1NASA Hubble Photo

Neutrino Physics

Boris KayserPASI

March 14-15, 2012Part 1

2

What Are Neutrinos Good For?Energy generation in the sun starts with the reaction —

!

p + p"d + e+ +#Spin: 1

212

12

121

Without the neutrino, angular momentumwould not be conserved.

Uh, oh ……

3

The Neutrinos

The neutrinos are spin – 1/2, electrically neutral, leptons.

The only known forces they experience arethe weak force and gravity.

Their weak interactions are successfully describedby the Standard Model.

This means that their interactions with other matterhave very low strength.

Thus, neutrinos are difficult to detect and study.

Neutrinos and photons are by far the most abundantNeutrinos and photons are by far the most abundantelementary particles in the universe.elementary particles in the universe.

There are 340 There are 340 neutrinos/cc.neutrinos/cc.

4

The Neutrino Revolution(1998 – …)

Neutrinos have nonzero masses!

Leptons mix!

Neutrino masses suggest, via theSee-Saw picture, new physics

far above the LHC energy scale.

5

The discovery of neutrino massesand leptonic mixing has come

from the observation ofneutrino flavor changeneutrino flavor change(neutrino oscillation)(neutrino oscillation).

6

The Physics ofThe Physics ofNeutrino OscillationNeutrino Oscillation

—— Preliminaries Preliminaries

7

The Neutrino FlavorsWe define the three known flavors of neutrinos, νe, νµ, ντ, by W boson decays:

Wνe

eW νµ

µW

ντ

τ

Detectorνµ

µ

WShort Journey

eAs far as we know, neither

nor any other change of flavor in the ν → interaction everoccurs. With α = e, µ, τ, να makes only α (e ≡ e, µ ≡ µ, τ ≡ τ).

8

If neutrinos have masses, and leptons mix,we can have —

Give ν time to change character

νµ ντ

The last 13 years have brought us compellingevidence that such flavor changes actually occur.

ντ

τ

W

Detectorνµ

µ

π

Long Journey

Neutrino Flavor Change

9

(Mass)2

ν1

ν2

ν3

Mass (νi) ≡ mi

There must be some spectrumof neutrino mass eigenstates νi:

Flavor Change Requires Neutrino MassesNeutrino Masses

10

Flavor Change Requires Leptonic Leptonic MixingMixing

|να > = Σ U*αi |νi> .Neutrino of flavor Neutrino of definite mass mi α = e, µ, or τ PMNS Leptonic Mixing Matrix

i

The neutrinos νe,µ,τ of definite flavor(W → eνe or µνµ or τντ)

must be superpositions of the mass eigenstates:

There must be at least 3 mass eigenstates νi,because there are 3 orthogonal neutrinosof definite flavor να.

11

This mixing is easily incorporated into the StandardModel (SM) description of the νW interaction.

For this interaction, we then have —

!

LSM = "g2

! L#$%&L#W%

" + & L#$%!L#W%

+( )#=e,µ,'(

= "g2

! L#$%U#i&LiW%

" + & Li$%U#i

*!L#W%+( )

#=e,µ,'i = 1,2,3

(

Left-handed

Taking mixing into account

If neutrino masses are described by an extension ofthe SM, and there are no new leptons, U is unitaryunitary.

Semi-weakcoupling

12

The Meaning of U

!

Ue1 Ue2 Ue3Uµ1 Uµ2 Uµ3U"1 U" 2 U" 3

#

$

% % %

&

'

( ( ( !

"1

!

"2

!

"3

!

µ

!

"!

e

!

U

!

=

!

"i

!

! "#

W+

!

g2U"i

The e row of U: The linear combination ofneutrino mass eigenstates that couples to e.

The ν1 column of U: The linear combination ofcharged-lepton mass eigenstates that couples to ν1 .

!

"i

!

!"#

W+

!

g2U"i*

!

!"+

13

Slides onThe Physics ofThe Physics of

Neutrino OscillationNeutrino Oscillation go here.

14

Suppose an experiment cannot see the small splitting

!

"m2

!

P "# $"%&#( ) = sin2 2'#% sin2 1.27(m2 eV 2( ) L km( )

E GeV( ))

* +

,

- .

Parameters that are ≤ 1

!

P "# $"#( ) =1% sin2 2&## sin2 1.27'm2 eV 2( ) L km( )

E GeV( )(

) *

+

, -

(Mass)2Invisible if

Δm2 L/E = O(1)

!

sin2 2"## = sin2 2"#$1 + sin2 2"#$2

Then —

( ) ( )

( ) ( )

No CP

15

Suppose the ν3 component of νe may be neglected

!

P "e #"x( ) = sin2 2$ sin2 1.27%m2 eV 2( ) L km( )E GeV( )

&

' (

)

* +

!

P "e #"e( ) =1$ sin2 2% sin2 1.27&m2 eV 2( ) L km( )E GeV( )

'

( )

*

+ ,

A neutrino born as νe will oscillate betweenνe and one other effective flavor, νx, which is thecombination of ν1 and ν2 that is orthogonal to νe .

νx is a linear combination of νµ and ντ.

Equal

No CP

( )

( )

( )

( )

16

Neutrino Flavor Change In Matter

This raises the effective mass of νe, and lowers that of νe.

involvesW

e

eνe

νe

νe

νe e

e

Wor

Coherent forward scattering via thisW-exchange interaction leads to

an extra interaction potential energy —

VW =+√2GFNe, νe

–√2GFNe, νe

Fermi constant Electron density

17

The fractional importance of matter effects on anoscillation involving a vacuum splitting Δm2 is —

[√2GFNe] / [Δm2/2E] ≡ x .

Interactionenergy

Vacuumenergy

The matter effect —

— Grows with neutrino energy E

— Is sensitive to Sign(Δm2)

— Reverses when ν is replaced by ν

This last is a “fake CP violation”, butthe matter effect is negligible when x << 1.

18

What WeWhat WeHave LearnedHave Learned

Renata

Zukanovic

h Funcha

l

19

(Mass)2

ν1

ν2ν3

or

ν1

ν2ν3

Δm221 = 7.4 x 10–5 eV2, Δm2

32 = 2.3 x 10–3 eV2~ ~

Normal Inverted

The (Mass)2 Spectrum

20

The 3 X 3 Unitary Mixing Matrix

!

LSM = "g2

! L#$%&L#W%

" + & L#$%!L#W%

+( )#=e,µ,'(

= "g2

! L#$%U#i&LiW%

" + & Li$%U#i

*!L#W%+( )

#=e,µ,'i = 1,2,3

(

Caution: We are assuming the mixing matrix U to be3 x 3 and unitary.

!

(CP) ! L"#$U"i%LiW$

&( )(CP)&1 = % Li#$U"i!L"W$

+

Phases in U will lead to CP violation, unless theyare removable by redefining the leptons.

21

Uαi describes —

νi α

W+

–

Uαi ∼ 〈α W+⏐H⏐νi 〉–

When ⏐νi〉 → ⏐eiϕ νi〉 , Uαi → eiϕ Uαi

When ⏐α 〉 → ⏐eiϕ α 〉, Uαi → e–iϕ Uαi– –

Thus, one may multiply any column, or any row, of U bya complex phase factor without changing the physics.

Some phases may be removed from U in this way.

22

Exception: If the neutrino mass eigenstatesare their own antiparticles, then —

Charge conjugate

νi = νic = Cνi

T

One is no longer free to phase-redefineνi without consequences.

U can contain additional CP-violating phases.

23

How Many Mixing Angles andCP Phases Does U Contain?

Real parameters before constraints: 18

Unitarity constraints —

Each row is a vector of length unity: – 3

Each two rows are orthogonal vectors: – 6

Rephase the three α : – 3

Rephase two νi , if νi ≠ νi: – 2

Total physically-significant parameters: 4

Additional (Majorana) CP phases if νi = νi : 2

!

U"i*U#i

i$ = %"#

24

How Many Of The ParametersAre Mixing Angles?

The mixing angles are the parametersin U when it is real.

U is then a three-dimensional rotation matrix.

Everyone knows such a matrix isdescribed in terms of 3 angles.

Thus, U contains 3 mixing angles.Summary

Mixing anglesCP phases if νi ≠ νi

CP phases if νi = νi

3 31

25

The Mixing Matrix U

!

U =

1 0 00 c23 s230 "s23 c23

#

$

% % %

&

'

( ( ( )

c13 0 s13e"i*

0 1 0"s13e

i* 0 c13

#

$

% % %

&

'

( ( ( )

c12 s12 0"s12 c12 00 0 1

#

$

% % %

&

'

( ( (

)

ei+1 /2 0 00 ei+2 /2 00 0 1

#

$

% % %

&

'

( ( (

cij ≡ cos θijsij ≡ sin θij

θ12 ≈ 34°, θ23 ≈ 39-51°,

0.023 < sin22θ13 < 0.17

δ and θ13 ≠ 0 would lead to P(να→ νβ) ≠ P(να→ νβ). CP violation

sin22θ13 = 0.092 ± 0.016 (stat) ± 0.005 (syst) (Daya Bay)

Majorana CPphases

26

!

P " µ #" e( ) $ P "µ #"e( ) = 2cos%13 sin2%13 sin2%12 sin2%23 sin&

' sin (m231L4E

)

* +

,

- . sin (m232

L4E

)

* +

,

- . sin (m221

L4E

)

* +

,

- .

All mixing angles must be nonzero for CP in oscillation.

There Is Nothing SpecialAbout θ13

For example —

In the factored form of U, one can putδ next to θ12 instead of θ13.