On the Importance of Neutrino Mass A. Para, Fermilab Is it really important? Why? Who cares? What is a Neutrino ? What is Mass ? Keys to the Puzzle ? More questions than answers..

11 Greatest Unanswered Questions of Physics What is dark matter ? What is dark energy ? How were the elements from iron to uranium made? Do neutrinos have mass ? … Are protons unstable ? What is gravity ? Are there additional dimensions ? How did the Universe begin ? Discover February 2002

Particle Physics at the End of the XX Century:Theory of Matter and Forces Periodic table of elementary particles

Expanding our Ignorance: Composition of the Universe 65+-10% Dark(vacuum) energy 30+-7% Dark matter 4.5+-0.5% Ordinary matter 0.5% Stars 0.5% Neutrinos 0.02% C,N,O,…,Fe,… Unknown, not understood Known, poorly understood “Us” N(n) >~109N(protons, neutrons, electrons)

Theory of Matter and Forces: the Right-handed Stuff? Right-handed SU(2) singlets No neutrinos! Do not participate in weak interactions, we know of their existence because of their strong/electromagnetic interactions Left-handed SU(2) doublets Quark <-> lepton symmetry (anomaly free)

Quarks and charged leptons Neutrinos are special Neutrinos Members of SU(2) doublets (left-handed), no singlets Electric charge = 0 obey Dirac equation? Majorana equation? Do have anitparticles? Are self-conjugate? Magnetic moments? Sterile neutrinos? Quarks and charged leptons members of SU(2) doublets (left-handed) and singlets (right handed) Electric charges 1/3, 2/3, 1 4-component Dirac spinors Have antiparticles distinct from particles Are these facts/questions related?

Enigma of Masses of Elementary Particles Masses of all charged fermions within a given generation are the same within a factor of 10 Masses of neutrinos are a factor ~109 smaller Why ??? What makes masses so different? Notice: if mn~me we would not be here to ask such questions !

The meaning of Mass: A Worldline of a Massive Particle in its Rest Frame Q(t) is a spinor of a massless particle with momentum t R.H. L.H.

A Massive Particle in its Rest Frame What are R,L ? R L Interaction with vacuum changes left-handed particle into right-handed one Electron case L = left handed electron R = right handed electron (not positron! Because of charge conservation) Neutrino case L = left handed neutrino R = right handed antineutrino?? right handed neutrino??

CPT transformation of a spinor fL C f P f CPT Invariance implies: fL fR T fR

From Schrodinger to Dirac Non-relativistic Schrodinger Klein-Gordon Non-positive probabibility Dirac Square root of K-G

g matrices, Weyl representation

The ‘other’ square root Majorana Which equation describes neutrino? Dirac? Majorana? This question arises only for neutral fermions

Dirac neutrino vs Majorana neutrino Lorentz Boost, E, B C P T C P T

A General Lagrangian (Neutral Fermions) Left, right handed fields

The physical states are eigenstates of the mass matrix See-saw mechanism The physical states are eigenstates of the mass matrix Let all fermions have the same Dirac mass MD (~ mq or ml), ML=0 if MR>>MD than mn<<ml Is neutrino a Majorana particle? Is a very heavy Majorana mass an explanation for the smallness of the observed mass eigenstate? Are we witnessing a first sign of the physics at very high energies?

Neutrino Masses: a Key to the Mass Generation Mechanism? Possible examples: m1 : m2 : m3 = mu2 : mc2 : mt2 mn ~ mq2/Mx See-saw mechanism for Majorana neutrinos New interactions at the scale Mx m1 : m2 : m3 = mu : mc : mt mn ~ mq Top members of weak doublets couple to the same Higgs field m1 : m2 : m3 = me : mm : mt mn ~ ml ‘Leptonic’ Higgs generates mass of leptons

Direct measurements of neutrino mass Techniques time of flight (SN1987a) particle decay kinematics beta decay spectrum shape (ne) muon momentum in pion decay (nm) invariant mass studies of multiparticle semileptonic decays (nt) Advantages sensitive to absolute mass scale purely kinematical observables no assumptions about n properties

Neutrino Masses: Experimental Progress J. Wilkerson points without error bars represent upper limits note: different scale for different neutrinos types

Tritium beta decay spectrum n p+e-+ne

Two leading experiments: Troitsk and Mainz

Breakthrough technique: MAC-E-Filter Magnetic Adiabatic Collimation followed by Electrostatic Filter Integrating high pass filter: high intensity Large acceptance ~ 2p High resolution, DE~2-6 eV at E=20 keV Developed specifically for tritium beta decay experiments

New Twist: Neutrino Mixing (SuperK 1997) Weak eigenstates are mixtures of mass eigenstates Large mixing angle q12 ~ 35o Large mixing angle q23 ~ 45o Mixing angle q13 ~ small

What is an electron neutrino? p Electron (muon,tau) neutrino is not a mass eigenstate Electron (muon, tau) neutrino is a coherent mixture of mass eigenstates e n ne What do neutrino mass experiments measure?

b-decay spectrum and neutrino mixing The beta spectrum shape depends on: the neutrino masses the number of neutrino mass eigenstates the leptonic mixing matrix elements An “effective mass” : mb 2 = S |Uei |2 mni 2

Neutrino Oscillations: Tool for Measuring Mass Differences If neutrinos have mass, then it is likely that flavor and mass eigenstates are different  Neutrino Oscillations Example: two families of neutrinos Amplitude Oscillation frequency

Neutrino Interferometry, or How do Neutrinos Oscillate? Components of the initial state have different time evolution => Y(t)  Y(0) Amplitude Amplitude 3-slit interference Experiment: mass difference  difference in optical path length

Oscillation Probability where

Neutrino Oscillations Primer if all masses are equal i.e. Neutrino oscillations are sensitive to mass differences only. oscillates as a function of L/E for Appearance experiment. : disappearance experiment :total number of neutrinos is conserved If Uai is complex then hence T (or CP) violation

Neutrino Oscillations Disappearance experiment: Start with neutrinos of type x (say nm), detect the flux at a distance L, Fnm(L)< Fnm(0) Appearance experiment: Start with neutrinos of type x (say nm), detect the neutrinos of type y (say nt), at a distance L Does really happen?

How does the Sun ‘work’? (H. Bethe) Solar model Tiny fraction

Detecting Solar Neutrinos SuperKamiokande: Electron neutrino scatters elastically of an atomic electron Scattered electrons follow the direction of the incoming neutrino R. Davis, Homestake: 680 ton of CCl4 ~ 15 atoms of 37Ar produced per month !!!

Solar Neutrino Results (~1999) Only about 50% of the predicted flux is detected Solar neutrino ‘problem’

n Reactions in heavy water (SNO) ne + d ® p + p + e- Ethres= 1.4 MeV Charged Current Reaction: • 6-9 events per day • ne flux and energy spectrum • Some directional sensitivity (1 - 1/3cosqe)  ne: 1.75(15) x 106 cm-2 s-1 nSSM: 5.05 x 106 cm-2 s-1 Elastic Scattering Reaction: • 1-2.5 events per day • Directional sensitivity (very forward peaked) CC ne e- W n p nx + e- ® nx + e- Ethres = 0 MeV ES nmt: 3.69(113) x 106 cm-2 s-1 ntotal: 5.44(99) x 106 cm-2 s-1 ne ne ne n e- n W Z W e- e- e- ne e- e-

KamLAND: the ultimate proof of solar neutrino oscillations

Disappearing electron antineutrinos Reactor neutrinos (== electron antineutrinos!!) disappear at distances ~ 100 km consistent with solar neutrino experiment Dm2 ~ 1-14 x 10-5 eV2 Solar neutrino problem no longer a problem Neutrinos oscillate

Atmospheric Neutrinos SuperK n Earth

Results from Super-K Experiment nm flux reduced by about 50% for long flight path if it is a result of the neutrino oscillations, then : the dominant mode is nm to nt mixing angle is very large Dm2 :

Long Baseline Neutrino Oscillation Exp’s Reproduce atmospheric effect using accelerator produced n-beam K2K (KEK to SuperK) L = 250 km Now MINOS (Fermilab to Minnesota) L = 730 km 2003 CNGS (Cern to Gran Sasso, Italy) L = 750 km 2005?

Oscillation Experiment The MINOS Beamline Two Detector Neutrino Oscillation Experiment (Start 2005) Far Detector (5.4 ktons) : - 8m diameter by 1” steel plates - 4cm wide solid scintillator strips - Steel magnetized at 1.5 T Det. 2 Det. 1

Do Neutrinos Oscillate? Decay? Travel in Extra Dimensions Expected event spectrum Observed (perhaps?) event spectrum Observed energy distribution of nm CC interactions provide a measure of the nm survival probability as a function of En

Three outstanding questions ~ 2003 Neutrino mass pattern: This ? Or that? Electron component of n3 (sin22q13) Complex phase of s  CP violation in a neutrino sector  (?) baryon number of the universe

The key: nm  ne oscillation experiment A. Cervera et al., Nuclear Physics B 579 (2000) 17 – 55, expansion to second order in

Neutrino Propagation in Matter Matter effects reduce mass of ne and increase mass of ne Matter effects increase Dm223 for normal hierarchy and reduce Dm223 for inverted hierarchy

Anatomy of Bi-probability ellipses Minakata and Nunokawa, hep-ph/0108085 ~cosd Observables are: P Interpretation in terms of sin22q13, d and sign of Dm223 depends on the value of these parameters and on the conditions of the experiment: L and E d ~sind sin22q13

NuMI Beam + Off-axis Detector(s) Search for nm to ne transition Measure mixing angle sin22q13 Search for CP violation in a neutrino sector

How about the nature of neutrino? Dirac or Majorana particle? Does it have a distinct antiparticle? Is it its own antiparticle?

Masses of Nuclei: even A Case Lowest energy state reachable only through two simultaneous weak beta decays  very low rate, very long lifetimes (exceeding age of the Universe)

Neutrinoless Double b decay: Key to the Nature of the Neutrino Two beta decays If (neutrino=antineutrino) {they can ‘annihilate’ each other} Process allowed only for a Majorana neutrino

Electron Spectrum From Double b Decay: from Theory to Practice Energy resolution High rates capabilities

Double Beta Decay Experiments: Results Isotope Experiment 48Ca HEP Beijing >1.1x1022* 23-50 76Ge Heidelberg-Moscow >5.7x1025 2-8 IGEX >0.8x1025 82Se Irvine >2.7x1022 4-14 NEMO 2 >9.5x1021 96Zr >1.3x1021 100Mo LBL >2.2x1022* 3-111 UCI >2.6x1021 Osaka 5.5x1022 2 NEMO2 >5x1021 130Te Milano >1.4x1023 2-5 136Xe Caltech/PSI/Neuchatel >4.4x1023 150Nd >1.2x1021 5-6 Germanium diode cal. Te02 cryo calorim. Xe TPC

What do 0nbb Experiments Measure? Where: a phase space factor a nuclear matrix element (QRPA, NSM,..) If CP is conserved Majorana phases

The quest for 20-50 meV sensitivity CUORE – 210 kg of 130Te, Grand Sasso EXO - (liguid or gaseous) 136Xe WIPP? Homestake? GENIUS - 1t of enriched 76Ge in liquid N2 shield MAJORANA – 500 kg of enriched segmented 76Ge detectors MOON – thin foils of (enriched?) 100 Mo Homestake? Japan? Large mass of the source material, enriched if possible Innovative background suppression Intermediate steps

Large scale clusters Large scale structures originate from fluctuations of the primordial mass/energy distribution Significant contribution of the mass/energy in a form of fast moving neutrinos would tend to wash out fluctuations

Weighing Neutrinos with Galaxy Surveys Large scale cluster formation Fraction of energy in neutrinos Sloan Sky Survey of Bright Red Galaxies W. Hu, D.J. Eisenstein, M. Tegmark, PRL80, p5255, 1998

The pattern and absolute scale of n masses Key issues in particle physics hierarchical or degenerate neutrino mass spectrum understanding the scale of new physics beyond SM potential insight into origin of fermion masses Nature of the neutrino Cosmology and astrophysics connection early universe, relic neutrinos (HDM), structure formation, anisotropies of CMBR supernovae, r-process, origin of elements potential influence on UHE cosmic rays

(Instead of) Conclusions We are living in interesting times. It is fun to study neutrinos

Stellar Evolution

Supernova Explosion

Supernova 1987A February 1984 March 8,1987 Seven years later..

Supernova as a Neutrino Laboratory (Examples) Neutrino mass: If neutrinos have mass m then neutrinos with different energies will travel with different speed. Difference of arrival time of neutrinos with energy E1 and E2: Neutrino lifetime: Neutrinos come from a distance L. Their lifetime must be such, that: SN1987A: mn<15 eV SN1987A: tn>5x1012 s

Neutrinos from Supernova 1987A Energy spectrum of neutrinos total energy radiated (1.4 solar masses) size of the resulting neutron star (15 km)

Dec 1930: A Desperate Remedy “I have done something very bad today by proposing a particle that cannot be detected; it is something no theorist should ever do.” W. Pauli

Weak Interactions Current-current interaction :Fermi 1934. Paper rejected by ‘Nature’ because “it contained speculations too remote from reality to be of interest to the reader” Modern version: is a projection operator onto left-handed states for fermions and right-handed states for antifermions Only left handed ferminos and right handed anti-fermions participate in weak interactions: Parity violation

Reines and Cowan: an Audacious Proposal (1946) Nuclear reactor will do the same 1956, Savannah River:”We are happy to inform you (Pauli) that we have definitely detected neutrinos…” 1995 Nobel Prize for Reines

How Many Neutrinos?

Energy Spectrum of Solar Neutrinos Two body reaction: line Three body decay: phase space, like muon decay spectrum

Neutrino survival probability Small Mixing P(ne → ne) Large Mixing Night Distortion of the observed energy spectrum differentiates between different oscillations scenarios Day LOW Just-so En (MeV)