Beyond the Standard Model- The elusive neutrinos - J.D. Vergados University of Ioannina, Ioannina, Greece. Visiting Professor, KAIST/CAPP/IBS/Daejeon Lctures on Neutrinos Nov-Dec/2014

Partial list of neutrino topics General Properties of Neutrinos. Neutrino mass and neutrino mixing Neutrino Oscillations. The elusive neutrino mass scale and experiments searching for it (astrophysics, decay experiments double beta decay) Neutrinoless Double Beta decay Neutrinos as a means for exploring the sky. Lctures on Neutrinos Nov-Dec/2014

Lctures on Neutrinos Nov-Dec/2014 The three Frontiers Lctures on Neutrinos Nov-Dec/2014

Ia: Some important stages in the life of neutrino It is elusive, but it does not really escape in neutron decay: n -> p+e-+(?) (Pauli 1930,1932, Fermi 1934). Bethe (1939) finds for it a role in our world. Without it our sun and the “stars cannot shine”. Symbolically: 4p ->He+2νe+2e++light Its direct discovery (Reiness & Cowan (1953) anti-νe  + p → n + e+ The neutrino is different from its antineutrino : νe+ 37Cl->37Ar+e- (yes!), anti-νe+ 37Cl->37Ar+e- (No!) (Davis, 1955) Neutrino violates sacred laws: The fall of parity (Lie &Yang, Wu et al 1956) Neutrino is prejudiced (always left handed!) (Goldhaber et al 1958) A new neutrino is born in 1947 (νμ since it always accompanies μ -), which is different from the old neutrino: νμ #νe ( Brookhaven experiments 1962) One more neutrino, ντ , is born. it appears always together with the lepton τ- (SPEAR, SLAC, 1976). It was shown that ντ #νe , ντ #νμ (Fermilab 1997) All these played a role in the formulation of the standard model (GSW, 1967-1971) Lctures on Neutrinos Nov-Dec/2014

The parity fall shook the world Lctures on Neutrinos Nov-Dec/2014

Ib: Modern history-Neutrino Oscillations The first concept of the 12 The first concept of the idea (Pontecorvo 1958) The first hints- The deficit of solar neutrinos (Davis 1960-1970) Oscillations of atmospheric neutrinos (Super K, 1998) The observations of solar neutrino oscillations (CHOOZE 1999, Sudbury Neutrino Observatory (SΝΟ) 2001) The further settlement of neutrino oscillations issues with reactor neutrinos (KamLAND , 2003). More precise measurement of the oscillation parameters. Measurement of θ13 :Τ2Κ 2011(upper and lower limits); definite result, Daya Bay, march 2012 Lctures on Neutrinos Nov-Dec/2014

Special neutrino features Two types of neutrinos i) Those produced in weak interactions: (ν0)L =(νe, νμ, ντ)L ii) the eigenstates of the world Ηamiltonian νL =(ν1, ν2, ν3)L with masses (m1, m2, m3) respectively. There exists a unitary transformation U (mixing matrix) connecting the two: (ν0)L =UPMNS (3x3 matrix)νL ---> e.g. νeL =Σj Uej νjL Lctures on Neutrinos Nov-Dec/2014

Neutrino Oscillations: An interesting quantum mechanical application Let us consider two neutrinos produced in weak interactions, να , νβ , say the electron and muon neutrinos. Suppose the are not eigenstates of the Ηamiltonian and the matrix mαβ=< νβ|H|να > is non diagonal. After diagonalizing it with a unitary transformstion we get the eigenstates, say ν1 , ν2 . Then ν1=cosθ να - sinθ νβ , ν2=sinθ να - cosθ νβ This can be inverted to yield να=cosθ ν1 + sinθ ν2 , νβ=-sinθ ν1 + cosθ ν2 Lctures on Neutrinos Nov-Dec/2014

Neutrino Oscillations- Period <-> oscillation length Lctures on Neutrinos Nov-Dec/2014

Lctures on Neutrinos Nov-Dec/2014 Neutrino Oscillations vs L/(Osc. Length) : θ≈π/5 (Solar), appearance(red) disappearance (green) Lctures on Neutrinos Nov-Dec/2014

Lctures on Neutrinos Nov-Dec/2014 Neutrino Oscillations- Appearance (solid curves)-disappearance (dot, dash) Θ=π/4 (thick, dotted): S-K Θ=π/5 (fine, dashed): solar. The vertical line indicates the expected events at we see a tiny fraction above the the value at L=0 (no oscillation) Can we see the full wave? Not so easy! It will not fit the detector! For Δm2=10-3 eV2, Eν=1 ΜeV  The detector size aught to be d=2.5 km ! Lctures on Neutrinos Nov-Dec/2014

Aspects of neutrino mass: Dirac mass Lctures on Neutrinos Nov-Dec/2014

Stability of matter <-> Conservation laws for charges How come the electron is stable? the process e-->νe +γ does not occur, since, if it did, it would violate charge conservation . There is no charged particle lighter than the electron! In all known process lepton number (the number of leptons minus the number of antileptons) is conserved The nuclear double beta decay without neutrinos: (A,Z)->(A,Z+2)+e- +e- Examined since the time of Maria Mayer, allowed by energy conservation in a number of nuclei has not been observed <-> Lepton number (lepton charge ) conservation How come the proton is stable? the process p->e++γ has not been observed. We postulate the existence of a baryon number B possessed only by p and n (assumed to carry B=1) and their heavier fermion simblings, which is conserved-> baryon number (baryon charge ) conservation With the exception of the electric charge, all other charges are related to a global symmetry. So these conservation laws are not sacred. Lctures on Neutrinos Nov-Dec/2014

Aspects of neutrino mass: Majorana mass (violates lepton number) Lctures on Neutrinos Nov-Dec/2014

Majorana Mass- two Higgs I=1/2 Lctures on Neutrinos Nov-Dec/2014

Aspects of neutrino mass (2): Majorana mass (violates lepton number) Lctures on Neutrinos Nov-Dec/2014

Lctures on Neutrinos Nov-Dec/2014 Neutrino masses (3): The see-saw mechanism (right handed ν with Μajorana mass term) Lctures on Neutrinos Nov-Dec/2014

Summary on Fermion masses The generation of the charged fermion masses is within the SM, but the actual matrices cannot be predicted. The can only be determined experimentally. The generation of neutrino masses is beyond the SM. There exist many semi-phenomenological models, but a yet no complete theory. The form of the mixing matrix is assumed by group theoretical techniques, but its entries will have to be determined experimentally, Lctures on Neutrinos Nov-Dec/2014

The see-saw mechanism! No Mν, but MD & MΝ Lctures on Neutrinos Nov-Dec/2014

Neutrino mixing. In all cases we have neutrino mixing We must distinguish between two types of neutrino states The weak eigenstates produced in weak interactions And the eigenstates of the Hamiltonian, which are stationary states. They are connected by a unitary transformation Lctures on Neutrinos Nov-Dec/2014

The leptonic mixing matrix: UPNMS (Pontecorvo-Maki-Nakagawa-Sakata) Lctures on Neutrinos Nov-Dec/2014

Lctures on Neutrinos Nov-Dec/2014 PART I NEUTRINO OSCILLATIONS Lctures on Neutrinos Nov-Dec/2014

Review of Neutrino Oscillations- 2 generations Lctures on Neutrinos Nov-Dec/2014

Lctures on Neutrinos Nov-Dec/2014 Neutrino Oscillations vs L/(Osc. Length) : θ≈π/5 (Solar), appearance(red) disappearance (green) Lctures on Neutrinos Nov-Dec/2014

Lctures on Neutrinos Nov-Dec/2014 Neutrino Oscillations- Appearance (solid curves)-disappearance (dot, dash) Θ=π/4 (thick, dotted): S-K Θ=π/5 (fine, dashed): solar. The vertical line indicates the expected events at we see a tiny fraction above the the value at L=0 (no oscillation) Can we see the full wave? Not so easy! It will not fit the detector! For Δm2=10-3 eV2, Eν=1 ΜeV  The detector size aught to be d=2.5 km ! Lctures on Neutrinos Nov-Dec/2014

Lctures on Neutrinos Nov-Dec/2014 For three generations It so happens that the two oscillation lengths are very different. So the two generation treatment used initially was reasonable Lctures on Neutrinos Nov-Dec/2014

Example of 3 Generations: Neutrino disappearance P(νe(0) -> νe (L)) |νe (0)>=cosθ13(cosθ12 |ν1> + sinθ12 |ν2>)+ sinθ13 |ν3> Lctures on Neutrinos Nov-Dec/2014

Lctures on Neutrinos Nov-Dec/2014 Electron Neutrino disappearance (three generations; two oscillation lengths ) L12≈50 L13 Near the source Far from the source Lctures on Neutrinos Nov-Dec/2014

Neutrino Oscillation Experiments Atmospheric Neutrinos, originating from cosmic rays (of moderately high energies). Reactor neutrinos, following nuclear decay. Low energy of the order of a few MeV* (only disappearance of electron neutrinos. The energy is below threshold for muon production) Accelerator neutrinos. Produced in accelerators. In the multi GeV range (both appearance and disappearance). *They confirmed the solar neutrino deficit. Solar neutrino deficit originated the idea of oscillations but they could not be seen expilicitly as such. So we will not discuss them. Lctures on Neutrinos Nov-Dec/2014

Atmospheric neutrinos: twice as many muon neutrinos produced! Lctures on Neutrinos Nov-Dec/2014

Atmospheric neutrino measurement Lctures on Neutrinos Nov-Dec/2014

Atmospheric neutrinos- Results Lctures on Neutrinos Nov-Dec/2014

Solar neutrinos: Production Lctures on Neutrinos Nov-Dec/2014

Solar neutrinos: The spectra p+p->d+e++νe 7Be->7Li+νe 8B->8Be+e++νe The needed elements were produced as follows: d+p->3He+γ 3He+ 3He+->4He+2p 3He+ 7He->7Be+γ 7Be+ p->8B+γ Lctures on Neutrinos Nov-Dec/2014

Solar neutrino experiments (not conclusive) Lctures on Neutrinos Nov-Dec/2014

Lctures on Neutrinos Nov-Dec/2014 Reactor Neutrinos (KamLAND experiment settled the issue of solar neutrinos) Lctures on Neutrinos Nov-Dec/2014

The Daya Bay reactor experiment Recall: |νe (0)>=cosθ13(cosθ12|ν1> + sinθ12 |ν2>)+ sinθ13|ν3> KamLAND looked at the large oscillation length and measured θ12 Daya Bay looked at the small and measured the small angle θ13 Lctures on Neutrinos Nov-Dec/2014

Lctures on Neutrinos Nov-Dec/2014 Information to be extracted from the standard neutrino oscillation data The three mixing angles: θ12 , θ13 , θ23 The absolute value of the mass squared differences, e.g. One sign, e.g. the first, can arbitrarily be chosen positive. The other can only be determined from the difference between neutrinos and antineutrinos. Not yet achieved Lctures on Neutrinos Nov-Dec/2014

Lctures on Neutrinos Nov-Dec/2014 The best fit values of all neutrino oscillation data, solar, atmospheric and reactor (KamLAND , CHOOZE, K2K, Daya Bay); F. Capozzi et al, arXiv:1312.2878 [hep-ph]. Lctures on Neutrinos Nov-Dec/2014

Neutrinos behave differently than quarks! Quark mixing matrix Lepton mixing matrix PNMS Lctures on Neutrinos Nov-Dec/2014

Lctures on Neutrinos Nov-Dec/2014 Since one of the signs of Δm2 is not known ->Two scenarios: Normal Hierarchy (NH) on the left and Invertited (IH) on the right. Lctures on Neutrinos Nov-Dec/2014

Lctures on Neutrinos Nov-Dec/2014 What is the hierarchy in the case of 3+1 light ν’s (not confirmed by MiniBooNE) Lctures on Neutrinos Nov-Dec/2014

Facts about neutrinos (after 70 years) --We know for some time that: There exist three distinct families of left handed neutrinos: (ν0)L =(νe,νμ,ντ)L These neutrinos are distinct from the associated antineutrinos How these neutrinos interact -- We have learned from neutrino oscillations that: the neutrinos are massive. We know the two mass squared differences. The neutrinos are admixed. We know all three mixing angles. Lctures on Neutrinos Nov-Dec/2014

Issues involving neutrinos (after 70 years) --We do not know: The absolute scale of their mass The value of the CP violating phase. The nature of the mass eigenstates, i.e whether they are of Majorana type (particle=antiparticle ) or Dirac type (particle # antiparticle) Lctures on Neutrinos Nov-Dec/2014

The main needed experiments for ν’s To determine the absolute mass scale: --Decay experiments: Sensitivity 0.2 eV (KATRIN) --Astrophysical and cosmological observations: Sensitivity sub eV --Neutrinoless (0ν) ββ- decay: Sensitivity meV, 1meV=10-3 eV To determine the CP violating phase : Neutrino oscillations involving both neutrinos and antineutrinos To settle the controversy of Dirac vs Majorana : Neutrinoless double beta decay Lctures on Neutrinos Nov-Dec/2014

Lctures on Neutrinos Nov-Dec/2014 PART II THE ELUSIVE SCALE OF NEUTRINO MASS Lctures on Neutrinos Nov-Dec/2014

Review: Issues not settled by Neutrino Oscillations: The nature of neutrinos , i.e. whether the neutrinos ere Majorana or Dirac type particles scale of neutrino masses (Not yet the sign of the expressions) the sign of Δm2 =m23 -m22 or Δm2 =m23 -m21 , (m2> m1) Thus the following scenarios emerge: Normal hierarchy: Δm2 >0 or m23 >m22 Inverted hierarchy: Δm2 <0 or m23 <m21 The Degenerate : Δm2<<m2ι , ι=1,2,3 Lctures on Neutrinos Nov-Dec/2014

The Mass Hierarchies - Flavor Content Lctures on Neutrinos Nov-Dec/2014

I: Neutrino mass scale in β decay Spectrum of triton beta decay Mass in the two scenarios Lctures on Neutrinos Nov-Dec/2014

Triton beta deacay:<mν>≤2.3eV Mass in the two scenarios N-H (N-S, upper) & I-H (N-S) lower) Measured mass as a function of m0 Lctures on Neutrinos Nov-Dec/2014

Lctures on Neutrinos Nov-Dec/2014 II:Cosmological bound (CMB, etc):mν≤ 0.71 Photοmetric red shift survey: mν ≤0.28 eV Mass in the two scenarios N-H (N-S, upper) & I-H (N-S), lower) Extracted mass as a function of m0 Lctures on Neutrinos Nov-Dec/2014

Lctures on Neutrinos Nov-Dec/2014 III: Neutrino mass in double beta decay: Ordinary Beta Decay of A(N,Z) is Forbidden Double Beta Decay of A(N,Z) is allowed N(A,Z)N(A,Z+2)+e- +e- (0ν ββ-decay) Δ=Q a fempto (10-15 m) laboratory! Lctures on Neutrinos Nov-Dec/2014

Lctures on Neutrinos Nov-Dec/2014 Measure the sum of the energies of the two electrons. 0ν ββ is a discreet line at the end point. 2ν ββ has a continuous spectrum. A need for good energy resolution. Lctures on Neutrinos Nov-Dec/2014

Lctures on Neutrinos Nov-Dec/2014 Diagrammatic Representation of 0ν-ββ decay (Light neutrino:Amplitude proportional to neutrino mass) Quark Level Nuclear Level Lctures on Neutrinos Nov-Dec/2014

Lctures on Neutrinos Nov-Dec/2014 0ν Double Beta decay lifetime For light neutrino nuclear and particle physics separate! 1. M0νββ Is the nuclear ME . It should be as large as possible. It is also very hard to calculate: The nuclei involved have complicated structure One encounters cancellations 2. G01: Kinematical well known function. It should be as large as possible. Q as large as possible 3. ην: Fundamental Particle Physics Τo be extracted from the data ! Still elusive after 70 years A Measurement of Lifetime involves the detection of the two produced electrons It is a Very hard task Very Low counting rate Terrible Backgrounds Lctures on Neutrinos Nov-Dec/2014

Lctures on Neutrinos Nov-Dec/2014 lower neutrino mass bound from 0ν ββ-decay: |<mν>| (JDV, Ejiri,Simkovic, ROP; arXiv:1205.0649) Μass in the two scenarios N-H (N-S, upper) & I-H (Ι-S) lower) Extracted mass as a function of m0 Lctures on Neutrinos Nov-Dec/2014

Lctures on Neutrinos Nov-Dec/2014 THE END Lctures on Neutrinos Nov-Dec/2014