Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to...
-
Upload
nguyennguyet -
Category
Documents
-
view
214 -
download
0
Transcript of Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to...
![Page 1: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/1.jpg)
Introduction to Neutrino PhysicsTommy Ohlsson
Royal Institute of Technology (KTH)
Stockholm Center for Physics, Astronomy, and Biotechnology
Stockholm, Sweden
Abisko, Norrbotten, Sweden – August 5-15, 2002
Tommy Ohlsson - Abisko 2002 – p.1/25
![Page 2: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/2.jpg)
� NewsNeutrino news from ICHEP 2002, Amsterdam, TheNetherlands, July 24-31, 2002 (where this lecture wasprepared):
� The results of the LSND experiment will be tested by the
MiniBooNE experiment, which will start in August 2002.
� CPT violation was suprisingly discussed a lot in the theory
talks as an alternative to neutrino oscillations in order to
also accommodate the results of the LSND experiment.
� KamLAND: First results @ PANIC 2002, Osaka, Japan
Tommy Ohlsson - Abisko 2002 – p.2/25
![Page 3: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/3.jpg)
Brief History & Introduction
� 4 December 1930: Wolfgang Pauli postulated theneutrino.
� 1933: Enrico Fermi and Francis Perrinconcluded that neutrinos are massless particles.
� 1946: Bruno Pontecorvo proposed that neutrinoscould be detected through the reaction
�����
� � � � � �
.
� 1956: Clyde L. Cowan, Jr. and Frederick Reinesdiscovered the electron antineutrino via inverse
-decay,
� � � � ��
. Nobel Prize
� 1957: Neutrino oscillations were considered byPontecorvo.
Tommy Ohlsson - Abisko 2002 – p.3/25
![Page 4: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/4.jpg)
Brief History & Introduction
� 1962: Mixing of two massive neutrinos wasintroduced and discussed by Z. Maki, M.Nakagawa, and S. Sakata.
� 1962: The muon neutrino was detected by thegroup of L.M. Lederman, M. Schwartz, and J.Steinberger at the Brookhaven NationalLaboratory. Nobel Prize
� 1978 & 1985: The Mikheyev–Smirnov–Wolfenstein (MSW) effect was found.
� 23 February 1987: About 25 neutrinos from thesupernova SN1987A were detected by theKamiokande (Japan), IMB (USA), and Baksan(Sovjet Union) experiments.
Tommy Ohlsson - Abisko 2002 – p.3/25
![Page 5: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/5.jpg)
Brief History & Introduction
� June 1998: The Super-Kamiokande experimentin Japan reported strong evidence for neutrinooscillations from their atmospheric neutrino dataand from which one can conclude that neutrinosare massive particles.
� July 2000: The tau neutrino was observed by theDONUT experiment at Fermilab.
� June 2001: The SNO experiment in Canadareported the first direct indication of anon-electron flavor component in the solarneutrino flux, i.e., the first stong evidence forsolar neutrino oscillations.
Tommy Ohlsson - Abisko 2002 – p.3/25
![Page 6: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/6.jpg)
Brief History & Introduction
� April 2002: Continuation of the success of theSNO experiment, which reported its first resultson the
� �
solar neutrino flux measurements vianeutral-current (NC) interactions. The totalneutrino flux measured via NC interactions isconsistent with the Standard Solar Model (SSM)predictions.
Tommy Ohlsson - Abisko 2002 – p.3/25
![Page 7: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/7.jpg)
Sources of Neutrinos
� The Sun
� The atmosphere (cosmic rays)
� Reactors
� Accelerators
� Supernovae
� The Earth (“natural radioactivity”)
� The Big Bang (so-called relic neutrinos)
...
Tommy Ohlsson - Abisko 2002 – p.4/25
![Page 8: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/8.jpg)
Neutrino FlavorsWhat is the number of neutrino flavors?
A combined SM fit to LEP data a:
A direct measurement of invisible decay width:
, i.e., there are three neutrino flavors.
aParticle Data Group, K. Hagiwara et al., Review of Particle Physics,
Phys. Rev. D 66, 010001 (2002), pdg.lbl.gov
Tommy Ohlsson - Abisko 2002 – p.5/25
![Page 9: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/9.jpg)
Neutrino FlavorsWhat is the number of neutrino flavors?
A combined SM fit to LEP data a:
� � ��
� � � ��
�� �
A direct measurement of invisible�
decay width:
� � ��
� � ��
�
, i.e., there are three neutrino flavors.
aParticle Data Group, K. Hagiwara et al., Review of Particle Physics,
Phys. Rev. D 66, 010001 (2002), pdg.lbl.gov
Tommy Ohlsson - Abisko 2002 – p.5/25
![Page 10: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/10.jpg)
Neutrino FlavorsWhat is the number of neutrino flavors?
A combined SM fit to LEP data a:
� � ��
� � � ��
�� �
A direct measurement of invisible�
decay width:
� � ��
� � ��
�
� � � �
, i.e., there are three neutrino flavors.
aParticle Data Group, K. Hagiwara et al., Review of Particle Physics,
Phys. Rev. D 66, 010001 (2002), pdg.lbl.gov
Tommy Ohlsson - Abisko 2002 – p.5/25
![Page 11: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/11.jpg)
Massive NeutrinosWithin the standard model of elementary particlephysics (SM), the neutrinos are massless particles.
Massive neutrinos would mean physics beyondthe SM.
Neutrinos are most certain massive particles.
The SM needs to be extended!
Tommy Ohlsson - Abisko 2002 – p.6/25
![Page 12: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/12.jpg)
Massive NeutrinosThe fermionic sector of the SM contains 13parameters, i.e.,
1. 9 mass parameters (quarks and charged leptons) and
2. 4 mixing parameters (CKM mixing matrix).
A trivial extension of the SM would mean 7 (Diraccase) or 9 (Majorana case) new parameters, i.e.,
1. 3 mass parameters (neutrinos) and
2. 4 or 6 (leptonic) mixing parameters (MNS mixing matrix).
� In total, the fermionic sector of the extended SMhas 20 or 22 parameters.
Tommy Ohlsson - Abisko 2002 – p.6/25
![Page 13: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/13.jpg)
Massive NeutrinosOne possible extension of the SM:Simplest new physics (NP): Add new fields to the SM. Thetrivial extension is to add � sterile neutrinos (right-handed SM
singlets) to the three active neutrinos [ ��� � � ��� � ��� � � � � �
].
Two types of mass terms arise from renormalizable terms:
���� � ��� ��� ��� �
� � �� �� ��� � ��� � � ��� � ! �#" � �#$ � % % % �'& � ( )
which can be written as
�+*�, � �
� � � �.- � � ��� � � � ���
�/� �.- �
� � �
� )� ��
where
�0- is the! � �21 (43 ! � �1 (
Dirac–Majorana neutrino mass matrix.
Tommy Ohlsson - Abisko 2002 – p.6/25
![Page 14: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/14.jpg)
The Seesaw MechanismThe seesaw mechanism is one of the most naturaldescriptions of the smallness of the neutrino masses.
One flavor Dirac–Majorana neutrino mass matrix:
where , , and are real mass parameters.
Diagonalization [ ]
Tommy Ohlsson - Abisko 2002 – p.7/25
![Page 15: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/15.jpg)
The Seesaw MechanismThe seesaw mechanism is one of the most naturaldescriptions of the smallness of the neutrino masses.
One flavor Dirac–Majorana neutrino mass matrix:
�
��� ���
��� ��� �
where ��� , � � , and �� are real mass parameters.
Diagonalization [ ]
Tommy Ohlsson - Abisko 2002 – p.7/25
![Page 16: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/16.jpg)
The Seesaw MechanismThe seesaw mechanism is one of the most naturaldescriptions of the smallness of the neutrino masses.
One flavor Dirac–Majorana neutrino mass matrix:
�
��� ���
��� ��� �
where ��� , � � , and �� are real mass parameters.
Diagonalization [
��
�
� �� �� � � �� � � ��
�
]
� �� � �
�� � ��
��
� �� � �� � � � � ��
Tommy Ohlsson - Abisko 2002 – p.7/25
![Page 17: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/17.jpg)
The Seesaw MechanismAssume that � � � �
and �� ��
� � � � � �� �
� $ �� �
� � � � �� � ��� �
which are called the seesaw mechanism formulas.
(Gell-Mann, Ramond & Slansky, 1979; Yanagida, 1979; Mohapatra & Senjanovic, 1980)Tommy Ohlsson - Abisko 2002 – p.7/25
![Page 18: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/18.jpg)
The Seesaw MechanismMatrix generalization of the seesaw mechanismformulas for more than one flavor:
�
� �
�� �
� � � � � �
� �
� �
�
where
� � � � ��
�� � �
� � � �
Here � is the effective neutrino mass matrix, � is
the Dirac mass matrix, and � is the Majorana mass
matrix. (see, e.g., Lindner, Ohlsson & Seidl, 2002)Tommy Ohlsson - Abisko 2002 – p.7/25
![Page 19: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/19.jpg)
The Masses of the NeutrinosAssuming that the neutrino mass eigenstates � � , � � ,and � � are the primary components of the neutrinoflavor states � � , ��� , and ��� , the present upper boundson the neutrino masses are:
� The electron neutrino: � ���� ���
� The muon neutrino: � �� �
�� � �
� The tau neutrino: � ���� �
�� �
However, this picture is not entirely true!
Tommy Ohlsson - Abisko 2002 – p.8/25
![Page 20: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/20.jpg)
Neutrino OscillationsNeutrino oscillations Neutrinos are massiveand mixed.
The neutrinos are particles that can be considered tobe governed by the Schrodinger equation, i.e., theneutrino states can be represented by quantummechanical states.
The relations between flavor and mass states andfields are:
where the ’s are matrix elements of the mixingmatrix .
Tommy Ohlsson - Abisko 2002 – p.9/25
![Page 21: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/21.jpg)
Neutrino OscillationsNeutrino oscillations Neutrinos are massiveand mixed.
The neutrinos are particles that can be considered tobe governed by the Schrodinger equation, i.e., theneutrino states can be represented by quantummechanical states.
The relations between flavor and mass states andfields are:
where the ’s are matrix elements of the mixingmatrix .
Tommy Ohlsson - Abisko 2002 – p.9/25
![Page 22: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/22.jpg)
Neutrino OscillationsNeutrino oscillations Neutrinos are massiveand mixed.
The neutrinos are particles that can be considered tobe governed by the Schrodinger equation, i.e., theneutrino states can be represented by quantummechanical states.
The relations between flavor and mass states andfields are:
� � � � ��
�� �� � � �� � �� � � � �
��� �
� � �� � �� � � � � � � ��
where the �� ’s are matrix elements of the mixingmatrix .
Tommy Ohlsson - Abisko 2002 – p.9/25
![Page 23: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/23.jpg)
Neutrino OscillationsThe time evolution of the neutrino mass eigenstates is:
��� � � � �
� � � ��� � ��� � � � �
�where � � � �� �
�� � �� � $��� � is the energy ofthe th neutrino mass eigenstate �� (ultra-relativisticneutrinos). Here � � and �� are the mass andmomentum of the th neutrino mass eigenstate,respectively.
Furthermore, we can assume that � � � ��� � � �
and
� �
.
Tommy Ohlsson - Abisko 2002 – p.9/25
![Page 24: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/24.jpg)
Neutrino OscillationsThus, neutrino oscillations among different neutrinoflavors occur with the transition probabilities
� � � �� � � � �
���� � � � �� � � � � � � �
�������
� � �
�� � �
� �� � � � ��� � ��� � � � �
������
�
which can be re-written as
��� � � � � � �
� ��
�� � � �� �� �� � � � � �� �� ���� ��� � ��� � ��
�
��
� ��
�� � � �! �� �� � � � � �� �� ���� ��� ��� � ��
� " � " # � � " � " "$ $ $ $
Tommy Ohlsson - Abisko 2002 – p.9/25
![Page 25: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/25.jpg)
The MSW EffectThe neutrino oscillation transition probabilities inmatter may differ drastically from the correspondingtransition probabilities in vacuum.
In particular, the presence of matter can lead toresonant amplification of the transition probabilitybetween two given types of neutrinos, even if thecorresponding transition probability in vacuum isstrongly suppressed by a small mixing.
This is the so-called MSW effect.
(Wolfenstein, 1978; Mikheyev & Smirnov, 1985, 1986)
Tommy Ohlsson - Abisko 2002 – p.10/25
![Page 26: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/26.jpg)
Matter EffectsThe Schrödinger equation in vacuum:
��
� � �� � �
� � �� � �
� � ��
��
��
...
��
�� �
where the total (free) Hamiltonian in the mass basis is
� � � � �� �� � � � � � � � � � � ��
Here are the number of flavors and � � � �� � � � �
.
Tommy Ohlsson - Abisko 2002 – p.11/25
![Page 27: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/27.jpg)
Matter EffectsThe Schrödinger equation in matter:In matter, we need to add the matter potential to thetotal Hamiltonian, i.e.,
� � �� � ���� � �� � �� � � �� � �
�
� � �� � � �� �
� �� � � �� � �� � � �� � � � � � �� � � ��
��
� �� � �
�
where is the mixing matrix relating the mass andflavor bases and is a constant, the matter densityparameter.
Note! Only one entry in the matrix
� is non-zero.
Tommy Ohlsson - Abisko 2002 – p.11/25
![Page 28: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/28.jpg)
Two Flavor Neutrino OscillationModels
In vacuum:
The mixing matrix:
where is the mixing angle.
The mass squared difference:
where and are the masses of the two neutrinomass eigenstates, respectively.MSW resonance condition:
The effective mixing angle in matter obtains itsmaximal value when the condition
is fulfilled. This condition is called the MSWresonance condition.
It follows that, if the MSW resonance condition is sat-
isfied, then the effective mixing angle in matter is
maximal, i.e., , independently of the value of
the vacuum mixing angle .
Tommy Ohlsson - Abisko 2002 – p.12/25
![Page 29: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/29.jpg)
Two Flavor Neutrino OscillationModels
In vacuum:
The mixing matrix:
�
� �� � � � � �
� � � � � � �� � �
where
�
is the mixing angle.
The mass squared difference:
where and are the masses of the two neutrinomass eigenstates, respectively.MSW resonance condition:
The effective mixing angle in matter obtains itsmaximal value when the condition
is fulfilled. This condition is called the MSWresonance condition.
It follows that, if the MSW resonance condition is sat-
isfied, then the effective mixing angle in matter is
maximal, i.e., , independently of the value of
the vacuum mixing angle .
Tommy Ohlsson - Abisko 2002 – p.12/25
![Page 30: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/30.jpg)
Two Flavor Neutrino OscillationModels
In vacuum:
The mixing matrix:
�
� �� � � � � �
� � � � � � �� � �
where
�
is the mixing angle.
The mass squared difference:
� �� � �� � � �� �
where � � and � � are the masses of the two neutrinomass eigenstates, respectively.
MSW resonance condition:
The effective mixing angle in matter obtains itsmaximal value when the condition
is fulfilled. This condition is called the MSWresonance condition.
It follows that, if the MSW resonance condition is sat-
isfied, then the effective mixing angle in matter is
maximal, i.e., , independently of the value of
the vacuum mixing angle .
Tommy Ohlsson - Abisko 2002 – p.12/25
![Page 31: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/31.jpg)
Two Flavor Neutrino OscillationModels
The transition probabilities:
� � � � � � �� � � � � � � � � � �� � � � � �� � �
� �
where
is the baseline length and is the neutrinoenergy.
0 Losc. 2L
osc.
L
0
1
Pee
(L)
0 Losc. 2L
osc.
L
0
1
Peµ
(L)
Losc.
=4πE/∆m2
Losc.
=4πE/∆m2si
n2 2θ
sin2
2θIt holds that � � � � � � � � � � � � � � �
MSWresonance condition:
The effective mixing angle in matter obtains itsmaximal value when the condition
is fulfilled. This condition is called the MSWresonance condition.
It follows that, if the MSW resonance condition is sat-
isfied, then the effective mixing angle in matter is
maximal, i.e., , independently of the value of
the vacuum mixing angle .
Tommy Ohlsson - Abisko 2002 – p.12/25
![Page 32: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/32.jpg)
Two Flavor Neutrino OscillationModels
In matter:The effective mixing angle in matter:
� � �� � � �
�
� � �� � �
� � �� � � �
� �� � � �� �
� � $
� �
The effective mass squared difference in matter:
� � �� � �
� � �� � � � �� � � �
�� �
�
Here is the matter density parameter.
� � � �� �
and
� � �� � �
MSWresonance condition:
The effective mixing angle in matter obtains itsmaximal value when the condition
is fulfilled. This condition is called the MSWresonance condition.
It follows that, if the MSW resonance condition is sat-
isfied, then the effective mixing angle in matter is
maximal, i.e., , independently of the value of
the vacuum mixing angle .
Tommy Ohlsson - Abisko 2002 – p.12/25
![Page 33: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/33.jpg)
Two Flavor Neutrino OscillationModels
MSW resonance condition:
The effective mixing angle in matter obtains itsmaximal value when the condition
is fulfilled. This condition is called the MSWresonance condition.
It follows that, if the MSW resonance condition is sat-
isfied, then the effective mixing angle in matter is
maximal, i.e., , independently of the value of
the vacuum mixing angle .
Tommy Ohlsson - Abisko 2002 – p.12/25
![Page 34: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/34.jpg)
Two Flavor Neutrino OscillationModels
MSW resonance condition:
The effective mixing angle in matter
� �
obtains itsmaximal value � � �
� � � �� �
when the condition
� �� � � �
�� �
is fulfilled. This condition is called the MSWresonance condition.
It follows that, if the MSW resonance condition is sat-
isfied, then the effective mixing angle in matter is
maximal, i.e., , independently of the value of
the vacuum mixing angle .
Tommy Ohlsson - Abisko 2002 – p.12/25
![Page 35: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/35.jpg)
Two Flavor Neutrino OscillationModels
MSW resonance condition:
The effective mixing angle in matter
� �
obtains itsmaximal value � � �
� � � �� �
when the condition
� �� � � �
�� �
is fulfilled. This condition is called the MSWresonance condition.
It follows that, if the MSW resonance condition is sat-
isfied, then the effective mixing angle in matter
� �
is
maximal, i.e.,� �
� �� �
, independently of the value of
the vacuum mixing angle
�
.Tommy Ohlsson - Abisko 2002 – p.12/25
![Page 36: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/36.jpg)
Three Flavor Neutrino Oscilla-tion Models
The formulas in matter are much more complicatedfor the three flavor case than for the two flavor case!
Using the Cayley–Hamilton formalism, one finds thetransition probabilities in matter:
where .
Tommy Ohlsson - Abisko 2002 – p.13/25
![Page 37: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/37.jpg)
Three Flavor Neutrino Oscilla-tion Models
The formulas in matter are much more complicatedfor the three flavor case than for the two flavor case!
Using the Cayley–Hamilton formalism, one finds thetransition probabilities in matter:
� � � � � �
� �
�
� � ��
� � �
� � �
� � �� � � � � � � � �
� � � � � � � � �
� � �� � �
�
� � �� � � � � � � � �
� �� � � � � � � � �
� � �� � �
� � �� ��� � � �
where
�� � � � � � � � � �� � �
.Tommy Ohlsson - Abisko 2002 – p.13/25
![Page 38: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/38.jpg)
Three Flavor Neutrino Oscilla-tion Models
Here:
� � ��
���� �� �
�
� � � � � �
� � � �� � � �
�
� �
The
� �’s ( � � ��
��
�
) are the eigenvalues of the matrix
�
.
(Ohlsson & Snellman, 2000; Ohlsson, 2001)
Tommy Ohlsson - Abisko 2002 – p.13/25
![Page 39: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/39.jpg)
Three Flavor Neutrino Oscilla-tion Models
The survival transition probability � � for neutrinosthat traverse the Earth as a function of the nadir angle�
and the neutrino energy : (Ohlsson, 2001)
Parameter values:� � � � � �� � �� �
,
� � � � � �
,
��� � �
,
� � � ��� � � � � �
, and
�� � � �� � �
.Tommy Ohlsson - Abisko 2002 – p.13/25
![Page 40: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/40.jpg)
Neutrino Experiments
Other sources of neutrinos:
e– + 7Be 7Li + νe
8B 2 4He + e+ + νe
Earth
Underground
νe detector
Solar corePrimary neutrino source
p + p D + e+ + νe
Cosmic-ray shower
π0
π+
µ+
νe
e+
νµ
νµ
Underground
νe, νe, νµ, νµ
detector
Atmospheric neutrino source
π+ µ+ + νµ
e+ + νe + νµ
π– µ– + νµ
e– + νe + νµ
30 meters
νe detectorNeutrinos νe, νµ, and νµ
Proton
beam
Pions
Copper beam stop
Muons and electrons
Water target
~30 kilometers
Sun
~10 8 kilometers
Tommy Ohlsson - Abisko 2002 – p.14/25
![Page 41: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/41.jpg)
Neutrino ExperimentsFive different types of neutrino oscillationexperiments: solar, atmospheric, accelerator, reactor,and cosmic.
Old experiments: Homestake, SAGE, GALLEX,
Kamiokande (solar); Baksan, NUSEX, Fréjus, IMB,
MACRO, Soudan, Kamiokande (atmospheric); NO-
MAD, CHORUS, LSND, KARMEN (accelerator);
Bugey, CHOOZ, Gösgen, Palo Verde (reactor)
Tommy Ohlsson - Abisko 2002 – p.14/25
![Page 42: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/42.jpg)
Neutrino ExperimentsPresent and new experiments:
� Solar: Super-Kamiokande, Hyper-Kamiokande,SNO, GNO, BOREXINO
� Atmospheric: Super-Kamiokande,Hyper-Kamiokande, MONOLITH
� Reactor: KamLAND
� Accelerator LBL: K2K, MINOS, CERN-LNGS,MiniBooNE, BooNE
� Cosmic: AMANDA, Baikal, Antares, IceCube
In the order of magnitude of 10 years: Neutrino factory
Tommy Ohlsson - Abisko 2002 – p.14/25
![Page 43: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/43.jpg)
The Solar Neutrino ProblemThe Sun is a source of neutrinos (solar neutrinos).The solar neutrinos can be detected on Earth usingunderground detectors. However, the measured fluxesof the solar neutrinos and the theoretical estimates forthe solar neutrino fluxes are different. The measuredflux is about one-half of the “expected” flux. This isthe solar neutrino problem.
SSM (BP2000): (Bahcall, Pinsonneault & Basu, 2001)
Experimental results: (Bilenky, Giunti & Grimus, 1999)
Experiment Ratio
Homestake
SAGE
GALLEX
Kamiokande
Super-Kamiokande
Solution: Neutrino oscillations(Best channels: with and [LMA])
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-4 10-3 10-2 10-1 1 10.
(Bahcall, Gonzalez-Garcia & Peña-Garay, 2002)
Tommy Ohlsson - Abisko 2002 – p.15/25
![Page 44: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/44.jpg)
The Solar Neutrino ProblemThe Sun is a source of neutrinos (solar neutrinos).The solar neutrinos can be detected on Earth usingunderground detectors. However, the measured fluxesof the solar neutrinos and the theoretical estimates forthe solar neutrino fluxes are different. The measuredflux is about one-half of the “expected” flux. This isthe solar neutrino problem.
SSM (BP2000): (Bahcall, Pinsonneault & Basu, 2001)
Experimental results: (Bilenky, Giunti & Grimus, 1999)
Experiment Ratio
Homestake
SAGE
GALLEX
Kamiokande
Super-Kamiokande
Solution: Neutrino oscillations(Best channels: with and [LMA])
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-4 10-3 10-2 10-1 1 10.
(Bahcall, Gonzalez-Garcia & Peña-Garay, 2002)
Tommy Ohlsson - Abisko 2002 – p.15/25
![Page 45: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/45.jpg)
The Solar Neutrino ProblemExperimental results: (Bilenky, Giunti & Grimus, 1999)
Experiment Ratio
Homestake
�$ � � � ��� ��
� �� ��
SAGE
�$ � � �$ � GALLEX
�$ � � �$ � Kamiokande
�$ � � �$ �
Super-Kamiokande
�$ � � ��� � �
� �� �
Solution: Neutrino oscillations(Best channels: with and [LMA])
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-4 10-3 10-2 10-1 1 10.
(Bahcall, Gonzalez-Garcia & Peña-Garay, 2002)
Tommy Ohlsson - Abisko 2002 – p.15/25
![Page 46: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/46.jpg)
The Solar Neutrino ProblemExperimental results: (Bilenky, Giunti & Grimus, 1999)
Experiment Ratio
Homestake
�$ � � � ��� ��
� �� ��
SAGE
�$ � � �$ � GALLEX
�$ � � �$ � Kamiokande
�$ � � �$ �
Super-Kamiokande
�$ � � ��� � �
� �� �
Solution: Neutrino oscillations(Best channels: ��� � ����� � with
��� �� �$ ��� � � � � � �
and
� � � � �
[LMA])
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-4 10-3 10-2 10-1 1 10.
(Bahcall, Gonzalez-Garcia & Peña-Garay, 2002)
Tommy Ohlsson - Abisko 2002 – p.15/25
![Page 47: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/47.jpg)
The Solar Neutrino ProblemSNO: (Ahmad et al., 2001, 2002)
CC: � � � � � � � � � � � ��� � � � � � � � � NC � �� � � � � � � �21 � � � � � ��� � � � � � � � �
ES: �� � � � � � � � � � � � � � �
0 1 2 3 4 5 60
1
2
3
4
5
6
7
8
)-1 s-2 cm6
(10eφ
)-1
s-2
cm
6 (
10τµφ SNO
NCφ
SSMφ
SNOCCφSNO
ESφ
Tommy Ohlsson - Abisko 2002 – p.15/25
![Page 48: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/48.jpg)
The Solar Neutrino Problem
The Sun as seen by the Super-Kamiokande detector!
Note! The detector is located in an old gold mine a few kilome-
ters below the surface of the Earth. Sun-light will never reach the
detector, but solar neutrinos will.Tommy Ohlsson - Abisko 2002 – p.15/25
![Page 49: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/49.jpg)
The Atmospheric NeutrinoProblem
Atmospheric neutrinos are produced in the followingreaction chain:
cosmic rays
�
air � � � ! � � ( � �
� � ! � � ( � � � � � � �
� � � � ��� �� � �� � � � � �
Naively, one concludes from the above reactionchain that
The “ratio of ratios”:
Atmospheric neutrino problem
Experimental results:
Solution: Neutrino oscillations(Best channel: with and )
Tommy Ohlsson - Abisko 2002 – p.16/25
![Page 50: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/50.jpg)
The Atmospheric NeutrinoProblem
Atmospheric neutrinos are produced in the followingreaction chain:
cosmic rays
�
air � � �� � �� � �
� ��� � ��� � � � � � � �
� � � � � � � � � � � ��
Naively, one concludes from the above reactionchain that
� ��� � ����� � ������ � � ��
� ��� � ����
!#"
The “ratio of ratios”:$ �
� �� � ��%� �'&( )+*� ��� � ���� �-, .
Atmospheric neutrino problem
Experimental results:
Solution: Neutrino oscillations(Best channel: with and )
Tommy Ohlsson - Abisko 2002 – p.16/25
![Page 51: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/51.jpg)
The Atmospheric NeutrinoProblem
� �
Atmospheric neutrino problem
Experimental results:
Solution: Neutrino oscillations(Best channel: with and )
Tommy Ohlsson - Abisko 2002 – p.16/25
![Page 52: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/52.jpg)
The Atmospheric NeutrinoProblem
� �
Atmospheric neutrino problem
Experimental results:
Solution: Neutrino oscillations(Best channel: with and )
Tommy Ohlsson - Abisko 2002 – p.16/25
![Page 53: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/53.jpg)
The Atmospheric NeutrinoProblem
� �
Atmospheric neutrino problem
Experimental results:
Solution: Neutrino oscillations(Best channel: � � � ��� with
��� ��� � � * �� �� � � & � �
and
� � � � �
)
Tommy Ohlsson - Abisko 2002 – p.16/25
![Page 54: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/54.jpg)
The Atmospheric NeutrinoProblem
Super-Kamiokande (1289 days): (Toshito, 2001)
050
100150200250300350400450
-1 -0.5 0 0.5 1cosθ
Num
ber
of E
vent
s Sub-GeV e-like
050
100150200250300350400450
-1 -0.5 0 0.5 1cosθ
Num
ber
of E
vent
s Sub-GeV µ-like
0
20
40
60
80
100
120
140
-1 -0.5 0 0.5 1cosθ
Num
ber
of E
vent
s Multi-GeV e-like
0
50
100
150
200
250
300
350
-1 -0.5 0 0.5 1cosθ
Num
ber
of E
vent
s Multi-GeV µ-like + PC
0
0.5
1
1.5
2
2.5
3
3.5
4
-1 -0.8 -0.6 -0.4 -0.2 0cosθ
Flu
x(10
-13 cm
-2s-1
sr-1
) Upward Through Going µ
0
0.2
0.4
0.6
0.8
1
1.2
1.4
-1 -0.8 -0.6 -0.4 -0.2 0cosθ
Upward Stopping µ
Tommy Ohlsson - Abisko 2002 – p.16/25
![Page 55: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/55.jpg)
The Accelerator SBL (LSND)Neutrino Problem
The only positive signature of neutrino oscillations ata laboratory experiment comes from the LSNDexperiment at Los Alamos.
However, only events, whichcorresponds to
with. (Aguilar et al., 2001)
Problem: A new mass squared difference, .
More than three flavors is necessary!
Solution: The LSND experiment is wrong! (easiest and most
possible); sterile neutrinos, CPT violation, . . . (not so possible)
Tommy Ohlsson - Abisko 2002 – p.17/25
![Page 56: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/56.jpg)
The Accelerator SBL (LSND)Neutrino Problem
The only positive signature of neutrino oscillations ata laboratory experiment comes from the LSNDexperiment at Los Alamos.However, only
� ��
� � ��
� ��
�
events, whichcorresponds to� � � �
��
� ��
� � � ��
� � � ��
� � �
with
� �� �� � � � ��
��
� � ��� �
. (Aguilar et al., 2001)
Problem: A new mass squared difference, .
More than three flavors is necessary!
Solution: The LSND experiment is wrong! (easiest and most
possible); sterile neutrinos, CPT violation, . . . (not so possible)
Tommy Ohlsson - Abisko 2002 – p.17/25
![Page 57: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/57.jpg)
The Accelerator SBL (LSND)Neutrino Problem
The only positive signature of neutrino oscillations ata laboratory experiment comes from the LSNDexperiment at Los Alamos.However, only
� ��
� � ��
� ��
�
events, whichcorresponds to� � � �
��
� ��
� � � ��
� � � ��
� � �
with
� �� �� � � � ��
��
� � ��� �
. (Aguilar et al., 2001)
Problem: A new mass squared difference, � �� �� � .
� �� � �� � �
� �� �� �
More than three flavors is necessary!
Solution: The LSND experiment is wrong! (easiest and most
possible); sterile neutrinos, CPT violation, . . . (not so possible)
Tommy Ohlsson - Abisko 2002 – p.17/25
![Page 58: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/58.jpg)
The Accelerator SBL (LSND)Neutrino Problem
The only positive signature of neutrino oscillations ata laboratory experiment comes from the LSNDexperiment at Los Alamos.However, only
� ��
� � ��
� ��
�
events, whichcorresponds to� � � �
��
� ��
� � � ��
� � � ��
� � �
with
� �� �� � � � ��
��
� � ��� �
. (Aguilar et al., 2001)
Problem: A new mass squared difference, � �� �� � .
� �� � �� � �
� �� �� �
More than three flavors is necessary!
Solution: The LSND experiment is wrong! (easiest and most
possible); sterile neutrinos, CPT violation, . . . (not so possible)Tommy Ohlsson - Abisko 2002 – p.17/25
![Page 59: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/59.jpg)
The Accelerator SBL (LSND)Neutrino Problem
The KARMEN experiment has excluded most of the region ofthe parameter space, which is favored by the LSND experiment.
The results of the LSND experiment will be further tested by the
MiniBooNE experiment, which starts running in August 2002.Tommy Ohlsson - Abisko 2002 – p.17/25
![Page 60: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/60.jpg)
Results from AnalysesSolar neutrinos: ��� -� ��� � oscillations
LMA: � �� � ���� � �� �� �
and�
� �
(Bahcall, Gonzalez-Garcia & Peña-Garay, 2001, 2002)
Further tests: KamLAND experiment
Atmospheric neutrinos: � �-� � oscillations
� �� � �
� ��
� � � � �� �and
�� � � � �
(Fukuda et al., 1998; Toshito, 2001; Shiozawa, 2002)
Further tests: Long-baseline experiments
Tommy Ohlsson - Abisko 2002 – p.18/25
![Page 61: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/61.jpg)
Results from AnalysesLSND experiment: �� �- ���� oscillations
� �� �� � � � ��
��
� ��� �
and
� � � � � � � ��
� �
(Athanassopoulos et al., 1996, 1998; Aguilar et al., 2001)
Further tests: MiniBooNE experiment
Reactor neutrinos (CHOOZ experiment):
� � � � �� ��
�
(Apollonio et al., 1999)
Three flavor models decouple into two twoflavor models.
Tommy Ohlsson - Abisko 2002 – p.18/25
![Page 62: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/62.jpg)
Wark’s Conclusions
�and m
ixin
gs
Dave War
CHEP�02
� masses�
University of Sussex/Tommy Ohlsson - Abisko 2002 – p.19/25
![Page 63: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/63.jpg)
Neutrino Oscillation Parame-ters
Definition (neutrino mass squared differences):
� �� � � � �� � � �� �
where � � ( � � ��
��
) is the mass of the �th neutrinomass eigenstate.
Neutrino mass squared differences:
: The small (or “solar”) masssquared difference
: The large (or“atmospheric”) mass squared difference
Consequence:Leptonic mixing parameters:
: The “solar” mixing angle
: The “reactor” mixing angle
: The “atmospheric” mixing angle
: The (leptonic) CP violation phase
The “standard” parameterization:
where and (for ).Transformation of any unitary matrix to the“standard” parameterization: (Ohlsson & Seidl, 2002)
The parameters of the “standard” parameterization:
Tommy Ohlsson - Abisko 2002 – p.20/25
![Page 64: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/64.jpg)
Neutrino Oscillation Parame-ters
Definition (neutrino mass squared differences):
� �� � � � �� � � �� �
where � � ( � � ��
��
) is the mass of the �th neutrinomass eigenstate.
Neutrino mass squared differences:
� � � � � ��� : The small (or “solar”) masssquared difference
�
�� � � � � � � � �� : The large (or
“atmospheric”) mass squared difference
Consequence:Leptonic mixing parameters:
: The “solar” mixing angle
: The “reactor” mixing angle
: The “atmospheric” mixing angle
: The (leptonic) CP violation phase
The “standard” parameterization:
where and (for ).Transformation of any unitary matrix to the“standard” parameterization: (Ohlsson & Seidl, 2002)
The parameters of the “standard” parameterization:
Tommy Ohlsson - Abisko 2002 – p.20/25
![Page 65: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/65.jpg)
Neutrino Oscillation Parame-ters
Definition (neutrino mass squared differences):
� �� � � � �� � � �� �
where � � ( � � ��
��
) is the mass of the �th neutrinomass eigenstate.
Neutrino mass squared differences:
� � � � � ��� : The small (or “solar”) masssquared difference
�
�� � � � � � � � �� : The large (or
“atmospheric”) mass squared difference
Consequence: � ��� � � � � � �� � � �
Leptonic mixing parameters:
: The “solar” mixing angle
: The “reactor” mixing angle
: The “atmospheric” mixing angle
: The (leptonic) CP violation phase
The “standard” parameterization:
where and (for ).Transformation of any unitary matrix to the“standard” parameterization: (Ohlsson & Seidl, 2002)
The parameters of the “standard” parameterization:
Tommy Ohlsson - Abisko 2002 – p.20/25
![Page 66: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/66.jpg)
Neutrino Oscillation Parame-ters
Leptonic mixing parameters:
� �� � � � �: The “solar” mixing angle
� �� � � � �: The “reactor” mixing angle
� � � � � �� : The “atmospheric” mixing angle
� � �� � �
: The (leptonic) CP violation phase
The “standard” parameterization:
where and (for ).Transformation of any unitary matrix to the“standard” parameterization: (Ohlsson & Seidl, 2002)
The parameters of the “standard” parameterization:
Tommy Ohlsson - Abisko 2002 – p.20/25
![Page 67: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/67.jpg)
Neutrino Oscillation Parame-ters
Leptonic mixing parameters:
� �� � � � �: The “solar” mixing angle
� �� � � � �: The “reactor” mixing angle
� � � � � �� : The “atmospheric” mixing angle
� � �� � �
: The (leptonic) CP violation phase
The “standard” parameterization:
� �
� � ��� � � � � � � � � � �
� � � � � � � � ��� � � � � � ��� � � � � � � � � � � � � �
� � � � � � � � �� � � � � � �� � � � � � � � � � � � � �� �
where
��
� ��� �� and �
� �� �� (for � � ��
��
).
Transformation of any unitary matrix to the“standard” parameterization: (Ohlsson & Seidl, 2002)
The parameters of the “standard” parameterization:
Tommy Ohlsson - Abisko 2002 – p.20/25
![Page 68: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/68.jpg)
Neutrino Oscillation Parame-ters
� 2 neutrino mass squared differences and 4leptonic mixing parameters, i.e., in total 6 neutrinooscillation parameters.
Note! Two neutrino flavors: 1 mass squared difference and 1leptonic mixing parameter.
Transformation of anyunitary matrix to the “standard”
parameterization: (Ohlsson & Seidl, 2002)
The parameters of the “standard” parameterization:
Tommy Ohlsson - Abisko 2002 – p.20/25
![Page 69: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/69.jpg)
Neutrino Oscillation Parame-ters
Transformation of any
�
unitary matrix to the“standard” parameterization: (Ohlsson & Seidl, 2002)
�
� � � � � �
�� � � � �
�� � � � �
�
� �� � �
�� � �
� � � �� �� �
The parameters of the “standard” parameterization:
Tommy Ohlsson - Abisko 2002 – p.20/25
![Page 70: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/70.jpg)
Neutrino Oscillation Parame-ters
Transformation of any
�
unitary matrix to the“standard” parameterization: (Ohlsson & Seidl, 2002)
�
� � � � � �
�� � � � �
�� � � � �
�
� �� � �
�� � �
� � � �� �� �
The parameters of the “standard” parameterization:
��� � � �� � � �������
�� ��� �
�����
���� � �� �� �� � ��� �
� �� � �� � � �������
� ���� �
�����
��� � � �� � �� � � �� � �� � � � � � ��� � � � � � �� � � � � �� � �
Tommy Ohlsson - Abisko 2002 – p.20/25
![Page 71: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/71.jpg)
Present Values of the NeutrinoOscillation Parameters
Parameter Best-fit value Range
� � ��� � � � � � � � !#" � � � � � � � � � �(99.73% CL)� !#" � � � � � � � � � � � " � � �" � � � � � � � � �
(90% CL)
�� � � � �
(99.73% CL)
�� � -
� ��
�
� � � � � �
(90% CL)
� �� - -
Bilarge leptonic mixing, i.e., and are largeand is small.
Note!Leptons (MNS): 2 large mixing angles and 1 small mixing angle
Quarks (CKM): 3 small mixing angles
Tommy Ohlsson - Abisko 2002 – p.21/25
![Page 72: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/72.jpg)
Present Values of the NeutrinoOscillation Parameters
Parameter Best-fit value Range
� � ��� � � � � � � � !#" � � � � � � � � � �(99.73% CL)� !#" � � � � � � � � � � � " � � �" � � � � � � � � �
(90% CL)
�� � � � �
(99.73% CL)
�� � -
� ��
�
� � � � � �
(90% CL)
� �� - -
� Bilarge leptonic mixing, i.e.,
�� � and
� � � are largeand
�� � is small.
Note!Leptons (MNS): 2 large mixing angles and 1 small mixing angle
Quarks (CKM): 3 small mixing angles
Tommy Ohlsson - Abisko 2002 – p.21/25
![Page 73: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/73.jpg)
Present Values of the NeutrinoOscillation Parameters
Parameter Best-fit value Range
� � ��� � � � � � � � !#" � � � � � � � � � �(99.73% CL)� !#" � � � � � � � � � � � " � � �" � � � � � � � � �
(90% CL)
�� � � � �
(99.73% CL)
�� � -
� ��
�
� � � � � �
(90% CL)
� �� - -
� Bilarge leptonic mixing, i.e.,
�� � and
� � � are largeand
�� � is small.
Note!Leptons (MNS): 2 large mixing angles and 1 small mixing angle
Quarks (CKM): 3 small mixing angles Tommy Ohlsson - Abisko 2002 – p.21/25
![Page 74: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/74.jpg)
Other Scenarios
� Neutrino decay(see, e.g., Lindner, Ohlsson & Winter, 2001, 2002)
� Neutrino decoherence(see, e.g., Ohlsson, 2001)
� Spin-flavor precession(Lim & Marciano, 1988; Akhmedov, 1988)
� Flavor changing neutrino interactions
� Non-standard neutrino interactions
� CPT violation(see, e.g., Bilenky, Freund, Lindner, Ohlsson & Winter, 2002)
...
Tommy Ohlsson - Abisko 2002 – p.22/25
![Page 75: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/75.jpg)
Neutrinos in AstrophysicsWhat is the absolute neutrino mass scale?
SN1987A
SN1987A data
Future galactic supernovae (Super-Kamiokande)
Tommy Ohlsson - Abisko 2002 – p.23/25
![Page 76: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/76.jpg)
Neutrinos in AstrophysicsWhat is the absolute neutrino mass scale?
SN1987A
SN1987A data � ��� � � �
Future galactic supernovae (Super-Kamiokande)
Tommy Ohlsson - Abisko 2002 – p.23/25
![Page 77: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/77.jpg)
Neutrinos in AstrophysicsWhat is the absolute neutrino mass scale?
SN1987A
SN1987A data � ��� � � �
Future galactic supernovae (Super-Kamiokande)
� �� � �Tommy Ohlsson - Abisko 2002 – p.23/25
![Page 78: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/78.jpg)
Neutrinos in AstrophysicsThe sum of the neutrino masses:
�
�� � �
� � �where the � � ’s are the masses of the neutrino masseigenstates.
Note! This quantity is often used in astrophysics and cosmology.
Tommy Ohlsson - Abisko 2002 – p.23/25
![Page 79: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/79.jpg)
Neutrinos in AstrophysicsFrom CMBR and large scale structure measurements:
� � ��
� � (@ 95% C.L.)
(Hannestad, 2002)
From CMBR, galaxy clustering, and Lyman �-forestmeasurements:
� ��
� � (@ 95% C.L.)
(Wang, Tegmark & Zaldarriaga, 2002)
From the 2dF Galaxy Redshift Survey measurements:
� � ��
� ��
� � � (@ 95% C.L.)
(Elgarøy et al., 2002)Tommy Ohlsson - Abisko 2002 – p.23/25
![Page 80: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/80.jpg)
Neutrinos in AstrophysicsIn the future, combination of CMBR fromMAP/Planck satellite with Sloan Digital Sky Surveymeasurements:
� ��
�
(Hu, Eisenstein & Tegmark, 1998)
Note!
An order of magnitude less than the present measurements!
Tommy Ohlsson - Abisko 2002 – p.23/25
![Page 81: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/81.jpg)
Summary✔ The number of light neutrino flavors are three.
✔ Neutrinos are massive and mixed.
✔ Neutrino oscillations occur among differentflavors.
✔ The SM has to be extended in order to includemassive neutrinos.
✔ New data soon from the following interestingexperiments: KamLAND, MiniBooNE, . . .
✔ In the far future: long-baseline experiments and aneutrino factory. In the meantime, theoreticaldevelopment!
Tommy Ohlsson - Abisko 2002 – p.24/25
![Page 82: Introduction to Neutrino Physics - KTH Teoretisk fysiktommy/abisko_ohlsson.pdf · Introduction to Neutrino Physics Tommy Ohlsson ... talks as an alternative to neutrino oscillations](https://reader036.fdocuments.us/reader036/viewer/2022070612/5b5a26467f8b9a24038bcd2f/html5/thumbnails/82.jpg)
Neutrino Physics in Progress
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002
Year
0
100
200
300
400
500
600
Num
ber
of p
aper
s
Neutrino @ hep-ph [2002-07-30](Number of papers at hep-ph per year containing the word "neutrino" in the title.)
� Now: � � �
papers/year in neutrino physics!Tommy Ohlsson - Abisko 2002 – p.25/25