icecube.wisc.eduhalzen/notes/week14-4.pdfPhysics of Massive Neutrinos Concha Gonzalez-Garcia Summary I+II+III In the SM: $ m 0 Œ neutrinos are left-handed ( helicity -1): m = 0 )

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


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


Summary I+II+III













Summary I+II+III













Summary I+II+III













Summary I+II+III













Summary I+II+III













Plan of Lecture IV

Emerging Picture and Some Lessons

3ν Oscillations

Some Lessons:

The Need of New Physics

The Possibility of Leptogenesis


• 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 ...


























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 ' ±∆m2

32 ' ±∆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


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 ' ±∆m2

32 ' ±∆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


3–ν Neutrino Oscillations

• In general one has to solve: id~ν

dt= H ~ν H = U · Hd

0 · U † + V

Hd0 =

1

2Eν

diag(

−∆m221, 0, ∆m2

32

)

V = diag(

±√

2GF Ne, 0, 0)

• Hierarchical approximation: ∆m221 � ∆m2

31 ∼ ∆m232

∗ For θ13 = 0 solar and atmospheric oscillations decouple ⇒ Normal≡ Inverted– Solar and KamLAND → ∆m2

21 = ∆m2� θ12 = θ�

– Atmospheric and LBL → ∆m231 = ∆M2

atm θ23 = θatm

∗ For θ13 6= 0

– Solar and KamLAND: P 3νee = c4

13P2νee (∆m2

12, θ12) + s413

– CHOOZ: PCHee ' 1 − 4c2

13s213 sin2

(

∆m2

31L

4E

)

– K2K+MINOS Probabilities Independent of θ12, ∆m221

4





0 · U † + V

Hd0 =

1

2Eν

diag(

−∆m221, 0, ∆m2

32

)

V = diag(

±√

2GF Ne, 0, 0)


31 ∼ ∆m232


21 = ∆m2� θ12 = θ�


atm θ23 = θatm

∗ For θ13 6= 0


13P2νee (∆m2

12, θ12) + s413


13s213 sin2

(

∆m2

31L

4E

)


4





0 · U † + V

Hd0 =

1

2Eν

diag(

−∆m221, 0, ∆m2

32

)

V = diag(

±√

2GF Ne, 0, 0)


31 ∼ ∆m232


21 = ∆m2� θ12 = θ�


atm θ23 = θatm

∗ For θ13 6= 0


13P2νee (∆m2

12, θ12) + s413


13s213 sin2

(

∆m2

31L

4E

)


4





0 · U † + V

Hd0 =

1

2Eν

diag(

−∆m221, 0, ∆m2

32

)

V = diag(

±√

2GF Ne, 0, 0)


31 ∼ ∆m232


21 = ∆m2� θ12 = θ�


atm θ23 = θatm

∗ For θ13 6= 0


13P2νee (∆m2

12, θ12) + s413


13s213 sin2

(

∆m2

31L

4E

)


4





0 · U † + V

Hd0 =

1

2Eν

diag(

−∆m221, 0, ∆m2

32

)

V = diag(

±√

2GF Ne, 0, 0)


31 ∼ ∆m232


21 = ∆m2� θ12 = θ�


atm θ23 = θatm

∗ For θ13 6= 0


13P2νee (∆m2

12, θ12) + s413


13s213 sin2

(

∆m2

31L

4E

)

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


3–ν Atmospheric Neutrino Oscillation: Effect of θ13



0 · U † + V

Hd0 =

1

2Eν

diag(

−∆m221, 0, ∆m2

32

)

V = diag(

±√

2GF Ne, 0, 0)


31 ∼ ∆m232 ⇒ neglect ∆m2

21 in ATM

Pantaleone 94; Used by many ...

Pee = 1 − 4s213,mc2

13,m S31

Pµµ = 1 − 4s213,mc2

13,ms423 S31 − 4s2

13,ms223c

223 S21 − 4c2

13,ms223c

223 S32

Peµ = 4s213,mc2

13,ms223 S31

Sij = sin2

„

∆µ2ij

4EνL

«

∆µ221 =

∆m232

2

“

sin 2θ13

sin 2θ13,m− 1

”

− EνVe

∆µ232 =

∆m232

2

“

sin 2θ13

sin 2θ13,m+ 1

”

+ EνVe

∆µ231 = ∆m2

32sin 2θ13

sin 2θ13,m

sin 2θ13,m =sin 2θ13

q

(cos 2θ13 ∓2EνVe

∆m231

)2 + sin2 2θ13





0 · U † + V

Hd0 =

1

2Eν

diag(

−∆m221, 0, ∆m2

32

)

V = diag(

±√

2GF Ne, 0, 0)


31 ∼ ∆m232 ⇒ neglect ∆m2

21 in ATM

Pantaleone 94; Used by many ...

Pee = 1 − 4s213,mc2

13,m S31

Pµµ = 1 − 4s213,mc2

13,ms423 S31 − 4s2

13,ms223c

223 S21 − 4c2

13,ms223c

223 S32

Peµ = 4s213,mc2

13,ms223 S31

Sij = sin2

„

∆µ2ij

4EνL

«

∆µ221 =

∆m232

2

“

sin 2θ13

sin 2θ13,m− 1

”

− EνVe

∆µ232 =

∆m232

2

“

sin 2θ13

sin 2θ13,m+ 1

”

+ EνVe

∆µ231 = ∆m2

32sin 2θ13

sin 2θ13,m


q


∆m231

)2 + sin2 2θ13



Ahkmedov,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/ N

eO

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 Oscillationss2

13=0.00, s223=0.35, ∆m2

21=0

s213=0.04, s2

23=0.35, ∆m221=0

s213=0.04, s2

23=0.65, ∆m221=0

Ne

Ne0− 1 = Peµr̄(s2

23 − 1r̄)

r̄ =Nµ0

Ne0

Peµ = 4s213,mc2

13,m sin2(

∆m2

31L

4Eν

sin 2θ13

sin 2θ13,m

)


r


∆m231

)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 ⇒ s2

23 < 12 ⇒ Ne(θ13) < Ne0

θ23 > π4 ⇒ s2

23 > 12 ⇒ Ne(θ13) > Ne0




-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/ N

eO

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 Oscillationss2

13=0.00, s223=0.35, ∆m2

21=0

s213=0.04, s2

23=0.35, ∆m221=0

s213=0.04, s2

23=0.65, ∆m221=0

Ne


23 − 1r̄)

r̄ =Nµ0

Ne0

Peµ = 4s213,mc2

13,m sin2(

∆m2

31L

4Eν

sin 2θ13

sin 2θ13,m

)


r


∆m231

)2 + sin2 2θ13



r ' 2 ⇒ θ23 < π4 ⇒ s2

23 < 12 ⇒ Ne(θ13) < Ne0

θ23 > π4 ⇒ s2

23 > 12 ⇒ Ne(θ13) > Ne0




-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/ N

eO

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 Oscillationss2

13=0.00, s223=0.35, ∆m2

21=0

s213=0.04, s2

23=0.35, ∆m221=0

s213=0.04, s2

23=0.65, ∆m221=0

Ne


23 − 1r̄)

r̄ =Nµ0

Ne0

Peµ = 4s213,mc2

13,m sin2(

∆m2

31L

4Eν

sin 2θ13

sin 2θ13,m

)


r


∆m231

)2 + sin2 2θ13



r ' 2 ⇒ θ23 < π4 ⇒ s2

23 < 12 ⇒ Ne(θ13) < Ne0

θ23 > π4 ⇒ s2

23 > 12 ⇒ Ne(θ13) > Ne0


∆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



0 · U † + V

Hd0 =

1

2Eν

diag(

−∆m221, 0, ∆m2

32

)

V = diag(

±√

2GF Ne, 0, 0)

• Neglecting θ13:

Pee = 1 − Pe2

Peµ = c223Pe2

Pµµ = 1 − c423Pe2 − 2s2

23c223

[

1 −√

1 − Pe2 cosφ]

Pe2 = sin2 2θ12,m sin2(

∆m2

21L

4Eν

sin 2θ12

sin 2θ12,m

)


√

(cos 2θ12 ∓ 2EνVe

∆m221

)2 + sin2 2θ12

φ ≈ (∆m231 + s2

12 ∆m221)

L2Eν



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



0 · U † + V

Hd0 =

1

2Eν

diag(

−∆m221, 0, ∆m2

32

)

V = diag(

±√

2GF Ne, 0, 0)

• Neglecting θ13:

Pee = 1 − Pe2

Peµ = c223Pe2

Pµµ = 1 − c423Pe2 − 2s2

23c223

[

1 −√

1 − Pe2 cosφ]


∆m2

21L

4Eν

sin 2θ12

sin 2θ12,m

)


√

(cos 2θ12 ∓ 2EνVe

∆m221

)2 + sin2 2θ12

φ ≈ (∆m231 + s2

12 ∆m221)

L2Eν



-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(c

223 − 1

r̄)


∆m2

21L

4Eν

sin 2θ12

sin 2θ12,m

)

sin 2θ12,m =sin2 2θ12

r

(cos 2θ12 ∓2EVe

∆m221

)2 + sin2 2θ12

For Sub-GeV:Pe2 =

(∆m221)

2

(2EVe)2sin2 2θ12 sin2 VeL

2

θ23 < π4 ⇒ c2

23 > 12 ⇒ Ne(θ13) > Ne0

θ23 > π4 ⇒ c2

23 < 12 ⇒ Ne(θ13) < Ne0

⇒ Sensitiv to Deviations from Maximal θ23

⇒ Sensitivity to Octant of θ23

(even for vanishing θ13)⇒ Effect proportional to (∆m2

21)2



-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(c

223 − 1

r̄)


∆m2

21L

4Eν

sin 2θ12

sin 2θ12,m

)

sin 2θ12,m =sin2 2θ12

r

(cos 2θ12 ∓2EVe

∆m221

)2 + sin2 2θ12

For Sub-GeV:Pe2 =

(∆m221)

2

(2EVe)2sin2 2θ12 sin2 VeL

2

θ23 < π4 ⇒ c2

23 > 12 ⇒ Ne(θ13) > Ne0

θ23 > π4 ⇒ c2

23 < 12 ⇒ Ne(θ13) < Ne0

⇒ Sensitiv to Deviations from Maximal θ23

⇒ Sensitivity to Octant of θ23

(even for vanishing θ13)⇒ Effect proportional to (∆m2

21)2


Beyond Hierarchical: Effect θ13 × ∆m221 in ATM

Smirnov, Peres 01,03, MC G-G, Maltoni 02For sub-GeV energies

Ne

N0e

− 1 ' Pe2r(c223 −

1

r) + 2s̃2

13r(s223 −

1

r) − rs̃13c̃

213 sin 2θ23(cos δCP R2 − sin δCP I2)

Pe2 = sin2 2θ12,m sin2 φm

2sin 2θ12,m = sin 2θ12

r

(cos 2θ12∓ 2EνVe

∆m221

)2+sin2 2θ12

R2 = −sin 2θ12,m cos 2θ12,m sin2 φm

2I2 = − 1

2sin 2θ12,m sin φm

θ̃13 ≈ θ13

“

1 + 2EνVe

∆m231

”

φ ≈ (∆m231 + s2

12 ∆m221)

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/3

δCP

= −π/3

δCP

= 0

δCP

= +π/3

δCP

= +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 eV

2]

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 eV

2]

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


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)) ε

− 12 (1 −O(λ) + ε) 1

2(1 + O(λ) − ε) 1√2

12(1 −O(λ) − ε) − 1

2(1 + O(λ) − ε) 1√2

λ ∼ 0.2

ε . 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



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)) ε

− 12 (1 −O(λ) + ε) 1

2(1 + O(λ) − ε) 1√2

12(1 −O(λ) − ε) − 1

2(1 + O(λ) − ε) 1√2

λ ∼ 0.2

ε . 0.2


1 O(λ) O(λ3)

O(λ) 1 O(λ2)

O(λ3) O(λ2) 1

λ ∼ 0.2



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)) ε

− 12 (1 −O(λ) + ε) 1

2(1 + O(λ) − ε) 1√2

12(1 −O(λ) − ε) − 1

2(1 + O(λ) − ε) 1√2

λ ∼ 0.2

ε . 0.2


1 O(λ) O(λ3)

O(λ) 1 O(λ2)

O(λ3) O(λ2) 1

λ ∼ 0.2


Open Questions

We still ignore: { (1) Is θ13 6= 0? How small?

(2) Is θ23 = π4 ? If not, is it > or <?

(3) Is there CP violation in the leptons (is δ 6= 0, π)?

(4) What is the ordering of the neutrino states?

(5) Are neutrino masses:hierarchical: mi − mj ∼ mi + mj ?degenerated: mi − mj � mi + mj ?

(6) Dirac or Majorana?

To answer (1)–(4):Proposed new generation ν osc experiments:

– Medium Baseline Reactor Experiment: Double-Chooz, Daya Bay

– Conventional (=from π decay) Superbeams: T2K, Nova (?)

– ν-factory: clean ν beam from µ decay

–νe or ν̄e beam from nuclear β decay (β beam)


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. . .






{

gauge invariant







× U(1)Lµ× U(1)Lτ









{

gauge invariant







× U(1)Lµ× U(1)Lτ









{

gauge invariant







× U(1)Lµ× U(1)Lτ









{

gauge invariant







× U(1)Lµ× U(1)Lτ









{

gauge invariant







× U(1)Lµ× U(1)Lτ









{

gauge invariant







× U(1)Lµ× U(1)Lτ



There is New Physics Beyond the SM

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






{

gauge invariant







× U(1)Lµ× U(1)Lτ





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−4NP

On

First NP effect ⇒ dim=5 operatorThere is only one! L5 =

Zνij

ΛNP

(

φ̃†LLj

)(

LcLi

φ̃∗)

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 GeV

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






∑

n

1

Λn−4NP

On


Zνij

ΛNP

(

φ̃†LLj

)(

LcLi

φ̃∗)


Zνij

2

v2

ΛNP




– mν >√

∆m2atm ∼ 0.05 eV ⇒ ΛNP < 1015 GeV







∑

n

1

Λn−4NP

On


Zνij

ΛNP

(

φ̃†LLj

)(

LcLi

φ̃∗)


Zνij

2

v2

ΛNP




– mν >√

∆m2atm ∼ 0.05 eV ⇒ ΛNP < 1015 GeV







∑

n

1

Λn−4NP

On


Zνij

ΛNP

(

φ̃†LLj

)(

LcLi

φ̃∗)


Zνij

2

v2

ΛNP




– mν >√

∆m2atm ∼ 0.05 eV ⇒ ΛNP < 1015 GeV







∑

n

1

Λn−4NP

On


Zνij

ΛNP

(

φ̃†LLj

)(

LcLi

φ̃∗)


Zνij

2

v2

ΛNP




– mν >√

∆m2atm ∼ 0.05 eV ⇒ ΛNP < 1015 GeV







∑

n

1

Λn−4NP

On


Zνij

ΛNP

(

φ̃†LLj

)(

LcLi

φ̃∗)


Zνij

2

v2

ΛNP




– mν >√

∆m2atm ∼ 0.05 eV ⇒ ΛNP < 1015 GeV







∑

n

1

Λn−4NP

On


Zνij

ΛNP

(

φ̃†LLj

)(

LcLi

φ̃∗)


Zνij

2

v2

ΛNP




– mν >√

∆m2atm ∼ 0.05 eV ⇒ ΛNP < 1015 GeV




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 =Zν

ij

ΛNP

(

φ̃†LLj

) (

LcLi

φ̃∗)


The See-Saw

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

Well above the electroweak (EW) scale

−LNP =1

2MRijνRiνR

cj + λν

ijνRiφ̃†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

) (

LcLi

φ̃∗)

⇒ mν = mTD

1

MR

mD

Thisis

thesee

-saw

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)


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


−LNP =1

2MRijνRiνR

cj + λν




E � MR


MR

(

φ̃†LLj

) (

LcLi

φ̃∗)

⇒ mν = mTD

1

MR

mD

Thisis

thesee

-saw






−LNP =1

2MRijνRiνR

cj + λν




E � MR


MR

(

φ̃†LLj

) (

LcLi

φ̃∗)

⇒ mν = mTD

1

MR

mD

Thisis

thesee

-saw






−LNP =1

2MRijνRiνR

cj + λν




E � MR


MR

(

φ̃†LLj

) (

LcLi

φ̃∗)

⇒ mν = mTD

1

MR

mD

Thisis

thesee

-saw






−LNP =1

2MRijνRiνR

cj + λν



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


MR

(

φ̃†LLj

) (

LcLi

φ̃∗)

⇒ mν = mTD

1

MR

mD

Thisis

thesee

-saw






−LNP =1

2MRijνRiνR

cj + λν




E � MR


MR

(

φ̃†LLj

) (

LcLi

φ̃∗)

⇒ mν = mTD

1

MR

mD

Thisis

thesee

-saw






−LNP =1

2MRijνRiνR

cj + λν




E � MR


MR

(

φ̃†LLj

) (

LcLi

φ̃∗)

⇒ mν = mTD

1

MR

mD

Thisis

thesee

-saw



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 equilibriumat 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




s = nbs ∼ 10−10








⇓YB,SM � 10−10




s = nbs ∼ 10−10








⇓YB,SM � 10−10




s = nbs ∼ 10−10








⇓YB,SM � 10−10




s = nbs ∼ 10−10








⇓YB,SM � 10−10




s = nbs ∼ 10−10








⇓YB,SM � 10−10




s = nbs ∼ 10−10








⇓YB,SM � 10−10


Leptogenesis

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

• If mν is generated via the See-saw mechanism

−LNP = 12MRijνRiνR

cj + λν

ijνRiφ̃†LLj ⇒ mν ∼ λ2〈φ〉2

MR

}(MνR3/λ2

3 . 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


Leptogenesis




cj + λν


MR

}(MνR3/λ2

3 . 1015 GeV)





∣

∣

T=MνR





Leptogenesis




cj + λν


MR

}(MνR3/λ2

3 . 1015 GeV)





∣

∣

T=MνR





Leptogenesis




cj + λν


MR

}(MνR3/λ2

3 . 1015 GeV)





∣

∣

T=MνR





Leptogenesis




cj + λν


MR

}(MνR3/λ2

3 . 1015 GeV)





∣

∣

T=MνR





Leptogenesis




cj + λν


MR

}(MνR3/λ2

3 . 1015 GeV)





∣

∣

T=MνR





Leptogenesis




cj + λν


MR

}(MνR3/λ2

3 . 1015 GeV)





∣

∣

T=MνR




Physics of Massive Neutrinos Concha Gonzalez-Garcia• In the the See-saw mechanism −LNP = 1

2MRijνRiνRcj + λν

ijνRiφ̃†LLj

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

8π

∑

i

(λλ†)2iiMνRi

– CP can be violated at 1-loop

l

νR

φ

6=

l̄

νR

φ̄

(This requires 3 lightgenerations and at least2νR)

εL =Γ(νR → φ lL) − Γ(νR → φ lL)

Γ(νR → φ lL) + Γ(νR → φ lL)= −

1

8π

X

k

Im[(λλ†)2k1]

(λλ†)11× f

„

MνRk

MνR1

«

⇒ |εL| . 0.1MνR1

〈φ〉2(mν3

− mν1)

YL =nνR

sεL d ∼ 10−3d εL 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



ijνRiφ̃†LLj


8π

∑

i

(λλ†)2iiMνRi


l

νR

φ

6=

l̄

νR

φ̄




1

8π

X

k

Im[(λλ†)2k1]

(λλ†)11× f

„

MνRk

MνR1

«

⇒ |εL| . 0.1MνR1

〈φ〉2(mν3

− mν1)

YL =nνR




∣

∣

T=MνR

⇒ m̃1 ≡(λλ†)211〈φ〉

2

MνR1

. 5 × 10−3eV



ijνRiφ̃†LLj


8π

∑

i

(λλ†)2iiMνRi


l

νR

φ

6=

l̄

νR

φ̄




1

8π

X

k

Im[(λλ†)2k1]

(λλ†)11× f

„

MνRk

MνR1

«

⇒ |εL| . 0.1MνR1

〈φ〉2(mν3

− mν1)

YL =nνR




∣

∣

T=MνR

⇒ m̃1 ≡(λλ†)211〈φ〉

2

MνR1

. 5 × 10−3eV



ijνRiφ̃†LLj


8π

∑

i

(λλ†)2iiMνRi


l

νR

φ

6=

l̄

νR

φ̄




1

8π

X

k

Im[(λλ†)2k1]

(λλ†)11× f

„

MνRk

MνR1

«

⇒ |εL| . 0.1MνR1

〈φ〉2(mν3

− mν1)

YL =nνR




∣

∣

T=MνR

⇒ m̃1 ≡(λλ†)211〈φ〉

2

MνR1

. 5 × 10−3eV



ijνRiφ̃†LLj


8π

∑

i

(λλ†)2iiMνRi


l

νR

φ

6=

l̄

νR

φ̄




1

8π

X

k

Im[(λλ†)2k1]

(λλ†)11× f

„

MνRk

MνR1

«

⇒ |εL| . 0.1MνR1

〈φ〉2(mν3

− mν1)

YL =nνR




∣

∣

T=MνR

⇒ m̃1 ≡(λλ†)211〈φ〉

2

MνR1

. 5 × 10−3eV


• In the See-saw mechanism −LNP = 12MRijνRiνR

cj + λν

ijνRiφ̃†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 εL ∼ 10−6

⇒ mνlight = mT

DM−1N mD has 3 physical phases

Oscillation experiments can only see one of these three phases

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


• In the See-saw mechanism −LNP = 12MRijνRiνR

cj + λν

ijνRiφ̃†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 εL ∼ 10−6

⇒ mνlight = mT

DM−1N mD has 3 physical phases

Oscillation experiments can only see one of these three phases

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


• The final YB depends on:

– εL the CP asymmetry

– MνR1the mass of the lightest νR

– m̃1 ≡ (λλ†)211

〈φ〉2MνR1

the 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


Summary

• Neutrino oscillation searches have shown us

– ∆m231 ∼ 2 × 10−3 eV2 and ∆m2

21 ∼ 8 × 10−5 eV2 ⇒ ν’s are massive

–|ULEP| '

0

B

@

1√2(1 + O(λ)) 1√

2(1 −O(λ)) ε

− 12(1 −O(λ) + ε) 1

2(1 + O(λ) − ε) 1√

212(1 −O(λ) − ε) − 1

2(1 + O(λ) − ε) 1√

2

1

C

A

λ ∼ 0.2

ε . 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


Summary


– ∆m231 ∼ 2 × 10−3 eV2 and ∆m2


–|ULEP| '

0

B

@

1√2(1 + O(λ)) 1√

2(1 −O(λ)) ε

− 12(1 −O(λ) + ε) 1

2(1 + O(λ) − ε) 1√

212(1 −O(λ) − ε) − 1

2(1 + O(λ) − ε) 1√

2

1

C

A

λ ∼ 0.2

ε . 0.2






– ΛNP . 1015 GeV




Summary


– ∆m231 ∼ 2 × 10−3 eV2 and ∆m2


–|ULEP| '

0

B

@

1√2(1 + O(λ)) 1√

2(1 −O(λ)) ε

− 12(1 −O(λ) + ε) 1

2(1 + O(λ) − ε) 1√

212(1 −O(λ) − ε) − 1

2(1 + O(λ) − ε) 1√

2

1

C

A

λ ∼ 0.2

ε . 0.2






– ΛNP . 1015 GeV




Summary


– ∆m231 ∼ 2 × 10−3 eV2 and ∆m2


–|ULEP| '

0

B

@

1√2(1 + O(λ)) 1√

2(1 −O(λ)) ε

− 12(1 −O(λ) + ε) 1

2(1 + O(λ) − ε) 1√

212(1 −O(λ) − ε) − 1

2(1 + O(λ) − ε) 1√

2

1

C

A

λ ∼ 0.2

ε . 0.2






– ΛNP . 1015 GeV




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


Conclusions



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







Conclusions



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






Documents

icecube.wisc.eduhalzen/notes/week14-4.pdfPhysics of Massive Neutrinos Concha Gonzalez-Garcia Summary I+II+III In the SM: $ m 0 Œ neutrinos are left-handed ( helicity -1): m = 0 )