Double beta decay and neutrino physics Osaka University M. Nomachi

Outline Weak interaction and neutrino property Exercise: Helicity Exercise: parity violation Neutrino mass Exercise: Seesaw mechanism Neutrino oscillation Exercise; Neutrino oscillation Oscillation experiments Neutrino mass measurement Beta decay Exercise: Beta ray energy spectrum Double beat decay

Beta decay In the modern view Weak interaction

Neutrino Lepton Spin ½ No charge Three generations Mass ??

Helicity spin Helicity = +1 Helicity = -1 spin Helicity = +1 Helicity is not Lorentz invariant

Free Dirac equation are 4x4 matrix Special relativity

Pseudo Scalar operator Chirality operator Diagonal representation In usual representation, βis diagonal

The solution of the Dirac equation is Helicity operator and its eigen states

Is zero for mass-less particle Helicity eigenstate = chirality eigenstate for mass-less particle Wrong helicity Chirality +1: Right handed -1: Left handed

Weak interaction Weak current Projection operator of negative (left handed) chirality In Weak interaction Electron and neutrino are always left handed While Positron and anti-neutrino are always right handed

Parity violation In Weak interaction Electron and neutrino are always left handed While Positron and anti-neutrino are always right handed mirror spin electron anti-neutrino We can know which is our world!

Beta decay of 60 Co ZZ Electron and anti-neutron spin Z electron Electron should be left handed Electron must have

Angular distribution ZZ For angular momentum conservation, spin must be down. Angular distribution will be Rotation of spin 1/2

Dirac particle and Majorana particle Dirac particle –Particle and anti-particle can be distinguished Majorana particle –Particle and anti-particle can not be distinguished

Mass Dirac mass Majorana mass Charge conjugate Charged particle cannot have Majorana mass.

Neutrino mass Neutrino may have both Dirac mass and Majorana mass. Dirac mass breaks chiral symmetry.

Mass eigenvalue

Seesaw mechanism Dirac mass will be the same order as the others. (0.1~10 GeV) Right handed Majorana mass will be at GUT scale GeV

Mixing and oscillation Time evolution Mixing

Mixing and oscillation Assuming Probability to be at t is

For small mass particle For non relativistic limit Mixing angle ⊿m2⊿m2

0.2 GeV fm or 0.2x10 -6 eV  m The value you have to remember

Atmospheric Neutrinos Figures from Prof. Y. Suzuki at TAUP 2005 Super Kamiokande DATA μ neutrino disappearance

Solar neutrino Nuclear fusion reaction in the sun is WEAK interaction. Electron neutrino disappearance

MNS matrix By Minakata

Δm 2 (atmospheric) Mass hierarchy Δm 2 (solar) m=0 Normal hierarchyInverted hierarchy Mass hierarchy is not derived from the oscillation measurements.

Beta ray spectrum The transition rate is the matrix element the density of final states Assuming plane wave

Phase space volume The number of state in momentum p in the volume V The transition rate will be

gives The transition rate will be Assuming neutrino mass is zero,

Because of the coulomb potential, the electron wave function is not plane wave. It causes the modification of the result Fermi-function consequently

Neutrino mass in beta decay The end point of beta-ray depends on neutrino mass.

Beta decay experiments KATRIN experiment 3 H beta decay, end point energy

Figure from

FINAL RESULTS FROM PHASE II OF THE MAINZ NEUTRINO MASS SEARCH IN TRITIUM BETA DECAY. Ch. Kraus et al.. Dec pp. Published in Eur.Phys.J.C40: ,2005 e-Print Archive: hep-ex/ Ch. Kraus et al.

Double beta decay

2) 0 neutrino double beta decay Neutrino has mass Neutrino is Majorana particle 1)2 neutrino double beta decay. d(n) u(p) W W e e ν ν T 1/2 (  ): ~ 1.15 x year d(n) u(p) W W e e ν ν T 1/2 (  ): > year Double beta decay

Lepton number non-conservation d(n) u(p) W W e e ν ν T 1/2 (  ): ~ 1.15 x year d(n) u(p) W W e e ν ν T 1/2 (  ): > year Lepton number 2 electron+2 2 anti neutrino-2 = Lepton number is conserved. (Baryon number is conserved.) Lepton number 2 electron+2 = Lepton number is NOT conserved. (Baryon number is conserved)

Mass measurement electron WW Mass term Probability of helicity flip (wrong helicity) is proportional to m.

Beta decay observable Double beta decay observable It should be larger than that of double beta decay measurements. It depends on the phase. Could be zero.

From NOON2004 summary by A. Yu. Smirnov νeνe νeνe 5meV 50meV Next generation experiments are aiming to explore 50meV region

Mass hierarchy 0.1 eV 10 meV

Double beta decay S.Elliott, Annu.Rev.Nucl.Part.Sci. 52, 115(2002) 100 Mo Background Natural radio activities Cosmogenic background 2 neutrino double beta decay

NEMO3

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 Hideaki OHSUMI for the NEMO-3 Collaboration APN04 Osaka July 2004 Trigger: 1 PMT > 150 keV 3 Geiger hits (2 neighbour layers + 1) Trigger rate = 7 Hz  events: 1 event every 1.5 minutes

(Data 14 Feb – 22 Mar. 2004) T 1/2 = 7.72  0.02 (stat)  0.54 (syst)  y 100 Mo 2  2 preliminary results 4.57 kg.y Cos(  ) Angular Distribution Background subtracted 2  2 Monte Carlo Data events 6914 g days S/B = 45.8 NEMO Mo E 1 + E 2 (keV) Sum Energy Spectrum events 6914 g days S/B = 45.8 NEMO Mo Data Background subtracted 2  2 Monte Carlo Hideaki OHSUMI for the NEMO-3 Collaboration APN04 Paris July 2004

 Analysis with 100 Mo V-A: T 1/2 (  ) > y V+A: T 1/2 > y with  E 1 - E 2  > 800 keV Majoron: T 1/2 > y with E single > 700 keV Hideaki OHSUMI for the NEMO-3 Collaboration APN04 Osaka July Mo     7.0 TOTAL Monte-Carlo 2.6<E 1 +E 2 < DATA 23.5  6.7 Radon M-C 32.3  Mo 2  2  M-C 100 Mo 6914 g 265 days Data  Monte-Carlo Radon Monte-Carlo E 1 +E 2 (MeV)  arbitrary unit PRELIMINARY 2.8<E 1 +E 2 <3. 2 Cu + nat Te Te 265 days Radon Monte-Carlo Data E 1 +E 2 (MeV) Cu + nat Te Te  3.4 ____ 2.6  ____ 2.6<E 1 +E 2 < <E 1 +E 2 <3. 2

MOON Osaka U., U. of Washington etc. 100 Mo + Plastic scintillator

CANDLES Osaka U. 48 Ca + CaF scintillator

Majorana Detector GOAL: Sensitive to effective Majorana mass near 50 meV 0  decay of 76 Ge potentially measured at 2039 keV Based on well known 76 Ge detector technology plus: –Pulse-shape analysis –Detector segmentation Requires: –Deep underground location –500 kg enriched 86% 76 Ge –many crystals, segmentation –Pulse shape discrimination –Time/Spatial Correlation –Special low-background materials n n p+p+ p+p+ e-e- e-e- e Reference Configuration

Homework Probability to have wrong helicity Beta ray angular distribution Seesaw mechanism Neutrino oscillation Beta ray energy spectrum