Neutrina, co nowego w teorii?

Neutrina,

co nowego w teorii?

Marek Zrałek Instytut Fizyki

Uniwersytetu Śląskiego

Streszczenie



Po odkryciu i rozwikłaniu problemu oscylacji, fizyka neutrin stała się w ostatnich latach jednym

z głównych elementów fizyki cząstek

elementarnych. Tak jak w przeszłości, również obecnie, odkrycia związane z neutrinami przynoszą

przełomowe informacje o oddziaływaniach elementarnych, astrofizyce i kosmologii.



Wykład będzie omawiać różne teoretyczne pomysły, o których usłyszeliśmy w ostatnim czasie. Tak więc

będzie mowa o problemie natury neutrin, o masie i zapachu, o neutrinach Mössbauera, o anomalii GSI

i wielu innych nowościach.

News

in the theory

of neutrino physics

Wrocław 9. 11. 2009

Marek Zrałek, Uniwersytet Śląski

4

Introduction

Neutrinos in the Standard Model (SM) Experimental facts

Neutrinos in the SM with small ν mass Neutrino mass beyond the SM

Questions

Conclusions and perspectives

Outline

πθ∞ν

ν

1) INTRODUCTION – What is behind us?

Neurinos always give a new and unexpected informations about elementary interactions

Lee & Yang (1956), Wu (1957) - P and C symmetries are broken in Nature,

In 1930, Pauli, remedy for the energy crisis observed in the beta decay,

In 1934, Fermi, neutrinos were used to construct the first theory of week interaction – Fermi theory for beta decay,

Majorana in 1937, particles which are the same are their antiparticles can exist – Majorana particles,

In 1987 neutrinos from the supernova SN87A were observed – the theory of supernova explosion was confirmed,

Gargamelle (1973), neutral currents exist – first indication about Z boson,

(Years 60-70), neutrinos are parts of the leptons doublets – Glashow, Weinberg & Salam of the unified model of

electromagnetic and week interaction was created – the Model Standard,

In In LEP, 1989, in Z decay - first observation that only three

generation of quarks and leptons exist in Nature,

1956 3

7 8

8 2

9 2

1960 9

1 4

2 6

3 20

4 18

5 12

6 9

7 9

8 29

9 70

1970 91

1 81

2 92

3 132

4 196

5 245

6 311

7 298

8 367

9 311

1980 432

1 412

2 318

3 227

4 375

5 344

6 541

7 598

8 498

9 449

1990 481

1 536

2 693

3 540

4 540

5 563

6 591

7 642

8 876

9 1006

2000 1195

1 1155

2 1119

3 1168

4 1001

5 1031

Superkamiokande, in 1998, first real

confirmation that atmospheric neutrinos

oscillate – neutrinos are massive particles – the Standard Model has to be extended

JJaak

How to extend

the Standard Model????

Between 1998 and 2003 – solar neutrino problem was resolved – first independent proof

that Bethe model of energy creation in stars –

hydrogen nucleosynthesis is correct

8

Neutrinos in

the Standard Model

2) Neutrinos in the Standard Model 2) Neutrinos in the Standard Model

1) There is no RH neutrinos,

2) There is only one Higgs doublet of SU(2)

, 3) Theory is renormalizable,

vanishing of neutrino But mass is not guaranteed

by any fundamental symmetry

As a consequense:

Neutrinos are

massless Neutrinos

are

massless

10

There are three flavour neutrinos:

L _e ,L _μ ,L _τ

Distinguished by three flavour

numbers

 F.Reines & C. Cowan (1956) - ν_e

 M. Schwartz, L. Lederman, J.

Steinberger (1962) – ν_μ

 DONAT Collaboration in Fermilab (2000) - ν_μ .

ν

, ν

, ν

From Z

decay- LEP- there are only

three flavour neutrinos

Neutrino interaction in the Standard

Model

From 1998 we know that neutrinos are massive, what kinds of mass term we have to add to the SM??

m

( ν

ν

+ ν

ν

)

Dirac mass?

or Majorana mass??

L m _i ^D (ν _iR ν _iL +ν _iL ν _iR )

m

( ν

ν + ν ν

)

m

( ν

ν

+ ν

ν

)

m

( ν

ν

+ ν

ν

)

1

Practical Dirac – Majorana Confusion Theorem

W obecnie prowadzonych eksperymentach

Differences in all observables for the Dirac and Majorana neutrinos smoothly vanish for mν 0

So in the frame of the new Standard Model

neutrinos:



 

m_i = E

K

 U

m

= E

In the present experiments:

(νSM)

→

What we know from

experiments??

14

3) Present experimental data

1) Very preciselly we know masses of charged leptons

m

 0.510998910 ± 0.000000013 MeV , m

 105.6583668 ± 0.0000038 MeV , m

 1776.84 ± 0.17 MeV

2) Neutrino masses we know indirectly

U

m

≤2 eV

From tritium beta decay

Δm

= (7.59

) ×10

eV

Δm

= (2.43 ± 0.13) ×10

eV

From oscillation experiments

U 

c₁₃c₁₂ c₁₃s₁₂ s₁₃e^−iδ

−s₁₂c₂₃ −c₁₂s₁₃s₂₃e^iδ c₁₂c₂₃ −s₁₂s₁₃s₂₃e^iδ c₁₃s₂₃ s₁₂s₂₃ −c₁₂s₁₃c₂₃e^iδ −c₁₂s₂₃ −s₁₂s₁₃c₂₃e^iδ c₁₃c₂₃

⎛

⎝

⎜⎜

⎜⎜

⎞

⎠

⎟⎟

⎟⎟

e

0 0 0 e

0

0 0 1

⎛

⎝

⎜ ⎜

⎜

⎞

⎠

⎟ ⎟

⎟

sin

(2 θ

)  0.87 ± 0.03

From oscillation experiments:

sin

(2 θ

) > 0.92

δ , φ , φ = ???

sin

(2 θ

) < 0.19

16

We do not know!!

A)The neutrino mass scheme:

✰ Mass hierarchy

✰ Inverse mass hierarchy

✰ Degenerate

B) Neutrino nature - Dirac or Majorana

C) Are the CP symmetry violated or no, phases

✰ Dirac - δ,

✰ Majorana - α

, α

D) Is mixing angle θ

different from zero

Neutrinos in the

New Standard Model

(νSM)

18

4) Neutrinos in the SM with massive neutrino

Durinng last two years two important properties of neutrino oscillation were discused:

• Mössbauer Neutrinos,

• Anomaly observed in the GSI

A(Z 1) A(Z)+ e ^ +  _e

MÖSSBAUER NEUTRINOS

W.P. Kells, J.P. Schiffer,1983 R.S. Raghavan,2006

3 H → ³ He + e ⁻ + ν _e

3 He + e ⁻ + ν _e → ³ H

For Tritium embedded into a cristal

M

 E

+ m

+ E

+ M

+ E

+ m

Δ  M

− M

^E

^{ − E}

^{− m}

E

≈0 E

≈ cost

E _ν

 Δ + E _B ⁻ E _R

Γ  h

τ ^{ 1.17 ×10}

−24

eV

τ  17.81 years

20

Even if we assume that various brodening effects degrade this value :

W. Potzel, 2006, R.S. Raghavan, 2006,

but W. Potzel in Ustron 2009 – probably observation of the effect in ³H - ³He will be unsuccessful

Energy difference for two relativistic neutrinos with energy E

Then for:

neutrinos

We obtain: Neutrinos

should not oscillate Neutrinos should not

oscillate

Do Mössbauer neutrinos oscillate ???

E.K.Akhmedov, J. Kopp, M. Lindner, 2008

No oscillation

But if: Neutrinos oscillate

Why is possible to have such big Δp??

For particles on mass shell:

In bound states, energy and momentum are not

connected by the on mass shell relation

Δm

= (2EΔE)

+ (2 pΔp)

m

 E

− p

If:

pΔ p  E Δ E

GSI, ArXiv:0801.2079

There are attempts to explain these observations as neutrino oscillation

Giunti; Ivanov, Reda and Kienle;

Lipkin; Peshkin; Burkardt, Lowe, Stephenson; Ivanov, Kryshen, Pitschmann, Kiele; Giunti;

Lipkin….

Litvinov et al. (GSI), Phys. Lett. B664, 163 (2008)

A. N. Ivanov at. al., arXiv:0801.2121, H. J. Lipkin, arXiv: 0801.1465,

arXiv:0805.0435 (The GSI method for

H. Kleinert, P. Kienle, arXiv:0803.2938.

Neutrino oscillation with

the period:

d

d 2

21

2 M

T m

p 

  



1) C.Giunti, arXiv:0801.4639,

2) H Kienert at al., arXiv:0808.2389,

No oscillation T

 2 π

ω ^

γ M

Δ m

24

Probability that measurement

of any observable A gives one of the eigenvalue a

, a

, .... a

Δ :

( P ) ˆ p _  Tr  _

1 2

ˆ ˆ ˆ ˆ

P P +P + ...+P

a a a

 

1 2

...

a a aN

p

 p + p + + p

There is no interference

⊂

p _Δ  T { ˆ P _Δ ρ }

ˆP

 ˆ P _a

+ ˆ P _a

+ .... ˆ P _a

In the two slits experiments:

x

x

A

A

2

1 2

( , ) ( )

x

p x x   dxp x ^{p x p x ( ) ( )   A x A x}

^{( ) ( ) + + A x A x}

^{( ) ( )}

26

Neutrinoless double beta decay

Even-even nuclei, candidate for (ββ)_0ν decay:

For the foreseeable future it will be impossible to calculate the NME direcly from QCD

Majorana Coll., nucl-ex/0311013

Decay half- life:

In the past years we have seen a significant improvement in the calculation of the NME

QRPA(Quasi-Particle-Random-

Phase-Approximation) ShM(Shell Modell)

P.Vogel,

arXiv:0807.2457

2

ei i

i=1

m_ 



m_  0.2 eV

2

ei i

i=1

m_ 



28

Neutrinos beyond

the Standard Model

5) Neutrinos beyond the SM

♳ MiniBOONE anomaly

♴ Problem of neutrino mass and mixing

♵ Neutrino oscillation beyond the SM

♶ Leptogenesis

MiniBooNE

Sizable excess (128.8 ± 43.4) at low energy (200-475 MeV) for

transition, is observed.

MiniBooNe coll.

arXiv:0812.2243

MiniBooNE coll.

arXiv:0904.1958

ν_μ→ ν_e

ν

→ ν

ν

→ ν

No significant excess of events has been observed for

oscillation at law (200-475 MeV ) and at high energy (475 -1250

MeV) regions.

In the same channel excess was

32

S.N. Ganienko, arXiv:0902.3802

There are a lot of papers which try to explain the electron neutrino excess:

Is there anomalous difference between neutrino and antineutrino properties ?? - result are inconclusive

 Extra – dimensions,

 Sterile neutrinos,

 CPT violating interaction,

 Neutrino –antineutrino

oscillation

x 10

33

In the present Higgs mechanism

e

e

e

e

e

H

H

H

H

Problem of Mass and Mixing

Why neutrino masses are so small, much smaller then charged

leptons

and quarks masses

10⁶

Why there two large mixing angles for leptons which contrasts

sharply

with the smallnest of the quark

mixing angles.

34

Why neutrino masses are very small, answer depends on neutrino nature

(I) Dirac neutrinos , or

(II) Majorana neutrinos

(I) Neutrina Diraca

Righ handed neutrino fields have to be added

 R







H

H

m

( ν

ν

+ ν

ν

)

m

( ν

ν

+ ν

ν

) m

( ν

ν

+ ν

ν

)

m

: λ

H ν

ν

H ≈ 175 GeV m

≈0.2 eV ⇒ λ

≈ 10

EXTRA

DIMENSIONS Resolutions:

EXTRA

DIMENSIONS

(II) Neutrina Majorany





NR

R

15

m

 M 10 GeV 

See-saw mechanism

Higgs triplet Δ: ρ ≈ 1 ⇒ Δ < 8GeV

Directly testable at LHC

Two Higgs doublet H:

(Δ LL )

1

M (HHLL)

m

: 1

M λ

H

M ≈ 10

− 10

GeV

R fermion singlet:

R

fermion triplet:

(See-saw II type)

(Type I see-saw)

36

Hierarchy problem scale ≈ 1TeV GUT scale ≈ 10

GeV

Planck skale ≈ 10

GeV

There is balance between

“naturalness”

“testability” and

U_{(3σ )} 

0.77 −0.86 0.50 −0.63 0.−0.22 0.22 −0.56 0.44 −0.73 0.57 −0.8 0.21−0.55 0.40 −0.71 0.59 −0.82

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

Problem of neutrino mass is connected with their mixing

U_TB 

2 3

1

3 0

− 1 6

1 3

1 2 1

6 − 1 3

1 2

⎛

⎝

⎜⎜

⎜⎜

⎜⎜

⎜

⎞

⎠

⎟⎟

⎟⎟

⎟⎟

⎟

Tri-bimaximal (TB) mixing pattern

sinθ₁₂  1

3 (1+ s) sinθ₂₃  1

2 (1+ a)

sinθ₁₃   2

If then TB is satisfied and would demand explanation. r, s , a = 1

If are closed to their current 2σ

bounds, then TB mixing would only be realized approximately

r, s, a

If TB is realized –

signal of underlying If TB is realized – family symmetry signal of underlying family symmetry

Then from spectral theorem neutrion mass matrix can be decomposed

M  m

Φ Φ

+ m

Φ Φ

+ m

Φ Φ

38

Where m

are the neutrino masses, and Φ

- appropriate eigenvectors, so

Φ

=

2

−1 1

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟ Φ

=

1 1

−1

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟ Φ

=

0 1 1

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟

U

 1

6 Φ

, 1

3 Φ

, 1

2 Φ

⎛

⎝⎜

⎞

⎠⎟

Large numbers of different flavour symmetry groups

continuous: SO(3),SU(3),….

and discrete: Z, S, A,…

Non-standard neutrino intraction and Neutrino

Oscillations

Different processes for neutrino production

π

→ μ

+ ν

π

→ μ

+ ν

n → p + e

+ ν

He →

Li e

ν

10

18

Ne →

F e

ν

p →  + e

+ ν

Neutrino superbeams,

Beta beams

Average E_cms  1.86 MeV

μ

→ e

+ ν

+ ν

μ

→ e

+ ν

+ ν

Neutrino factories

Processes for neutrino detection

ν

+

J

→

J

+ e

ν

+ e

→ ν

+ e

ν

+ e

→ ν

+ e

ν

+ d → p + p + e

ν

+ d → p + n + ν

ν_e + n → p + e⁻

ν

+

J

→

J

+ e

ν_e + p → n + e⁺

AJ_Z  ¹²C₆, ²⁰Ne₁₀, ³⁷Cl₁₇, ⁷¹Ga₃₁,¹⁰⁰Mo₄₂,¹²⁷ I₅₃

AJ^'_Z  ³⁷A₁₈, ⁷¹Ge₃₂,¹⁰⁰Tc₄₃,¹¹⁵S₅₀,¹²⁷Xe₅₄

For production and detection processes - complex current

L

 e

2 2 si θ

l

α, i

∑ ^γ

^{(1− γ}

^)U

^ν

^

^{+ h . c}

ν

↑  U

∑

^ν

^↑

Relativistic (anti)neutrinos are produced in pure Quantum Mechanical

flavour state

Neutrinos always with positive helicity

ν

↓  U

∑

^ν

^↓

Antineutrinos always with positive helicity

Z. Maki, M. Nakagawa, S. Sakata,

Neutrino propagation in the vacuum or in a matter – - neutral current

L

 e

4 si θ

cos θ

ν

i1,2,3

∑ ^γ

^{(1− γ}

^{) ν}

^Z

ν_β ↓  U^*_{β i}

∑

P P D D

ν_α ↑  U_{α i}

∑

ν_α ↓  U^*_{α i}

∑

ν_β ↑  U_{β i}

∑

No spin flip

No spin flip

D P

Number of the β neutrinos with energy E, which

reach detector in a unit time Number of the β

neutrinos with energy E, which

reach detector in a unit time

ΔN

(L, E) = ρ

(E) P

(L, E) σ

(E) N

Density of the initial α neutrin

os Density

of the initial α neutrin

os

Probability of theα to β neutrino

conversion

Probability of theα to β neutrino

conversion

Detection cross section of β neutrinos Detection cross

section of β neutrinos

Number of active scattering centres in a detector

Number of active scattering centres in a detector

Oscillation rate of neutrinos in a detector is described by the factorized formula

Oscillation rate is the same for Dirac and

Majorana neutrinos

There are models which predict

Nonstandard neutrino Interaction (NI) in the weak scale range, which can modify

neutrino production process,

 oscillation inside matter, and

 detection process

What we should modify to describe future

experiment with NI of neutrinos??

E.g. do not worry about gauge symmetry, and take dimensional six operators -

four-fermions effective Hamiltonian

H  4 G

2 ( 

)

( l

Γ

ν

)( ν

Γ

l

) + h . c .

i,k1 3

∑

δS,V ,T ε,ηL,R

∑

 Models which try to resolve problem of neutrino mass e.g. see-saw

 Charged Higgs,

 Right handed currents,

 Supersymmetric models.

First suggestion that neutrino oscillation experiments are sensitive to three ingredients, the production process, the time evolution and the detection, which is impossible to separate - in 1995

Y. Grossman,

Neutrio masses are uknown- but are very small, experiments cannot obserwed neutrinos as mass eigenstates. But the mass basis is well

define. Such states are process independent.

Neutrinos are produced by charged current

interaction. This process defines neutrino flavour.

Such states are process dependent:

l

l

ν

CC

CC

ν_i

DD

ν

= U

∑

^ν

ν

Detection process measures different state – the detection flavour neutrino states:

ν

= ∑ U

^ν

ν

l

P P

U

∝ ν

; f

H

l

; i

U

∝ l

; f

H

ν

; i

Production and detection flavour mixing matrices are constucted from production and detection interaction Hamiltonians

The probability of finding neutrinos in a states in the original beam at the time t is given by

P

( t )  ν

e

ν

Two kinds of such approaches using the necessary language of wave packets are possible to find in the literature

Kayser(81),Giunti,Kim,Lee(91),Rich(93) Grimus and Stckinger(96), MZ(98)

ν_β^D

P

D



a



 

Between two different points from production up

to detection place, neutrinos prapagate

virtually, they are not on the mass shell

Between two different points from production up

to detection place, neutrinos prapagate

virtually, they are not on the mass shell

1) First approach, full QFT

1) First approach, full QFT

) x - k(x 2

i 2

i 4

4 ik

2 k

1

i ^{1 2}

m k

m k

) (2

k 0 d

) x ( )

x ( T(

0 e

i



+



 ^  _p + _e







(t₁, r x₁)

(t², r x₂)

Grimus,Stockinger(96) Giunti(03),Beuthe(03)

a a

+ 



I

P

P





+ D

 D

50

2) Between P and D neutrinos are physical, but initial and final states are constructed using full QFT.

Having the interaction Lagrangian, we construct the S matrix:

 Te



S

i i

f ^ ( S - 1) i ^{ }  d

x H

(x)

In the first order

I F

P

N , P ... S P f 



+ 

a a

+ 



I

P

P

To get neutrino state, we have projected out all other degree of freedom So for the process

I I

F 4

I F

F

F

d x P H (x) P

N P 1

N P P 1

,

P

a a

a a

a a

a



 ^{ }

^{ }



C.Giunti JHEP 0211(2002)017

In these approaches as in the Standard Model:

1) Production and detection states are pure Quantum Mechanical states

2) It is possible to define flavour change probability

which factorize

ν

^ν

P

( t )  ν

e

ν

2

ΔN

(L ≈ t, E) = ρ

(E) P

(t) σ

(E) N

H  4 G

2 ( 

)

( l

Γ

ν

)( ν

Γ

l

) + h . c .

i,k1 3

∑

δS,V ,T ε,ηL,R

∑

Let us take the general interaction

μ

→ e

+ ν

+ ν

For muon decay:

(g

)

 

( U

)

( U

)

If there are different mixing for different operator and chirality:

ν

 ν (λ = −1) ν

= ν (λ = +1) SM

g

^{NI ν}

^{ ν (λ = +1)}

ν

= ν (λ = −1)

Neutrinos are produced

in

mixed state

g

But even if only NI scalar left-handed coupling is present:

g

→ 

U

≡ 

V

g

→ 

U

≡ 

U

There are two different mixing matrices for the

same chirality ---

what about neutrino states in such case, are they pure

or mixed??

1. We know what to do with any properties of accompanied particles, 2. We can check, when neutrino state is pure, and when it is mixed,

3. Any New Physic (NP) in neutrino interaction can be easy considered, 4. In very natural way we are able to take into account neutrino space

localization (wave packet approach) ,

5. We exactly know, when the formula for neutrino transition factorize,

6. For relativistic neutrino and their SM Left-Handed interaction, we reproduce

We propose to use the density matrix M.Ochman,R. Szafron,MZ, J.Phys.G35:065003,2008

(B) Beyond the Standard Model

(B.1)

is described by the density matrix (if the initial particles (l, A) are not polarized and polarization of the final particles (B) is not measured):

a

+  + 

l A B

Where the are the amplitudes for the production process:

( , ; , )

i A l B

A

l l l l

( )

(

) (

)

( ) l

l + A l  B l +  l

* , ; ,

, ,

1 A , ; , A , ; ,

a a a

l m a l l l

   ( l l l l ) ( l l l m )

l A B

i k i A l B k A l B

N

a 1 ( )  Tr

(B.2) There is no factorization for the detection rate

(E,L) P (E,L) (E)

a  a  

s



s

Generally the s

(E,L) cross section does not factorize

spins C

1 p 1

(E,L) = dLips A T=L)A

32 s p 2s 1

 a 

s



p

*



(

+ 

f i

Where now

 +  +

N(E,L)   _a (E) s _{a  } (E,L) N T

(B3) Dirac and Majorana neutrinos propagate in matter in a different way, so in principle both types of neutrinos can be distinguished in future oscillation experiments.

 Production and detection states are the same

(charge currents are responsible for production and detection), but

 Propagation in a matter distinguishes both types of

neutrinos (neutral currents are crucial).

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The road ahead:

EXPERIMENTS:

• Are neutrino Dirac or Majorana particles?

• What are absolute neutrino massea

• Is the 23 angle maximal?

• Does the 13 angle vanish?

• Is there CP volation in the lepton sector?

• Do the sterile neutrino exist?

THEORY

MASS PROBLEM

• To understand why neutrino mass is so tiny FLAVOUR PROBLEM

• Why the lepton and quarks mixing angles are so different?

• To understand SP symmetry breaking in the lepton sector PROBLEM OF INTERACTION

• Are there non-standard neurtino interaction in the TeV

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Large

statistic Future

neutrino experim

ents Large

statistic Future

neutrino experim

ents

Cosmological studies Dark matter, dark energy

Cosmological studies Dark matter, dark energy

LHC Large energy

LHC

2030 2030

Conclusions

During last years there was great progress in the

Lepton sector is completely different then the quark sector

To understand the neutrino masses we have to go beyond the SM

May be to understand the neutrinos we have to enlarge the number of dimensions

Neutrinos can give information about force unification

Neutrinos play the role in astrophysics and cosmology