1. Determining the absolute masses of neutrinos
Fu-Guang Cao
Massey University, New Zealand
Introduction
Experimental constraints
Theoretical constraints
A conjecture and neutrino masses
Summary
I will start with a brief introduction of basic properties of neutrinos, emphasizing the importance of determining the absolute neutrino mass scale.
I will then discuss experimental constraints, and theoretical constraints on the neutrino masses.
Experimental results usually provide constraints for some combinations of neutrino masses.
Theoretically, in the SM, neutrinos are massless and left-handed. To understand massive neutrinos one needs to go beyond the SM.
Various versions of the extension of the SM usually require the introduction of new particles and/or energy scales.
Thus, models beyond the SM generally cannot give firm prediction for the neutrinos masses.
However, I will argue that the extension of the SM will require higher level of symmetries. These symmetries will lead to some intrinsic relations for
lepton masses and quark masses. These relations may provide additional constraints for the neutrino masses.
I will discuss such relations and use the additional constraints together with neutrino oscillation data to determine the absolute masses of neutrinos.
I will finish with a brief summary.

2. 1. Introduction
History
Suggested by Pauli in 1930 in explaining the nuclear beta decay; formularized by Fermi in 1933; discovered by Cowan and Reines in the 1950s; no right-handed neutrinos in the SM
Importance for particle physics, nuclear physics, and astrophysics.
Difficulties in detection
Participating in only Weak interaction and travelling close to c make them very hard to detect.
Neutrinos are fascinating particles and continue surprising us with unexpected properties and phenomena.
Played an important role in the development of the SM since it was suggested by Pauli and incorporated by Fermi in his famous V-A coupling theory for the weak interaction.
Fermi’s theory is an effective theory and works well only at low energy.
Neutrinos are eventually included in the SM as massless particles.
Exist at the Big Bang.
Neutrinos are still the least understood fundamental particles, mainly because they
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NPB 2012, Shenzhen, 23/09/2012

3. Left-handedness vs. Non-zero masses
Neutrinos are ALWAYS left-handed.
Inverse beta decay processes, Goldhaber, Grodzins & Sunyar, 1958
Thus neutrinos are massless.
Neutrino oscillations are well established.
Thus neutrinos have non-zero masses.
Contradiction?
Hold clues for the extension of the SM.
The two properties about the neutrinos I want to discuss here are the left-handedness and non-zero masses.
The fact that neutrinos are always left-handed was established in 1950s via the study of inverse beta decay processes.
Must be massless. SR requirement. For an observer who moves faster than the neutrino, the LH neutrino turn into RH one.
(SuperKamiokande, 1998,).
Resolve this contradiction. Also hold clues for the extension of the SM.
A nucleus captures an electron, resulting an unstable nucleus and a neutrino; the unstable nucleus emits a gamma ray.
Measuring the handness of the gamma ray gives the handness of the neutrino.
F.-G. Cao, Massey University
NPB 2012, Shenzhen, 23/09/2012

4. Higgs-like particles PLB716 (2012) 30-61 PLB716 (2012) 1-29
To generate mass for particles we need turn to the Higgs mechanism.
The Higgs-like particle with a mass around 125 GeV has been observed by the two experimental groups at CERN. This is a tremendous victory of particle physics.
So we have more reasons to believe that the Higgs mechanism is THE mechanism to give mass to particles.
PLB716 (2012) 30-61
PLB716 (2012) 1-29
F.-G. Cao, Massey University
NPB 2012, Shenzhen, 23/09/2012

5. Mechanism for neutrino masses
Higgs mechanism
All particles acquire mass as they collide with the Higgs Boson. However, the collisions also change the handedness of the particle.
Dirac neutrinos
Right-handed neutrinos interact extremely weakly.
Majorana neutrinos: LH neutrino  RH antineutrino
Heavy RH neutrinos with mass M live a very short time.
Seesaw mechanism
Dirac neutrinos:
Tiny left-handed neutrino mass means that they interact 10^{-12} time weaker than other SM particles.
No-detection of the right-handed neutrinos means they interact even much much weaker than the LH neutrinos.
Majorana neutrinos:
Neutrinos and antineutrinos are identical, saving the left-handedness problem for the collision with Higgs boson:
left-handed neutrino=right-handed antineutrion. So we can argue that the collision with Higgs boson will turn a LH neutriono into a RH antineutrino.
We also need to introduce shortly-lived heavy RH neutrinos with mass M and M is not tied to the mass scale of the Higgs boson. Much heavier.
LH neutrinos colliding with the Higgs acquires mass m, and turn into a RH, heavy but shortly lived neutrino.
RH heavy collide with Higgs and transfer back to the light LH ones.
LH neutrino mass m/M^2.
Heavy particles are nature in the GUT theories.
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NPB 2012, Shenzhen, 23/09/2012

6. Fundamental questions about neutrinos
Dirac or Majorana neutrinos?
What are the absolute neutrino masses?
Do neutrinos violate CP symmetry?
Do sterile neutrinos exist?
What do neutrinos tell us about the models beyond the SM?
Are neutrinos their own anti-particles? Conservation of lepton number is retained or not.
Weak interaction vs heavy new particles.
TOF measurements from supernova suggested
Direct measurement using
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7. 2. Experimental constraints
Neutrino oscillations
Neutrinoless double beta decay
Beta decay
Cosmology
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8. Neutrino oscillations
Neutrino oscillations are sensitive to the neutrino mass squared difference
Allow two scenarios of neutrinos masses
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9. The absolute neutrino masses
Which hierarchy?
The absolute neutrino masses
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10. Neutrinoless double beta decay
Helicity has to flip
Even-even nuclei
Helicity has to flip, thus detect Majorana neutrinos.
Half life-time of even-even nuclei for which single beta decay is energetically forbidden or strongly suppressed. 2nu or 0 nu decay is allowed.
A hypothetical process can happen only if
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NPB 2012, Shenzhen, 23/09/2012

11. F.-G. Cao, Massey University
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12. Neutrinoless double beta decay: results
Future experiments could reach a sensitivity
General constraints is m_\beta\beta is smaller than a few hundreds millieVs.
Future experiments may improve the sensitivity to a few tens millieVs.
F.-G. Cao, Massey University
NPB 2012, Shenzhen, 23/09/2012

13. Neutrinoless double beta decay results
Before Daya Bay
After Daya Bay
Look at the dependence of m_\beta\beta on the lightest neutrino mass, we have this kind of plots.
The Daya bay measurement of \theta_13 affect the plot slightly.
Different colors represents different levels of confidence of exclusion.
A sensitivity of 10 millieVs may be able to distinguish IS and NS. Thus important.
S. M. Bilenky, arXiv:
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14. Beta decay experiments
Shape of the spectrum determines
Require high-precision measurement of the end-point part of the beta-spectrum of 3H decay
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15. Beta decay experiments
Results
Katrin may detect
The 95% C.L. upper bounds
The average neutrino mass
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NPB 2012, Shenzhen, 23/09/2012

16. Info from cosmology Provide constraints for
Cosmic microwave background anisotropies
Large-scale structure
Other observations
Depend on cosmology models
Results
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NPB 2012, Shenzhen, 23/09/2012

17. CMB anisotropies Launched in May 2009
A model with massless neutrinos;
Two models with massive neutrinos.
The Planck will reach a sensitivity of 0.2 eV .
The CMB temperature anisotropy spectrum; 3 years WMAP data; Y. Y. Wong, arXiv:
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18. Large-scale structure
Robertson
The large-scale matter power spectrum;
Y. Y. Wong, arXiv:
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19. 3. Theoretical constraints
Seesaw models: need new particles
Limited predictive power on the neutrino masses
GUTs suggest intriguing relations for the lepton and quark masses.
The empirical Koide relation
is respected with surprisingly high precision
and can be obtained using super-symmetric yukawaon models.
Relation does not depend on the energy scale, i.e. true for the pole mass as well as running mass.
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NPB 2012, Shenzhen, 23/09/2012

20. Models for the Koide relation
Koide’s mechanism
Assume U(3)-family nonet Higgs scalars with the U(3)-family being broken into SU(3) family
Higgs scalars couple to the charged leptons bilinearly
Octet, singlet,
The charged lepton mass matrix is given by the vacuum expectation values of the Higgs scalars
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NPB 2012, Shenzhen, 23/09/2012

21. Models for the Koide relation
Sumino’s mechanism
A flavor symmetry is gauged; cancellation of radiative corrections by photons and flavor gauge bosons.
Assume U(3)-family nonet Higgs scalars;
The relation is respected by the running masses as well.
F.-G. Cao, Massey University
NPB 2012, Shenzhen, 23/09/2012

22. 4. A conjecture and neutrino masses
Define Koide-like parameters for the lepton sector
Define Koide-like parameters for the quark sector via dividing quarks according to their mass instead of their electric charge or isospin (Rodejohann & Zhang; Kartavtsev)
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23. The Koide empirical relation is well satisfied for the heavy quarks.
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24. Additional constraint for neutrino masses!
A conjecture: intrinsic mass relations exist between leptons and quarks (FGC, PRD85 (2012)113003).
Quarks and leptons are to be commonly governed by a fundamental law of physics. Thus simple and pretty relations exist among quark and lepton masses.
K lepton heavy and K quark heavy differ by less than 0.3%, and K lepton and K quark differ by less than 5% when neutrino masses are ignored.
Expect K lepton light and K quark light is respected at higher degrees of accuracy than K lepton=K quark.
Additional constraint for neutrino masses!
F.-G. Cao, Massey University
NPB 2012, Shenzhen, 23/09/2012

25. normal inverted The inverted mass hierarchy is strongly disfavored.
Band represents the allowed 1 sigma range from the additional constraint.
The inverted mass hierarchy is strongly disfavored.
F.-G. Cao, Massey University
NPB 2012, Shenzhen, 23/09/2012

26. The normal mass hierarchy is consistent with the conjecture.
Current experimental constraints
m1 is 0.1 meV.
m2 is about 10 meV
m3 is about 50 meV
m1:m2:m3=1:100:500
F.-G. Cao, Massey University
NPB 2012, Shenzhen, 23/09/2012

27. Implications for the LHC
Use the seesaw mechanism to estimate the heavy neutrino masses.
Assuming diagonal matrices for the Dirac mass matrix and the Majorana mass matrix, we found that
Possibly accessible at the LHC
F.-G. Cao, Massey University
NPB 2012, Shenzhen, 23/09/2012

28. Additional constraint for neutrino masses!
5. Summary
Determining the absolute neutrino masses is important.
Constraints from current and near-future experiments are limited.
GUTs provide intrinsic relations for lepton masses and quark masses.
Additional constraint for neutrino masses!
The normal mass hierarchy is consistent with the conjecture.
F.-G. Cao, Massey University
NPB 2012, Shenzhen, 23/09/2012

29. Constraints from the conjecture
Summary
Constraints from the conjecture
Current experiments cannot distinguish the two mass hierarchies.
F.-G. Cao, Massey University
NPB 2012, Shenzhen, 23/09/2012