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Physics of Massive Neutrinos Concha Gonzalez-Garcia Plan of Lectures I. Standard Neutrino Properties and Mass Terms (Beyond Standard) II. Effects of ν Mass: Neutrino Oscillations (Vacuum) III. Matter Effects in Neutrino Oscillations IV. The Emerging Picture and Some Lessons

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Transcript of icecube.wisc.eduhalzen/notes/week14-4.pdfPhysics of Massive Neutrinos Concha Gonzalez-Garcia Summary...

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Plan of Lectures

    I. Standard Neutrino Properties and Mass Terms (Beyond Standard)

    II. Effects of ν Mass: Neutrino Oscillations (Vacuum)

    III. Matter Effects in Neutrino Oscillations

    IV. The Emerging Picture and Some Lessons

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Summary I+II+III

    • In the SM: ↔ mν ≡ 0– neutrinos are left-handed (≡ helicity -1): mν = 0 ⇒ chirality ≡ helicity– No distinction between Majorana or Dirac Neutrinos

    • mν 6= 0 → Need to extend SM to add mν– breaking total lepton number (L = Le + Lµ + Lτ ) → Majorana ν: ν = νC– conserving total lepton number → Dirac ν: ν 6= νC– Always Lepton Mixing≡ breaking of Le × Lµ × Lτ

    • Neutrino masses and mixing ⇒ Flavour oscillations• ν traveling through matter ⇒ Modification of oscillation pattern

    • Atmospheric, K2K and MINOS (+ negative SBL searches)⇒ νµ → ντ with ∆m2 ∼ 2 × 10−3 eV2 and tan2 θ ∼ 1

    • Solar and KamLAND⇒ νe → νµ, ντ with ∆m2 ∼ 8 × 10−5 eV2 and tan2 θ ∼ 0.4

    • Can we fit all toegether? What can we learn from all this?Answer: Today

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Summary I+II+III

    • In the SM: ↔ mν ≡ 0– neutrinos are left-handed (≡ helicity -1): mν = 0 ⇒ chirality ≡ helicity– No distinction between Majorana or Dirac Neutrinos

    • mν 6= 0 → Need to extend SM to add mν– breaking total lepton number (L = Le + Lµ + Lτ ) → Majorana ν: ν = νC– conserving total lepton number → Dirac ν: ν 6= νC– Always Lepton Mixing≡ breaking of Le × Lµ × Lτ

    • Neutrino masses and mixing ⇒ Flavour oscillations• ν traveling through matter ⇒ Modification of oscillation pattern

    • Atmospheric, K2K and MINOS (+ negative SBL searches)⇒ νµ → ντ with ∆m2 ∼ 2 × 10−3 eV2 and tan2 θ ∼ 1

    • Solar and KamLAND⇒ νe → νµ, ντ with ∆m2 ∼ 8 × 10−5 eV2 and tan2 θ ∼ 0.4

    • Can we fit all toegether? What can we learn from all this?Answer: Today

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Summary I+II+III

    • In the SM: ↔ mν ≡ 0– neutrinos are left-handed (≡ helicity -1): mν = 0 ⇒ chirality ≡ helicity– No distinction between Majorana or Dirac Neutrinos

    • mν 6= 0 → Need to extend SM to add mν– breaking total lepton number (L = Le + Lµ + Lτ ) → Majorana ν: ν = νC– conserving total lepton number → Dirac ν: ν 6= νC– Always Lepton Mixing≡ breaking of Le × Lµ × Lτ

    • Neutrino masses and mixing ⇒ Flavour oscillations• ν traveling through matter ⇒ Modification of oscillation pattern

    • Atmospheric, K2K and MINOS (+ negative SBL searches)⇒ νµ → ντ with ∆m2 ∼ 2 × 10−3 eV2 and tan2 θ ∼ 1

    • Solar and KamLAND⇒ νe → νµ, ντ with ∆m2 ∼ 8 × 10−5 eV2 and tan2 θ ∼ 0.4

    • Can we fit all toegether? What can we learn from all this?Answer: Today

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Summary I+II+III

    • In the SM: ↔ mν ≡ 0– neutrinos are left-handed (≡ helicity -1): mν = 0 ⇒ chirality ≡ helicity– No distinction between Majorana or Dirac Neutrinos

    • mν 6= 0 → Need to extend SM to add mν– breaking total lepton number (L = Le + Lµ + Lτ ) → Majorana ν: ν = νC– conserving total lepton number → Dirac ν: ν 6= νC– Always Lepton Mixing≡ breaking of Le × Lµ × Lτ

    • Neutrino masses and mixing ⇒ Flavour oscillations• ν traveling through matter ⇒ Modification of oscillation pattern

    • Atmospheric, K2K and MINOS (+ negative SBL searches)⇒ νµ → ντ with ∆m2 ∼ 2 × 10−3 eV2 and tan2 θ ∼ 1

    • Solar and KamLAND⇒ νe → νµ, ντ with ∆m2 ∼ 8 × 10−5 eV2 and tan2 θ ∼ 0.4

    • Can we fit all toegether? What can we learn from all this?Answer: Today

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Summary I+II+III

    • In the SM: ↔ mν ≡ 0– neutrinos are left-handed (≡ helicity -1): mν = 0 ⇒ chirality ≡ helicity– No distinction between Majorana or Dirac Neutrinos

    • mν 6= 0 → Need to extend SM to add mν– breaking total lepton number (L = Le + Lµ + Lτ ) → Majorana ν: ν = νC– conserving total lepton number → Dirac ν: ν 6= νC– Always Lepton Mixing≡ breaking of Le × Lµ × Lτ

    • Neutrino masses and mixing ⇒ Flavour oscillations• ν traveling through matter ⇒ Modification of oscillation pattern

    • Atmospheric, K2K and MINOS (+ negative SBL searches)⇒ νµ → ντ with ∆m2 ∼ 2 × 10−3 eV2 and tan2 θ ∼ 1

    • Solar and KamLAND⇒ νe → νµ, ντ with ∆m2 ∼ 8 × 10−5 eV2 and tan2 θ ∼ 0.4

    • Can we fit all toegether? What can we learn from all this?Answer: Today

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Summary I+II+III

    • In the SM: ↔ mν ≡ 0– neutrinos are left-handed (≡ helicity -1): mν = 0 ⇒ chirality ≡ helicity– No distinction between Majorana or Dirac Neutrinos

    • mν 6= 0 → Need to extend SM to add mν– breaking total lepton number (L = Le + Lµ + Lτ ) → Majorana ν: ν = νC– conserving total lepton number → Dirac ν: ν 6= νC– Always Lepton Mixing≡ breaking of Le × Lµ × Lτ

    • Neutrino masses and mixing ⇒ Flavour oscillations• ν traveling through matter ⇒ Modification of oscillation pattern

    • Atmospheric, K2K and MINOS (+ negative SBL searches)⇒ νµ → ντ with ∆m2 ∼ 2 × 10−3 eV2 and tan2 θ ∼ 1

    • Solar and KamLAND⇒ νe → νµ, ντ with ∆m2 ∼ 8 × 10−5 eV2 and tan2 θ ∼ 0.4

    • Can we fit all toegether? What can we learn from all this?Answer: Today

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Plan of Lecture IV

    Emerging Picture and Some Lessons

    3ν Oscillations

    Some Lessons:

    The Need of New Physics

    The Possibility of Leptogenesis

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    • We have learned:∗ Atmospheric νµ disappear (> 15σ) most likely to ντ∗ K2K: accelerator νµ disappear at L ∼ 250 Km with E-distortion (∼ 2.5–4σ)

    ∗ MINOS: accelerator νµ disappear at L ∼ 735 Km with E-distortion (∼ 5σ)

    ∗ Solar νe convert to νµ or ντ (> 7σ)

    ∗ KamLAND: reactor νe disappear at L ∼ 200 Km with E-distortion (& 3σ CL)

    ∗ LSND found evidence for νµ → νe but it is not confirmed

    All this implies that neutrinos are massive

    • We have important information (mostly constraints) from:∗ The line shape of the Z: Nweak = 3

    ∗ Limits from Short Distance Oscillation Searches at Reactor and Accelerators

    ∗ Direct mass measurements: 3H →3 He + e− + ν̄e and ν-less ββ decay

    ∗ From Astrophysics and Cosmology: BBN, CMBR, LSS ...

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    • We have learned:∗ Atmospheric νµ disappear (> 15σ) most likely to ντ∗ K2K: accelerator νµ disappear at L ∼ 250 Km with E-distortion (∼ 2.5–4σ)

    ∗ MINOS: accelerator νµ disappear at L ∼ 735 Km with E-distortion (∼ 5σ)

    ∗ Solar νe convert to νµ or ντ (> 7σ)

    ∗ KamLAND: reactor νe disappear at L ∼ 200 Km with E-distortion (& 3σ CL)

    ∗ LSND found evidence for νµ → νe but it is not confirmed

    All this implies that neutrinos are massive

    • We have important information (mostly constraints) from:∗ The line shape of the Z: Nweak = 3

    ∗ Limits from Short Distance Oscillation Searches at Reactor and Accelerators

    ∗ Direct mass measurements: 3H →3 He + e− + ν̄e and ν-less ββ decay

    ∗ From Astrophysics and Cosmology: BBN, CMBR, LSS ...

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    • We have learned:∗ Atmospheric νµ disappear (> 15σ) most likely to ντ∗ K2K: accelerator νµ disappear at L ∼ 250 Km with E-distortion (∼ 2.5–4σ)

    ∗ MINOS: accelerator νµ disappear at L ∼ 735 Km with E-distortion (∼ 5σ)

    ∗ Solar νe convert to νµ or ντ (> 7σ)

    ∗ KamLAND: reactor νe disappear at L ∼ 200 Km with E-distortion (& 3σ CL)

    ∗ LSND found evidence for νµ → νe but it is not confirmed

    All this implies that neutrinos are massive

    • We have important information (mostly constraints) from:∗ The line shape of the Z: Nweak = 3

    ∗ Limits from Short Distance Oscillation Searches at Reactor and Accelerators

    ∗ Direct mass measurements: 3H →3 He + e− + ν̄e and ν-less ββ decay

    ∗ From Astrophysics and Cosmology: BBN, CMBR, LSS ...

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Solar+Atmospheric+Reactor+LBL 3ν Oscillations

    U : 3 angles, 1 CP-phase+ (2 Majorana phases)

    0

    @

    1 0 0

    0 c23 s23

    0 −s23 c23

    1

    A

    0

    @

    c13 0 s13eiδ

    0 1 0

    −s13e−iδ 0 c13

    1

    A

    0

    @

    c21 s12 0

    −s12 c12 0

    0 0 1

    1

    A

    Two mass schemes

    M

    sola

    r

    sola

    r

    atm

    osm m 1 3

    ∆ 2

    ∆ m

    2

    m 3

    m 2

    ∆ m

    m 1

    m 2

    NORMAL INVERTED

    2

    2ν oscillation analysis ⇒ ∆m221 = ∆m2� � ∆M2atm ' ±∆m232 ' ±∆m231

    Generic 3ν mixing effects:– Effects due to θ13– Difference between Inverted and Normal– Interference of two wavelength oscillations– CP violation due to phase δ

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Solar+Atmospheric+Reactor+LBL 3ν Oscillations

    U : 3 angles, 1 CP-phase+ (2 Majorana phases)

    0

    @

    1 0 0

    0 c23 s23

    0 −s23 c23

    1

    A

    0

    @

    c13 0 s13eiδ

    0 1 0

    −s13e−iδ 0 c13

    1

    A

    0

    @

    c21 s12 0

    −s12 c12 0

    0 0 1

    1

    A

    Two mass schemes

    M

    sola

    r

    sola

    r

    atm

    osm m 1 3

    ∆ 2

    ∆ m

    2

    m 3

    m 2

    ∆ m

    m 1

    m 2

    NORMAL INVERTED

    2

    2ν oscillation analysis ⇒ ∆m221 = ∆m2� � ∆M2atm ' ±∆m232 ' ±∆m231Generic 3ν mixing effects:

    – Effects due to θ13– Difference between Inverted and Normal– Interference of two wavelength oscillations– CP violation due to phase δ

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    3–ν Neutrino Oscillations

    • In general one has to solve: i d~νdt

    = H ~ν H = U · Hd0 · U † + V

    Hd0 =1

    2Eνdiag

    (

    −∆m221, 0, ∆m232)

    V = diag(

    ±√

    2GF Ne, 0, 0)

    • Hierarchical approximation: ∆m221 � ∆m231 ∼ ∆m232∗ For θ13 = 0 solar and atmospheric oscillations decouple ⇒ Normal≡ Inverted

    – Solar and KamLAND → ∆m221 = ∆m2� θ12 = θ�– Atmospheric and LBL → ∆m231 = ∆M2atm θ23 = θatm

    ∗ For θ13 6= 0– Solar and KamLAND: P 3νee = c413P 2νee (∆m212, θ12) + s413

    – CHOOZ: PCHee ' 1 − 4c213s213 sin2(

    ∆m231

    L

    4E

    )

    – K2K+MINOS Probabilities Independent of θ12, ∆m221

    4

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    3–ν Neutrino Oscillations

    • In general one has to solve: i d~νdt

    = H ~ν H = U · Hd0 · U † + V

    Hd0 =1

    2Eνdiag

    (

    −∆m221, 0, ∆m232)

    V = diag(

    ±√

    2GF Ne, 0, 0)

    • Hierarchical approximation: ∆m221 � ∆m231 ∼ ∆m232∗ For θ13 = 0 solar and atmospheric oscillations decouple ⇒ Normal≡ Inverted

    – Solar and KamLAND → ∆m221 = ∆m2� θ12 = θ�– Atmospheric and LBL → ∆m231 = ∆M2atm θ23 = θatm

    ∗ For θ13 6= 0– Solar and KamLAND: P 3νee = c413P 2νee (∆m212, θ12) + s413

    – CHOOZ: PCHee ' 1 − 4c213s213 sin2(

    ∆m231

    L

    4E

    )

    – K2K+MINOS Probabilities Independent of θ12, ∆m221

    4

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    3–ν Neutrino Oscillations

    • In general one has to solve: i d~νdt

    = H ~ν H = U · Hd0 · U † + V

    Hd0 =1

    2Eνdiag

    (

    −∆m221, 0, ∆m232)

    V = diag(

    ±√

    2GF Ne, 0, 0)

    • Hierarchical approximation: ∆m221 � ∆m231 ∼ ∆m232∗ For θ13 = 0 solar and atmospheric oscillations decouple ⇒ Normal≡ Inverted

    – Solar and KamLAND → ∆m221 = ∆m2� θ12 = θ�– Atmospheric and LBL → ∆m231 = ∆M2atm θ23 = θatm

    ∗ For θ13 6= 0– Solar and KamLAND: P 3νee = c413P 2νee (∆m212, θ12) + s413

    – CHOOZ: PCHee ' 1 − 4c213s213 sin2(

    ∆m231

    L

    4E

    )

    – K2K+MINOS Probabilities Independent of θ12, ∆m221

    4

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    3–ν Neutrino Oscillations

    • In general one has to solve: i d~νdt

    = H ~ν H = U · Hd0 · U † + V

    Hd0 =1

    2Eνdiag

    (

    −∆m221, 0, ∆m232)

    V = diag(

    ±√

    2GF Ne, 0, 0)

    • Hierarchical approximation: ∆m221 � ∆m231 ∼ ∆m232∗ For θ13 = 0 solar and atmospheric oscillations decouple ⇒ Normal≡ Inverted

    – Solar and KamLAND → ∆m221 = ∆m2� θ12 = θ�– Atmospheric and LBL → ∆m231 = ∆M2atm θ23 = θatm

    ∗ For θ13 6= 0– Solar and KamLAND: P 3νee = c413P 2νee (∆m212, θ12) + s413

    – CHOOZ: PCHee ' 1 − 4c213s213 sin2(

    ∆m231

    L

    4E

    )

    – K2K+MINOS Probabilities Independent of θ12, ∆m221

    4

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    3–ν Neutrino Oscillations

    • In general one has to solve: i d~νdt

    = H ~ν H = U · Hd0 · U † + V

    Hd0 =1

    2Eνdiag

    (

    −∆m221, 0, ∆m232)

    V = diag(

    ±√

    2GF Ne, 0, 0)

    • Hierarchical approximation: ∆m221 � ∆m231 ∼ ∆m232∗ For θ13 = 0 solar and atmospheric oscillations decouple ⇒ Normal≡ Inverted

    – Solar and KamLAND → ∆m221 = ∆m2� θ12 = θ�– Atmospheric and LBL → ∆m231 = ∆M2atm θ23 = θatm

    ∗ For θ13 6= 0– Solar and KamLAND: P 3νee = c413P 2νee (∆m212, θ12) + s413

    – CHOOZ: PCHee ' 1 − 4c213s213 sin2(

    ∆m231

    L

    4E

    )

    – K2K+MINOS Probabilities Independent of θ12, ∆m221 4

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    3–ν Atmospheric Neutrino Oscillation: Effect of θ13

    • In general one has to solve: i d~νdt

    = H ~ν H = U · Hd0 · U † + V

    Hd0 =1

    2Eνdiag

    (

    −∆m221, 0, ∆m232)

    V = diag(

    ±√

    2GF Ne, 0, 0)

    • Hierarchical approximation: ∆m221 � ∆m231 ∼ ∆m232 ⇒ neglect ∆m221 in ATM

    Pantaleone 94; Used by many ...

    Pee = 1 − 4s213,mc

    213,m S31

    Pµµ = 1 − 4s213,mc

    213,ms

    423 S31 − 4s

    213,ms

    223c

    223 S21 − 4c

    213,ms

    223c

    223 S32

    Peµ = 4s213,mc

    213,ms

    223 S31

    Sij = sin2

    ∆µ2ij4Eν

    L

    «

    ∆µ221 =∆m2

    32

    2

    sin 2θ13sin 2θ13,m

    − 1”

    − EνVe

    ∆µ232 =∆m2

    32

    2

    sin 2θ13sin 2θ13,m

    + 1”

    + EνVe

    ∆µ231 = ∆m232

    sin 2θ13sin 2θ13,m

    sin 2θ13,m =sin 2θ13

    q

    (cos 2θ13 ∓2EνVe∆m2

    31

    )2 + sin2 2θ13

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    3–ν Atmospheric Neutrino Oscillation: Effect of θ13

    • In general one has to solve: i d~νdt

    = H ~ν H = U · Hd0 · U † + V

    Hd0 =1

    2Eνdiag

    (

    −∆m221, 0, ∆m232)

    V = diag(

    ±√

    2GF Ne, 0, 0)

    • Hierarchical approximation: ∆m221 � ∆m231 ∼ ∆m232 ⇒ neglect ∆m221 in ATM

    Pantaleone 94; Used by many ...

    Pee = 1 − 4s213,mc

    213,m S31

    Pµµ = 1 − 4s213,mc

    213,ms

    423 S31 − 4s

    213,ms

    223c

    223 S21 − 4c

    213,ms

    223c

    223 S32

    Peµ = 4s213,mc

    213,ms

    223 S31

    Sij = sin2

    ∆µ2ij4Eν

    L

    «

    ∆µ221 =∆m2

    32

    2

    sin 2θ13sin 2θ13,m

    − 1”

    − EνVe

    ∆µ232 =∆m2

    32

    2

    sin 2θ13sin 2θ13,m

    + 1”

    + EνVe

    ∆µ231 = ∆m232

    sin 2θ13sin 2θ13,m

    sin 2θ13,m =sin 2θ13

    q

    (cos 2θ13 ∓2EνVe∆m2

    31

    )2 + sin2 2θ13

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    3–ν Atmospheric Neutrino Oscillation: Effect of θ13Ahkmedov,Dighe,Lipari,Smirnov 99; Petcov, Maris 98; Palomares, Petcov, 03

    -1 -0.5 0 0.5 10.8

    0.9

    1

    1.1

    1.2

    1.3

    Ne

    / Ne0

    SK sub-GeV (e)

    Normal

    -1 -0.5 0 0.5 1

    cosθ

    0.8

    0.9

    1

    1.1

    1.2

    1.3

    Ne/

    NeO

    SK multi-GeV (e)

    Normal

    -1 -0.5 0 0.5 10.8

    0.9

    1

    1.1

    1.2

    1.3

    SK sub-GeV (e)

    Inverted

    -1 -0.5 0 0.5 1

    cos θ

    0.8

    0.9

    1

    1.1

    1.2

    1.3

    SK multi-GeV (e)

    Inverted

    No Oscillationss213=0.00, s

    223=0.35, ∆m

    221=0

    s213=0.04, s223=0.35, ∆m

    221=0

    s213=0.04, s223=0.65, ∆m

    221=0

    Ne

    Ne0− 1 = Peµr̄(s223 − 1r̄ )

    r̄ =Nµ0Ne0

    Peµ = 4s213,mc

    213,m sin

    2(

    ∆m231

    L

    4Eνsin 2θ13

    sin 2θ13,m

    )

    sin 2θ13,m =sin 2θ13

    r

    (cos 2θ13 ∓2EνVe∆m2

    31

    )2 + sin2 2θ13

    • Multi-GeV : Enhancement due to MatterLarger Effect in NormalPossible Sensitivity to Mass Ordering

    • Sub-GeV: Vacuum Osc: Smaller Effect

    r ' 2 ⇒ θ23 <π4 ⇒ s223 < 12 ⇒ Ne(θ13) < Ne0

    θ23 >π4 ⇒ s223 > 12 ⇒ Ne(θ13) > Ne0

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    3–ν Atmospheric Neutrino Oscillation: Effect of θ13Ahkmedov,Dighe,Lipari,Smirnov 99; Petcov, Maris 98; Palomares, Petcov, 03

    -1 -0.5 0 0.5 10.8

    0.9

    1

    1.1

    1.2

    1.3

    Ne

    / Ne0

    SK sub-GeV (e)

    Normal

    -1 -0.5 0 0.5 1

    cosθ

    0.8

    0.9

    1

    1.1

    1.2

    1.3

    Ne/

    NeO

    SK multi-GeV (e)

    Normal

    -1 -0.5 0 0.5 10.8

    0.9

    1

    1.1

    1.2

    1.3

    SK sub-GeV (e)

    Inverted

    -1 -0.5 0 0.5 1

    cos θ

    0.8

    0.9

    1

    1.1

    1.2

    1.3

    SK multi-GeV (e)

    Inverted

    No Oscillationss213=0.00, s

    223=0.35, ∆m

    221=0

    s213=0.04, s223=0.35, ∆m

    221=0

    s213=0.04, s223=0.65, ∆m

    221=0

    Ne

    Ne0− 1 = Peµr̄(s223 − 1r̄ )

    r̄ =Nµ0Ne0

    Peµ = 4s213,mc

    213,m sin

    2(

    ∆m231

    L

    4Eνsin 2θ13

    sin 2θ13,m

    )

    sin 2θ13,m =sin 2θ13

    r

    (cos 2θ13 ∓2EνVe∆m2

    31

    )2 + sin2 2θ13

    • Multi-GeV : Enhancement due to MatterLarger Effect in NormalPossible Sensitivity to Mass Ordering

    • Sub-GeV: Vacuum Osc: Smaller Effect

    r ' 2 ⇒ θ23 <π4 ⇒ s223 < 12 ⇒ Ne(θ13) < Ne0

    θ23 >π4 ⇒ s223 > 12 ⇒ Ne(θ13) > Ne0

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    3–ν Atmospheric Neutrino Oscillation: Effect of θ13Ahkmedov,Dighe,Lipari,Smirnov 99; Petcov, Maris 98; Palomares, Petcov, 03

    -1 -0.5 0 0.5 10.8

    0.9

    1

    1.1

    1.2

    1.3

    Ne

    / Ne0

    SK sub-GeV (e)

    Normal

    -1 -0.5 0 0.5 1

    cosθ

    0.8

    0.9

    1

    1.1

    1.2

    1.3

    Ne/

    NeO

    SK multi-GeV (e)

    Normal

    -1 -0.5 0 0.5 10.8

    0.9

    1

    1.1

    1.2

    1.3

    SK sub-GeV (e)

    Inverted

    -1 -0.5 0 0.5 1

    cos θ

    0.8

    0.9

    1

    1.1

    1.2

    1.3

    SK multi-GeV (e)

    Inverted

    No Oscillationss213=0.00, s

    223=0.35, ∆m

    221=0

    s213=0.04, s223=0.35, ∆m

    221=0

    s213=0.04, s223=0.65, ∆m

    221=0

    Ne

    Ne0− 1 = Peµr̄(s223 − 1r̄ )

    r̄ =Nµ0Ne0

    Peµ = 4s213,mc

    213,m sin

    2(

    ∆m231

    L

    4Eνsin 2θ13

    sin 2θ13,m

    )

    sin 2θ13,m =sin 2θ13

    r

    (cos 2θ13 ∓2EνVe∆m2

    31

    )2 + sin2 2θ13

    • Multi-GeV : Enhancement due to MatterLarger Effect in NormalPossible Sensitivity to Mass Ordering

    • Sub-GeV: Vacuum Osc: Smaller Effect

    r ' 2 ⇒ θ23 <π4 ⇒ s223 < 12 ⇒ Ne(θ13) < Ne0

    θ23 >π4 ⇒ s223 > 12 ⇒ Ne(θ13) > Ne0

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    ∆m221 effects in ATM Data

    Smirnov, Peres 99,01; Fogli, Lisi, Marrone 01; MC G-G, Maltoni 02; MCG-G, Maltoni, Smirnov hep-ph/0408170

    • In general one has to solve: i d~νdt

    = H ~ν H = U · Hd0 · U † + V

    Hd0 =1

    2Eνdiag

    (

    −∆m221, 0, ∆m232)

    V = diag(

    ±√

    2GF Ne, 0, 0)

    • Neglecting θ13:

    Pee = 1 − Pe2Peµ = c

    223Pe2

    Pµµ = 1 − c423Pe2 − 2s223c223[

    1 −√

    1 − Pe2 cosφ]

    Pe2 = sin2 2θ12,m sin

    2(

    ∆m221

    L

    4Eνsin 2θ12

    sin 2θ12,m

    )

    sin 2θ12,m =sin 2θ12

    (cos 2θ12 ∓ 2EνVe∆m221

    )2 + sin2 2θ12

    φ ≈ (∆m231 + s212 ∆m221) L2Eν

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    ∆m221 effects in ATM Data

    Smirnov, Peres 99,01; Fogli, Lisi, Marrone 01; MC G-G, Maltoni 02; MCG-G, Maltoni, Smirnov hep-ph/0408170

    • In general one has to solve: i d~νdt

    = H ~ν H = U · Hd0 · U † + V

    Hd0 =1

    2Eνdiag

    (

    −∆m221, 0, ∆m232)

    V = diag(

    ±√

    2GF Ne, 0, 0)

    • Neglecting θ13:

    Pee = 1 − Pe2Peµ = c

    223Pe2

    Pµµ = 1 − c423Pe2 − 2s223c223[

    1 −√

    1 − Pe2 cosφ]

    Pe2 = sin2 2θ12,m sin

    2(

    ∆m221

    L

    4Eνsin 2θ12

    sin 2θ12,m

    )

    sin 2θ12,m =sin 2θ12

    (cos 2θ12 ∓ 2EνVe∆m221

    )2 + sin2 2θ12

    φ ≈ (∆m231 + s212 ∆m221) L2Eν

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    ∆m221 effects in ATM Data

    -1 -0.5 0 0.5 10.8

    0.9

    1

    1.1

    1.2

    1.3

    Ne

    / Ne0

    SK sub-GeV (e)

    Normal

    -1 -0.5 0 0.5 10.8

    0.9

    1

    1.1

    1.2

    1.3

    SK sub-GeV (e)

    Inverted

    -1 -0.5 0 0.5 1

    cos θ

    0.8

    0.9

    1

    1.1

    1.2

    1.3

    Ne

    / Ne0

    SK multi-GeV (e)

    Normal

    -1 -0.5 0 0.5 1

    cos θ

    0.8

    0.9

    1

    1.1

    1.2

    1.3

    SK multi-GeV (e)

    Inverted

    Ne

    Ne0− 1 = Pe2r̄(c223 − 1r̄ )

    Pe2 = sin2 2θ12,m sin

    2(

    ∆m221

    L

    4Eνsin 2θ12

    sin 2θ12,m

    )

    sin 2θ12,m =sin2 2θ12

    r

    (cos 2θ12 ∓2EVe∆m2

    21

    )2 + sin2 2θ12

    For Sub-GeV:Pe2 =

    (∆m221)2

    (2EVe)2sin2 2θ12 sin

    2 VeL

    2

    θ23 <π4 ⇒ c223 > 12 ⇒ Ne(θ13) > Ne0

    θ23 >π4 ⇒ c223 < 12 ⇒ Ne(θ13) < Ne0

    ⇒ Sensitiv to Deviations from Maximal θ23⇒ Sensitivity to Octant of θ23

    (even for vanishing θ13)⇒ Effect proportional to (∆m221)2

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    ∆m221 effects in ATM Data

    -1 -0.5 0 0.5 10.8

    0.9

    1

    1.1

    1.2

    1.3

    Ne

    / Ne0

    SK sub-GeV (e)

    Normal

    -1 -0.5 0 0.5 10.8

    0.9

    1

    1.1

    1.2

    1.3

    SK sub-GeV (e)

    Inverted

    -1 -0.5 0 0.5 1

    cos θ

    0.8

    0.9

    1

    1.1

    1.2

    1.3

    Ne

    / Ne0

    SK multi-GeV (e)

    Normal

    -1 -0.5 0 0.5 1

    cos θ

    0.8

    0.9

    1

    1.1

    1.2

    1.3

    SK multi-GeV (e)

    Inverted

    Ne

    Ne0− 1 = Pe2r̄(c223 − 1r̄ )

    Pe2 = sin2 2θ12,m sin

    2(

    ∆m221

    L

    4Eνsin 2θ12

    sin 2θ12,m

    )

    sin 2θ12,m =sin2 2θ12

    r

    (cos 2θ12 ∓2EVe∆m2

    21

    )2 + sin2 2θ12

    For Sub-GeV:Pe2 =

    (∆m221)2

    (2EVe)2sin2 2θ12 sin

    2 VeL

    2

    θ23 <π4 ⇒ c223 > 12 ⇒ Ne(θ13) > Ne0

    θ23 >π4 ⇒ c223 < 12 ⇒ Ne(θ13) < Ne0

    ⇒ Sensitiv to Deviations from Maximal θ23⇒ Sensitivity to Octant of θ23

    (even for vanishing θ13)⇒ Effect proportional to (∆m221)2

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Beyond Hierarchical: Effect θ13 × ∆m221 in ATMSmirnov, Peres 01,03, MC G-G, Maltoni 02

    For sub-GeV energiesNe

    N0e− 1 ' Pe2r(c223 −

    1

    r) + 2s̃213r(s

    223 −

    1

    r) − rs̃13c̃213 sin 2θ23(cos δCP R2 − sin δCP I2)

    Pe2 = sin2 2θ12,m sin

    2 φm2

    sin 2θ12,m =sin 2θ12

    r

    (cos 2θ12∓ 2EνVe∆m2

    21

    )2+sin2 2θ12

    R2 = −sin 2θ12,m cos 2θ12,m sin2 φm

    2I2 = −

    12sin 2θ12,m sin φm

    θ̃13 ≈ θ13“

    1 + 2EνVe∆m2

    31

    φ ≈ (∆m231 + s212 ∆m

    221)

    L2Eν

    -1 -0.5 0 0.5 1cos θ

    1.05

    1.1

    1.15

    1.2

    1.25

    Ne

    / N0 e

    Normal

    -1 -0.5 0 0.5 1cos θ

    Invertedδ

    CP = −π

    δCP

    = −2π/3δ

    CP = −π/3

    δCP

    = 0

    δCP

    = +π/3δ

    CP = +2π/3

    δCP

    = +π

  • Physics of Massive Neutrinos Concha Gonzalez-GarciaGlobal Analysis: Three Neutrino OscillationsM.C. G-G, M.Maltoni, ArXiV/0704.1800

    0.3 0.4 0.5 0.6 0.7

    tan2 θ12

    6

    7

    8

    9

    10

    ∆m2 21

    [10-

    5 eV

    2 ]

    0 0.01 0.02 0.03 0.04 0.05

    sin2 θ13

    0.3 0.5 1 2 3

    tan2 θ23

    -4

    -2

    0

    2

    4

    ∆m2 31

    [10-

    3 eV

    2 ]

    0 0.01 0.02 0.03 0.04 0.05

    sin2 θ13

    0 0.01 0.02 0.03 0.04 0.05

    sin2 θ13

    0

    60

    120

    180

    240

    300

    360

    δ CP

    0 5 10 15

    ∆m221 [10-5

    eV2]

    0

    5

    10

    15

    ∆χ2

    w/o K

    amLand

    0.3 0.4 0.5 0.6 0.7 0.8

    tan2 θ12

    -4 -2 0 2 4

    ∆m231 [10-3

    eV2]

    0

    5

    10

    15

    ∆χ2

    w/o

    LB

    L

    0.3 0.5 1 2 3

    tan2 θ23

    0 0.05 0.1 0.15

    sin2 θ13

    0

    5

    10

    15

    ∆χ2

    ATM only

    ATM

    +CH

    OO

    Z

    + LB

    L

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Global Analysis: Three Neutrino Oscillations

    The derived ranges:

    ∆m221 = 7.7+0.22−0.21

    (

    +0.67−0.61

    )

    × 10−5 eV2∣

    ∣∆m231∣

    ∣ = 2.37 ± 0.17 (0.46) × 10−3 eV2

    |ULEP |3σ =

    0

    @

    0.79 → 0.86 0.50 → 0.61 0.00 → 0.20

    0.25 → 0.53 0.47 → 0.73 0.56 → 0.79

    0.21 → 0.51 0.42 → 0.69 0.61 → 0.83

    1

    A

    with structure

    |ULEP| '

    1√2(1 + O(λ)) 1√

    2(1 −O(λ)) �

    − 12 (1 −O(λ) + �) 12(1 + O(λ) − �) 1√212(1 −O(λ) − �) − 12(1 + O(λ) − �) 1√2

    λ ∼ 0.2� . 0.2

    very different from quark’s |UCKM| '

    1 O(λ) O(λ3)O(λ) 1 O(λ2)O(λ3) O(λ2) 1

    λ ∼ 0.2

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Global Analysis: Three Neutrino Oscillations

    The derived ranges:

    ∆m221 = 7.7+0.22−0.21

    (

    +0.67−0.61

    )

    × 10−5 eV2∣

    ∣∆m231∣

    ∣ = 2.37 ± 0.17 (0.46) × 10−3 eV2

    |ULEP |3σ =

    0

    @

    0.79 → 0.86 0.50 → 0.61 0.00 → 0.20

    0.25 → 0.53 0.47 → 0.73 0.56 → 0.79

    0.21 → 0.51 0.42 → 0.69 0.61 → 0.83

    1

    A

    with structure

    |ULEP| '

    1√2(1 + O(λ)) 1√

    2(1 −O(λ)) �

    − 12 (1 −O(λ) + �) 12(1 + O(λ) − �) 1√212(1 −O(λ) − �) − 12(1 + O(λ) − �) 1√2

    λ ∼ 0.2� . 0.2

    very different from quark’s |UCKM| '

    1 O(λ) O(λ3)O(λ) 1 O(λ2)O(λ3) O(λ2) 1

    λ ∼ 0.2

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Global Analysis: Three Neutrino Oscillations

    The derived ranges:

    ∆m221 = 7.7+0.22−0.21

    (

    +0.67−0.61

    )

    × 10−5 eV2∣

    ∣∆m231∣

    ∣ = 2.37 ± 0.17 (0.46) × 10−3 eV2

    |ULEP |3σ =

    0

    @

    0.79 → 0.86 0.50 → 0.61 0.00 → 0.20

    0.25 → 0.53 0.47 → 0.73 0.56 → 0.79

    0.21 → 0.51 0.42 → 0.69 0.61 → 0.83

    1

    A

    with structure

    |ULEP| '

    1√2(1 + O(λ)) 1√

    2(1 −O(λ)) �

    − 12 (1 −O(λ) + �) 12(1 + O(λ) − �) 1√212(1 −O(λ) − �) − 12(1 + O(λ) − �) 1√2

    λ ∼ 0.2� . 0.2

    very different from quark’s |UCKM| '

    1 O(λ) O(λ3)O(λ) 1 O(λ2)O(λ3) O(λ2) 1

    λ ∼ 0.2

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Open Questions

    We still ignore: { (1) Is θ13 6= 0? How small?(2) Is θ23 = π4 ? If not, is it > or

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Some Lessons: New Physics

    A fermion mass can be seen as at a Left-Right transition

    mffLfR (this is not SU(2)L gauge invariant)

    If the SM is the fundamental theory:– All terms in lagrangian (including masses) must be

    {

    gauge invariant

    renormalizable (dim ≤ 4 )– A gauge invariant fermion mass is generated

    by interaction with the Higgs field λffLφfR → mf = λfv(v ≡ Higgs vacuum expectation value ∼ 250 GeV)

    – But there are no right-handed neutrinos⇒ No renormalizable gauge-invariant operator for tree level ν mass

    – SM gauge invariance also implies the accidental symmetryG

    globalSM = U(1)B × U(1)Le × U(1)Lµ × U(1)Lτ⇒ mν = 0 to all orders

    Thus the most striking implication of ν masses:

    There is New Physics Beyond the SMAnd it is also the only solid evidence! To go further one has to be cautious. . .

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Some Lessons: New Physics

    A fermion mass can be seen as at a Left-Right transition

    mffLfR (this is not SU(2)L gauge invariant)

    If the SM is the fundamental theory:– All terms in lagrangian (including masses) must be

    {

    gauge invariant

    renormalizable (dim ≤ 4 )– A gauge invariant fermion mass is generated

    by interaction with the Higgs field λffLφfR → mf = λfv(v ≡ Higgs vacuum expectation value ∼ 250 GeV)

    – But there are no right-handed neutrinos⇒ No renormalizable gauge-invariant operator for tree level ν mass

    – SM gauge invariance also implies the accidental symmetryG

    globalSM = U(1)B × U(1)Le × U(1)Lµ × U(1)Lτ⇒ mν = 0 to all orders

    Thus the most striking implication of ν masses:

    There is New Physics Beyond the SMAnd it is also the only solid evidence! To go further one has to be cautious. . .

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Some Lessons: New Physics

    A fermion mass can be seen as at a Left-Right transition

    mffLfR (this is not SU(2)L gauge invariant)

    If the SM is the fundamental theory:– All terms in lagrangian (including masses) must be

    {

    gauge invariant

    renormalizable (dim ≤ 4 )

    – A gauge invariant fermion mass is generatedby interaction with the Higgs field λffLφfR → mf = λfv

    (v ≡ Higgs vacuum expectation value ∼ 250 GeV)

    – But there are no right-handed neutrinos⇒ No renormalizable gauge-invariant operator for tree level ν mass

    – SM gauge invariance also implies the accidental symmetryG

    globalSM = U(1)B × U(1)Le × U(1)Lµ × U(1)Lτ⇒ mν = 0 to all orders

    Thus the most striking implication of ν masses:

    There is New Physics Beyond the SMAnd it is also the only solid evidence! To go further one has to be cautious. . .

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Some Lessons: New Physics

    A fermion mass can be seen as at a Left-Right transition

    mffLfR (this is not SU(2)L gauge invariant)

    If the SM is the fundamental theory:– All terms in lagrangian (including masses) must be

    {

    gauge invariant

    renormalizable (dim ≤ 4 )– A gauge invariant fermion mass is generated

    by interaction with the Higgs field λffLφfR → mf = λfv(v ≡ Higgs vacuum expectation value ∼ 250 GeV)

    – But there are no right-handed neutrinos⇒ No renormalizable gauge-invariant operator for tree level ν mass

    – SM gauge invariance also implies the accidental symmetryG

    globalSM = U(1)B × U(1)Le × U(1)Lµ × U(1)Lτ⇒ mν = 0 to all orders

    Thus the most striking implication of ν masses:

    There is New Physics Beyond the SMAnd it is also the only solid evidence! To go further one has to be cautious. . .

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Some Lessons: New Physics

    A fermion mass can be seen as at a Left-Right transition

    mffLfR (this is not SU(2)L gauge invariant)

    If the SM is the fundamental theory:– All terms in lagrangian (including masses) must be

    {

    gauge invariant

    renormalizable (dim ≤ 4 )– A gauge invariant fermion mass is generated

    by interaction with the Higgs field λffLφfR → mf = λfv(v ≡ Higgs vacuum expectation value ∼ 250 GeV)

    – But there are no right-handed neutrinos⇒ No renormalizable gauge-invariant operator for tree level ν mass

    – SM gauge invariance also implies the accidental symmetryG

    globalSM = U(1)B × U(1)Le × U(1)Lµ × U(1)Lτ⇒ mν = 0 to all orders

    Thus the most striking implication of ν masses:

    There is New Physics Beyond the SMAnd it is also the only solid evidence! To go further one has to be cautious. . .

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Some Lessons: New Physics

    A fermion mass can be seen as at a Left-Right transition

    mffLfR (this is not SU(2)L gauge invariant)

    If the SM is the fundamental theory:– All terms in lagrangian (including masses) must be

    {

    gauge invariant

    renormalizable (dim ≤ 4 )– A gauge invariant fermion mass is generated

    by interaction with the Higgs field λffLφfR → mf = λfv(v ≡ Higgs vacuum expectation value ∼ 250 GeV)

    – But there are no right-handed neutrinos⇒ No renormalizable gauge-invariant operator for tree level ν mass

    – SM gauge invariance also implies the accidental symmetryG

    globalSM = U(1)B × U(1)Le × U(1)Lµ × U(1)Lτ⇒ mν = 0 to all orders

    Thus the most striking implication of ν masses:

    There is New Physics Beyond the SMAnd it is also the only solid evidence! To go further one has to be cautious. . .

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Some Lessons: New Physics

    A fermion mass can be seen as at a Left-Right transition

    mffLfR (this is not SU(2)L gauge invariant)

    If the SM is the fundamental theory:– All terms in lagrangian (including masses) must be

    {

    gauge invariant

    renormalizable (dim ≤ 4 )– A gauge invariant fermion mass is generated

    by interaction with the Higgs field λffLφfR → mf = λfv(v ≡ Higgs vacuum expectation value ∼ 250 GeV)

    – But there are no right-handed neutrinos⇒ No renormalizable gauge-invariant operator for tree level ν mass

    – SM gauge invariance also implies the accidental symmetryG

    globalSM = U(1)B × U(1)Le × U(1)Lµ × U(1)Lτ⇒ mν = 0 to all orders

    Thus the most striking implication of ν masses:

    There is New Physics Beyond the SM

    And it is also the only solid evidence! To go further one has to be cautious. . .

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Some Lessons: New Physics

    A fermion mass can be seen as at a Left-Right transition

    mffLfR (this is not SU(2)L gauge invariant)

    If the SM is the fundamental theory:– All terms in lagrangian (including masses) must be

    {

    gauge invariant

    renormalizable (dim ≤ 4 )– A gauge invariant fermion mass is generated

    by interaction with the Higgs field λffLφfR → mf = λfv(v ≡ Higgs vacuum expectation value ∼ 250 GeV)

    – But there are no right-handed neutrinos⇒ No renormalizable gauge-invariant operator for tree level ν mass

    – SM gauge invariance also implies the accidental symmetryG

    globalSM = U(1)B × U(1)Le × U(1)Lµ × U(1)Lτ⇒ mν = 0 to all orders

    Thus the most striking implication of ν masses:

    There is New Physics Beyond the SMAnd it is also the only solid evidence! To go further one has to be cautious. . .

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Lessons: The Scale of 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 =

    Zνij

    ΛNP

    (

    φ̃†LLj

    )(

    LcLiφ̃∗)

    which after symmetry breakinginduces a ν Majorana mass (Mν)ij =

    Zνij

    2

    v2

    ΛNP

    L5 breaks total lepton and lepton flavour numbersImplications:– It is natural that ν mass is the first evidence of NP

    – Naturally mν � other fermions masses ∼ λfv– mν >

    ∆m2atm ∼ 0.05 eV ⇒ ΛNP < 1015 GeVBut this is scale was already known to particle physicists...

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Lessons: The Scale of 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 =

    Zνij

    ΛNP

    (

    φ̃†LLj

    )(

    LcLiφ̃∗)

    which after symmetry breakinginduces a ν Majorana mass (Mν)ij =

    Zνij

    2

    v2

    ΛNP

    L5 breaks total lepton and lepton flavour numbersImplications:– It is natural that ν mass is the first evidence of NP

    – Naturally mν � other fermions masses ∼ λfv– mν >

    ∆m2atm ∼ 0.05 eV ⇒ ΛNP < 1015 GeVBut this is scale was already known to particle physicists...

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Lessons: The Scale of 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 =

    Zνij

    ΛNP

    (

    φ̃†LLj

    )(

    LcLiφ̃∗)

    which after symmetry breakinginduces a ν Majorana mass (Mν)ij =

    Zνij

    2

    v2

    ΛNP

    L5 breaks total lepton and lepton flavour numbersImplications:– It is natural that ν mass is the first evidence of NP

    – Naturally mν � other fermions masses ∼ λfv– mν >

    ∆m2atm ∼ 0.05 eV ⇒ ΛNP < 1015 GeVBut this is scale was already known to particle physicists...

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Lessons: The Scale of 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 =

    Zνij

    ΛNP

    (

    φ̃†LLj

    )(

    LcLiφ̃∗)

    which after symmetry breakinginduces a ν Majorana mass (Mν)ij =

    Zνij

    2

    v2

    ΛNP

    L5 breaks total lepton and lepton flavour numbersImplications:– It is natural that ν mass is the first evidence of NP

    – Naturally mν � other fermions masses ∼ λfv– mν >

    ∆m2atm ∼ 0.05 eV ⇒ ΛNP < 1015 GeVBut this is scale was already known to particle physicists...

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Lessons: The Scale of 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 =

    Zνij

    ΛNP

    (

    φ̃†LLj

    )(

    LcLiφ̃∗)

    which after symmetry breakinginduces a ν Majorana mass (Mν)ij =

    Zνij

    2

    v2

    ΛNP

    L5 breaks total lepton and lepton flavour numbers

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

    – Naturally mν � other fermions masses ∼ λfv– mν >

    ∆m2atm ∼ 0.05 eV ⇒ ΛNP < 1015 GeVBut this is scale was already known to particle physicists...

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Lessons: The Scale of 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 =

    Zνij

    ΛNP

    (

    φ̃†LLj

    )(

    LcLiφ̃∗)

    which after symmetry breakinginduces a ν Majorana mass (Mν)ij =

    Zνij

    2

    v2

    ΛNP

    L5 breaks total lepton and lepton flavour numbersImplications:– It is natural that ν mass is the first evidence of NP

    – Naturally mν � other fermions masses ∼ λfv– mν >

    ∆m2atm ∼ 0.05 eV ⇒ ΛNP < 1015 GeV

    But this is scale was already known to particle physicists...

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Lessons: The Scale of 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 =

    Zνij

    ΛNP

    (

    φ̃†LLj

    )(

    LcLiφ̃∗)

    which after symmetry breakinginduces a ν Majorana mass (Mν)ij =

    Zνij

    2

    v2

    ΛNP

    L5 breaks total lepton and lepton flavour numbersImplications:– It is natural that ν mass is the first evidence of NP

    – Naturally mν � other fermions masses ∼ λfv– mν >

    ∆m2atm ∼ 0.05 eV ⇒ ΛNP < 1015 GeVBut this is scale was already known to particle physicists...

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Lessons: The Scale of New Physics

    mν >√

    ∆m2atm ∼ 0.05eV ⇒ 1010 < ΛNP < 1015GeV New Physics Scaleclose to Grand Uni-fication scale

    Also the generated neutrino mass term is Majorana :⇒ It violates total lepton number

    L5 =Zνij

    ΛNP

    (

    φ̃†LLj

    ) (

    LcLiφ̃∗)

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    The See-Saw

    Simplest NP: add right-handed νR (=SM singlet) neutrinos

    Well above the electroweak (EW) scale

    −LNP =1

    2MRijνRiνR

    cj + λ

    νijνRiφ̃

    †LLj + h.c..

    νR is a EW singlet ⇒ MRij >> EW scaleBelow EW symmetry breaking scale (E � MR):a) mD = λνv ∼ mass of other fermions is generatedb) νR are so heavy that can be “integrated out”⇒

    E � MR

    LNP ⇒ L5 =(λνT λν)ij

    MR

    (

    φ̃†LLj

    ) (

    LcLiφ̃∗)

    ⇒ mν = mTD1

    MRmD

    This

    isthe

    see-sa

    w

    Lessons:– LNP contains 18 parameters which we want to know– L5 contains 9 parameters which we can measure⇒ Same O5 can give very different LNP⇒ It is difficult to “imply” bottom-up (model independently)

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    The See-SawSimplest NP: add right-handed νR (=SM singlet) neutrinos

    Well above the electroweak (EW) scale

    −LNP =1

    2MRijνRiνR

    cj + λ

    νijνRiφ̃

    †LLj + h.c..

    νR is a EW singlet ⇒ MRij >> EW scaleBelow EW symmetry breaking scale (E � MR):a) mD = λνv ∼ mass of other fermions is generatedb) νR are so heavy that can be “integrated out”⇒

    E � MR

    LNP ⇒ L5 =(λνT λν)ij

    MR

    (

    φ̃†LLj

    ) (

    LcLiφ̃∗)

    ⇒ mν = mTD1

    MRmD

    This

    isthe

    see-sa

    w

    Lessons:– LNP contains 18 parameters which we want to know– L5 contains 9 parameters which we can measure⇒ Same O5 can give very different LNP⇒ It is difficult to “imply” bottom-up (model independently)

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    The See-SawSimplest NP: add right-handed νR (=SM singlet) neutrinos

    Well above the electroweak (EW) scale

    −LNP =1

    2MRijνRiνR

    cj + λ

    νijνRiφ̃

    †LLj + h.c..

    νR is a EW singlet ⇒ MRij >> EW scaleBelow EW symmetry breaking scale (E � MR):a) mD = λνv ∼ mass of other fermions is generatedb) νR are so heavy that can be “integrated out”⇒

    E � MR

    LNP ⇒ L5 =(λνT λν)ij

    MR

    (

    φ̃†LLj

    ) (

    LcLiφ̃∗)

    ⇒ mν = mTD1

    MRmD

    This

    isthe

    see-sa

    w

    Lessons:– LNP contains 18 parameters which we want to know– L5 contains 9 parameters which we can measure⇒ Same O5 can give very different LNP⇒ It is difficult to “imply” bottom-up (model independently)

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    The See-SawSimplest NP: add right-handed νR (=SM singlet) neutrinos

    Well above the electroweak (EW) scale

    −LNP =1

    2MRijνRiνR

    cj + λ

    νijνRiφ̃

    †LLj + h.c..

    νR is a EW singlet ⇒ MRij >> EW scale

    Below EW symmetry breaking scale (E � MR):a) mD = λνv ∼ mass of other fermions is generatedb) νR are so heavy that can be “integrated out”⇒

    E � MR

    LNP ⇒ L5 =(λνT λν)ij

    MR

    (

    φ̃†LLj

    ) (

    LcLiφ̃∗)

    ⇒ mν = mTD1

    MRmD

    This

    isthe

    see-sa

    w

    Lessons:– LNP contains 18 parameters which we want to know– L5 contains 9 parameters which we can measure⇒ Same O5 can give very different LNP⇒ It is difficult to “imply” bottom-up (model independently)

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    The See-SawSimplest NP: add right-handed νR (=SM singlet) neutrinos

    Well above the electroweak (EW) scale

    −LNP =1

    2MRijνRiνR

    cj + λ

    νijνRiφ̃

    †LLj + h.c..

    νR is a EW singlet ⇒ MRij >> EW scaleBelow EW symmetry breaking scale (E � MR):a) mD = λνv ∼ mass of other fermions is generatedb) νR are so heavy that can be “integrated out”

    E � MR

    LNP ⇒ L5 =(λνT λν)ij

    MR

    (

    φ̃†LLj

    ) (

    LcLiφ̃∗)

    ⇒ mν = mTD1

    MRmD

    This

    isthe

    see-sa

    w

    Lessons:– LNP contains 18 parameters which we want to know– L5 contains 9 parameters which we can measure⇒ Same O5 can give very different LNP⇒ It is difficult to “imply” bottom-up (model independently)

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    The See-SawSimplest NP: add right-handed νR (=SM singlet) neutrinos

    Well above the electroweak (EW) scale

    −LNP =1

    2MRijνRiνR

    cj + λ

    νijνRiφ̃

    †LLj + h.c..

    νR is a EW singlet ⇒ MRij >> EW scaleBelow EW symmetry breaking scale (E � MR):a) mD = λνv ∼ mass of other fermions is generatedb) νR are so heavy that can be “integrated out”⇒

    E � MR

    LNP ⇒ L5 =(λνT λν)ij

    MR

    (

    φ̃†LLj

    ) (

    LcLiφ̃∗)

    ⇒ mν = mTD1

    MRmD

    This

    isthe

    see-sa

    w

    Lessons:– LNP contains 18 parameters which we want to know– L5 contains 9 parameters which we can measure⇒ Same O5 can give very different LNP⇒ It is difficult to “imply” bottom-up (model independently)

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    The See-SawSimplest NP: add right-handed νR (=SM singlet) neutrinos

    Well above the electroweak (EW) scale

    −LNP =1

    2MRijνRiνR

    cj + λ

    νijνRiφ̃

    †LLj + h.c..

    νR is a EW singlet ⇒ MRij >> EW scaleBelow EW symmetry breaking scale (E � MR):a) mD = λνv ∼ mass of other fermions is generatedb) νR are so heavy that can be “integrated out”⇒

    E � MR

    LNP ⇒ L5 =(λνT λν)ij

    MR

    (

    φ̃†LLj

    ) (

    LcLiφ̃∗)

    ⇒ mν = mTD1

    MRmD

    This

    isthe

    see-sa

    w

    Lessons:– LNP contains 18 parameters which we want to know– L5 contains 9 parameters which we can measure⇒ Same O5 can give very different LNP⇒ It is difficult to “imply” bottom-up (model independently)

  • Physics of Massive Neutrinos Concha Gonzalez-GarciaLeptogenesis

    Baryogenesis and the SM

    • From Nucleosytesys and CMBR data ⇒ YB =nb − nb

    s =nbs ∼ 10−10

    • YB can be dynamically generated ifThree Sakharov Conditions are verified:

    – Baryon number is violated– C and CP are violated– Departure from thermal equilibrium

    • The SM verifies these conditions:

    → Conserves B −L but violates B + L→ CP violation due to δCKM→ Departure from thermal equilibrium

    at Electroweak Phase Transition• But the SM fails on two points:

    – With the bound of SM Higgs mass the EWPT is not strong first order PT– CKM CP violation is too suppressed

    ⇓YB,SM � 10−10

  • Physics of Massive Neutrinos Concha Gonzalez-GarciaLeptogenesis

    Baryogenesis and the SM

    • From Nucleosytesys and CMBR data ⇒ YB =nb − nb

    s =nbs ∼ 10−10

    • YB can be dynamically generated ifThree Sakharov Conditions are verified:

    – Baryon number is violated– C and CP are violated– Departure from thermal equilibrium

    • The SM verifies these conditions:

    → Conserves B −L but violates B + L→ CP violation due to δCKM→ Departure from thermal equilibrium

    at Electroweak Phase Transition• But the SM fails on two points:

    – With the bound of SM Higgs mass the EWPT is not strong first order PT– CKM CP violation is too suppressed

    ⇓YB,SM � 10−10

  • Physics of Massive Neutrinos Concha Gonzalez-GarciaLeptogenesis

    Baryogenesis and the SM

    • From Nucleosytesys and CMBR data ⇒ YB =nb − nb

    s =nbs ∼ 10−10

    • YB can be dynamically generated ifThree Sakharov Conditions are verified:

    – Baryon number is violated– C and CP are violated– Departure from thermal equilibrium

    • The SM verifies these conditions:

    → Conserves B −L but violates B + L→ CP violation due to δCKM→ Departure from thermal equilibrium

    at Electroweak Phase Transition• But the SM fails on two points:

    – With the bound of SM Higgs mass the EWPT is not strong first order PT– CKM CP violation is too suppressed

    ⇓YB,SM � 10−10

  • Physics of Massive Neutrinos Concha Gonzalez-GarciaLeptogenesis

    Baryogenesis and the SM

    • From Nucleosytesys and CMBR data ⇒ YB =nb − nb

    s =nbs ∼ 10−10

    • YB can be dynamically generated ifThree Sakharov Conditions are verified:

    – Baryon number is violated– C and CP are violated– Departure from thermal equilibrium

    • The SM verifies these conditions:

    → Conserves B −L but violates B + L→ CP violation due to δCKM→ Departure from thermal equilibrium

    at Electroweak Phase Transition• But the SM fails on two points:

    – With the bound of SM Higgs mass the EWPT is not strong first order PT– CKM CP violation is too suppressed

    ⇓YB,SM � 10−10

  • Physics of Massive Neutrinos Concha Gonzalez-GarciaLeptogenesis

    Baryogenesis and the SM

    • From Nucleosytesys and CMBR data ⇒ YB =nb − nb

    s =nbs ∼ 10−10

    • YB can be dynamically generated ifThree Sakharov Conditions are verified:

    – Baryon number is violated– C and CP are violated– Departure from thermal equilibrium

    • The SM verifies these conditions:

    → Conserves B −L but violates B + L→ CP violation due to δCKM→ Departure from thermal equilibrium

    at Electroweak Phase Transition

    • But the SM fails on two points:– With the bound of SM Higgs mass the EWPT is not strong first order PT– CKM CP violation is too suppressed

    ⇓YB,SM � 10−10

  • Physics of Massive Neutrinos Concha Gonzalez-GarciaLeptogenesis

    Baryogenesis and the SM

    • From Nucleosytesys and CMBR data ⇒ YB =nb − nb

    s =nbs ∼ 10−10

    • YB can be dynamically generated ifThree Sakharov Conditions are verified:

    – Baryon number is violated– C and CP are violated– Departure from thermal equilibrium

    • The SM verifies these conditions:

    → Conserves B −L but violates B + L→ CP violation due to δCKM→ Departure from thermal equilibrium

    at Electroweak Phase Transition• But the SM fails on two points:

    – With the bound of SM Higgs mass the EWPT is not strong first order PT– CKM CP violation is too suppressed

    ⇓YB,SM � 10−10

  • Physics of Massive Neutrinos Concha Gonzalez-GarciaLeptogenesis

    Baryogenesis and the SM

    • From Nucleosytesys and CMBR data ⇒ YB =nb − nb

    s =nbs ∼ 10−10

    • YB can be dynamically generated ifThree Sakharov Conditions are verified:

    – Baryon number is violated– C and CP are violated– Departure from thermal equilibrium

    • The SM verifies these conditions:

    → Conserves B −L but violates B + L→ CP violation due to δCKM→ Departure from thermal equilibrium

    at Electroweak Phase Transition• But the SM fails on two points:

    – With the bound of SM Higgs mass the EWPT is not strong first order PT– CKM CP violation is too suppressed

    ⇓YB,SM � 10−10

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Leptogenesis

    • From the analysis of oscillation data ⇒ mν3 & 0.05 eV

    • If mν is generated via the See-saw mechanism

    −LNP = 12MRijνRiνRcj + λνijνRiφ̃†LLj ⇒ mν ∼λ2〈φ〉2MR

    }(MνR3/λ23 . 1015 GeV)⇒ Lepton Number is Violated (MR)

    ⇒ New Sources of CP violation λ

    ⇒ Decay of νR can be out of equilibrium(if ΓνR � Universe expansion rate) ⇒ ΓνR � H

    T=MνR

    ⇓Leptogenesis ≡ generation of lepton asymmetry YL

    • At the electroweak transition sphaleron processes:⇒ YL is transformed in YB ' −YL2

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Leptogenesis

    • From the analysis of oscillation data ⇒ mν3 & 0.05 eV

    • If mν is generated via the See-saw mechanism

    −LNP = 12MRijνRiνRcj + λνijνRiφ̃†LLj ⇒ mν ∼λ2〈φ〉2MR

    }(MνR3/λ23 . 1015 GeV)⇒ Lepton Number is Violated (MR)

    ⇒ New Sources of CP violation λ

    ⇒ Decay of νR can be out of equilibrium(if ΓνR � Universe expansion rate) ⇒ ΓνR � H

    T=MνR

    ⇓Leptogenesis ≡ generation of lepton asymmetry YL

    • At the electroweak transition sphaleron processes:⇒ YL is transformed in YB ' −YL2

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Leptogenesis

    • From the analysis of oscillation data ⇒ mν3 & 0.05 eV

    • If mν is generated via the See-saw mechanism

    −LNP = 12MRijνRiνRcj + λνijνRiφ̃†LLj ⇒ mν ∼λ2〈φ〉2MR

    }(MνR3/λ23 . 1015 GeV)⇒ Lepton Number is Violated (MR)

    ⇒ New Sources of CP violation λ

    ⇒ Decay of νR can be out of equilibrium(if ΓνR � Universe expansion rate) ⇒ ΓνR � H

    T=MνR

    ⇓Leptogenesis ≡ generation of lepton asymmetry YL

    • At the electroweak transition sphaleron processes:⇒ YL is transformed in YB ' −YL2

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Leptogenesis

    • From the analysis of oscillation data ⇒ mν3 & 0.05 eV

    • If mν is generated via the See-saw mechanism

    −LNP = 12MRijνRiνRcj + λνijνRiφ̃†LLj ⇒ mν ∼λ2〈φ〉2MR

    }(MνR3/λ23 . 1015 GeV)

    ⇒ Lepton Number is Violated (MR)

    ⇒ New Sources of CP violation λ

    ⇒ Decay of νR can be out of equilibrium(if ΓνR � Universe expansion rate) ⇒ ΓνR � H

    T=MνR

    ⇓Leptogenesis ≡ generation of lepton asymmetry YL

    • At the electroweak transition sphaleron processes:⇒ YL is transformed in YB ' −YL2

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Leptogenesis

    • From the analysis of oscillation data ⇒ mν3 & 0.05 eV

    • If mν is generated via the See-saw mechanism

    −LNP = 12MRijνRiνRcj + λνijνRiφ̃†LLj ⇒ mν ∼λ2〈φ〉2MR

    }(MνR3/λ23 . 1015 GeV)⇒ Lepton Number is Violated (MR)

    ⇒ New Sources of CP violation λ

    ⇒ Decay of νR can be out of equilibrium(if ΓνR � Universe expansion rate) ⇒ ΓνR � H

    T=MνR

    ⇓Leptogenesis ≡ generation of lepton asymmetry YL

    • At the electroweak transition sphaleron processes:⇒ YL is transformed in YB ' −YL2

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Leptogenesis

    • From the analysis of oscillation data ⇒ mν3 & 0.05 eV

    • If mν is generated via the See-saw mechanism

    −LNP = 12MRijνRiνRcj + λνijνRiφ̃†LLj ⇒ mν ∼λ2〈φ〉2MR

    }(MνR3/λ23 . 1015 GeV)⇒ Lepton Number is Violated (MR)

    ⇒ New Sources of CP violation λ

    ⇒ Decay of νR can be out of equilibrium(if ΓνR � Universe expansion rate) ⇒ ΓνR � H

    T=MνR

    ⇓Leptogenesis ≡ generation of lepton asymmetry YL

    • At the electroweak transition sphaleron processes:⇒ YL is transformed in YB ' −YL2

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Leptogenesis

    • From the analysis of oscillation data ⇒ mν3 & 0.05 eV

    • If mν is generated via the See-saw mechanism

    −LNP = 12MRijνRiνRcj + λνijνRiφ̃†LLj ⇒ mν ∼λ2〈φ〉2MR

    }(MνR3/λ23 . 1015 GeV)⇒ Lepton Number is Violated (MR)

    ⇒ New Sources of CP violation λ

    ⇒ Decay of νR can be out of equilibrium(if ΓνR � Universe expansion rate) ⇒ ΓνR � H

    T=MνR

    ⇓Leptogenesis ≡ generation of lepton asymmetry YL

    • At the electroweak transition sphaleron processes:⇒ YL is transformed in YB ' −YL2

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia• In the the See-saw mechanism −LNP = 12MRijνRiνRcj + λνijνRiφ̃†LLj

    – In the Early Universe decay of heavy νR: Γ(νR → φ lL) =1

    i

    (λλ†)2iiMνRi

    – CP can be violated at 1-loop

    l

    νR

    φ

    6=

    νR

    φ̄

    (This requires 3 lightgenerations and at least2νR)

    �L =Γ(νR → φ lL) − Γ(νR → φ lL)

    Γ(νR → φ lL) + Γ(νR → φ lL)= −

    1

    X

    k

    Im[(λλ†)2k1]

    (λλ†)11× f

    MνRkMνR1

    «

    ⇒ |�L| . 0.1MνR1〈φ〉2

    (mν3 − mν1)

    YL =nνRs

    �L d ∼ 10−3d �L nνR ≡ density of νR (d < 1 ≡ dilution factor)

    Out of Equilibrium condition ΓνR � H∣

    T=MνR⇒ m̃1 ≡ (λλ

    †)211〈φ〉2

    MνR1. 5 × 10−3eV

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia• In the the See-saw mechanism −LNP = 12MRijνRiνRcj + λνijνRiφ̃†LLj

    – In the Early Universe decay of heavy νR: Γ(νR → φ lL) =1

    i

    (λλ†)2iiMνRi

    – CP can be violated at 1-loop

    l

    νR

    φ

    6=

    νR

    φ̄

    (This requires 3 lightgenerations and at least2νR)

    �L =Γ(νR → φ lL) − Γ(νR → φ lL)

    Γ(νR → φ lL) + Γ(νR → φ lL)= −

    1

    X

    k

    Im[(λλ†)2k1]

    (λλ†)11× f

    MνRkMνR1

    «

    ⇒ |�L| . 0.1MνR1〈φ〉2

    (mν3 − mν1)

    YL =nνRs

    �L d ∼ 10−3d �L nνR ≡ density of νR (d < 1 ≡ dilution factor)

    Out of Equilibrium condition ΓνR � H∣

    T=MνR⇒ m̃1 ≡ (λλ

    †)211〈φ〉2

    MνR1. 5 × 10−3eV

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia• In the the See-saw mechanism −LNP = 12MRijνRiνRcj + λνijνRiφ̃†LLj

    – In the Early Universe decay of heavy νR: Γ(νR → φ lL) =1

    i

    (λλ†)2iiMνRi

    – CP can be violated at 1-loop

    l

    νR

    φ

    6=

    νR

    φ̄

    (This requires 3 lightgenerations and at least2νR)

    �L =Γ(νR → φ lL) − Γ(νR → φ lL)

    Γ(νR → φ lL) + Γ(νR → φ lL)= −

    1

    X

    k

    Im[(λλ†)2k1]

    (λλ†)11× f

    MνRkMνR1

    «

    ⇒ |�L| . 0.1MνR1〈φ〉2

    (mν3 − mν1)

    YL =nνRs

    �L d ∼ 10−3d �L nνR ≡ density of νR (d < 1 ≡ dilution factor)

    Out of Equilibrium condition ΓνR � H∣

    T=MνR⇒ m̃1 ≡ (λλ

    †)211〈φ〉2

    MνR1. 5 × 10−3eV

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia• In the the See-saw mechanism −LNP = 12MRijνRiνRcj + λνijνRiφ̃†LLj

    – In the Early Universe decay of heavy νR: Γ(νR → φ lL) =1

    i

    (λλ†)2iiMνRi

    – CP can be violated at 1-loop

    l

    νR

    φ

    6=

    νR

    φ̄

    (This requires 3 lightgenerations and at least2νR)

    �L =Γ(νR → φ lL) − Γ(νR → φ lL)

    Γ(νR → φ lL) + Γ(νR → φ lL)= −

    1

    X

    k

    Im[(λλ†)2k1]

    (λλ†)11× f

    MνRkMνR1

    «

    ⇒ |�L| . 0.1MνR1〈φ〉2

    (mν3 − mν1)

    YL =nνRs

    �L d ∼ 10−3d �L nνR ≡ density of νR (d < 1 ≡ dilution factor)

    Out of Equilibrium condition ΓνR � H∣

    T=MνR⇒ m̃1 ≡ (λλ

    †)211〈φ〉2

    MνR1. 5 × 10−3eV

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia• In the the See-saw mechanism −LNP = 12MRijνRiνRcj + λνijνRiφ̃†LLj

    – In the Early Universe decay of heavy νR: Γ(νR → φ lL) =1

    i

    (λλ†)2iiMνRi

    – CP can be violated at 1-loop

    l

    νR

    φ

    6=

    νR

    φ̄

    (This requires 3 lightgenerations and at least2νR)

    �L =Γ(νR → φ lL) − Γ(νR → φ lL)

    Γ(νR → φ lL) + Γ(νR → φ lL)= −

    1

    X

    k

    Im[(λλ†)2k1]

    (λλ†)11× f

    MνRkMνR1

    «

    ⇒ |�L| . 0.1MνR1〈φ〉2

    (mν3 − mν1)

    YL =nνRs

    �L d ∼ 10−3d �L nνR ≡ density of νR (d < 1 ≡ dilution factor)

    Out of Equilibrium condition ΓνR � H∣

    T=MνR⇒ m̃1 ≡ (λλ

    †)211〈φ〉2

    MνR1. 5 × 10−3eV

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    • In the See-saw mechanism −LNP = 12MRijνRiνRcj + λνijνRiφ̃†LLj

    Mν =

    (

    0 mD

    mTD MR

    )

    mD = λ〈φ〉 is a 3 × 3 matrix

    MR is a 3 × 3 symmetric matrix

    ⇒ Mν has 6 physical phases

    ⇒ It is easy to generate �L ∼ 10−6

    ⇒ mνlight = mTDM−1N mD has 3 physical phasesOscillation experiments can only see one of these three phases

    ⇒ No direct correspondence between CPV in leptogenesis and CPV in oscillations

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    • In the See-saw mechanism −LNP = 12MRijνRiνRcj + λνijνRiφ̃†LLj

    Mν =

    (

    0 mD

    mTD MR

    )

    mD = λ〈φ〉 is a 3 × 3 matrix

    MR is a 3 × 3 symmetric matrix

    ⇒ Mν has 6 physical phases

    ⇒ It is easy to generate �L ∼ 10−6

    ⇒ mνlight = mTDM−1N mD has 3 physical phasesOscillation experiments can only see one of these three phases

    ⇒ No direct correspondence between CPV in leptogenesis and CPV in oscillations

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    • The final YB depends on:

    – �L the CP asymmetry

    – MνR1 the mass of the lightest νR

    – m̃1 ≡ (λλ†)2

    11〈φ〉2

    MνR1the effective neutrino mass

    – m2ν1 + m2ν2

    + m2ν3 the sum of the light neutrinos mass squared

    • To generate the required YB :

    – MνR1 & 4 × 108 GeV

    – mν3 . 0.12 eV

    – Large CP phasesThe CP violating phase relevant for leptogenesismay not be the same as the one relevant for oscillations

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Summary

    • Neutrino oscillation searches have shown us

    – ∆m231 ∼ 2 × 10−3 eV2 and ∆m221 ∼ 8 × 10−5 eV2 ⇒ ν’s are massive

    –|ULEP| '

    0

    B

    @

    1√2(1 + O(λ)) 1√

    2(1 −O(λ)) �

    − 12(1 −O(λ) + �) 1

    2(1 + O(λ) − �) 1√

    212(1 −O(λ) − �) − 1

    2(1 + O(λ) − �) 1√

    2

    1

    C

    A

    λ ∼ 0.2� . 0.2

    ⇒ Different from UCKM

    • mν 6= 0 ⇒ Need to extend SM It can be done:

    (a) breaking total lepton number → Majorana ν : ν = νC(b) conserving total lepton number → Dirac ν : ν 6= νC

    • Majorana ν′s are more Natural: appear generically if SM is a LE effective theory– ΛNP . 1015 GeV

    – Results Fit well with GUT expectations

    – Leptogenesis may explain the baryon asymmetry

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Summary

    • Neutrino oscillation searches have shown us

    – ∆m231 ∼ 2 × 10−3 eV2 and ∆m221 ∼ 8 × 10−5 eV2 ⇒ ν’s are massive

    –|ULEP| '

    0

    B

    @

    1√2(1 + O(λ)) 1√

    2(1 −O(λ)) �

    − 12(1 −O(λ) + �) 1

    2(1 + O(λ) − �) 1√

    212(1 −O(λ) − �) − 1

    2(1 + O(λ) − �) 1√

    2

    1

    C

    A

    λ ∼ 0.2� . 0.2

    ⇒ Different from UCKM

    • mν 6= 0 ⇒ Need to extend SM It can be done:

    (a) breaking total lepton number → Majorana ν : ν = νC(b) conserving total lepton number → Dirac ν : ν 6= νC

    • Majorana ν′s are more Natural: appear generically if SM is a LE effective theory– ΛNP . 1015 GeV

    – Results Fit well with GUT expectations

    – Leptogenesis may explain the baryon asymmetry

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Summary

    • Neutrino oscillation searches have shown us

    – ∆m231 ∼ 2 × 10−3 eV2 and ∆m221 ∼ 8 × 10−5 eV2 ⇒ ν’s are massive

    –|ULEP| '

    0

    B

    @

    1√2(1 + O(λ)) 1√

    2(1 −O(λ)) �

    − 12(1 −O(λ) + �) 1

    2(1 + O(λ) − �) 1√

    212(1 −O(λ) − �) − 1

    2(1 + O(λ) − �) 1√

    2

    1

    C

    A

    λ ∼ 0.2� . 0.2

    ⇒ Different from UCKM

    • mν 6= 0 ⇒ Need to extend SM It can be done:

    (a) breaking total lepton number → Majorana ν : ν = νC(b) conserving total lepton number → Dirac ν : ν 6= νC

    • Majorana ν′s are more Natural: appear generically if SM is a LE effective theory– ΛNP . 1015 GeV

    – Results Fit well with GUT expectations

    – Leptogenesis may explain the baryon asymmetry

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Summary

    • Neutrino oscillation searches have shown us

    – ∆m231 ∼ 2 × 10−3 eV2 and ∆m221 ∼ 8 × 10−5 eV2 ⇒ ν’s are massive

    –|ULEP| '

    0

    B

    @

    1√2(1 + O(λ)) 1√

    2(1 −O(λ)) �

    − 12(1 −O(λ) + �) 1

    2(1 + O(λ) − �) 1√

    212(1 −O(λ) − �) − 1

    2(1 + O(λ) − �) 1√

    2

    1

    C

    A

    λ ∼ 0.2� . 0.2

    ⇒ Different from UCKM

    • mν 6= 0 ⇒ Need to extend SM It can be done:

    (a) breaking total lepton number → Majorana ν : ν = νC(b) conserving total lepton number → Dirac ν : ν 6= νC

    • Majorana ν′s are more Natural: appear generically if SM is a LE effective theory– ΛNP . 1015 GeV

    – Results Fit well with GUT expectations

    – Leptogenesis may explain the baryon asymmetry

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Conclusions

    • Still open questions { Is θ13 6= 0?Is there CP violation in the leptons (is δ 6= 0, π)?Is θ23 large or maximal?Normal or Inverted mass ordering?Are neutrino masses:hierarchical: mi − mj ∼ mi + mj ?degenerated: mi − mj � mi + mj ?

    Dirac or Majorana? what about the Majorana Phases?. . .

    • To answer:Proposed new generation ν osc experiments:

    – LBL with Conventional Superbeams and/or β beams and/or ν-factory:– Medium Baseline Reactor Experiment

    Also no-oscillation experiments:

    – ν-less ββ decay,3H beta decay– Interesting input from cosmological data

    Rich and Challenging Experimental Program

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Conclusions

    • Still open questions { Is θ13 6= 0?Is there CP violation in the leptons (is δ 6= 0, π)?Is θ23 large or maximal?Normal or Inverted mass ordering?Are neutrino masses:hierarchical: mi − mj ∼ mi + mj ?degenerated: mi − mj � mi + mj ?

    Dirac or Majorana? what about the Majorana Phases?. . .• To answer:

    Proposed new generation ν osc experiments:

    – LBL with Conventional Superbeams and/or β beams and/or ν-factory:– Medium Baseline Reactor Experiment

    Also no-oscillation experiments:

    – ν-less ββ decay,3H beta decay– Interesting input from cosmological data

    Rich and Challenging Experimental Program

  • Physics of Massive Neutrinos Concha Gonzalez-Garcia

    Conclusions

    • Still open questions { Is θ13 6= 0?Is there CP violation in the leptons (is δ 6= 0, π)?Is θ23 large or maximal?Normal or Inverted mass ordering?Are neutrino masses:hierarchical: mi − mj ∼ mi + mj ?degenerated: mi − mj � mi + mj ?

    Dirac or Majorana? what about the Majorana Phases?. . .• To answer:

    Proposed new generation ν osc experiments:

    – LBL with Conventional Superbeams and/or β beams and/or ν-factory:– Medium Baseline Reactor Experiment

    Also no-oscillation experiments:

    – ν-less ββ decay,3H beta decay– Interesting input from cosmological data

    Rich and Challenging Experimental Program