Neutrina, co nowego w teorii?

Marek Zrałek Instytut Fizyki

Uniwersytetu Śląskiego

1

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. 2

3

News in the theory

of neutrino physicsWrocław

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

νπθ∞ν

5

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,

6

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 37 88 29 2

1960 91 42 63 204 185 126 97 98 299 70

1970 911 812 923 1324 1965 2456 3117 2988 3679 311

1980 4321 4122 3183 2274 3755 3446 5417 5988 4989 449

1990 4811 5362 6933 5404 5405 5636 5917 6428 8769 1006

2000 11951 11552 11193 11684 10015 10316 10947 8298 6137

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

9

2) Neutrinos in the Standard Model

1) There is no RH neutrinos, 2) There is only one Higgs doublet of SU(2)L, 3) Theory is renormalizable,

Butvanishing of neutrino

mass is not guaranteed by any

fundamental symmetry

As a consequense:

Neutrinos are

massless

10

There are three flavour neutrinos:

Le,Lμ ,Lτ

Distinguished by three flavour

numbers

F.Reines & C. Cowan (1956) - νe

M. Schwartz, L. Lederman, J. Steinberger (1962) – νμ

DONAT Collaboration in Fermilab (2000) - νμ .

νe,ν μ ,

ν τ

From Z0 decay- LEP- there are only three flavour neutrinos

11

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??

mMLi (ν

ciRνiL +νiLν

ciR )

Dirac mass?

or Majorana mass??

L

R

mDi (νiRνiL +νiLνiR )

mMRi (ν

ciLνiR +νiRν

ciL)

mDi (νiRνiL +νiLνiR )

mMLi (ν

ciRνiL +νiLν

ciR )

12

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 For three neutrinos:

a, b a, b

mi = E

Ka, l Ul , a*

mi = EIn the present experiments:

(νSM)

→

13

What we know from

experiments??

14

3) Present experimental data

1) Very preciselly we know masses of charged leptons

me 0.510998910 ±0.000000013 MeV ,μ μ 105.6583668 ±0.0000038 MeV ,

μ τ 1776.84 ±0.17 MeV

2) Neutrino masses we know indirectly

Uei2 mi

2 ≤2 eVFrom tritium beta decay

Δm212 = (7.59−0.21

+0.14 ) ×10−5 eV 2

Δm322 = (2.43 ± 0.13) ×10−3eV 2

From oscillation

experiments

15

U

c13c12 c13s12 s13e−i

−s12c23 −c12s13s23ei c12c23 −s12s13s23e

i c13s23 s12s23 −c12s13c23e

i −c12s23 −s12s13c23ei c13c23

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

eiφ1 0 00 eiφ2 00 0 1

⎛

⎝⎜⎜⎜

⎞

⎠⎟⎟⎟

sin2 (2θ12 )0.87 ±0.03

From oscillation experiments:

sin2 (2θ23)> 0.92

, φ1, φ2 = ???sin2 (2θ13)< 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 - α1, α2 D) Is mixing angle θ13 different from zero

17

Neutrinos in the

New Standard Model(νSM)

18

4) Neutrinos in the SM with massive neutrinoDurinng last two years two important properties of neutrino oscillation were discused: • Mössbauer Neutrinos,

• Anomaly observed in the GSI

A(Z 1) A(Z)+ e +νe

MÖSSBAUER NEUTRINOS W.M.Visscher, 1959W.P. Kells, J.P. Schiffer,1983R.S. Raghavan,2006

19

3H → 3He + e−+νe

3He + e−+νe →3H

For Tritium embedded into a cristal

M Z−1 Eν + μ ν + ER + MZ + Ee + μ e

Δ M Z −1 − M Z EB −Ee −μ e

ER ≈0EB ≈coνsτ

EνeΔ + EB −ER

Γ

hτ1.17 ×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:Atmospheric neutrinos

We obtain:

Neutrinosshould not oscillate

21

Do Mössbauer neutrinos oscillate ???

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

No oscillation

But if: Neutrinos oscillateWhy 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 (e.g. eigenstate of harmonic oscillator has definite energy but not momentum)

Δm2 = (2EΔE)2 + (2 pΔp)2

m2 E2 −π2

If:

pΔπEΔE

22

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….

23

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 studying neutrino mass difference – For Pedestrians),

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

Neutrino oscillation with

the period:

dd 2

21

2 MTm

π

Δ

1) C.Giunti, arXiv:0801.4639,2) H Kienert at al., arXiv:0808.2389,3) M.Peshkin, arXiv:0804.4891, arXiv:0811.1765,

No oscillation

Td 2π

M

Δμ 212

24

Probability that measurement of any observable A gives one of the

eigenvalue a1, a2, .... aN Δ :

ˆ( P )p Tr Δ Δ

1 2ˆ ˆ ˆ ˆP P +P + .....+P

Na a aΔ

1 2...

Na a ap p p pΔ + + +

There is no interference

⊂

pΔ T{P̂Δ}

P̂Δ P̂a1 + P̂a2 +....P̂aN

25

In the two slits experiments:

1x2x

1A

2A

2

1

1 2( , ) ( )x

x

p x x dxp x2

1 2( ) ( ) ( )p x A x A x +2

1 2( ) ( ) ( )p x A x A x +

26

Neutrinoless double beta decayEven-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:

27

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

2ei i

i=1

m (U ) mν

m 0.2 eVν

2ei i

i=1

m (U ) mν

28

Neutrinos beyond

the Standard Model

29

5) Neutrinos beyond the SM

♳ MiniBOONE anomaly

♴ Problem of neutrino mass and mixing

♵ Neutrino oscillation beyond the SM

♶ Leptogenesis

MiniBooNE

31

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

for

transition, is observed.

MiniBooNe coll. arXiv:0812.2243

MiniBooNE coll. arXiv:0904.1958νμ → νe

νμ → νe

νμ → νe

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

observed by LSND

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 106

33

In the present Higgs mechanism

Le ReLe Re Le

H

H

H

H

Lν

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 RνLν Rν LνH

H

mDi (νiRνiL +νiLνiR )

mMLi (ν

ciRνiL +νiLν

ciR )

mMRi (ν

ciLνiR +νiRν

ciL)

mν : λν H νiRνiL

H ≈175 ΓeVmν ≈0.2 eV ⇒ λν ≈10

−12 Resolutions: EXTRA DIMENSIONS

35

(II) Neutrina Majorany

Lν LνRN

R

15Nm M 10 GeV

See-saw mechanism

Higgs triplet Δ: ≈1⇒ Δ < 8GeV

Directly testable at LHC

Two Higgs doublet H:

(ΔLL)

1M

(HHLL) mν :

1M

λν H 2

M ≈1013 −1016ΓeVR fermion singlet:

1M

HLR

R3 fermion triplet: 1M

HLR3

(See-saw II type)

(Type I see-saw)

(Type III see-saw)

36

Hierarchy problem scale ≈ 1TeVGUT scale ≈ 1016 GeV Planck skale ≈ 1019 GeV

There is balance

between “naturalness”

and“testability”

U(3s ) 0.77−0.86 0.50−0.63 0.−0.220.22−0.56 0.44 −0.73 0.57−0.80.21−0.55 0.40−0.71 0.59−0.82

⎛

⎝⎜⎜

⎞

⎠⎟⎟

Problem of neutrino mass is connected with their mixing

UTB

23

13

0

−16

13

12

16

−13

12

⎛

⎝

⎜⎜⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟⎟⎟

Tri-bimaximal (TB) mixing pattern

sinθ12 13(1+ s)

sinθ23 12(1+a)

sinθ13 2

37

If then TB is satisfiedand 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 family symmetry

Then from spectral theorem neutrion mass matrix can be decomposed

Mν μ 1

6Φ1Φ

+1 +

μ 2

3Φ2Φ

+2 +

μ 3

2Φ3Φ

+3

38

Where mi are the neutrino masses, and Φi - appropriate eigenvectors, so

Φ1 =2−11

⎛

⎝⎜⎜

⎞

⎠⎟⎟ Φ2 =

11−1

⎛

⎝⎜⎜

⎞

⎠⎟⎟ Φ3 =

011

⎛

⎝⎜⎜

⎞

⎠⎟⎟

UMNS 16Φ1,

13Φ2 ,

12Φ3

⎛⎝⎜

⎞⎠⎟

Large numbers of different flavour symmetry groups continuous: SO(3),SU(3),….and discrete: Z, S, A,…

39

Non-standard neutrino intraction and Neutrino

Oscillations

Different processes for neutrino production

π + → μ+ +νμ

π −→ μ−+νμ

n→ π+ e−+νe 26He→ 3

6Li e−νe

1018Ne→ 9

18Φ e+νep→ ν+ e+ +νe

Neutrino superbeams, Off axis neutrino beams

Beta beams Average Ecms 1.937 MeV

Average Ecms 1.86 MeV

μ−→ e− +ν μ +ν e

μ+ → e+ +ν μ +ν e

Neutrino factories

Processes for neutrino detection

νe + A JZ → A J 'Z +1 + e−

νa + e− → ν α + e− νa + e− → ν α + e−

νa + d → p + p + e− νa + d → p + n +ν α

νe + n → p + e−

νe + A JZ → A J 'Z −1 + e+

νe + p → n + e+

A JZ 12C6 ,20Ne10 ,

37Cλ17 ,71Γa31,

100Mo42 ,127 I53

A J 'Z 37A18 ,

71Γe32 ,100Tc43,

115Sν50 ,127Xe54

For production and detection processes - complex current

LCC e

2 2 siνθ

λaa , i∑ μ (1−5 )Uaiνiμ

−+h.c

νβ ↑ Uβ ii

∑ ν i ↑

Relativistic (anti)neutrinos are produced in pure Quantum Mechanical

flavour state

Neutrinos always with positive helicity

νa ↓ U *α i

i∑ ν i ↓

Antineutrinos always with positive helicityZ. Maki, M. Nakagawa, S. Sakata,

Prog.Theor.Phys. 28(1962)870

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

LNC e

4siνθ cosθ

νii1,2,3∑ μ (1−5 )νiZμ

νβ ↓ U *β i

i∑ ν i ↓

P Dνa ↑ Uα i

i∑ ν i ↑

νa ↓ U *α i

i∑ ν i ↓

νβ ↑ Uβ ii

∑ ν i ↑

No spin flip

No spin flip

DP

Number of the β neutrinos with energy E, which reach detector in a unit time

ΔND (L, E) = ρα (E) Pα →β (L,E) σ β (E) ND

Density of the

α initial neutrin

os

Probability of theα to β neutrino conversion

Detection cross section ofβ neutrinos

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 4ΓΦ

2(e ,h

)i,k(λaΓνi,e )(νk,hΓλβ )+ h.c.

i,k1

3

∑S,V ,Te ,hL,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, Phys.Lett.B359,141(1995)

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:

la

la

ν i

CC

CC

ν i

D

νaP = Uα , i

P

i∑ ν i

νaP

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

νaD = Uα , i

D

i∑ ν i

νβD lβ

CC

P

Ua , iP 2

∝ νi; fP H P λa ;iP2

Uβ, iΔ 2

∝ λβ ; fΔ H Δ νi;iΔ2

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 byνβ

D

Pa→ β (τ) νβP e−iHτ νa

Δ2

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) Cardall(00), Giunti(02), Beuthe(03)

νβD

49

P

D

βa νν

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

)x-k(x2i

2i

4

4

ik2k1i21

mkmk

)(2kd0)x()x(T(0 ie

i

++

eπνν

(t1,rx1)

(t2 , rx2 )

Grimus,Stockinger(96)

Giunti(03),Beuthe(03)

aa ν+ FI PP

ββν FI DD +

OK - if Hamiltonian describing production and detection includes NI

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:

H x)(x d- I

4

TeSi

iif (x) Hxdi1)-S( I4

In the first order

IFP P ......P,N Sf + aaa νaa ν+ FI PP

To get neutrino state, we have projected out all other degree of freedom

So for the process

IIF4

IFFF P(x)HPxdN1PP

N1P,P a

aa

aaaaa νν iS

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

νaP νβ

D

Pa→ β (τ) νβP e−iHτ νa

Δ2

ΔND (L ≈ t,E) = ρα (E) Pα →β (t) σ β (E) ND

H 4ΓΦ

2(e ,h

)i,k(λaΓνi,e )(νk,hΓλβ )+ h.c.

i,k1

3

∑S,V ,Te ,hL,R

∑

Let us take the general interaction

μ−→ e− + ν μ + ν eFor muon decay:

(ge ,h )i,k e ,h

(Ue )e, i(Uh

)μ,k*

If there are different mixing for different operator and chirality:

νμ ν(λ = −1)

νe = ν (λ = +1)SM

gR,RS NI νμ ν(λ = +1)

νe = ν (λ = −1)

Neutrinos are

produced in

mixed state

gL ,LV

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

gL ,LS → L,L

S Uμ,kS* ≡L,L

S V μ,k*

gL ,LV → L,L

V Uμ,kV * ≡L,L

V Uμ,k*

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 the standard formulae.

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

(B) Beyond the Standard Model(B.1) Initial neutrino states are not pure, they are mixed even for

relativistic neutrinos. State of the neutrinos produced in the process

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 ν+ + il A B

Where the are the amplitudes for the production process:

( , ; , )i A l BAa λ λ λ λ( ) ( ) ( ) ( )l A B il A Ba λ λ λ ν λ+ +

*, ; ,

, ,

1 A , ; , A , ; ,a a aλ μ

λ λ λa

λ λ λ λ λ λ λ μ ( ) ( )l A B

i k i A l B k A l BN1a( )Tr

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

(E,L) P (E,L) (E)a β a β βs s

Generally the (E,L) cross section does not factorizea βs

spinsC

p1 1(E,L) = dLips A T=L)A32 s p 2s 1

β a βa βs

π*

(+ f

i

Where now

A is the amplitude for the detection processβk C Dβν + +l

TN(E,L) (E) (E,L) Na a β s

(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).

57

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

scale?

58

Large statistic

Future neutrino

experiments

Cosmological studiesDark matter, dark energy

Large energy

LHC

2030

59

Conclusions During last years there was great progress in the neutrino physics

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 GUT

Neutrinos play the role in astrophysics and cosmology