• Open questions in physics

• : mechanism & EFT

III. Neutrinos

New “Periodic Table”

Courtesy: R.D. McKeown

Not physical states

Missing Solar Neutrinos…

Courtesy: R.D. McKeown

Neutrino Oscillations: What We’ve Learned & What’s Unknown

The status of the present knowledge of the neutrinooscillation

phenomenais schematicallydepicted in this slide.Three quantities areunknown at present:a) The mass m1

b) The angle 13

c) Whether the normal or

inverted hierarchy is

realized.Courtesy: P. Vogel

Neutrino Masses and Mixing: Scales

Courtesy: R.D. McKeown

Maki – Nakagawa – Sakata Matrix

CP violation

Future ReactorExperiment!

Courtesy: R.D. McKeown

νL νR( )mD

mD M

⎛

⎝ ⎜

⎞

⎠ ⎟

νL

νR

⎛

⎝ ⎜

⎞

⎠ ⎟

mν =mD

2

M<<mD

“Seesaw mechanism”

M

The Mass Puzzle

Courtesy: R.D. McKeown

Very heavy neutrino

}Familiar light neutrino

{

The Mixing Angle Puzzle

Why so different???Why so different???

Courtesy: R.D. McKeown

• What is the absolute value of m ? Why is m so tiny ?

• What is the mass hierarchy ?

• Is the neutrino its own antiparticle?

• What is 13 ?

• Do neutrinos violate CP?

• How do neutrinos affect/reflect astrophysical phenomena ?

Open Questions

-Decay: LNV? Mass Term?

€

e−

€

e−

€

M

€

W −

€

W −

€

A Z,N( )

€

A Z − 2,N + 2( )0.1

1

10

100

1000

Effective

( )Mass meV

12 3 4 5 6 7

12 3 4 5 6 7

12 3 4 5 6 7

1 ( )Minimum Neutrino Mass meV

U1e=.866δm2

sol=7meV

2

U2e=.5δm2

atm=2meV

2

U 3e =

Inverted

Normal

Degenerate

Dirac Majorana

-decayLong baseline

?

?

Theory Challenge: matrix elements+ mechanism

€

mν

EFF= Uek

2mk e2iδ

k

∑

€

e−

€

e−

€

χ 0

€

˜ e −

€

u

€

u

€

d

€

d

€

˜ e −€

e−

€

e−

€

M

€

W −

€

W −

€

u

€

u

€

d

€

d

mEFF & neutrino spectrum

Normal Inverted

See-saw mechanism

Leptogenesis

L LR

H H

Lepton Asym -> Baryon Asym

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

GERDA CUORE

EXO Majorana

Majorana or Dirac

Or equivalently, is the total lepton number conserved?

Courtesy: P. Vogel

& Lepton Number Violation

0e– e–

u d d u

()R L

W W

Whatever processes cause , its observation would imply the existence of a Majorana mass term:

Schechter and Valle,82

By adding only Standard model interactions we obtain

()R ()L Majorana mass term Courtesy: P. Vogel

Decay vs. 2 Decay

virtual state of the intermediate nucleus virtual state of the intermediate nucleus

Courtesy: P. Vogel

Decay vs. 2 Decay

2.0

1.5

1.0

0.5

0.01.00.80.60.40.20.0

Ke/Q

30

20

10

0

1.101.000.90Ke/Q

assumed 2%resolution

2

ratio 1:100

ratio1:106

Courtesy: P. Vogel

-Decay: Theoretical Challenges

Dirac Majorana

Theory Challenge: matrix elements+ mechanism

€

mν

EFF= Uek

2mk e2iδ

k

∑

€

e−

€

e−

€

χ 0

€

˜ e −

€

u

€

u

€

d

€

d

€

˜ e −€

e−

€

e−

€

M

€

W −

€

W −

€

u

€

u

€

d

€

d

Light M exchange: can we determine m

Shell Model vs. QRPA

Configs near Fermi surface

Levels above Fermi surface

Vogel et al: reduce QRPA spread by calibrating gPP to T2

Decay Matrix Elements

Why it is difficult to calculatethe matrix elements accurately?

Contributions of differentangular momenta J of theneutron pair that is transformed in the decay into the proton pair with the same J.

Note the opposite signs, and thus tendency to cancel, between the J = 0 (pairing) and the J 0(ground state correlations) parts.

The same restricted s.p. space is used for QRPA and NSM. There is a reasonable agreement between the two methodsCourtesy: P. Vogel

Decay Matrix Elements

Full estimated range of M within QRPA framework and comparison with NSM (higher order currents now included in NSM) Courtesy: P. Vogel

-Decay: Theoretical Challenges

Dirac Majorana

Theory Challenge: matrix elements+ mechanism

€

mν

EFF= Uek

2mk e2iδ

k

∑

€

e−

€

e−

€

χ 0

€

˜ e −

€

u

€

u

€

d

€

d

€

˜ e −€

e−

€

e−

€

M

€

W −

€

W −

€

u

€

u

€

d

€

d

Mechanism: does light M exchange dominate ?

How to calc effects reliably ? How to disentangle H & L ?

O(1) for ~ TeV

-Decay: Mechanism & m

0.1

1

10

100

1000

Effective

( )Mass meV

12 3 4 5 6 7

12 3 4 5 6 7

12 3 4 5 6 7

1 ( )Minimum Neutrino Mass meV

U1e=.866δm2

sol=7meV

2

U2e=.5δm2

atm=2meV

2

U 3e =

Inverted

Normal

Degeneratesignal equivalent to degenerate hierarchy

Loop contribution to m of inverted hierarchy scale

-Decay: Theoretical Challenges

Dirac Majorana

Theory Challenge: matrix elements+ mechanism

€

mν

EFF= Uek

2mk e2iδ

k

∑

€

e−

€

e−

€

χ 0

€

˜ e −

€

u

€

u

€

d

€

d

€

˜ e −€

e−

€

e−

€

M

€

W −

€

W −

€

u

€

u

€

d

€

d

Mechanism: does light M exchange dominate ?

How to calc effects reliably ? How to disentangle H & L ?

O(1) for ~ TeV

€

u

€

d€

u

€

d

€

e−

€

e−

€

N

€

N€

π

€

π€

e−

€

e−

Prezeau, R-M, Vogel: EFT

Does operator power counting suffice?

€

n

€

n

€

p

€

p

€

ˆ O 0νββL

- decay Mechanism: EFT

€

e−

€

e−

€

M

€

W −

€

W −

€

u

€

u

€

d

€

d

€

e−

€

e−

€

χ 0

€

˜ e −

€

u

€

u

€

d

€

d

€

˜ e −

€

e−

€

e−

€

A Z,N( )

€

A Z + 2,N − 2( )€

u

€

d€

u

€

d

€

e−

€

e−

4 quark operator: low energy EFT

How do we compute & separate heavy particle exchange effects?

- decay in EFT I

We have a clear separation of scales

€

>>>χ >> kF

L-violating new physics

Non-perturbative QCD

Nuclear dynamics

Effective Field Theory

Systematically and effectively organizing our ignorance

Weak: MW

Hadronic: χ

Nuclear: kF

Scale separation

€

LEFF =GF

2C j

j

∑ (Λχ ) p Λχ( )j

“Low-energy constants” parameterizing non-perturbative QCD

Nuclear operators reflecting symmetries of short distance physics

Power counting

- decay in EFT II

€

N

€

N€

π

€

π€

e−

€

e−

€

N

€

N€

π€

e−

€

e−

€

N

€

N

€

e−

€

e−

Tractable nuclear operators

Systematic operator classification

- decay in EFT III

€

N

€

N€

π

€

π€

e−

€

e−

€

N

€

N€

π€

e−

€

e−

€

N

€

N

€

e−

€

e−

€

Kππ p−2

€

KπNN p−1

€

KNNNN p0

Kππ, KπNN , KNNNN can be O ( p0 ), O ( p1 ), etc.

- decay in EFT IV

Operator classification

€

μ =MWEAK

€

μ =M HAD

Spacetime & chiral transformation properties

L(q,e) Lπ,N,e

- decay in EFT V

Operator classification

€

μ =MWEAK

L(q,e) =

€

GF2

Λββ

C j (μ) ˆ O j++ e Γ je

c + h.c.j=1

14

∑

€

ˆ O 1+ab = q Lγ μτ aqL q Rγ μτ bqR e.g.

- decay: a = b = +

- decay in EFT VI

Operator classification

€

μ =MWEAK

€

ˆ O 1+ab = q Lγ μτ aqL q Rγ μτ bqR

€

qL → LqL

€

qR → RqR

€

L

R= exp i

r θ L

R

⋅r τ

2PL

R

⎛

⎝ ⎜

⎞

⎠ ⎟

Chiral transformations: SU(2)L x SU(2)R

€

ˆ O 1+ab ∈ (3L , 3R )

Parity transformations: qL qR

- decay: a = b = +

€

ˆ O 1+++ ↔ ˆ O 1+

++

- decay in EFT VI

Hadronic basis

€

XRa = ξ τ a ξ +

€

XLa = ξ + τ a ξ

€

ξ =exp ir τ ⋅

r π 2( ), ,

Chiral transformations

€

ˆ O 1+++ ~ Tr XR

+ XL+

( ) ~2

Fπ2

π − π − +L

No derivatives Kππ ~ O (p0)

- decay in EFT VIII

Hadronic basis

Chiral transformations

€

ˆ O 3+++ ~ Tr Dμ XL

+ Dμ XL+ + L ↔ R( )[ ] ~

2

Fπ2

∂ μπ − ∂μπ − +L

Two derivatives Kππ ~ O (p2)

€

ˆ O 3+++ = q Lτ +γ μqL q Lτ +γ μqL + q Rτ +γ μqR q Rτ +γ μqR

€

5L ,1R( )⊕ 1L ,5R( )

- decay in EFT: Implications

€

N

€

N€

π

€

π€

e−

€

e−

€

N

€

N€

π€

e−

€

e−

€

N

€

N

€

e−

€

e−

€

KNNNN p0

€

KπNN p−1

€

Kππ p−2

Prezeau, R-M, & VogelL(q,e) =

€

GF2

Λββ

C j (μ) ˆ O j++ e Γ je

c + h.c.j=1

14

∑

Chiral properties of Oj++

determine p-dependence of KππKπNN , KNNNN

€

ˆ O 1+++ ∈ (3L , 3R ) Kππ ~ O (p0)

€

ˆ O 3+++ ∈ (5, 1)⊕ (1, 5) Kππ ~ O (p2)

€

e−

€

e−

€

χ 0

€

˜ e −

€

u

€

u

€

d

€

d

€

˜ e −

€

ˆ O 1+++ ∈ (3L , 3R )

€

ˆ O 3+++ ∈ (5L , 1R )⊕ (1L , 5R )

€

ˆ O 1+++ ∈ (3L , 3R )

No WR - WL

mixing

WR - WL mix

RPV SUSY

€

M

€

W −

€

W −

€

u

€

u

€

d

€

d

€

e−

€

e−

An open question

Is the power counting of operators sufficient to understand weak matrix elements in nuclei ?

€

n

€

n

€

p

€

p

€

ˆ O 0νββL

76Ge76Se€

g9 2ν

( )2

€

p3 2π

( )2, f5 2

π( )

2

€

l =0,K ,9

€

′l =0,K ,5

An open question

Is the power counting of operators sufficient to understand weak matrix elements in nuclei ?

€

l =0,K ,9

€

′l =0,K ,5

€

ˆ O 0νββL

e.g.

€

M fi ~ p0

€

l = ′l =0

€

ˆ O 0νββL= 0

€

M fi ~ p0

€

l =2, ′ l = 0

€

ˆ O 0νββL= 2

€

M fi ~ p4

€

l =0, ′ l = 2

€

ˆ O 0νββL= 2

€

M fi ~ p0

€

l =4, ′ l = 0

€

ˆ O 0νββL= 4

etc.

-Decay: Interpretation

0.1

1

10

100

1000

Effective

( )Mass meV

12 3 4 5 6 7

12 3 4 5 6 7

12 3 4 5 6 7

1 ( )Minimum Neutrino Mass meV

U1e=.866δm2

sol=7meV

2

U2e=.5δm2

atm=2meV

2

U 3e =

Inverted

Normal

Degenerate

Dirac Majorana

Theory Challenge: matrix elements+ mechanism

€

mν

EFF= Uek

2mk e2iδ

k

∑

€

e−

€

e−

€

χ 0

€

˜ e −

€

u

€

u

€

d

€

d

€

˜ e −€

e−

€

e−

€

M

€

W −

€

W −

€

u

€

u

€

d

€

d

If the existence of the decay is established:

• What mechanism?

• Which additional isotopes ?

-Decay: Mechanism & m

- SM extensions with low ( TeV) scale LNV **

** In absence of fine-tuning or hierarchies in flavor couplings. Important caveat! See: V. Cirigliano et al., PRL93,231802(2004)

Left-right symmetric model,R-parity violating SUSY, etc.possibly unrelated tom

2

R ~ O(π1312

R = Bμe/Bμe» 10-2

Bμe = (μe)/(μeμe) μ(Z,A) e- + (Z,A))

μ(Z,A) μ + (Z,A))Bμe =

Lepton Flavor & Number Violation

Present universe Early universe

Weak scale Planck scale

log10(μ / μ0)

€

S−1

€

L−1

€

Y−1

€

μ

€

e

€

€

μ

€

e

€

A Z,N( )

€

A Z,N( )

MEG: Bμ->e ~ 5 x 10-14

Mu2e: Bμ->e ~ 5 x 10-17

??

R = Bμ->e

Bμ->e

Also PRIME

Lepton Flavor & Number Violation

€

μ

€

e

€

€

μ

€

e

€

A Z,N( )

€

A Z,N( )

MEG: Bμ!e ~ 5 x 10-14

Mu2e: Bμ!e ~ 5 x 10-17

€

μ

€

e

€

*

€

e

€

e

€

˜ ν

€

μ

€

e

€

*

€

e+

€

e+

€

Δ−−

Logarithmic enhancements of R

Low scale LFV: R ~ O(1) GUT scale LFV: R ~ O

€

e−

€

e−

€

M

€

W −

€

W −

€

u

€

u

€

d

€

d

€

e−

€

e−

€

χ 0

€

˜ e −

€

u

€

u

€

d

€

d

€

˜ e −

0decay

Light M exchange ?

Heavy particle exchange ?

Raidal, Santamaria; Cirigliano, Kurylov, R-M, Vogel

k11/ ~ 0.09 for mSUSY ~ 1 TeV

μ->e LFV Probes of RPV:

k11/ ~ 0.008 for mSUSY ~ 1 TeV

μ->e LFV Probes of RPV:

• What is the absolute value of m ? Why is m so tiny ?

• What is the mass hierarchy ?

• Is the neutrino its own antiparticle?

• What is 13 ?

• Do neutrinos violate CP?

• How do neutrinos affect/reflect astrophysical phenomena ?

Open Questions

Precision Neutrino Property Studies

Neutrino Mass: Terrestrial vs Cosmological

WMAP & BeyondKATRIN, Mare

0.1

1

10

100

1000

Effective

( )Mass meV

12 3 4 5 6 7

12 3 4 5 6 7

12 3 4 5 6 7

1 ( )Minimum Neutrino Mass meV

U1e=.866δm2

sol=7meV

2

U2e=.5δm2

atm=2meV

2

U 3e =

Inverted

Normal

Degenerate

Energy Density Power Spectrum

Beacom, Bell, Dodelson

New interactions

Precision Neutrino Property Studies

Mixing, hierarchy, & CPV

€

U =

Ue1 Ue2 Ue 3

Uμ1 Uμ 2 U μ 3

Uτ 1 Uτ 2 Uτ 3

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

=

1 0 0

0 cosθ23 sinθ23

0 −sinθ23 cosθ23

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟×

cosθ13 0 e−iδ CP sinθ13

0 1 0

−e iδ CP sinθ13 0 cosθ13

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟×

cosθ12 sinθ12 0

−sinθ12 cosθ12 0

0 0 1

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟×

1 0 0

0 e iα / 2 0

0 0 e iα / 2+iβ

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

Mini Boone

Long baseline oscillation studies:

CPV?

Normal or Inverted ?

Daya Bay

Double Chooz

T2K

Precision Neutrino Property Studies

Solar Neutrinos

KamLAND Borexino SNO+ LENS

Ice Cube

High energy solar s

DM + EWB

EM vs. luminosity: MNSP unitarity? Solar model?