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

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

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 ' ±∆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

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

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



= H ~ν H = U · Hd0 · U † + V

Hd0 =1

2Eνdiag

(

−∆m221, 0, ∆m232)

V = diag(

±√

2GF Ne, 0, 0)





∆m231

L

4E

)


4



= H ~ν H = U · Hd0 · U † + V

Hd0 =1

2Eνdiag

(

−∆m221, 0, ∆m232)

V = diag(

±√

2GF Ne, 0, 0)





∆m231

L

4E

)


4



= H ~ν H = U · Hd0 · U † + V

Hd0 =1

2Eνdiag

(

−∆m221, 0, ∆m232)

V = diag(

±√

2GF Ne, 0, 0)





∆m231

L

4E

)


4



= H ~ν H = U · Hd0 · U † + V

Hd0 =1

2Eνdiag

(

−∆m221, 0, ∆m232)

V = diag(

±√

2GF Ne, 0, 0)





∆m231

L

4E

)

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

3–ν Atmospheric Neutrino Oscillation: Effect of θ13


= 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

“


+ 1”

+ EνVe

∆µ231 = ∆m232


sin 2θ13,m =sin 2θ13

q

(cos 2θ13 ∓2EνVe∆m2

31

)2 + sin2 2θ13

3–ν Atmospheric Neutrino Oscillation: Effect of θ13


= 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

“


− 1”

− EνVe

∆µ232 =∆m2

32

2

“


+ 1”

+ EνVe

∆µ231 = ∆m232



q


31

)2 + sin2 2θ13

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

)


r


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


-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


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

)


r


31

)2 + sin2 2θ13



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

θ23 >π4 ⇒ s223 > 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/

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


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

)


r


31

)2 + sin2 2θ13



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

θ23 >π4 ⇒ s223 > 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


= 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

)


√

(cos 2θ12 ∓ 2EνVe∆m221

)2 + sin2 2θ12

φ ≈ (∆m231 + s212 ∆m221) L2Eν


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


= 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]


2(

∆m221

L

4Eνsin 2θ12

sin 2θ12,m

)


√

(cos 2θ12 ∓ 2EνVe∆m221

)2 + sin2 2θ12

φ ≈ (∆m231 + s212 ∆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(c223 − 1r̄ )


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


-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 )


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

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)


2 φm2


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

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


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


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)) �

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

λ ∼ 0.2� . 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

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. . .





{

gauge invariant












{

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)










{

gauge invariant












{

gauge invariant












{

gauge invariant












{

gauge invariant







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








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...




∑

n

1

Λn−4NPOn


Zνij

ΛNP

(

φ̃†LLj

)(

LcLiφ̃∗)


Zνij

2

v2

ΛNP



√





∑

n

1

Λn−4NPOn


Zνij

ΛNP

(

φ̃†LLj

)(

LcLiφ̃∗)


Zνij

2

v2

ΛNP



√





∑

n

1

Λn−4NPOn


Zνij

ΛNP

(

φ̃†LLj

)(

LcLiφ̃∗)


Zνij

2

v2

ΛNP



√





∑

n

1

Λn−4NPOn


Zνij

ΛNP

(

φ̃†LLj

)(

LcLiφ̃∗)


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


√





∑

n

1

Λn−4NPOn


Zνij

ΛNP

(

φ̃†LLj

)(

LcLiφ̃∗)


Zνij

2

v2

ΛNP



√

∆m2atm ∼ 0.05 eV ⇒ ΛNP < 1015 GeV

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




∑

n

1

Λn−4NPOn


Zνij

ΛNP

(

φ̃†LLj

)(

LcLiφ̃∗)


Zνij

2

v2

ΛNP



√



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∗)

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)

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


−LNP =1

2MRijνRiνR

cj + λ

νijνRiφ̃

†LLj + h.c..


E � MR


MR

(

φ̃†LLj

) (

LcLiφ̃∗)

⇒ mν = mTD1

MRmD

This

isthe

see-sa

w




−LNP =1

2MRijνRiνR

cj + λ

νijνRiφ̃

†LLj + h.c..


E � MR


MR

(

φ̃†LLj

) (

LcLiφ̃∗)

⇒ mν = mTD1

MRmD

This

isthe

see-sa

w




−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


MR

(

φ̃†LLj

) (

LcLiφ̃∗)

⇒ mν = mTD1

MRmD

This

isthe

see-sa

w




−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


MR

(

φ̃†LLj

) (

LcLiφ̃∗)

⇒ mν = mTD1

MRmD

This

isthe

see-sa

w




−LNP =1

2MRijνRiνR

cj + λ

νijνRiφ̃

†LLj + h.c..


E � MR


MR

(

φ̃†LLj

) (

LcLiφ̃∗)

⇒ mν = mTD1

MRmD

This

isthe

see-sa

w




−LNP =1

2MRijνRiνR

cj + λ

νijνRiφ̃

†LLj + h.c..


E � MR


MR

(

φ̃†LLj

) (

LcLiφ̃∗)

⇒ mν = mTD1

MRmD

This

isthe

see-sa

w

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



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





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



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 = 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

Leptogenesis







∣

∣

T=MνR



Leptogenesis







∣

∣

T=MνR



Leptogenesis




}(MνR3/λ23 . 1015 GeV)

⇒ Lepton Number is Violated (MR)



∣

∣

T=MνR



Leptogenesis







∣

∣

T=MνR



Leptogenesis







∣

∣

T=MνR



Leptogenesis







∣

∣

T=MνR


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

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)

�L =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

„

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


8π

∑

i

(λλ†)2iiMνRi


l

νR

φ

6=

l̄

νR

φ̄




1

8π

X

k

Im[(λλ†)2k1]

(λλ†)11× f

„

MνRkMνR1

«

⇒ |�L| . 0.1MνR1〈φ〉2

(mν3 − mν1)

YL =nνRs



∣


†)211〈φ〉2

MνR1. 5 × 10−3eV


8π

∑

i

(λλ†)2iiMνRi


l

νR

φ

6=

l̄

νR

φ̄




1

8π

X

k

Im[(λλ†)2k1]

(λλ†)11× f

„

MνRkMνR1

«

⇒ |�L| . 0.1MνR1〈φ〉2

(mν3 − mν1)

YL =nνRs



∣


†)211〈φ〉2

MνR1. 5 × 10−3eV


8π

∑

i

(λλ†)2iiMνRi


l

νR

φ

6=

l̄

νR

φ̄




1

8π

X

k

Im[(λλ†)2k1]

(λλ†)11× f

„

MνRkMνR1

«

⇒ |�L| . 0.1MνR1〈φ〉2

(mν3 − mν1)

YL =nνRs



∣


†)211〈φ〉2

MνR1. 5 × 10−3eV


8π

∑

i

(λλ†)2iiMνRi


l

νR

φ

6=

l̄

νR

φ̄




1

8π

X

k

Im[(λλ†)2k1]

(λλ†)11× f

„

MνRkMνR1

«

⇒ |�L| . 0.1MνR1〈φ〉2

(mν3 − mν1)

YL =nνRs



∣


†)211〈φ〉2

MνR1. 5 × 10−3eV

• 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

• 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

• 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

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

Summary



–|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







Summary



–|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







Summary



–|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







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:

Proposed new generation ν osc experiments:





Conclusions


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

Proposed new generation ν osc experiments:

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

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