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  • Neutrinoless Double Beta Decay and Particle Physics

    Werner Rodejohann

    (MPIK, Heidelberg)

    Teilchentee

    8/12/11

    1

  • Outline

    (A, Z) (A, Z + 2) + 2 e (0) Lepton Number Violation

    Introduction

    Standard Interpretation (neutrino physics)

    Non-Standard Interpretations (BSM 6= neutrino physics)

    review on 0 and particle physics:

    W.R., Int. J. Mod. Phys. E20, 1833-1930 (2011)

    2

  • Why should we probe Lepton Number Violation (LNV)?

    L and B accidentally conserved in SM

    effective theory: L = LSM + 1 LLNV + 12 LLFV, BNV, LNV + . . .

    baryogenesis: B is violated

    B, L often connected in GUTs

    GUTs have seesaw and Majorana neutrinos

    (chiral anomalies: JB,L = c G G 6= 0 with JB =

    qi qi and

    JL =

    i i)

    Lepton Number Violation as important as Baryon Number Violation(0 is much more than a neutrino mass experiment)

    3

  • What is Neutrinoless Double Beta Decay?

    (A, Z) (A, Z + 2) + 2 e (0)

    second order in weak interaction: G4F rare!

    not to be confused with (A, Z) (A, Z + 2) + 2 e + 2 e (2)(which occurs more often but is still rare)

    4

  • Need to forbid single decay:

    even/even even/even either direct (0) or two simultaneous decays with virtual (energetically

    forbidden) intermediate state (2)

    5

  • '(

    )#*

    +

    ,-,-

    Slide by A. Giuliani

    6

  • Upcoming experiments: exciting time!!

    current best limit from 2001. . .

    Name Isotope source = detector; calorimetric with source 6= detector

    high energy res. low energy res. event topology event topology

    CANDLES 48Ca X

    COBRA 116Cd (and 130Te) X

    CUORE 130Te X

    DCBA 82Se or 150Nd X

    EXO 136Xe X

    GERDA 76Ge X

    KamLAND-Zen 136Xe X

    LUCIFER 82Se or 100Mo or 116Cd X

    MAJORANA 76Ge X

    MOON 82Se or 100Mo or 150Nd X

    NEXT 136Xe X

    SNO+ 150Nd X

    SuperNEMO 82Se or 150Nd X

    XMASS 136Xe X

    multi-isotope determination good for 3 reasons

    7

  • Experiment Isotope Mass of Sensitivity Status Start of

    Isotope [kg] T 01/2 [yrs] data-taking

    GERDA 76Ge 18 3 1025 running 2011

    40 2 1026 in progress 2012

    1000 6 1027 R&D 2015

    CUORE 130Te 200 6.5 1026 in progress 2013

    2.1 1026

    hline MAJORANA 76Ge 30-60 (1 2) 1026 in progress 2013

    1000 6 1027 R&D 2015

    EXO 136Xe 200 6.4 1025 in progress 2011

    1000 8 1026 R&D 2015

    SuperNEMO 82Se 100-200 (1 2) 1026 R&D 2013-15

    KamLAND-Zen 136Xe 400 4 1026 in progress 2011

    1000 1027 R&D 2013-15

    SNO+ 150Nd 56 4.5 1024 in progress 2012

    500 3 1025 R&D 2015

    8

  • Interpretation of Experiments

    Master formula:

    0 = Gx(Q, Z) |Mx(A, Z) x|2

    Gx(Q, Z): phase space factor

    Mx(A, Z): nuclear physics

    x: particle physics

    9

  • Interpretation of Experiments

    Master formula:

    0 = Gx(Q, Z) |Mx(A, Z) x|2

    Gx(Q, Z): phase space factor; calculable

    Mx(A, Z): nuclear physics; problematic

    x: particle physics; interesting

    10

  • 3 Reasons for Multi-isotope determination

    1.) credibility

    2.) test NME calculation

    T 01/2(A1, Z1)

    T 01/2(A2, Z2)=

    G(Q2, Z2) |M(A2, Z2)|2G(Q1, Z1) |M(A1, Z1)|2

    systematic errors drop out, ratio sensitive to NME model

    3.) test mechanism

    T 01/2(A1, Z1)

    T 01/2(A2, Z2)=

    Gx(Q2, Z2) |Mx(A2, Z2)|2Gx(Q1, Z1) |Mx(A1, Z1)|2

    particle physics drops out, ratio of NMEs sensitive to mechanism

    11

  • Experimental Aspects

    particle theory:

    (T 01/2)1 (particle physics)2

    experimentally:

    (T 01/2)1

    a M t without background

    a

    M t

    B Ebackground-dominated

    Note: factor 2 in particle physics is combined factor of 16 in M t B E

    12

  • Standard Interpretation

    Neutrinoless Double Beta Decay is mediated by light and massive Majorana

    neutrinos (the ones which oscillate) and all other mechanisms potentially leading

    to 0 give negligible or no contribution

    W

    i

    i

    W

    dL

    dL

    uL

    eL

    eL

    uL

    Uei

    q

    Uei

    13

  • L 6= 0: Neutrinoless Double Beta DecayIm

    Rem

    mm

    ee

    ee

    ee

    (1)

    (3)

    (2)

    | |

    | || | e

    e.

    .

    eem

    2i2i

    Amplitude proportional to coherent sum (effective mass):

    |mee|

    U2ei mi =

    |Ue1|2 m1 + |Ue2|2 m2 e2i + |Ue3|2 m3 e2i

    actually,

    U2ei miq2 m2i

    U2ei miq2

    14

  • U =

    0

    BB@

    c12 c13 s12 c13 s13 ei

    s12 c23 c12 s23 s13 ei

    c12 c23 s12 s23 s13 ei

    s23 c13

    s12 s23 c12 c23 s13 ei

    c12 s23 s12 c23 s13 ei

    c23 c13

    1

    CCA

    =

    0

    BB@

    1 0 0

    0 c23 s23

    0 s23 c23

    1

    CCA

    | {z }

    0

    BB@

    c13 0 s13 ei

    0 1 0

    s13 ei 0 c13

    1

    CCA

    | {z }

    0

    BB@

    c12 s12 0

    s12 c12 0

    0 0 1

    1

    CCA

    | {z }

    atmospheric and SBL reactor solar and

    LBL accelerator LBL reactor

    15

  • U =

    0

    BB@

    c12 c13 s12 c13 s13 ei

    s12 c23 c12 s23 s13 ei

    c12 c23 s12 s23 s13 ei

    s23 c13

    s12 s23 c12 c23 s13 ei

    c12 s23 s12 c23 s13 ei

    c23 c13

    1

    CCA

    =

    0

    BB@

    1 0 0

    0 c23 s23

    0 s23 c23

    1

    CCA

    | {z }

    0

    BB@

    c13 0 s13 ei

    0 1 0

    s13 ei 0 c13

    1

    CCA

    | {z }

    0

    BB@

    c12 s12 0

    s12 c12 0

    0 0 1

    1

    CCA

    | {z }

    atmospheric and SBL reactor solar and

    LBL accelerator LBL reactor0

    BBB@

    1 0 0

    0q

    1

    2

    q1

    2

    0q

    1

    2

    q1

    2

    1

    CCCA

    0

    BB@

    1 0 0

    0 1 0

    0 0 1

    1

    CCA

    0

    BBB@

    q2

    3

    q1

    30

    q1

    3

    q2

    30

    0 0 1

    1

    CCCA

    (sin2 23 =1

    2) (sin2 13 = 0) (sin

    212 =

    1

    3)

    m2A

    m2A

    m2

    16

  • U =

    0

    BB@

    c12 c13 s12 c13 s13 ei

    s12 c23 c12 s23 s13 ei

    c12 c23 s12 s23 s13 ei

    s23 c13

    s12 s23 c12 c23 s13 ei

    c12 s23 s12 c23 s13 ei

    c23 c13

    1

    CCA

    =

    0

    BB@

    1 0 0

    0 c23 s23

    0 s23 c23

    1

    CCA

    | {z }

    0

    BB@

    c13 0 s13 ei

    0 1 0

    s13 ei 0 c13

    1

    CCA

    | {z }

    0

    BB@

    c12 s12 0

    s12 c12 0

    0 0 1

    1

    CCA

    | {z }

    atmospheric and SBL reactor solar and

    LBL accelerator LBL reactor0

    BBB@

    1 0 0

    0q

    1

    2

    q1

    2

    0q

    1

    2

    q1

    2

    1

    CCCA

    0

    BB@

    1 0

    0 1 0

    0 1

    1

    CCA

    0

    BBB@

    q2

    3

    q1

    30

    q1

    3

    q2

    30

    0 0 1

    1

    CCCA

    (sin2 23 =1

    2) (sin2 13 =

    2) (sin2 12 =1

    3)

    m2A

    m2A

    m2

    17

  • Tri-bimaximal Mixing

    UTBM =

    23

    13 0

    16

    13

    12

    16

    13

    12

    Harrison, Perkins, Scott (2002)

    with mass matrix

    (m)TBM = UTBM m

    diag U

    TBM =

    A B B

    12 (A + B + D) 12 (A + B D) 12 (A + B + D)

    A =1

    3

    (2 m1 + m2 e

    2i)

    , B =1

    3

    (m2 e

    2i m1)

    , D = m3 e2i

    Flavor symmetries. . .

    18

  • 19

  • The usual plot

    20

  • Crucial points

    NH: can be zero!

    IH: cannot be zero! |mee|inhmin =

    m2A c213 cos 212

    gap between |mee|inhmin and |mee|normax

    QD: cannot be zero! |mee|QDmin = m0 c213 cos 212 QD: cannot distinguish between normal and inverted ordering

    21

  • 0 and Ue3

    0.0001 0.001 0.01 0.1 1m @eVD

    0.0001

    0.001

    0.01

    0.1

    1

    mee@eVD Dm31

    2 < 0

    Dm312 > 0

    sin2 213 = 0

    Dis

    fav

    ore

    db

    yC

    osm

    olo

    gy

    Disfavored by 0

    0.0001 0.001 0.01 0.1 1m @eVD

    0.0001

    0.001

    0.01

    0.1

    1

    mee@eVD

    0.0001 0.001 0.01 0.1 1m @eVD

    0.0001

    0.001

    0.01

    0.1

    1

    mee@eVD Dm31

    2 < 0

    Dm312 > 0

    sin2 213 = 0.10

    Dis

    fav

    ore

    db

    yC

    osm

    olo

    gy

    Disfavored by 0

    0.0001 0.001 0.01 0.1 1m @eVD

    0.0001

    0.001

    0.01

    0.1

    1

    mee@eVD

    22

  • Plot against other observables

    0.01 0.1m (eV)

    10-3

    10-2

    10-1

    100

    (eV

    )

    Normal

    CPV(+,+)(+,-)(-,+)(-,-)

    0.01 0.1

    Inverted

    CPV(+)(-)

    12

    10-3

    10-2

    10-1

    100

    (eV

    )0.1 1

    mi (eV)

    Normal

    CPV(+,+)(+,-)(-,+)(-,-)

    0.1 1

    Inverted

    CPV(+)(-)

    Complementarity of |mee| = U2ei mi , m =

    |Uei|2 m2i and =

    mi

    23

  • Neutrino Mass Matrix

    24

  • Which mass ordering with which life-time?

    m |mee|NH

    m2A

    m2 + |Ue3|2m2A

    m2 + |Ue3|2

    m2Ae2i()

    0.05 eV 0.01 eV 0.003 eV T 01/2 > 102829 yrsIH 2

    m2A

    m2A

    m2A

    1 sin2 212 sin2 0.1 eV 0.05 eV 0.03 eV T 01/2 > 102627 yrs

    QD 3m0 m0 m0

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