Neutrino Physics Caren Hagner Universität Hamburg Caren Hagner Universität Hamburg Part 3: Absolute neutrino mass Introduction beta decay double beta decay

Evidence for Neutrino Oscillations: Neutrino oscillations were observed in 2 regions: Solar neutrinos and reactor neutrinos v e → v μ,τ with Δm 2 ≈ 8·10 -5 eV 2, large mixing Atmospheric neutrinos and accelerator neutrinos v μ → v τ,(s) mit Δm 2 ≈ 2·10 -3 eV 2, maximal mixing LSND? Anti-v μ → Anti-v e with Δm 2 ≈ 1 eV 2 (Tested by MiniBooNE) Neutrino oscillations were observed in 2 regions: Solar neutrinos and reactor neutrinos v e → v μ,τ with Δm 2 ≈ 8·10 -5 eV 2, large mixing Atmospheric neutrinos and accelerator neutrinos v μ → v τ,(s) mit Δm 2 ≈ 2·10 -3 eV 2, maximal mixing LSND? Anti-v μ → Anti-v e with Δm 2 ≈ 1 eV 2 (Tested by MiniBooNE) Neutrinos have mass! m lightest v ? (3)

Nature of Neutrino Mass I Neutrino fields v(x) with mass m are described by the Dirac equation: The left-handed and right-handed components are: This leads to a system of two coupled equations: With m=0 one obtains the decoupled Weyl equations: From Goldhaber experiment one knows that v L is realized. With m=0 there is no need to have v R. Therefore there were no v R in the Standard Model. 4 component spinor 2 components each

Dirac mass term Dirac Mass Term The neutrino mass term in L could have exactly the same form as the mass term of the quarks and charged leptons: m Must add v R (right handed SU(2) singlets) to standard model! Problem: When the mechanism is the same, why are the masses so small? m t = ± 5.1 GeV; m b = ( ) GeV; m τ = ± 0.29 MeV; m 3 < 2eV Lepton number is conserved! Footnote: A Lorentz invariant mass term must link a chirally left-handed field with a chirally right handed field

Majorana Particles Because neutrinos carry no electric charge (and no color charge), there is the possibility: particle ≡ anti-particle Majorana particle particle anti-particle (charge conjugate field): for a Majorana particle: But what about experiments? Anti-neutrinos(reactor): Neutrinos (solar): observed! not observed! There are two different states per flavor but the difference could be due to left-handed and right-handed states!

Majorana Mass Term Note that is a left-handed field and is a right-handed field Footnote: A Lorentz invariant mass term must link a chirally left-handed field with a chirally right handed field Let’s try vLvL left handed field (v L ) c right handed field mLmL ok! works too! Lepton number violation!

Construct the Majorana fields: Eigenstates of the interaction: v L and v R Mass eigenstates: Φ 1 (mass m L ), Φ 2 (mass m R )

Dirac-Majorana Mass Term mass matrix M mass term for each flavor: In order to obtain the mass eigenstates one must diagonalize M: find unitary U with with with the mass eigenstates:and mass eigenvalues:

What if… 1. m L = m R = 0: pure Dirac case θ = 45, m 1 =m 2 =m D. 2 degenerate Majorana states can be combined to form 1 Dirac state. 2. m D = 0: pure Majorana case θ = 0, m 1 =m L m 2 =m R 3. m R ≫ m D, m L = 0: seesaw model θ = m D /m R ≪ 1 per neutrino flavor: one very light Majorana neutrino v 1L = v L one very heavy Majorana neutrino v 2L = (v R ) c m D of the order of lepton masses, m R reflects scale of new physics ⇒ explains small neutrino masses! mRmR mDmD

Lower Limit of Neutrino Mass Super-K (atmospheric neutrinos):  m 2 atm = 2.5 × eV 2  m(ν i ) ≥ 0.05 eV This sets the energy scale for mass search!

Which mass hierarchy? v1v1 v2v2 Δm solar v3v3 Δm atm inverted hierarchy v3v3 v1v1 v2v2 Δm solar Δm atm normal hierarchy 0.05 eV - Lightest neutrino mass not known - Δm 2 atm 0 ? ? 0 v3v3 v1v1 v2v2 ≲ 2 eV quasi-degenerate 0

Neutrino Mass Measurements Strategies cosmology &structure formation D.N. Spergel et al:  m < 0.69 eV (95%CL) S.W. Allen et al:  m = 0.56 eV (best fit) 0  decay: NEMO3 76 LNGS ´90-´03 (71.7 kg×y) |m ee |= eV 2  SuperK, SNO, OMNIS + grav.waves: potential for ~1eV sensitivity? astrophysics: supernova time of flight measurements ? 3H3H 187 Re β decay kinematics: - Microcalorimeters - MAC-E spectrometers e < 2eV

β-decay u d d u d u n p W-W- e-e- veve q = 2/3 - 1/3 -1/3 = 0 q = 2/3 + 2/3 -1/3 = 1 Total kinetic energy Q ≈ maximal kinetic energy of electron

Tritium β-Decay: Mainz/Troitsk E 0 = 18.6 keV dN/dE = K × F(E,Z) × p × E tot × (E 0 -E e ) × [ (E 0 -E e ) 2 – m 2 ] 1/2

Problem: All experiments measured negative Δm 2 ! electrostatic spectrometers with MAC-E filter Only recently solved by electrostatic spectrometers with MAC-E filter

principle of an electrostatic filter with magnetic adiabatic collimation (MAC-E) adiabatic magnetic guiding of  ´s along field lines in stray B-field of s.c. solenoids: B max = 6 T B min = 3×10 -4 T energy analysis by static retarding E-field with varying strength: high pass filter with integral  transmission for E>qU

results from the MAINZ experiment Mainz Data (1998,1999,2001)

KATRIN ~70 m beamline, 40 s.c. solenoids The KArlsruhe TRItium Neutrino Experiment

KATRIN Main Spectrometer  stainless steel vessel (Ø=10m & l=22m) on HV potential  minimisation of bg  UHV: p ≤ mbar  „massless“ inner electrode system UHV requirements: outgassing < mbar l/s inner surface ~ 800m 2 volume to pump ~ 1500m 3 Ziel: Commissioning 2008

187 Re  -decay:  -calorimeters MIBETA experiment (Milano, Como, Trento) array of 10 AgReO 4 crystals M.Sisti et al, NIM A520(2004)125 A.Nucciotti et al, NIM A520(2004)148 C. Arnaboldi et al, PRL 91, (2003) E 0 = 2.46 keV T op ~ mK

free fit parameters:   endpoint energy  m 2   spectrum normal.  pile-up amplitude  background level 187 Re  decay  -calorimeters Kurie plot of 6.2 × Re  decay events above 700 eV fit range: 0.9 to 4 keV fit function m 2 = -112 ± 207 ± 90 eV 2 m < 15 eV (90%CL) (2 eV in 2007?) dN/dE = K × F(E,Z) × p × E tot × (E 0 -E e ) × [ (E 0 -E e ) 2 – m 2 ] 1/2

Double-beta decay 2 -  decay u e - d d e - W u e e W 0 -  decay e - e - d d u u W W e e Lepton number violation ΔL = 2 Lepton number violation ΔL = 2 Summenenergie der Elektronen (E/Q)

Neutrinoless Double Beta Decay d d u u e eW W n n p p v = v 0v Double Beta Decay: (A,Z)  (A,Z+2) + 2e - neutrino  anti-neutrino Majorana-neutrino: only for Majorana-neutrino and m V > 0!

Neutrinoless Double Beta Decay Effective neutrino mass in 0νββ-decay: Compare to β-decay: Phase space factor Transition matrix element Effective neutrino mass

Dirac CP-Phase Majorana CP-Phases Complex phases in the mixing matrix Cancellation possible!

in eV Masse des leichtesten Neutrinos in eV normale Hierarchie invertierte Hierarchie

0v Doppel-Beta Experimente: Ergebnisse Heidelberg-Moskau Collaboration, Eur.Phys.J. A12 (2001) 147 IGEX Collaboration, hep-ex/ , Phys. Rev. C59 (1999) × – 2.1 all 90%CL HM-K IGEX

Jedoch: ein Teil der HdM Kollaboration veröffentlicht Evidenz für 0v Doppel-Beta Zerfall! (Q = 2039 keV für 76 Ge Doppel-Beta Zerfall) ?

Zukunft: Heidelberg Ge Initiative (MPIK Heidelberg) Phase I: 20kg angereichertes (86%) 76 Ge, vgl. HDM Phase II: 100 kgJahre, 0.1 – 0.3 eV Phase III: O(1t) angereichertes 76 Ge, 10meV

CUORICINO 11 modules, 4 detector each, crystal dimension 5x5x5 cm 3 crystal mass 790 g 4 x 11 x 0.79 = kg of TeO 2 2 modules, 9 detector each, crystal dimension 3x3x6 cm 3 crystal mass 330 g 9 x 2 x 0.33 = 5.94 kg of TeO 2 2v Doppelbeta mit 130 Te (Q=2529 keV) 18 crystals 3x3x6 cm crystals 5x5x5 cm kg of TeO 2 Start in 2003 Suche nach 0v Doppelbeta: T 1/2 0v ( 130 Te) > 7.5 x y < eV 2v Doppelbeta mit 130 Te (Q=2529 keV) 18 crystals 3x3x6 cm crystals 5x5x5 cm kg of TeO 2 Start in 2003 Suche nach 0v Doppelbeta: T 1/2 0v ( 130 Te) > 7.5 x y < eV

array of 988 bolometers grouped in 19 colums with 13 flours of 4 crystals 750 kg TeO 2 => 600 kg Te = 203 kg 130 Te IL PROGETTO CUORE

3 m 4 m B (25 G) 20 sectors Source : 10 kg of  isotopes cylindrical, S = 20 m 2, e ~ 60 mg/cm 2 Tracking detector : drift wire chamber operating in Geiger mode (6180 cells) Gas: He + 4% ethyl alcohol + 1% Ar + 0.1% H 2 O Calorimeter : 1940 plastic scintillators coupled to low radioactivity PMTs Magnetic field: 25 Gauss Gamma shield: Pure Iron (e = 18 cm) Neutron shield: 30 cm water (ext. wall) 40 cm wood (top and bottom) (since march 2004: water  boron) Able to identify e , e ,  and  The NEMO3 detector Fréjus Underground Laboratory : 4800 m.w.e.

Drift distance 100 Mo foil Transverse view Longitudinal view Run Number: 2040 Event Number: 9732 Date: Geiger plasma longitudinal propagation Scintillator + PMT Deposited energy: E 1 +E 2 = 2088 keV Internal hypothesis: (  t) mes –(  t) theo = 0.22 ns Common vertex: (  vertex)  = 2.1 mm Vertex emission (  vertex) // = 5.7 mm Vertex emission Transverse view Longitudinal view Run Number: 2040 Event Number: 9732 Date: Criteria to select  events: 2 tracks with charge < 0 2 PMT, each > 200 keV PMT-Track association Common vertex Internal hypothesis (external event rejection) No other isolated PMT (  rejection) No delayed track ( 214 Bi rejection)  events selection in NEMO-3 Typical  2 event observed from 100 Mo

100 Mo kg Q  = 3034 keV  decay isotopes in NEMO-3 detector 82 Se kg Q  = 2995 keV 116 Cd 405 g Q  = 2805 keV 96 Zr 9.4 g Q  = 3350 keV 150 Nd 37.0 g Q  = 3367 keV Cu 621 g 48 Ca 7.0 g Q  = 4272 keV nat Te 491 g 130 Te 454 g Q  = 2529 keV  measurement External bkg measurement  search (All the enriched isotopes produced in Russia)

100 Mo  likelihood analysis Ec 1 +Ec 2 (keV) Data  Monte-Carlo Radon Monte-Carlo 100 Mo 6914 g days 4.10 kg.y PRELIMINARY Xavier Sarazin for the NEMO-3 Collaboration Neutrino 2004 Paris June 2004 Data  Monte-Carlo Radon Monte-Carlo  T 1/2 = Mo 6914 g days 4.10 kg.y Ec 1 +Ec 2 (keV) Previous limit V-A: T 1/2 (  ) > y (Elegant V, Ejiri et al., 2001) V-A: T 1/2 (  ) > y (90% C.L.) -Log(Likelihood) x   N  N tot ee < 0.7 – 1.2 eV

Double Beta Decay: Future to t13

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