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.

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 F.-G. Cao, Massey University NPB 2012, Shenzhen, 23/09/2012

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

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

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. F.-G. Cao, Massey University NPB 2012, Shenzhen, 23/09/2012

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 F.-G. Cao, Massey University NPB 2012, Shenzhen, 23/09/2012

2. Experimental constraints Neutrino oscillations Neutrinoless double beta decay Beta decay Cosmology F.-G. Cao, Massey University NPB 2012, Shenzhen, 23/09/2012

Neutrino oscillations Neutrino oscillations are sensitive to the neutrino mass squared difference Allow two scenarios of neutrinos masses F.-G. Cao, Massey University NPB 2012, Shenzhen, 23/09/2012

The absolute neutrino masses Which hierarchy? The absolute neutrino masses F.-G. Cao, Massey University NPB 2012, Shenzhen, 23/09/2012

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 F.-G. Cao, Massey University NPB 2012, Shenzhen, 23/09/2012

F.-G. Cao, Massey University NPB 2012, Shenzhen, 23/09/2012

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

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:1203.5250 F.-G. Cao, Massey University NPB 2012, Shenzhen, 23/09/2012

Beta decay experiments Shape of the spectrum determines Require high-precision measurement of the end-point part of the beta-spectrum of 3H decay F.-G. Cao, Massey University NPB 2012, Shenzhen, 23/09/2012

Beta decay experiments Results Katrin may detect The 95% C.L. upper bounds The average neutrino mass F.-G. Cao, Massey University NPB 2012, Shenzhen, 23/09/2012

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

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:1111.1436 F.-G. Cao, Massey University NPB 2012, Shenzhen, 23/09/2012

Large-scale structure Robertson The large-scale matter power spectrum; Y. Y. Wong, arXiv:1111.1436 F.-G. Cao, Massey University NPB 2012, Shenzhen, 23/09/2012

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. F.-G. Cao, Massey University NPB 2012, Shenzhen, 23/09/2012

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 F.-G. Cao, Massey University NPB 2012, Shenzhen, 23/09/2012

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

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) F.-G. Cao, Massey University NPB 2012, Shenzhen, 23/09/2012

The Koide empirical relation is well satisfied for the heavy quarks. F.-G. Cao, Massey University NPB 2012, Shenzhen, 23/09/2012

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

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

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

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

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

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