiv:0707.3492]

  • DAMA/R&DDAMA/LXe low bckg DAMA/Ge for sampling meas.




    + by-products and small scale expts.: INR-Kiev+ neutron meas.: ENEA-Frascati+ in some studies on bb decays (DST-MAE project): IIT Kharagpur, India


  • DAMA/LXe: results on CNC processes

    • Electron decay into invisible channels [Astrop.P.5(1996)217]

    • Nuclear level excitation of 129Xe during CNC processes


    • N, NN decay into invisible channels in 129Xe [PLB493(2000)12]

    • Electron decay: e- νeγ [PRD61(2000)117301]

    • CNC decay 136Xe 136Cs [Beyond the Desert(2003)365]

    • N, NN, NNN decay into invisible channels in 136Xe

    [EPJA27 s01 (2006) 35]

    • CNC decay 139La 139Ce [UJP51(2006)1037]

    DAMA/R&D set-up: results on CNC processes

    • Possible Pauli exclusion principle violation


    • CNC processes [PRC60(1999)065501 ]

    • Electron stability and non-paulian transitions in Iodine

    atoms (by L-shell) [PLB460(1999)235]

    DAMA/NaI: results on CNC processes and PEPv

  • 25 x 9.7 kg NaI(Tl) in a 5x5 matrix

    Two Suprasil-B light guides directly coupled to each bare crystal

    Two PMTs working in coincidence at the single ph. el. threshold

    5.5-7.5 phe/keV

    DAMA/LIBRA set-up

    • All the materials selected for low radioactivity

    • Multicomponent passive shield (>10 cm of Cu, 15 cm of Pb + Cd foils,

    10/40 cm Polyethylene/paraffin, about 1 m concrete, mostly outside the


    • Three-level system to exclude Radon from the detectors

    Glove-box for


    Electronics + DAQ


    Glove-box for


    Electronics + DAQ


    • Calibrations in the same running conditions as production runs

    • Installation in air conditioning + huge heat capacity of shield

    • Monitoring/alarm system; many parameters acquired with the production data

    • Pulse shape recorded by Waweform Analyzer Acqiris DC270 (2chs per detector), 1 Gsample/s, 8 bit, bandwidth 250 MHz

    • Data collected from single photoelectron up to MeV region, despite the hardware optimization was done for the low energy

  • The new DAMA/LIBRA set-up ~250 kg NaI(Tl)(Large sodium Iodide Bulk for RAre processes)

    detectors during installation; in the

    central and right up detectors the

    new shaped Cu shield surrounding

    light guides (acting also as optical

    windows) and PMTs was not yet


    Residual contaminations in the new DAMA/LIBRA NaI(Tl) detectors:

    232Th, 238U and 40K at level of 10-12 g/g

    installing DAMA/LIBRA detectors

    assembling a DAMA/ LIBRA detector

    filling the inner Cu box with further shield

    closing the Cu box

    housing the detectors

  • ...calibration procedures

    • Radiopurity,performances, procedures, etc.: NIMA592(2008)297• Results on DM particles: DM Annual Modulation Signature: EPJC56(2008)333, EPJC67(2010)39

    Results on rare processes: PEP violation in Na and I: EPJC62(2009)327

  • 1) Search for non-paulian nuclear processes

    This process was studied in 1997 with

    DAMA/NaI set-up obtaining a sensitivity of

    > 0.7 × 1025 y for 23Na (68% C.L.)

    > 0.9 × 1025 y for 127I (68% C.L.)

    Example of a process PEP violating:deexcitation of a nucleon from the shell Ni to theN0 lower (full) shell

    The energy is converted to another nucleon atshell N through strong interaction, resulting toexcitation to the unbound region (analogy:Augér emission)

    PEP forbidden transitions (1/2)Underground experimental site and highly radiopure set-up allow to reduce

    background due to PEP-allowed transitions induced by cosmic rays and due

    to environmental radioactivity



    internal ’s

    PLB 408 (1997) 439

  • Electronic configuration schema of I anion (54 electrons) in Na+I- crystal




    s p d

    example of a PEP violating transition of Iodine electron to the full L-shell followedby the atomic shells rearrangement

    The total released energy (X-ray + Augér electrons) is approximately equal to L-shell ionization potential ( ≈ 5 keV)

    PEP violating electron

    PEP forbidden transitions (2/2)

    2) Search for non-paulian electronic transitions to L-shell

    In 1999 DAMA searched for this process in DAMA/NAI obtaining the sensitivity:

    τ > 4.2×1024 yr (68% C.L.) [P. Belli et al., PLB 460 (1999) 236]

  • PEP-violating nuclear processes (1/2)

    Above 10 MeV background due to very high energy muons

    possibly surviving the mountain.

    Continous line:

    bkg muon events

    evaluated by MC

    not present in the

    inner core (veto)

    For E > 10 MeV:

    17 events in the

    upper/lower plane

    of detector (10


    0 events in the

    central planes of

    detector (14 cryst.)

    EPJC 62 (2009) 327570h running time, optimized for very high energy

    For PEP violatingnuclear processes:events where just one detector fires

    Mainly particlesfrom internal contaminants

  • I II II II I




    I II II II I

    Lower limit on the mean life for non-paulianproton emission in frame b) (90% C.L.):

    > 2 x 1025 y for 23Na > 2.5 x 1025 y for 127I

    cautious approach:

    PEP-violating nuclear processes (2/2)


    a) Fermi momentum distribution with

    kF = 255 Mev/c

    b) 56Fe momentum distribution accounting

    for correlation effects

    EPJC 62 (2009) 327

  • Exposure: 0.53 ton × yr

    This limit can also be related to a possible finite size of the electron in composite models of

    quarks and leptons providing superficial violation of the PEP

    de2 < 1.28 10-47 (90% C.L.).

    PV > 4.7 x 1030 s (90% C.L.)


    considering normal electromagneticdipole transition to Iodine K-shell:

    0 ≈ 6 x 10-17 s

    one order of magnitude more stringent

    than the previous one (ELEGANTS V)

    PEP-violating electron processes

    The obtained upper limit on the electron size is:

    r0 < 5.710-18 cm (energy scale E > 3.5 TeV)

    [PRL 68(1992)1826]

    EPJC 62 (2009) 327

  • Possible electron decay CNC:


    e-→νe ν ν


    e-+(A,Z) → νe+(A,Z)* [CNC electron capture]

    (A,Z) → νe+(A,Z+1)*+νe [CNC β-decay]

    electron disappearance

    Searches for invisible decays are also related with extra-dimensions:

    Probably, our world is a brane inside higher-dimensional space

    Particles can escape from the brane to extra dimensions

    “The presence and properties of the extra dimensions will be investigated

    by looking for any loss of energy from our 3-brane into the bulk” [N.Arkani-Hamed et al., PLB 429(1998)263]

    Thus we could expect disappearance of e, p, n...

    η(p→nothing) = 9.2×1034 y η(e → nothing) = 9.0×1025 yr[S.L.Dubovsky, JHEP 01(2002)012]

  • CNC Electron capture (1/5)e-+(A,Z) → νe+(A,Z)* This process is more probable by K-shell electrons!

    In NaI(Tl) detectors the possible excited states that can be produced by this process are: 127I four possible excited states: 57.6 keV, 202.8 keV, 375 keV and 418 keV23Na one excited state at 440 keV

    We search for γ emitted in de-excitation processes

    238.6 keV(212Pb)

    338.3 keV(228Ac)

    DAMA/LIBRA high-energy distribution

    This process is followed by relaxation of the atomic shellswith emissions at energy = electron disappeared boundingenergy Eb

    Na: EK = 1.1 keV

    I: EK = 33.3 keV

    We choose preliminarly to study the production of 127I in the excited level 418 keV

    To improve our sensitivity and reduce the background we search for events in coincidence

    Each CNC electron capture in Iodine produces X-rays/Augér electrons at 33.3 keV and γ emission due to de-

    excitation processes of 127I (for example for the 418 keV level γ energies 418 keV, 203 keV and 360 keV)

    Exposure 0.87 ton × yr

  • CNC Electron capture (2/5)With Montecarlo simulation (3600000 events) we obtain:

    Expected distribution for

    events in coincidence

    with multiplicity 2

    Peak at 33.3 keV Fixing the energy

    window 24.7-41.9keV

    in one detector

    We expect a peak

    at energy 418 keV

    due to 127I de-


    Selection of events in coincidence with multiplicity 2 in DAMA/LIBRA (0.87 ton×yr

    exposure) in the energy window 24.7-41.9 keV for the first one and 371.6-464.4 keV for

    the second one gives 26273 candidates events for this process

    Using 1ζ-approach we obtain for the expected signal S < 162 events (68% C.L.)

    Considering that each Iodine has 2 electron in K-shell we obtain:

    η > 1.9 × 1024 yr (68% C.L.)

    Efficiency for this

    coincidence is 4.5%

    EGSnrc Montecarlo simulation EGS





    rlo s




  • CNC Electron capture (3/5)

    Montecarlo expectation Experimental data

    The experimental data with multiplicity 2 don’t show the expected structures for

    events in coincidence: No evidence for any signal!

    No correlated events in coincidence!

    Comparison of experimental data distribution

    with Montecarlo expectation

  • CNC Electron capture (4/5)Data selection with multiplicity 2 and the first event

    in the energy window 24.7-41.9 keV reduces the

    background of a factor larger than 103

    Fittting data with a sum of an exponential function

    for the continous background and the expected peak

    we obtain: S = - (260 ± 296) events


    Best limits previously obtained for this process by:

    DAMA/NaI for the production of excited levels of 127I: η> 2.4·1023 yr

    [P.Belli et al., PRC 60(1999)065501]

    DAMA/LXe for the production of excited levels of 129Xe: η>3.7·1024 yr

    [P.Belli et al., PLB 465(1999)315]

    The obtained limit is the best one available for this process in NaI(Tl)

    Using Feldman and Cousins procedure:

    S < 264 events (90% C.L.), corresponding to:

    τ>1.2 × 1024 yr (90% C.L.)

  • CNC Electron capture (5/5)The transition probability for the CNC process can be written in therm of a process

    mediated by photon exchange or by W-boson exchange:

    [Nuclear Data Sheet 112(2011)1647; T. Kibèdi et al., NIMA 589(2008)202]

    The CC process can be estimated theoretically (i-initial state, f-final state, n all the

    possible intermediate states)

    Considering the excited state at 418 keV and the obtained limit: τ > 1.2 × 1024 yr (90% C.L.)

  • Preliminary analysis exploits the total DAMA/LIBRA published

    exposure: 0.87 ton × yr212Pb γ-emission at 238.6 keV estimated by MC considering the

    experimental energy resolution

    Fit of the energy distribution in the region [193, 293] keV with a

    sum of: (i) an exponential; (ii) energy distribution due to 212Pb

    decay; (iii) the possible signal due to the CNC process searched

    for obtained activity of the possible e → νeγ decay

    (χ2/d.o.f. = 1.2): A = - (1.2±1.3) mBq

    By Feldman & Cousins procedure: A

  • Further analysis: we selected the 7 detectors (of the 25 ones in DAMA/LIBRA) which have thelower contribution from 212Pb residual contamination in the set-up; exposure is 0.25 ton × yr

    The same fitting procedure used above has been applied in the same energy range

    The fit (χ2/d.o.f. = 1.1) gives for the possible e → νeγ decay the

    activity: A=−(1.0 ± 2.2) mBq

    Using Feldmann and Cousins procedure: A 2.0×1026 yr (90% C.L.) [P.Belli et al., PRD 1(2000)117301]

    -10.96 kg HP-Ge HD-MW: τ > 1.9×1026 yr (68% C.L.) [H.V. Klapdor-Kleingrothaus et al., PLB 644(2007)109]

    - ~4 ton PXE scintillator BOREXINO: τ > 4.6×1026 yr (90% C.L.) [H. O. Back et al., PLB 525(2002)29]

    Our best limit: τ > 4.0×1025 yr

    ε2e→γν < 2.6×10−98

    It is the best-one with NaI(Tl) detectors, the previous one

    was: η > 3.5×1023 yr [E.L. Koval’chuk et al. JETP Lett. 29, 145 (1979)]

    Exposure 0.25 ton × yr

    e-→γνe (2/3)

  • e-→γνe (3/3)This process gives the most restrictive limit on ε2 (

  • Process τ (yr) (this work) τ (yr) (previous best limit) [Ref.]

    e-→νγ>1.3×1025 (68% C.L.)

    >4.6×1026 (90% C.L.) [H. O. Back et al., PLB 525(2002)29]

    (in NaI) >3.5×1023 (68% C.L.) [E.L. Koval’chuk et al., JETPL29(1979)145 ]

    EC-CNC (127I) >1.2×1024 (90% C.L.) >2.4·1023 (90% C.L.) [P.Belli et al., PRC 60(1999)065501]

    We obtain the best limits available on the life-time of CNC processes for NaI(Tl)

    detectors and the best limits available on CNC electron capture.

    For the PEP-forbidden transitions the obtained limits on electron transition

    probability by DAMA/LIBRA is the best available in literature.

    For nuclear transition BOREXINO obtained a more stringent limit in 2010

    Processδ2 (yr) DAMA/LIBRA

    [EPJC 62 (2009) 327]δ2 (yr) (best limit by other experiments) [Ref.]



  • Process ε2 (this work) ε2 (previous best limit) [Ref.]


  • Perspectives for further CNC investigations with DAMA/LIBRA (1/2)

    Other possible studies:

    Complete the search for 23Na and 127I CNC

    Electron-Capture investigating other excited


    Search for possible nucleons disappearance

    (neutron, proton, diproton...)

    Study for possible electrons disappearance

    Possible studies on electron disappearance from L-shelll can be pursued

    Considering ηe→invisible (from K-shell) ≈ 0.024 ηe→invisible (from L-shell) [PLB 460

    (1999) 236] and that the electron PEP-forbidden transitions give the same

    experimental signal of electron disappearance for this electron’s decay

    From ηe→invisible (K-shell) < 4.7 × 1030 s we can estimate an experimental

    sensitivity for ηe→invisible (from L-shell) ≈ 1025 years

    CNC processes are correlated to other fundamental questions, in particular

    searches for invisible decays are related also with: extra-dimensions and Pauli

    Exclusion Principle violation

  • [S.L.Dubovsky, JHEP 01(2002)012]

    Search for particle disappearance can constrain theoretical models with

    extradimensions where particles are considered localized in a three-brane

    world. In this scenario particles at low energy are described by the

    eigenvalue: E=E0-iΓ/2 where Γ is a resonance which can be interpreted as a

    four-dimensional metastable particle

    Particles disappearance is due to tunneling from the three-brane world to the

    extra-dimension. Γ depends on the number of extradimensions “n”

    For electron disappearance considering k ≈ Planck mass ≈ 1019 GeV the best

    available limit on ηe→nothing constrains the number of extradimension to n > 2

    (ηe→nothing for n=3 is 9×1025 yr)

    The estimated sensitivity on ηe→nothing could be used to give a more stringent

    limit on the number of extradimensions

    Perspectives for further CNC investigations with DAMA/LIBRA (2/2)

  • Search for non-paulianelectronic transitions to L-shell

    Accessible sensitivity with

    DAMA/LIBRA ηe→invisible ≈ 10

    25 years

    The lowering of the software energy

    threshold of the experiment down to about 1

    keV may give the possibility to investigate for

    the first time processes involving Sodium K-

    shell (≈1 keV)

    Perspectives for PEP investigations with DAMA/LIBRA

    Search for non-paulian electronic transitions to K-shellDAMA/LIBRA upgrade (2010)

    • Replacement of all the PMTs with higher Q.E. ones

    • Goal: lowering the energy thresholds

    PLB 460 (1999) 236

  • “If something in fundamental physics can be tested, then it absolutely must be tested“ [L.B. Okun]