The Neutrino – Massless or Massive?courses.theophys.kth.se/5A1387/lecture18.pdfNeutrino...

The Neutrino – Massless orMassive?Tommy Ohlsson

[email protected]

Royal Institute of Technology (KTH) &

Royal Swedish Academy of Sciences (KVA)

Stockholm

Theoretical Particle Physics – Lecture 18

May 8, 2007

Tommy Ohlsson - Lecture 18, 2007 – p.1/16

Pauli’s Letter4th of December 1930

Dear Radioactive Ladies and Gentlemen,

As the bearer of these lines, to whom I graciously ask you to listen,will explain to you in more detail, how because of the “wrong”statistics of the N and

�

Li nuclei and the continuous beta spectrum, Ihave hit upon a desperate remedy to save the “exchange theorem”of statistics and the law of conservation of energy. Namely, thepossibility that there could exist in the nuclei electrically neutralparticles, that I wish to call neutrons, which have spin 1/2 and obeythe exclusion principle and which further differ from light quanta inthat they do not travel with the velocity of light. The mass of theneutrons should be of the same order of magnitude as the electronmass and in any event not larger than 0.01 proton masses. Thecontinuous beta spectrum would then become understandable bythe assumption that in beta decay a neutron is emitted in addition tothe electron such that the sum of the energies of the neutron and theelectron is constant. . .


Pauli’s LetterI agree that my remedy could seem incredible because one shouldhave seen these neutrons much earlier if they really exist. But onlythe one who dare can win and the difficult situation, due to thecontinuous structure of the beta spectrum, is lighted by a remark ofmy honoured predecessor, Mr Debye, who told me recently inBruxelles: “Oh, It’s well better not to think about this at all, like newtaxes”. From now on, every solution to the issue must be discussed.Thus, dear radioactive people, look and judge.Unfortunately, I cannot appear in Tubingen personally since I amindispensable here in Zurich because of a ball on the night of 6/7December. With my best regards to you, and also to Mr Back.

Your humble servant,

W. Pauli


Pauli’s LetterWolfgang Ernst Pauli (April 25, 1900 – December 15, 1958)

Austrian physicist who postulated the “neutrino”.


NeutrinosNeutrinos are:

elementary particles (s.c. leptons – same familyas the electron)

divided in (at least) three different s.c. flavors

electrically uncharged (neutral) and interactingonly via the weak force

nearly massless (i.e. they have very smallmasses)

very elusive (i.e. they have very smallcross-sections)

But:The neutrino is the most frequent particle in theUniverse.


Different Neutrinos andCharged Leptons

Family 1 2 3

Neutrino ��

Charged lepton � � � � �

It is unclear if the neutrinos are their own antiparticles,i.e. if they are s.c. Majorana particles, or not.

Neutrino Year discovered Discovered by

1956 C.L. Cowan, Jr. & F. Reines

1962 L.M. Lederman, M. Schwartz & J. Steinberger

2000 DONUT collaboration at Fermilab, USA


Different Neutrinos andCharged Leptons

Family 1 2 3

Neutrino ��

Charged lepton � � � � �

It is unclear if the neutrinos are their own antiparticles,i.e. if they are s.c. Majorana particles, or not.

Neutrino Year discovered Discovered by

�� 1956 C.L. Cowan, Jr. & F. Reines

�� 1962 L.M. Lederman, M. Schwartz & J. Steinberger

�� 2000 DONUT collaboration at Fermilab, USA


Neutrino Sourcesthe Sun ( � ��

neutrinos per second)

the atmosphere (from cosmic rays)

accelerators

nuclear power plants ( � ��

neutrinos persecond)

”natural radioactivity”

supernovae explosions ( � ��

neutrinos persecond)

”Big Bang”, cosmic point-sources

etc.


Solar NeutrinosThe Sun:

The Standard Solar Model (SSM) predicts that the Sun shinesbecause of fusion reactions in the core of the Sun.

SSM: � ��

neutrinos per secondThe distance betweeen the Sun and the Earth:

� ��

��

m

Ca 70 billion solar neutrinos passes through yourthumbnail of ca 1 per second!




SSM: � ��


� ��

��

m

��

��

��

� � ��

Ca 70 billion solar neutrinos passes through yourthumbnail of ca 1 per second!




SSM: � ��


� ��

��

m

��

��

��

� � ��

� Ca 70 billion solar neutrinos passes through yourthumbnail of ca 1 ��

per second!


How Many Different Types ofNeutrinos Are There?

Experimental studies of

�

-decays at LEP: a

��

��

� � �

� There are three neutrino flavors.

aParticle Data Group, W.-M. Yao et al., Review of Particle Physics, J. Phys. G

33, 1 (2006), pdg.lbl.gov



The number of different neutrinos from astrophysicaldata:(S. Hannestad, 2003)1. WMAP + Wang + 2dFGRS + HST + SN-Ia:

�� (@ 95 % C.L.)

+ BBN (

�� och

�

):

� � � � � � � � � � (@ 95 % C.L.)

2. WMAP + 2dFGRS:

� � � � � � � � � �

3. WMAP:

� � � � � � � ��

4. Hannestad & Raffelt, 2006:� � ��

(@ 95 % C.L.)



The number of different neutrinos from ”Big Bang”nucleosynthesis:

(S. Burles, K.M. Nollett och M.S. Turner, 1999)

� There are three neutrino flavors.


Neutrino OscillationsQuantum mechanics:Neutrinos are massive and mixed � Neutrino oscillationsNeutrino mixing:

��

��

� ��

� ��

�

The leptonic mixing matrix:

� �

��

� � �

� � � �

� � � � � �

��

� ��

”atmospheric neutrinos”

��

� � � � ��

� � �

� � � � ��

��

� ��

”reactor neutrinos”

��

� � � � � �

� � � � � � �

� � ��

��

� ��

”solar neutrinos”

�

where �� ! � " � � and # � � � $&% " � �.


Neutrino OscillationsA graphical representation of neutrino mixing:


Neutrino OscillationsThe Pontecorvo formula:

� �� $% � � "�� amplitude

� $% �

� � ��

frequency

��

where

�

is the mixing angle,��

is the masssquared difference,

�� is the neutrino energy, and�

is the baseline length.It holds that:

� �� ! "$# � �� % � "$# � ��% � � � �

� ��% � �% �


Neutrino OscillationsA graphical representation of neutrino oscillations in atwo-flavor approximation:


Neutrino OscillationExperiments

Experiment: Super-Kamiokande

Measurements of atmospheric neutrinos and solarneutrinos.Reaction: Elastic scattering �� % � �

June 1998: Strong evidence for that neutrinooscillations occur and that neutrinos are massive.



Atmospheric neutrinos – Super-Kamiokande (1289 days)

Neutrino fluxes

”Up-going”:�! � " � � � � " � � � � �

”Down-going”:�! � " � � � " � �

(T. Toshito, 2001)



Solar neutrinos – Super-Kamiokande (1258 days)

The angular distribution of solar neutrino candidates

S. Fukuda et al., Phys. Rev. Lett. 86 (2001) 5651, The Sun in ”neutrino light”

hep-ex/0103032.



Solar neutrinos – SNO (Q.R. Ahmad et al., 2001, 2002)

CC: � � � � �� NC �� % � � � ��

ES: �� % � ��

CC � ��

NC � ��

ES � ��

� � ��

� �! " � � � �� [

� � � # � � � � �� ]Tommy Ohlsson - Lecture 18, 2007 – p.9/16

Mixing Angles and MassSquared Differences

Definition (leptonic mixing and mixing angles):

�

� � � � � � � � � � � � � � ��

� � � � � � � � � � � � � � � � � ��

� � � � � � � � � � � � � � � ��

where

�� $% " � � and�� ! � " � �.

Definition (neutrino mass squared differences):

� � ��

where � � ( � � � � � � �

) is the mass for the �th neutrinomass eigenstate.Mixing angles and mass squared differences are fundamentalneutrino parameters in neutrino oscillation experiments.

Currentvalues (June 30, 2006) of the fundamental three-flavorneutrino oscillation parameters [including data fromthe Sun, the atmosphere, reactors (KamLAND &CHOOZ), and accelerators (K2K & MINOS)]:

Parameter Best-fit value Interval (3 )

-

-

Nearly bimaximal leptonic mixing, i.e., andare large and is small.



Current values (June 30, 2006) of the fundamentalthree-flavor neutrino oscillation parameters [includingdata from the Sun, the atmosphere, reactors(KamLAND & CHOOZ), and accelerators (K2K &MINOS)]:

Parameter Best-fit value Interval (3 �)� � ��

� � � ��

� � � ��

"� � � ��

� � � ��

� � � � ��

� �

"� � -

� � � ��

� �

" � � ��

� � � ��

� � � � ��

�

�� -

��

Nearly bimaximal leptonic mixing, i.e., andare large and is small.



Current values (June 30, 2006) of the fundamentalthree-flavor neutrino oscillation parameters [includingdata from the Sun, the atmosphere, reactors(KamLAND & CHOOZ), and accelerators (K2K &MINOS)]:

Parameter Best-fit value Interval (3 �)� � ��

� � � ��

� � � ��

"� � � ��

� � � ��

� � � � ��

� �

"� � -

� � � ��

� �

" � � ��

� � � ��

� � � � ��

�

�� -

��

� Nearly bimaximal leptonic mixing, i.e.,

"� � and

" � �

are large and

"� � is small.


Comparison: Quarks andLeptons

Quark mixing can be represented by a similar mixingmatrix as the one for leptonic mixing. This mixingmatrix is usually called the CKM matrix. The values ofthe mixing angles are:

� � � #� � � � � � � � � � � � � � � � #� � � � � � � � � � � � � � #� � � � � � � � � � �

� � � #��

The leptonic mixing matrix is sometimes called theMNS or PMNS matrix. The values of the mixing anglesare:

Quarks (CKM): 3 small mixing anglesLeptons (MNS): 2 large mixing angles and 1 smallmixing angle


Comparison: Quarks andLeptons

Quark mixing can be represented by a similar mixingmatrix as the one for leptonic mixing. This mixingmatrix is usually called the CKM matrix. The values ofthe mixing angles are:

� � � #� � � � � � � � � � � � � � � � #� � � � � � � � � � � � � � #� � � � � � � � � � �

� � � #��

The leptonic mixing matrix is sometimes called theMNS or PMNS matrix. The values of the mixing anglesare:

� #! �� #! �� #! �� #! ��

Quarks (CKM): 3 small mixing anglesLeptons (MNS): 2 large mixing angles and 1 smallmixing angle


Open Questions Concerningthe Neutrino Parameters

The standard model (SM) for particle physics, whichassumes that neutrinos are massless, have 18 freeparameters. The neutrino parameters are six. Thus,the SM for massive neutrinos have 24 free parameters.

What is the sign of

� � �� ?

Do we have normal mass hierarchy,i.e.. � �

� � � � � �? Or do we have invertedmass hierarchy, i.e. � � � � �

� � �?

What is the upper bound on the mixing angle

"� �?

There is ongoing research in order to determineor at least make the upper bound better for themixing angle

"� �.

What is the value of the CP-violating phase

� � ?This parameter is so far totally undetermined!


The Absolute Neutrino MassScale

What are the masses of the neutrino masseigenstates, i.e. what are the values of � � , � � , and� �?

� 3 masses

From neutrino oscillations and neutrino oscillationexperiments, one can only determine the masssquared differences and .In addition, one does not know the sign of .

2 mass squared differences

Thus, one cannot determine the absolute neutrinomass scale via neutrino oscillation experiments!


The Absolute Neutrino MassScale

What are the masses of the neutrino masseigenstates, i.e. what are the values of � � , � � , and� �?

� 3 masses

From neutrino oscillations and neutrino oscillationexperiments, one can only determine the masssquared differences

� � �� and

� � �� .

In addition, one does not know the sign of

� � �� .

� 2 mass squared differences

Thus, one cannot determine the absolute neutrinomass scale via neutrino oscillation experiments!


Neutrino MassesAssume that the neutrino mass eigenstates � � , � � , and� � are the primary components of the neutrino flavoreigenstates � � , �� , and �� . Then, the present upperbound on the neutrino masses are:

The electron neutrino:� � � � ��

(

� � � � �� )

The muon neutrino: � � � � ��

� � ��

( � � �% � ��

� � )

The tau neutrino: � � � � � ��

� ��

( � � � � � � � )

But:

One should instead determine the upper bounds on the masses of

the neutrino mass eigenstates, since they are the only states that

have well-defined masses.


Neutrino MassesThe sum of neutrino masses:

� � �

� � �where �� is the mass for the �th neutrino

mass eigenstate.


Neutrino MassesSome upper bounds on the sum of neutrino masses� � from cosmological data (@ 95 % C.L.):

Authors Upper boundElgarøy et al. (2002) 1.8 eV

Sanchez et al. (2005) 1.2 eV

Goobar et al. (2006) 0.62 eV

Fukugita et al. (2006) 2.0 eV

Spergel et al. (2006) 0.68 eV

Seljak et al. (2006) 0.17 eV

(Ø. Elgarøy and O. Lahav, 2006)

� � � � � � �


Determination of the Masses?If one assumes a normal mass hierarchy,i.e. � �

� � � � � � , and uses the measured values ofthe mass squared differences from neutrino oscillationexperiments and the cosmological upper bound on thesum of neutrino masses. Can one then determine theneutrino masses?

Solve the non-linear system of equations:

This system of equations has a valid solution!





��

��

� � � ��

� ��

� ��

��

� �

� � � � � � � � � � ��

� � � � �






��

��

� � � ��

� ��

� ��

��

� �

� � � � � � � � � � ��

� � � � �


� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �


Summary✔ Neutrinos are very elusive particles, but are the

most frequent particles in the Universe.

��

✔ Neutrinos are massive and mixed. �

Oscillations occur among different flavors.

✔ There are most probably three neutrino flavors.

✔ The absolute neutrino mass scale is not known.

✔ Three of the six neutrino parameters need to bebetter determined.

✔ The sum of neutrino masses (for the neutrinomass eigenstates) is

� �

eV.


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