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Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia P HENOMENOLOGY WITH M ASSIVE N EUTRINOS Concha Gonzalez-Garcia (YITP Stony Brook & ICREA U. Barcelona ) UB, June 1tth, 2016 Neutrino Flavour Transition: Data and Interpretation Some Implications for/from Cosmology http://www.nu-fit.org

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  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    PHENOMENOLOGY WITH MASSIVE

    NEUTRINOS

    Concha Gonzalez-Garcia

    (YITP Stony Brook & ICREA U. Barcelona )

    UB, June 1tth, 2016

    Neutrino Flavour Transition: Data and Interpretation

    Some Implications for/from Cosmology

    http://www.nu-fit.org

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    p

    Sources of ν’s

    Concha Gonzalez-Garcia

    The Big Bang

    ρν = 330/cm3

    pν =0.0004 eVSN1987

    Eν ∼ MeV

    ExtraGalactic

    Eν & 30 TeV

    The Sun

    νe

    ΦEarthν = 6× 1010ν/cm2sEν ∼ 0.1–20 MeV

    Atmospheric ν′s

    νe, νµ, νe, νµΦν ∼ 1ν/cm2sHuman Body

    Φν = 340× 106ν/day

    Nuclear Reactors

    νe

    Eν ∼ few MeV

    Accelerators

    Eν ≃ 0.3–30 GeVEarth’s radioactivity

    Φν ∼ 6× 106ν/cm2s

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Neutrinos in the Standard Model

    The SM is a gauge theory based on the symmetry group

    SU(3)C × SU(2)L × U(1)Y ⇒ SU(3)C × U(1)EM

    With three generation of fermions

    (1, 2)− 12 (3, 2)16

    (1, 1)−1 (3, 1) 23(3, 1)− 13

    (

    νee

    )

    L

    (

    ui

    di

    )

    LeR u

    iR d

    iR

    (

    νµµ

    )

    L

    (

    ci

    si

    )

    LµR c

    iR s

    iR

    (

    νττ

    )

    L

    (

    ti

    bi

    )

    LτR t

    iR b

    iR

    Three and only three

    There is no νR

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Neutrinos in the Standard Model

    The SM is a gauge theory based on the symmetry group

    SU(3)C × SU(2)L × U(1)Y ⇒ SU(3)C × U(1)EM

    With three generation of fermions

    (1, 2)− 12 (3, 2)16

    (1, 1)−1 (3, 1) 23(3, 1)− 13

    (

    νee

    )

    L

    (

    ui

    di

    )

    LeR u

    iR d

    iR

    (

    νµµ

    )

    L

    (

    ci

    si

    )

    LµR c

    iR s

    iR

    (

    νττ

    )

    L

    (

    ti

    bi

    )

    LτR t

    iR b

    iR

    Three and only three

    There is no νR⇒Accidental global symmetry: B × Le × Lµ × Lτ (hence L = Le + Lµ + Lτ )⇒

    ν strictly massless

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    • By 2016 we have observed with high (or good) precision:∗ Atmospheric νµ & ν̄µ disappear most likely to ντ (SK,MINOS, ICECUBE)∗ Accel. νµ & ν̄µ disappear at L ∼ 300/800 Km (K2K, T2K/ MINOS, NOνA)∗ Some accelerator νµ appear as ντ at L ∼ 700 Km ( OPERA)∗ Some accelerator νµ appear as νe at L ∼ 300/800 Km ( T2K, MINOS,NOνA)∗ Solar νe convert to νµ/ντ (Cl, Ga, SK, SNO, Borexino)∗ Reactor νe disappear at L ∼ 200 Km (KamLAND)∗ Reactor νe disappear at L ∼ 1 Km (D-Chooz, Daya Bay, Reno)

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    • By 2016 we have observed with high (or good) precision:∗ Atmospheric νµ & ν̄µ disappear most likely to ντ (SK,MINOS, ICECUBE)∗ Accel. νµ & ν̄µ disappear at L ∼ 300/800 Km (K2K, T2K/ MINOS, NOνA)∗ Some accelerator νµ appear as ντ at L ∼ 700 Km ( OPERA)∗ Some accelerator νµ appear as νe at L ∼ 300/800 Km ( T2K, MINOS,NOνA)∗ Solar νe convert to νµ/ντ (Cl, Ga, SK, SNO, Borexino)∗ Reactor νe disappear at L ∼ 200 Km (KamLAND)∗ Reactor νe disappear at L ∼ 1 Km (D-Chooz, Daya Bay, Reno)

    All this implies that Lα are violated

    and There is Physics Beyond SM

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    The New Minimal Standard Model

    • Minimal Extension to allow for LFV ⇒ give Mass to the Neutrino

    ∗ Introduce νR AND impose L conservation ⇒ Dirac ν 6= νc:L = LSM −MννLνR + h.c.

    ∗ NOT impose L conservation ⇒ Majorana ν = νcL = LSM − 12MννLνCL + h.c.

    _ _

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    The New Minimal Standard Model

    • Minimal Extension to allow for LFV ⇒ give Mass to the Neutrino

    ∗ Introduce νR AND impose L conservation ⇒ Dirac ν 6= νc:L = LSM −MννLνR + h.c.

    ∗ NOT impose L conservation ⇒ Majorana ν = νcL = LSM − 12MννLνCL + h.c.

    • The charged current interactions of leptons are not diagonal (same as quarks)g√2W+µ

    ij

    (

    U ijLEP ℓi γµ Lνj + U ijCKM U

    i γµ LDj)

    + h.c.

    j

    W+

    l_

    i

    ν

    W+

    _

    i

    uj

    d

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garciaν Mass Oscillations in Vacuum

    • If neutrinos have mass, a weak eigenstate |να〉 produced in lα + N →να + N ′

    is a linear combination of the mass eigenstates (|νi〉) : |να〉=n∑

    i=1

    Uαi |νi〉

    • After a distance L it can be detected with flavour β with probability

    Pαβ = δαβ − 4n∑

    j 6=i

    Re[U⋆αiUβiUαjU⋆βj ]sin

    2

    (

    ∆ij2

    )

    + 2∑

    j 6=i

    Im[U⋆αiUβiUαjU⋆βj ]sin (∆ij)

    ∆ij2 =

    (Ei−Ej)L2 = 1.27

    (m2i−m2j )

    eV2L/E

    Km/GeV

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garciaν Mass Oscillations in Vacuum

    • If neutrinos have mass, a weak eigenstate |να〉 produced in lα + N →να + N ′

    is a linear combination of the mass eigenstates (|νi〉) : |να〉=n∑

    i=1

    Uαi |νi〉

    • After a distance L it can be detected with flavour β with probability

    Pαβ = δαβ − 4n∑

    j 6=i

    Re[U⋆αiUβiUαjU⋆βj ]sin

    2

    (

    ∆ij2

    )

    + 2∑

    j 6=i

    Im[U⋆αiUβiUαjU⋆βj ]sin (∆ij)

    ∆ij2 =

    (Ei−Ej)L2 = 1.27

    (m2i−m2j )

    eV2L/E

    Km/GeV

    No information on ν mass scale nor Majorana versus Dirac

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garciaν Mass Oscillations in Vacuum

    • If neutrinos have mass, a weak eigenstate |να〉 produced in lα + N →να + N ′

    is a linear combination of the mass eigenstates (|νi〉) : |να〉=n∑

    i=1

    Uαi |νi〉

    • After a distance L it can be detected with flavour β with probability

    Pαβ = δαβ − 4n∑

    j 6=i

    Re[U⋆αiUβiUαjU⋆βj ]sin

    2

    (

    ∆ij2

    )

    + 2∑

    j 6=i

    Im[U⋆αiUβiUαjU⋆βj ]sin (∆ij)

    ∆ij2 =

    (Ei−Ej)L2 = 1.27

    (m2i−m2j )

    eV2L/E

    Km/GeV

    No information on ν mass scale nor Majorana versus Dirac

    • For 2-ν: Pαα = 1− Posc DisappearPosc = sin

    2(2θ) sin2(

    1.27∆m2L

    E

    )

    Appear

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Matter Effects

    • If ν cross matter regions (Sun, Earth...) it interacts coherently

    – But Different flavours

    have different interactions :

    νe, νµ, ντ only νe

    Z W

    ν ν ν e

    e,N e,Ne ν

    ⇒ Effective potential in ν evolution : Ve 6= Vµ,τ ⇒ ∆V ν = −∆V ν̄ =√2GFNe

    ⇒ Modification of mixing angle and oscillation wavelength ≡ MSW effect

    • The mixing angle in matter

    sin(2θm) =∆m2 sin(2θ)

    (∆m2 cos(2θ)− 2E∆V )2 + (∆m2 sin(2θ))2

    • For solar neutrinos in adiabatic regime P (νe → νe) = 12 [1 + cos(2θm) cos(2θ)]

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia• By 2016 we have observed with high (or good) precision:∗ Atmospheric νµ & ν̄µ disappear most likely to ντ (SK,MINOS, ICECUBE)∗ Accel. νµ & ν̄µ disappear at L ∼ 300/800 Km (K2K, T2K, MINOS, NOνA)∗ Some accelerator νµ appear as ντ at L ∼ 700 Km ( OPERA)∗ Some accelerator νµ appear as νe at L ∼ 300/800 Km ( T2K, MINOS,NOνA)∗ Solar νe convert to νµ/ντ (Cl, Ga, SK, SNO, Borexino)∗ Reactor νe disappear at L ∼ 200 Km (KamLAND)∗ Reactor νe disappear at L ∼ 1 Km (D-Chooz, Daya Bay, Reno)

    • Confirmed:

    SK

    MINOS/T2K/NOvA

    (km/MeV)eν

    /E0L20 30 40 50 60 70 80 90 100

    Surv

    ival

    Pro

    babi

    lity

    0

    0.2

    0.4

    0.6

    0.8

    1

    eνData - BG - Geo Expectation based on osci. parameters

    determined by KamLAND

    KamLAND

    Daya-Bay/RENO/D-Chooz

    Vacuum oscillation L/E pattern with 2 frequencies

    MSW conversion in Sun

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia3ν Flavour Parameters

    • For for 3 ν’s : 3 Mixing angles + 1 Dirac Phase + 2 Majorana Phases

    ULEP =

    1 0 0

    0 c23 s23

    0 −s23 c23

    c13 0 s13eiδcp

    0 1 0

    −s13e−iδcp 0 c13

    c21 s12 0

    −s12 c12 0

    0 0 1

    eiη1 0 0

    0 eiη2 0

    0 0 1

    • Two Possible Orderings

    M

    sola

    r

    sola

    r

    atm

    os

    m m 1 3

    2

    ∆ m

    2

    m 3

    m 2

    ∆ m

    m 1

    m 2

    NORMAL INVERTED

    2

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia3ν Flavour Parameters

    • For for 3 ν’s : 3 Mixing angles + 1 Dirac Phase + 2 Majorana Phases

    ULEP =

    1 0 0

    0 c23 s23

    0 −s23 c23

    c13 0 s13eiδcp

    0 1 0

    −s13e−iδcp 0 c13

    c21 s12 0

    −s12 c12 0

    0 0 1

    eiη1 0 0

    0 eiη2 0

    0 0 1

    • Two Possible Orderings

    M

    sola

    r

    sola

    r

    atm

    os

    m m 1 3

    2

    ∆ m

    2

    m 3

    m 2

    ∆ m

    m 1

    m 2

    NORMAL INVERTED

    2

    Experiment Dominant Dependence Important Dependence

    Solar Experiments → θ12 ∆m221 , θ13Reactor LBL (KamLAND) → ∆m221 θ12 , θ13Reactor MBL (Daya Bay, Reno, D-Chooz) → θ13 ∆m2atmAtmospheric Experiments → θ23 ∆m2atm, θ13 ,δcpAcc LBL νµ Disapp (Minos,T2K,NOvA) → ∆m2atm θ23Acc LBL νe App (Minos,T2K,NOvA) → θ13 δcp , θ23

    ×

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia3 ν Flavour Parameters: Status in 6/2016

    Global 6-parameter fit http://www.nu-fit.org (ArXiv:1409.5439)Maltoni, Schwetz, Martinez-Soler, Esteban, MCG-G

    0.2 0.25 0.3 0.35 0.4

    sin2 θ12

    0

    5

    10

    15

    ∆χ2

    6.5 7 7.5 8 8.5

    ∆m221 [10-5

    eV2]

    0.3 0.4 0.5 0.6 0.7

    sin2 θ23

    0

    5

    10

    15

    ∆χ2

    -2.6 -2.4 -2.2

    ∆m232 [10-3

    eV2] ∆m231

    2.2 2.4 2.6 2.8

    0.015 0.02 0.025 0.03

    sin2 θ13

    0

    5

    10

    15

    ∆χ2

    0 90 180 270 360δCP

    NO, IO (LEM)

    NO, IO (LID)

    NuFIT 2.1 (2016)

    0.2 0.25 0.3 0.35 0.4

    sin2 θ12

    6.5

    7

    7.5

    8

    8.5

    ∆m2 21

    [10-

    5 eV

    2 ]

    0.015 0.02 0.025 0.03

    sin2 θ13

    0.015

    0.02

    0.025

    0.03

    sin2

    θ 13

    0

    90

    180

    270

    360

    δ CP

    0.3 0.4 0.5 0.6 0.7

    sin2 θ23

    -2.8

    -2.6

    -2.4

    -2.2

    2.2

    2.4

    2.6

    2.8

    ∆m2 32

    [1

    0-3

    eV2 ]

    m2 31

    NuFIT 2.1 (2016)

    θ23 6= 45

    θ23 < 45 ?

    N/I

    ?

    δcp

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    3ν Analysis: Leptonic CP violation

    • “Hint” CP phase around δCP = 3π2 (maximal)

    0 90 180 270δCP

    0

    2

    4

    6

    8

    10

    12

    14

    ∆χ2

    0 90 180 270 360δCP

    NuFIT 2.0 (updated)

    + DeepCore+ T2K ν+ NOνA (LEM, LID)

    NuFIT 2.1 (2016)

    IO NO

    • Leptonic Jarslog Determinant

    0.025 0.03 0.035 0.04

    JCPmax

    = c12 s12 c23 s23 c213 s13

    0

    5

    10

    15

    ∆χ2

    -0.04 -0.02 0 0.02 0.04

    JCP = JCPmax

    sinδCP

    NO, IO (LEM)

    NO, IO (LID)

    NuFIT 2.1 (2016)

    Potentially much larger than the quark sector JCMK =(

    3.06+0.21−0.20)

    × 10−5

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Issues with the Solar Fluxes

    – Newer determination of abundance of heavy

    elements in solar surface give lower values

    – Solar Models with these lower metalicities

    fail in reproducing helioseismology data

    – Two sets of SSM:Starting from Bahcall etal 05, Serenelli etal 0909.2668

    GS98 uses older metalicities

    AGSXX uses newer metalicities

    Flux GS98 AGSS09 Diff (%)cm−2 s−1

    pp/1010 5.97 6.03 (1± 0.005) 0.8

    pep/108 1.41 1.44 (1± 0.010) 2.1

    hep/103 7.91 8.18 (1± 0.15) 3.4

    7Be/109 5.08 4.64 (1± 0.06) 8.8

    8B/106 5.88 4.85 (1± 0.12) 17.7

    13N/108 2.82 2.07(1+0.14−0.13) 26.7

    15O/108 2.09 1.47 (1+0.16−0.15) 30.0

    17F/1016 5.65 3.48 (1+0.17−0.16) 38.4

    Most difference in CNO fluxes

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Issues with the Solar Fluxes

    – Newer determination of abundance of heavy

    elements in solar surface give lower values

    – Solar Models with these lower metalicities

    fail in reproducing helioseismology data

    – Two sets of SSM:Starting from Bahcall etal 05, Serenelli etal 0909.2668

    GS98 uses older metalicities

    AGSXX uses newer metalicities

    Flux GS98 AGSS09 Diff (%)cm−2 s−1

    pp/1010 5.97 6.03 (1± 0.005) 0.8

    pep/108 1.41 1.44 (1± 0.010) 2.1

    hep/103 7.91 8.18 (1± 0.15) 3.4

    7Be/109 5.08 4.64 (1± 0.06) 8.8

    8B/106 5.88 4.85 (1± 0.12) 17.7

    13N/108 2.82 2.07(1+0.14−0.13) 26.7

    15O/108 2.09 1.47 (1+0.16−0.15) 30.0

    17F/1016 5.65 3.48 (1+0.17−0.16) 38.4

    Most difference in CNO fluxes

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Issues with the Solar Fluxes

    – Newer determination of abundance of heavy

    elements in solar surface give lower values

    – Solar Models with these lower metalicities

    fail in reproducing helioseismology data

    – Two sets of SSM:Starting from Bahcall etal 05, Serenelli etal 0909.2668

    GS98 uses older metalicities

    AGSXX uses newer metalicities

    –Impact in Osc Parameter Determination

    Neglegeable ⇒ Possible to Invertand Extract Fluxes from Data.

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Learning how the Sun Shines with ν ′s

    Results of Oscillation analysis with solar flux normalizations free: fi =Φi

    ΦGS98i

    Bergstrom,MCG-G,Maltoni,Peña-Garay,Serenelli, Song,

    ArXiv:1601:00972

    Present limit on CNO:

    LCNOL⊙

    < 2% (3σ)

    Test of Luminosity Constraint:

    L⊙(ν − inferred)L⊙

    = 1.04± 0.07

    Comparing with the Models:

    Both statistically equally probable

    New experiments needed

    more sensitive to CNO fluxes

    New models with new Nuclear Rates

    New problems with Helioseismology

    Bergstrom,MCG-G,Maltoni,

    Peña-Garay,Serenelli,Song, in preparation

  • Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaBeyond 3ν’s: Light Sterile Neutrinos

    • Several Observations which can be Interpreted as Oscillations with ∆m2 ∼ eV2Reactor Anomaly

    New reactor flux calculation

    ⇒ Deficit in data at L . 100 m

    0.7

    0.8

    0.9

    1

    1.1

    1.2

    1.3

    obse

    rved

    / pr

    edic

    ted

    oldnew

    Bug

    ey 4

    RO

    VN

    O

    Bug

    ey 3

    Goe

    sgen

    ILL

    Kra

    snoy

    arsk

    } } } 235

    U23

    8 U23

    9 Pu

    241 P

    u

    Explained as νe disappearance

    Kopp etal, ArXiv 1303.3011

    Gallium AnomalyAcero, Giunti, Laveder, 0711.4222Giunti, Laveder,1006.3244

    Radioactive Sources (51Cr, 37Ar)

    in calibration of Ga Solar Exp;

    νe + 71Ga → 71Ge + e−

    Give a rate lower than expected

    R =Nobs

    NthBahc

    = 0.86± 0.05 (2.8σ)

    Explained as νe disappearance

    10� 3

    10� 2

    10�1

    10�1

    100

    101

    �Ue42

    �m

    412�eV2�

    95� CL

    Gallium

    C�12

    Kopp etal, ArXiv 1303.3011

    LSND, MiniBoone

    νµ → νe and ν̄µ → ν̄e

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Light Sterile Neutrinos

    • These explanations require 3+Ns mass eigenstates → Ns sterile neutrinos

    • Problem: fit togetherνe → νe disapp (REACT,Gallium,Solar, LSND/KARMEN)νµ → νe app (LSND,KARMEN,NOMAD,MiniBooNE,E776,ICARUS)νµ → νµ disapp (CDHS,ATM,MINOS,MiniBooNE)

    • Generically: P (νe → νµ) ∼ |U∗eiUµi| [i =heavier state(s)]

    But |Uei| constrained by P (νe → νe) disappearance dataAnd |Uµi| constrained by P (νµ → νµ) disappearance data}⇒ Severe tension

  • Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaLight Sterile Neutrinos:3+1

    • Comparing the parameters required to explain signals with bounds from disapp

    Kopp etal, ArXiv 1303.3011

    10�4 10� 3 10� 2 10�110�1

    100

    101

    sin 2 2 Θ Μe

    �m

    2

    disappearance

    appearance

    Giunti etal, ArXiv 1308.5288

    sin22ϑeµ

    ∆m412

    [e

    V2 ]

    10−4 10−3 10−2 10−1 110−1

    1

    10

    +

    10−4 10−3 10−2 10−1 110−1

    1

    10

    +

    3+1 − GLO

    68.27% CL90.00% CL95.45% CL99.00% CL99.73% CL

    3+1 − 3σνe DISνµ DISDISAPP

    Somewhat different conclusions

    Further Disfavoured by ICECUBE

    sin

    2

    24

    10

    −1

    10

    0

    10

    1

    ∆m

    2

    41

    /eV

    2

    SuperK

    MINOS

    M

    B

    /

    S

    B

    ν

    C

    D

    H

    S

    IceCube 90% CL

    90% CL sensitivity

    (68% and 95%)

    Kopp et al. (2013)

    10

    −2

    10

    −1

    10

    0

    sin

    2

    24

    10

    −2

    10

    −1

    10

    0

    ∆m

    2

    41

    /eV

    2

    SuperK

    MIN

    OS

    M

    B

    /

    S

    B

    ν

    C

    D

    H

    S

    IceCube 99% CL

    99% CL sensitivity

    (68% and 95%)

    Kopp et al. (2013)

  • Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaLight Sterile Neutrinos:3+1

    • Comparing the parameters required to explain signals with bounds from disapp

    Kopp etal, ArXiv 1303.3011

    10�4 10� 3 10� 2 10�110�1

    100

    101

    sin 2 2 Θ Μe

    �m

    2

    disappearance

    appearance

    Giunti etal, ArXiv 1308.5288

    sin22ϑeµ

    ∆m412

    [e

    V2 ]

    10−4 10−3 10−2 10−1 110−1

    1

    10

    +

    10−4 10−3 10−2 10−1 110−1

    1

    10

    +

    3+1 − GLO

    68.27% CL90.00% CL95.45% CL99.00% CL99.73% CL

    3+1 − 3σνe DISνµ DISDISAPP

    Somewhat different conclusions

    Further Disfavoured by ICECUBE

    sin

    2

    24

    10

    −1

    10

    0

    10

    1

    ∆m

    2

    41

    /eV

    2

    SuperK

    MINOS

    M

    B

    /

    S

    B

    ν

    C

    D

    H

    S

    IceCube 90% CL

    90% CL sensitivity

    (68% and 95%)

    Kopp et al. (2013)

    10

    −2

    10

    −1

    10

    0

    sin

    2

    24

    10

    −2

    10

    −1

    10

    0

    ∆m

    2

    41

    /eV

    2

    SuperK

    MIN

    OS

    M

    B

    /

    S

    B

    ν

    C

    D

    H

    S

    IceCube 99% CL

    99% CL sensitivity

    (68% and 95%)

    Kopp et al. (2013)

    More steriles help? Arguelles etal ArXiv:1602.00671

    More latter...

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Neutrino Mass Scale: Laboratory Probes

    Single β decay : Dirac or Majorana ν mass modify spectrum endpoint

    νm

    K (T)

    QT

    m2νe =∑

    m2j |Uej |2 = c213c212m21 + c213s212m22 + s213m23Present bound: mνe ≤ 2.2 eV (at 95 % CL)Katrin (2016?) Sensitivity to mνe ∼ 0.2 eV

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Neutrino Mass Scale: Laboratory Probes

    Single β decay : Dirac or Majorana ν mass modify spectrum endpoint

    νm

    K (T)

    QT

    m2νe =∑

    m2j |Uej |2 = c213c212m21 + c213s212m22 + s213m23Present bound: mνe ≤ 2.2 eV (at 95 % CL)Katrin (2016?) Sensitivity to mνe ∼ 0.2 eV

    ν-less Double-β decay: ⇔ Majorana ν′s

    n

    p

    W

    n

    p

    e−

    e−

    If mν only source of ∆L T0ν1/2 =

    meG0ν M

    2nucl m

    2ee

    mee = |∑

    U2ejmj |

    =∣

    ∣c213c212m1 e

    iη1 + c213s212m2 e

    iη2 + s213m3 e−iδCP

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    0νββ Decay: Present

    Bounds from 136Xe (EXO and KamLAND-ZEN), 76Ge (Gerda) and 130Te (Cuore-0)

    (eV)lightestm

    4103

    10 210 110

    (eV

    )m

    310

    210

    110

    1

    IH

    NH

    Xe)136

    KamLAND-Zen (

    A

    50 100 150

    Ca

    Ge

    SeZr

    Mo

    CdTe

    Te

    Xe

    Nd

    KamLAND-Zen Coll. ArXiv:1505.02889

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    The Emerging Picture

    • At least two neutrinos are massive ⇒ There is NP

    • Oscillations DO NOT determine the lightest mass but β decay:∑

    mνi ≤ 2 eV/c2⇒ Heaviest ν is at least 1 millon de times lighter than the electron

    • Dirac or Majorana?: We do not know

    • Three mixing angles are non-zero (and relatively large) ⇒ very different from CKM

    – The two arising questions

    ∗ Why are neutrinos so light?

    The Origin of Neutrino Mass

    ∗ Why are lepton mixing so different from quark’s?

    The Flavour Puzzle

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Bottom-up: Light ν from Generic New Physics

    If SM is an effective low energy theory, for E ≪ ΛNP– The same particle content as the SM and same pattern of symmetry breaking

    – But there can be non-renormalizable

    (dim> 4) operatorsL = LSM+

    n

    1

    Λn−4NPOn

    First NP effect ⇒ dim=5 operatorThere is only one!

    L5 =ZνijΛNP

    (

    LL,iφ̃)(

    φ̃TLCL,j

    )

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Bottom-up: Light ν from Generic New Physics

    If SM is an effective low energy theory, for E ≪ ΛNP– The same particle content as the SM and same pattern of symmetry breaking

    – But there can be non-renormalizable

    (dim> 4) operatorsL = LSM+

    n

    1

    Λn−4NPOn

    First NP effect ⇒ dim=5 operatorThere is only one!

    L5 =ZνijΛNP

    (

    LL,iφ̃)(

    φ̃TLCL,j

    )

    which after symmetry breaking

    induces a ν Majorana mass(Mν)ij = Z

    νij

    v2

    ΛNP

    Implications:

    – It is natural that ν mass is the first evidence of NP

    – Naturally mν ≪ other fermions masses ∼ λfv if ΛNP >> v

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Bottom-up: Light ν from Generic New Physics

    If SM is an effective low energy theory, for E ≪ ΛNP– The same particle content as the SM and same pattern of symmetry breaking

    – But there can be non-renormalizable

    (dim> 4) operatorsL = LSM+

    n

    1

    Λn−4NPOn

    First NP effect ⇒ dim=5 operatorThere is only one!

    L5 =ZνijΛNP

    (

    LL,iφ̃)(

    φ̃TLCL,j

    )

    which after symmetry breaking

    induces a ν Majorana mass(Mν)ij = Z

    νij

    v2

    ΛNP

    Implications:

    – It is natural that ν mass is the first evidence of NP

    – Naturally mν ≪ other fermions masses ∼ λfv if ΛNP >> v

    – mν >√

    ∆m2atm ∼ 0.05 eV for Zν ∼ 1⇒ ΛNP ∼ 1015GeV⇒ ΛNP ∼ GUT scale

    ⇒ Leptogenesis possible[ But if Zν ∼ (Ye)2 ⇒ ΛNP ∼ TeV scale ]

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Implications: Leptogenesis

    • Majorana mν ⇒ Lepton # violated ⇒ Matter-Antimatter asymmetry possible

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Implications: Leptogenesis

    • Majorana mν ⇒ Lepton # violated ⇒ Matter-Antimatter asymmetry possible

    • How? In the Early Universe via decay of heavy state N related to ν-mass generation

    – If /CP : Γ(N → X l) 6= Γ(N → X l)– And decay is out of equilibrium:

    (ΓN ≪ Universe expansion rate)

    }∆ L is generatedSM sphaleron processes ⇒∆ L is transformed in ∆ B

    • Today µB = − gtoday∗

    gend∗asph N

    endL ≃ − 3.92106.75 2879N endL ≃ 10−2 N endL

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Implications: Leptogenesis

    • Majorana mν ⇒ Lepton # violated ⇒ Matter-Antimatter asymmetry possible

    • How? In the Early Universe via decay of heavy state N related to ν-mass generation

    – If /CP : Γ(N → X l) 6= Γ(N → X l)– And decay is out of equilibrium:

    (ΓN ≪ Universe expansion rate)

    }∆ L is generatedSM sphaleron processes ⇒∆ L is transformed in ∆ B

    • Today µB = − gtoday∗

    gend∗asph N

    endL ≃ − 3.92106.75 2879N endL ≃ 10−2 N endL

    • To obtain N endL : solve Boltzman Eqs. with all relevant processes⇒ Details and connection to ν parameters are model dependent

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Leptogenesis connection to ν’s: Challenge

    O5 is generated for example by tree-level exchange of singlet (Ni ≡ (1, 1)0) (Type-I) ortriplet fermions (Ni ≡ Σi ≡ (1, 3)0) (Type-III) or a scalar triplet ∆ ≡ (1, 3)1 (Type-II)

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Leptogenesis connection to ν’s: Challenge

    O5 is generated for example by tree-level exchange of singlet (Ni ≡ (1, 1)0) (Type-I) ortriplet fermions (Ni ≡ Σi ≡ (1, 3)0) (Type-III) or a scalar triplet ∆ ≡ (1, 3)1 (Type-II)

    • For fermionic see-saw −LNP = −iNi/DNi + 12MNijNci Nj + λναjLαφ̃Nj [.τ ]⇒ O5 = (λ

    νTλν)αβΛNP

    (

    Lαφ̃)(

    φ̃TLCβ

    )

    with ΛNP = MN

    • For scalar see-saw −LNP = f∆αβLα ∆LCβ +M2∆ |∆|2 + κφT ∆† φ . . .

    ⇒ O5 = f∆αβΛNP(

    Lαφ̃)(

    φ̃TLCβ

    )

    with ΛNP =M2∆κ

    Very different HE physics, but same LE ν parameters

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Leptogenesis connection to ν’s: Example

    • Generically in these see-saw models successfull leptogenesis⇒ Lower bound on heavy decaying particle (for enough asymmetry)⇒ Upper bound on light neutrino mass (for not too much washout)

    • For example in Type-I see-saw

    10-6

    10-5

    10-4

    10-3

    10-2

    10-1

    1

    m 1 HeVL

    109

    1010

    1011

    1012

    M1HGeVL

    msol

    matm

    10-6

    10-5

    10-4

    10-3

    10-2

    10-1

    1

    m 1 HeVL

    108

    109

    1010

    1011

    1012

    M1HGeVL

    msol

    matm

    Abada, Josse-Michaux

    Zero Initial Abundance thermal initial abundance

    ⇒ Lower bound on right-handed neutrino mass:M1 & 3× 109 GeV (for zero initial abundance)M1 & 6× 108 GeV (for thermal initial abundance)

    ⇒ Upper bound on neutrino mass m̄ =√

    m21 +m22 +m

    23 . O(eV)

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Light massive ν in Cosmology

    Relic ν′s: Effects in several cosmological observations at several epochs

    Primordial Cosmic Microwave Large Scale

    Nucleosynthesis Background Structure Formation

    BBN CMB LSS

    T ∼ MeV T . eVNumber of ν′s (Neff ) Neff and

    Observables also depend on all other cosmological parameters

    See also talk by V. Niro on Friday and posters by Cuesta and Giusarma

  • Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaBBN & Neff

    • In general at T < me we can always write ρr =[

    1 +7

    8×(

    4

    11

    )43

    Neff

    ]

    ργ

    ∆Neff = Neff − 3 (exactly -3.04) parametrizes:– Any new relativistic states (accounting for their decoupling temperature

    – Possible new ν-interactions (which change the relation between Tγ and Tν )

  • Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaBBN & Neff

    • In general at T < me we can always write ρr =[

    1 +7

    8×(

    4

    11

    )43

    Neff

    ]

    ργ

    ∆Neff = Neff − 3 (exactly -3.04) parametrizes:– Any new relativistic states (accounting for their decoupling temperature

    – Possible new ν-interactions (which change the relation between Tγ and Tν )

    • At BBN Neff > 3 :⇒ Faster expansion of Universe⇒ Weak Interac freeze-out earlier⇒ Larger nnnp ⇒ Larger

    4He abundanceB

    url

    es,N

    oll

    et,

    Tu

    rner

    (19

    99

    )

  • Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaBBN & Neff

    • In general at T < me we can always write ρr =[

    1 +7

    8×(

    4

    11

    )43

    Neff

    ]

    ργ

    ∆Neff = Neff − 3 (exactly -3.04) parametrizes:– Any new relativistic states (accounting for their decoupling temperature

    – Possible new ν-interactions (which change the relation between Tγ and Tν )

    • At BBN Neff > 3 :⇒ Faster expansion of Universe⇒ Weak Interac freeze-out earlier⇒ Larger nnnp ⇒ Larger

    4He abundanceB

    url

    es,N

    oll

    et,

    Tu

    rner

    (19

    99

    )

    Cyburt etal arXiv:1505.0176

    BBN 4He and Deut: Neff = 2.85± 0.28

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    CMB: Effects of Neutrinos

    • CMB almost unaffected by 3 ν’s if they are relativistic at recombination zrec = 1089

    At recombination T recγ ≃ 3000 K≃ 0.26 eV ⇒ T recν =(

    4

    11

    )13

    T recγ ≃ 0.18 eV

    The mean momenta of the neutrino 〈pν〉rec =7π4

    180ξ(3)T recν = 0.58 eV

    So ν’s direct effect of CMB if∑

    mνi > O(eV)

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    CMB: Effects of Neutrinos

    • CMB almost unaffected by 3 ν’s if they are relativistic at recombination zrec = 1089

    At recombination T recγ ≃ 3000 K≃ 0.26 eV ⇒ T recν =(

    4

    11

    )13

    T recγ ≃ 0.18 eV

    The mean momenta of the neutrino 〈pν〉rec =7π4

    180ξ(3)T recν = 0.58 eV

    So ν’s direct effect of CMB if∑

    mνi > O(eV)

    • For 3 lighter ν′s effect is indirect (and small):fν =

    ΩνΩm

    6= 0 changes background evolution(time of matter-radiation equality)

    6000

    5000

    4000

    3000

    2000

    1000

    01400120010008006004002002

    l(l+

    1) C

    l / 2

    π (

    µK)2

    l

    no ν’sfν=0

    fν=0.1

    J. Lesgourgues & S.Pastor Phys. Rep.(2006)

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    CMB: Effect of Neutrinos

    • CMB almost unaffected by 3 ν’s if they are relativistic at recombination zrec = 1089

    At recombination T recγ ≃ 3000 K≃ 0.26 eV ⇒ T recν =(

    4

    11

    )13

    T recγ ≃ 0.18 eV

    The mean momenta of the neutrino 〈pν〉rec =7π4

    180ξ(3)T recν = 0.58 eV

    So ν’s direct effect of CMB if∑

    mνi > O(eV)

    • For 3 lighter ν′s effect is indirect (and small):fν =

    ΩνΩm

    6= 0 changes background evolution(time of matter-radiation equality)

    6000

    5000

    4000

    3000

    2000

    1000

    01400120010008006004002002

    l(l+

    1) C

    l / 2

    π (

    µK)2

    l

    fν=0

    fν=0.1, fixed (ωc, ΩΛ)fν=0.1, fixed (ωc, h)

    J. Lesgourgues & S.Pastor Phys. Rep.(2006)

    • But parameter degeneracies:Same effect by change of

    other cosmological parameters

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    CMB: Effect of Neutrinos

    • CMB almost unaffected by 3 ν’s if they are relativistic at recombination zrec = 1089

    At recombination T recγ ≃ 3000 K≃ 0.26 eV ⇒ T recν =(

    4

    11

    )13

    T recγ ≃ 0.18 eV

    The mean momenta of the neutrino 〈pν〉rec =7π4

    180ξ(3)T recν = 0.58 eV

    So ν’s direct effect of CMB if∑

    mνi > O(eV)

    • For more than 3 ν′s: a change in Neff changes the time of matter-radiation equality

    1 + zeq =ΩmΩr

    =Ωmh

    2

    Ωγh21

    1 + 0.2271Neff

    • The ratio 1st/3rd peak in CMB ⇒ zeq = 3386± 69 but Neff degenerated with Ωm

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    CMB: Effect of Neutrinos

    • CMB almost unaffected by 3 ν’s if they are relativistic at recombination zrec = 1089

    At recombination T recγ ≃ 3000 K≃ 0.26 eV ⇒ T recν =(

    4

    11

    )13

    T recγ ≃ 0.18 eV

    The mean momenta of the neutrino 〈pν〉rec =7π4

    180ξ(3)T recν = 0.58 eV

    So ν’s direct effect of CMB if∑

    mνi > O(eV)

    • For more than 3 ν′s: a change in Neff changes the time of matter-radiation equality

    1 + zeq =ΩmΩr

    =Ωmh

    2

    Ωγh21

    1 + 0.2271Neff

    • The ratio 1st/3rd peak in CMB ⇒ zeq = 3386± 69 but Neff degenerated with ΩmThe conclusions is:

    Combined analysis of Several Observables to break Degeneracies

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Matter Power Spectrum: Effects of ν’s

    • Contrary to CDM, ν′s move at speed vν ∼ min[

    c, 3Tνmν

    ]

    ⇒ They can travel freely over distances λFS ∼vν

    H(t)

    ⇒ They affect structures formed over scales k with 2πa(t)k

    ≤ λFS

    k ≥ knr ≃ 0.018Ω1/2mmν1 eV

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Matter Power Spectrum: Effects of ν’s

    • Contrary to CDM, ν′s move at speed vν ∼ min[

    c, 3Tνmν

    ]

    ⇒ They can travel freely over distances λFS ∼vν

    H(t)

    ⇒ They affect structures formed over scales k with 2πa(t)k

    ≤ λFS

    k ≥ knr ≃ 0.018Ω1/2mmν1 eV

    • If all DM formed of ν′s (Hot Dark Matter) no structure formed with k ≥ knr⇒ Pure HDM Ruled out by Observations

    ⇒ Subdominant contribution of ν′s to DM Constrained by Observations

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Matter Power Spectrum: Effects of ν’s

    • In a Universe with CDM+ν′s with fν =ΩνΩm

    ≪ 1

    ∆P (k)

    P (k)≃ −8fν ≃ −0.09

    mνi1 eV

    1

    Ωmh2for k ≫ knr

    0

    0.2

    0.4

    0.6

    0.8

    1

    1.2

    110-110-210-310-4

    P(k

    )f ν /

    P(k

    )f ν=

    0

    k (h/Mpc)

    knrknr fν

    0.01

    0.02

    0.03

    0.1

    J. Lesgourgues & S.Pastor Phys. Rep.(2006)

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Cosmological Analysis by Planck

    arXiv:1502.01589

    −0.12

    −0.08

    −0.04

    0.00

    ΩK

    0.4

    0.8

    1.2

    1.6

    Σm

    ν[e

    V]

    2.4

    3.2

    4.0

    4.8

    Neff

    0.24

    0.28

    0.32

    YP

    −0.030

    −0.015

    0.000

    0.015

    dn

    s/d

    lnk

    0.06

    0.12

    0.18

    0.24

    r 0.0

    02

    0.021 0.022 0.023

    Ωbh2

    −2.0

    −1.5

    −1.0

    −0.5

    w

    0.11 0.12 0.13 0.14

    Ωch2

    0.93 0.96 0.99 1.02

    ns

    45 60 75 90

    H0

    0.60 0.75 0.90 1.05

    σ8

    Range of Bounds

    Model Observables Σmν (eV) 95%

    ΛCDM+mν Planck TT + lowP ≤ 0.72ΛCDM+mν Planck TT + lowP + lensing ≤ 0.68ΛCDM+mν Planck TT,TE,EE + lowP+lensing ≤ 0.59ΛCDM+mν Planck TT,TE,EE + lowP ≤ 0.49ΛCDM+mν Planck TT + lowP + lensing + BAO + SN + H0 ≤ 0.23ΛCDM+mν Planck TT,TE,EE + lowP+ BAO ≤ 0.17

    2.4 3.0 3.6 4.2

    Neff

    0.0

    0.2

    0.4

    0.6

    0.8

    1.0

    P/P

    max

    Planck+WP+highL

    +BAO

    +H0

    +BAO+H0

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Neutrino Mass Scale

    Single β decay : Dirac or Majorana ν mass modify spectrum endpoint

    νm

    K (T)

    QT

    m2νe =∑

    m2j |Uej |2 = c213c212m21 + c213s212m22 + s213m23Present bound: mνe ≤ 2.2 eV (at 95 % CL)Katrin (2016?) Sensitivity to mνe ∼ 0.2 eV

    ν-less Double-β decay: ⇔ Majorana ν′s sensitive to Majorana phases

    n

    p

    W

    n

    p

    e−

    e−

    If mν only source of ∆L (T0ν1/2)

    −1 ∝ (mee)2

    mee = |∑

    U2ejmj |

    =∣

    ∣c213c212m1 e

    iη1 + c213s212m2 e

    iη2 + s213m3 e−iδCP

    Present Bounds: mee < 0.06−0.76 eV

    COSMO Neutrino mass (Dirac or Majorana)

    modify the growth of structures∑

    mi

  • Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaNeutrino Mass Scale: The Cosmo-Lab Connection

    Global oscillation analysis

    ⇒ Correlations mνe , mee and∑

    mν(Fogli et al (04))

    Nufit (95%)

    Width due to range in oscillation

    parameters very narrow

    High precision determination of

    mνe and∑

    mi can give informa-

    tion on ordering

    Wide band due to unknown Majorana

    phases ⇒ Possible Det of Maj phasesIf Matrix Element Uncertainty Reduced

  • Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaNeutrino Mass Scale: The Cosmo-Lab Connection

    Global oscillation analysis

    ⇒ Correlations mνe , mee and∑

    mν(Fogli et al hep-ph/0408045)

    Nufit (95%)

    Presently only Bounds

    • From Tritium β decay (Mainz & Troisk expe)mνe < 2.2 eV (95%)

    Katrin (2016?) Sensitivity to mνe ∼ 0.2 eV• From 0νββ decay for Majorana Neutrinos

    mee < 0.06− 0.15 eV (90%)Goal of Next Decade ⇒ mee at IO

    • From Analysis of Cosmological dataBound on

    mν changes with:cosmo parameters fix in analysis

    cosmo observables considered

    Model Observables Σmν (eV) 95%

    ΛCDM+mν Planck TT + lowP ≤ 0.72ΛCDM+mν Planck TT + lowP + lensing ≤ 0.68ΛCDM+mν Planck TT,TE,EE + lowP+lensing ≤ 0.59ΛCDM+mν Planck TT,TE,EE + lowP ≤ 0.49ΛCDM+mν Planck TT + lowP + lensing + BAO + SN + H0 ≤ 0.23ΛCDM+mν Planck TT,TE,EE + lowP+ BAO ≤ 0.17

    See also talk by V. Niro on Friday and posters by Cuesta

    and Giusarma

  • Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaMixed Light Sterile Neutrinos in Cosmology

    One light νs mixed with 3 ν′as contributes to ρ as Neff .

    From evol eq for 3 + 1 ensemble one finds

    ⇒ So if “explaination” to SBL anomalies1 νs contributes as much as 1 νa

    But analysis of cosmo data in ΛCDM+r + νs tells us

    Plank+WP+high-l+BAO

    J. Bergstrom, etal, ArXiv:1407.3806

  • Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaLight Sterile ν ′s in Cosmology and New Interactions

    • In string inspired E6 models, 3 light νR’s with new interactions(Z ′ with coupling Y νRZ′ = cosβ

    5√40

    − 1√24

    sinβ)

    • In these scenarios ∆Neff = 3×(

    TνRTνL

    )4

    = 3×(

    g(TdecνR)

    g(TdecνR)

    )43

    Determined by σ(ν̄RνR → f̄f) mediated by Z ′ (ie MZ′ and coupling parameter β)

    [GeV]Z’M

    310 410

    [MeV

    ]Rν de

    cT

    310

    π = 0.41 βπ = 0.42 β

    π = 0.5 βπ = 0.3 βπ = 0.7 βπ = 0.8 βπ = 0.1 β

    = 0β

    [GeV]Z’M

    310 410

    eff

    N∆

    0

    0.5

    1

    1.5

    2

    2.5π = 0.41 β

    π = 0.5 βπ = 0.3 βπ = 0.6 βπ = 0.7βπ = 0.2 βπ = 0.8βπ = 0.1 βπ = 0.9β

    = 0β

    A.

    So

    lag

    ure

    n-B

    easc

    oa,

    MC

    G-G

    arX

    iv:1

    21

    0.6

    35

    0

    ⇒ Interplay between cosmological determination of ∆Neff and Z ′ LHC searches

  • Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaSummary

    • Neutrino oscillation searches have shown us

    ∆m221 = 7.49× 10−5 eV2 (2.3%)

    ∆m231 = 2.48× 10−3 eV2 NO

    ∆m232 = −2.47× 10−3 eV2 IO

    (1.8%)

    sin2 θ12 = 0.308 (4%) sin2 θ23 =

    0.579 IO

    0.479 NO(7.2%) sin2 θ13 = 0.022 (4.8%)

    ⇒ ULEP Very different from UCKM

    • mν 6= 0⇒ Need to extend SM NP breaking total L → Majorana ν : ν = νC

    NP conserving total L → Dirac ν : ν 6= νC

    • Still ignore or not significantly determinedMajorana/Dirac? mν scale leptonic /CP? Ordering?

    Standing Puzzles: SBL anomalies light sterile ν’s?}⇒ New experiments

    • More physics than ν masses: VLI, NSI, Solar Physics, Cosmological effects . . .

    • Majorana ν′s: generic if SM is LE effective theory and explain ν lightnessΛNP ∼ 1015 GeV Fits OK in GUTLeptogenesis may explain the baryon asymmetry

    • ν′s example of interplay Particle Physics-Cosmology to learn about BSM physics

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Atmospheric Neutrinos

    Atmospheric νe,µ are produced by the interaction of cosmic rays (p, He . . . ) with the

    atmosphere

    -

    _

    +

    ( )

    ( )

    ( ) ( )

    Rµ/e=

    Nµν

    νe

    N

    πp , He

    νµµ+_

    e

    ννµ e

    +_

    Nπ+_π+

    2N

    N

    νν µ+

    +~

  • Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaAtmospheric Neutrinos: Results

    • SKI+II+III+IV data:

    -1 -0.5 0 0.5 10

    100

    200

    300

    400

    500

    Sub-GeV (e)

    -1 -0.5 0 0.5 10

    100

    200

    300

    400

    500

    Mid-GeV (e)

    -1 -0.5 0 0.5 10

    100

    200

    300

    400

    Multi-GeV (e)

    -1 -0.5 0 0.5 10

    100

    200

    300

    400

    500

    Sub-GeV (µ)

    -1 -0.5 0 0.5 10

    150

    300

    450

    600

    750

    Mid-GeV (µ)

    -1 -0.5 0 0.5 10

    100

    200

    300

    Multi-GeV FC (µ)

    -1 -0.5 0 0.5 10

    100

    200

    300

    400

    500

    Multi-GeV PC (µ)

    -1 -0.75 -0.5 -0.25 00

    50

    100

    150

    200

    250

    Stopping (µ)

    -1 -0.75 -0.5 -0.25 00

    200

    400

    600

    800

    Through (µ)

    cos(zenith)

    p, He

    π , Kµ

    e

    νeνµ

    detector

    atmosphere

    EARTH

    νµ

    down-going

    up-going

    zenithangle

    L ≈1.2×104 km

    L −~ 10-30 km

    L ≈104 km

    L ≈500 km

    [not to scale]

    +−

    +− +−

    +−

    0

    1

    2

    3

    4

    5

    0

    0.005

    0.01

    0.015

    subGeV

    multiGeV

    stoppingmuons

    through-goingmuons

    10 10 10 10 10 10 10-1 0 1 2 3 4 5

    E , GeV

    dN

    /dln

    E, (

    Kt.

    yr)-

    1

    (m .yr.ster)2

    -1

    ν

  • Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaAtmospheric Neutrinos: Results

    • SKI+II+III+IV data:

    -1 -0.5 0 0.5 10

    100

    200

    300

    400

    500

    Sub-GeV (e)

    -1 -0.5 0 0.5 10

    100

    200

    300

    400

    500

    Mid-GeV (e)

    -1 -0.5 0 0.5 10

    100

    200

    300

    400

    Multi-GeV (e)

    -1 -0.5 0 0.5 10

    100

    200

    300

    400

    500

    Sub-GeV (µ)

    -1 -0.5 0 0.5 10

    150

    300

    450

    600

    750

    Mid-GeV (µ)

    -1 -0.5 0 0.5 10

    100

    200

    300

    Multi-GeV FC (µ)

    -1 -0.5 0 0.5 10

    100

    200

    300

    400

    500

    Multi-GeV PC (µ)

    -1 -0.75 -0.5 -0.25 00

    50

    100

    150

    200

    250

    Stopping (µ)

    -1 -0.75 -0.5 -0.25 00

    200

    400

    600

    800

    Through (µ)

    cos(zenith)

    p, He

    π , Kµ

    e

    νeνµ

    detector

    atmosphere

    EARTH

    νµ

    down-going

    up-going

    zenithangle

    L ≈1.2×104 km

    L −~ 10-30 km

    L ≈104 km

    L ≈500 km

    [not to scale]

    +−

    +− +−

    +−

    0

    1

    2

    3

    4

    5

    0

    0.005

    0.01

    0.015

    subGeV

    multiGeV

    stoppingmuons

    through-goingmuons

    10 10 10 10 10 10 10-1 0 1 2 3 4 5

    E , GeV

    dN

    /dln

    E, (

    Kt.

    yr)-

    1

    (m .yr.ster)2

    -1

    ν

    νe

    inag

    reem

    ent

    wit

    hS

    M

    → νµ Deficitgrows with L

    → νµ Deficitdecreases with E

  • Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaAtmospheric Neutrinos: Results

    • SKI+II+III+IV data:

    -1 -0.5 0 0.5 10

    100

    200

    300

    400

    500

    Sub-GeV (e)

    -1 -0.5 0 0.5 10

    100

    200

    300

    400

    500

    Mid-GeV (e)

    -1 -0.5 0 0.5 10

    100

    200

    300

    400

    Multi-GeV (e)

    -1 -0.5 0 0.5 10

    100

    200

    300

    400

    500

    Sub-GeV (µ)

    -1 -0.5 0 0.5 10

    150

    300

    450

    600

    750

    Mid-GeV (µ)

    -1 -0.5 0 0.5 10

    100

    200

    300

    Multi-GeV FC (µ)

    -1 -0.5 0 0.5 10

    100

    200

    300

    400

    500

    Multi-GeV PC (µ)

    -1 -0.75 -0.5 -0.25 00

    50

    100

    150

    200

    250

    Stopping (µ)

    -1 -0.75 -0.5 -0.25 00

    200

    400

    600

    800

    Through (µ)

    cos(zenith)

    Best explained by νµ → ντ

    0.3 0.5 1 2 3

    tan2 θ

    0

    1

    2

    3

    4

    5

    ∆m2

    [10-

    3 eV

    2 ]

    ∆m2 ∼ 2.4 × 10−3 eV2

    tan2 θ ∼ 1 ⇒ θ ∼ π4

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    νµ Disappearance in Accelerator ν Fluxes

    T2K:

    νµ produced in Tokai (Japan)

    detected in SK at ∼ 250 Km

    MINOS, NOνA

    νµ produced en Fermilab (Illinois)

    detected in Minnesota at ∼ 800 Km

    Lectures by G. Feldman

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Long Baseline Experiments: νµ Disappearance

    K2K/T2K 2004–: spectral distortion MINOS 2006–: spectral distortion

    NOνA: 2015–

    νµ oscillations with ∆m2 ∼ 2.5× 10−3 eV2 and mixing compatible with π4

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Solar Neutrinos

    • Sun shines by nuclear fusion of protons into He

    And only νe are produced

    • Two main chains of nuclear reactionspp Chain : CNO cycle:

    N13

    C12 C13

    N15 N14

    O15

    O16 O17

    F17

    =0.707MeV

    =0.999MeV

    =0.997MeV

    He4p p

    p p

    p p

    e+

    e+

    e+

    He4

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Solar Neutrinos: Fluxes

    PP CHAIN Eν (MeV)

    (pp)

    p + p →2 H + e+ + νe ≤ 0.42

    (pep)

    p + e− + p →2 H + νe 1.552

    (7Be)

    7Be + e− →7 Li + νe 0.862(90%)

    0.384 (10%)

    (hep)

    2He + p →4 He + e+ + νe ≤ 18.77

    (8B)

    8B →8 Be∗ + e+ + νe ≤ 15

    CNO CHAIN Eν (MeV)

    (13N)

    13N →13 C + e+ + νe ≤ 1.199

    (15O)

    15O →15 N + e+ + νe ≤ 1.732

    (17F)

    17F →17 O + e+ + νe ≤ 1.74

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Solar Neutrinos: Results

    radio

    -ch

    emic

    alre

    alti

    me

    Experiment Detection Flavour Eth (MeV)

    Homestake 37Cl(ν, e−)37Ar νe Eν > 0.81

    Sage + 71Ga(ν, e−)71Ge νe Eν > 0.23Gallex+GNO

    Kam ⇒ SK ES νxe− → νxe− νe, νµ/τ

    (

    σµτσe

    ≃ 16

    )

    Ee > 5

    SNO CC νed → ppe− νe Te > 5

    NC νxd → νxp n νe, νµ/τ Tγ > 5

    ES νxe− → νxe− νe, νµ/τ Te > 5

    Borexino νxe− → νxe− νe, νµ/τ Eν = 0.862

    Experiments measuring νe observe a deficit

    Deficit is energy dependent

    Deficit disappears in NC

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    • Real Time experiments can also give information on Energy and Direction of ν′sand can search for Energy and Time variations of the effect

    • From SK (also from SNO)

    Energy Dependence

    0.2

    0.4

    0.6

    0.8

    5 10 15 20Energy(MeV)

    Dat

    a/S

    SM

    BP

    2004

    Deficit indep Eν & 5 MeV

    Day-Night Variation

    Not significant

    Seasonal Variation

    1

    2

    3

    4

    1998 2000 2002 2004 2006YEAR

    Flu

    x (x

    106 /

    cm2 /

    s)

    Nothing beyond 1R2

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Solar Neutrinos: Oscillation Solutions

    10-12

    10-11

    10-10

    10-9

    10-8

    10-7

    10-6

    10-5

    10-4

    10-3

    10-4 10-3 10-2 10-1 1 10.

    RATES ONLY GLOBALSK and SNO E and t dependence

    SMA

    LMA

    LOW

    VAC

    LMA

    ∆m2 ∼ 5× 10−5 eV2

    tan2 θ ∼ 0.4 ⇒ θ ∼ π6Different frequency and flavour

    than ATM and LBL

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Terrestrial test of LMA: KamLAND

    Lectures by K. Heeger

    KamLAND: Detector of ν̄e produced in nuclear reactors in Japan at an average distance

    of 180 Km

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Terrestrial test of LMA: KamLAND

    KamLAND: Detector of ν̄e produced in nuclear reactors in Japan at an average distance

    of 180 Km

    Results of KamLAND

    compared with Pee for

    θ = 35◦ y ∆m2 = 7.5× 10−5 (eV/c2)2

    (km/MeV)eν

    /E0L20 30 40 50 60 70 80 90 100

    Surv

    ival

    Pro

    babi

    lity

    0

    0.2

    0.4

    0.6

    0.8

    1

    eνData - BG - Geo Expectation based on osci. parameters

    determined by KamLAND

  • Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaMedium Baseline Reactor Experiments

    Lectures by K. Heeger

    • Searches for ν̄e → ν̄e disappearance at L ∼ Km (E/L ∼ 10−3 eV2)• Relative measurement: near and far detectors

    Daya-Bay Reno

  • Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaDaya-Bay and Reno Reactor Experiments

    • Searches for ν̄e → ν̄e disappearance at L ∼ Km (E/L ∼ 10−3 eV2)• Relative measurement: near and far detectors

    Daya-Bay: 4 Near+ 4 Far

    Described with ∆m2 ∼ 2.5× 10−3eV2(as νµ ATM and LBL acc but for νe)

    and θ ∼ 9◦

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    Long Baseline Experiments: νe Appearance

    • Observation of νµ → νe transitions with E/L ∼ 10−3 eV2

    T2K MINOS

    NOνA also

    Well described with νµ → νe oscillations with ∆m2 ∼ 2× 10−3 eV2 and θ ∼ 11◦

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    ν Oscillations: Lab Searches at Short Distance

    Lectures by B. Louis

    Appearance Experiment

    L

    αν sourceν ν detectorSearches for β

    β

    αdiff

    Experiment 〈E/MeVL/m

    〉 α β

    CCFR 100 νµ, νe ντ

    E531 25 νµ, νe ντ

    Nomad 13 νµ, νe ντ

    Chorus 13 νµ, νe ντ

    E776 2.5 νµ νe

    Karmen2 2.5 ν̄µ ν̄e

    LSND 3 ν̄µ ν̄e

    Miniboone 3 νµ νeν̄µ ν̄e

    ICARUS 1 νµ νe

    Disappearance Experiment

    αν sourceν να detector ναdetectorI II

    Φα Ι Φα ΙΙLL

    I

    II

    α Ι α ΙΙandCompares ΦΦ to look for loss

    Experiment 〈E/MeVL/m

    〉 α

    CDHSW 1.4 νµ

    BugeyIII 0.05 ν̄e

    Chooz 0.005 ν̄e

  • Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia

    LSND and MiniBooNE

    • LSND: Main signal for ν̄µ → ν̄e with Eν ∼ 0.03 GeV and L = 30 m• MiniBooNE: Search for νµ → νe and ν̄µ → ν̄e with Eν = 0.3− 2 GeV and L = 540 m

    Compatibility (?)

    for ∆m2 ∼ eV2

    a third osc frequency?