Endpoint spectra of tritium and rhenium beta decays for massive neutrinos

Rastislav DvornickýDepartment of Nuclear Physics & Biophysics

Comenius University, Bratislava Slovakia

supervisor - Fedor Šimkovic

14-th Lomonosov conference on Elementary Particle Physics

NeutrinoNeutrino was suggested in y. 1930 by Pauli to explain the continuity of β

spectrum as a spin 1/2 particle obeying Fermi-Dirac statistics

I have done aterrible thingI invented a particle thatcannot bedetectedW. Pauli

Tübingen

Neutrino oscillations

Pontecorvo-Maki-Nakagawa-Sakata

matrix

Flavoreigenstates

Masseigenstates

oscillations ⇒ massive neutrinos

Zh.Eksp.Teor.Fiz.,32(1957)

Maki,Nakagawa,Sakata.Prog.Theor.Phys.28(1962)870

)4

(sin2sin)(2

22

EtmP e

Δ=→ ϑνν μ

0νββ-decay

Absolute mass scale of neutrinos ?

3H decay

Cosmology

Solar neutrinos

Atmospheric neutrinos

1998SuperKamiokande

1968Homestake

We need 3 mass eigenstatesTo explain 2 different Δm2

m22-m1

2=Δmsol2≈ 3.10-5 eV2

m32-m2

2=Δmatm2≈ 2.10-3 eV2

Double beta decay

Observed for 10 isotopes: 48Ca, 76Ge, 82Se, 96Zr,100Mo.116Cd. 128Te, 130Te, 150Nd, 238U, T1/2 ≈1018-1024 years

Enrico Fermi1934

..)()()1()(2 5 chxjxxeG

H e +−= μμβ

β νγγ

Maria GöppertMayer 1935

eeAZAZ ν~22),(),2( ++→− −

0νββ decay

−+→− eAZAZ 2),(),2(

20 m≈Γ νββ 3

232

221

21

3121 meUmeUmUm ie

iee

αα ++=

2=ΔL

neutrino origin

Tritium – 3H

1. low endpoint – Q=18.6 keV2. super-allowed nuclear transition

(spectrum shape)3. short half-live T1/2 = 12.32 y4. simple molecular structure

KATRIN experiment

KArlsruheTRItiumNeutrinoexperiment

Direct measurementof neutrino mass

Measuring last300 eV of endpoint

2010 – startdata taking

Weinheimer, Nucl.Phys.Proc.Suppl. 168,5(2007)

Tritium beta decay

ν~33 ++→ −eHeH

22222GTAFV MgMgM +=

Q=18.6 keV

Differentialspectrum

Kurie plot

Both – Fermi &Gamow-Tellertransitions (T1/2=12.32 y)

Tritium beta decay

ν~++→ −epn

ν~33 ++→ −eHeH

++ → 2/12/1

( )[ ]2222max

21

νmMmMM

E feif

e −−+= νmMME fie −−≅max

Spin – isospin propertiesare identical

Elementary particle treatment (Kim & Primakoff, Phys.Rev. 139, B 1447(1965))

Exact relativistic treatment of tritium β decay. Recoil effect taken into account (3.4 eV less than standard Q value)

Nucleus as elementary particle

Beta decay on free nucleons.Relativistic calculation.No nuclear matrix elements.

Šimkovic, Dvornický, Faessler:Phys. Rev. C77,055502(2008)

Approximation withkeeping dominant terms

Relativistic Kurie plot

22

33

2AV

udFT ggVGB +=

π

( ) 2/1)()2()( νν mymyyByK T ++=

Tritium beta decay

247.132.12exp2/1 =⇒= AgyT

Rhenium beta decay

1. the lowest known Q value 2.47 keV2. T1/2= 4.35 x 1010 y ~ age of universe3. natural abundance 187Re is 63%

MARE experiment

-we don’t bother with energy loses-no corrections for atomic or molecular structure

MicrocalorimeterArrays for aRhenium Experiment

Re-187

Os−187

ßi,

calorimetersource=detector

T1/2=4.35 × 1010 y - low radioactivitycalorimetersource=detector

Rhenium beta decay

Δ Jπ = 2- first unique transition187Re →187Os+e-+νe

5/2+→1/2- higher partial waves of leptons

whole spectrum is measured

Rhenium beta decay

p-waves have to be taken into account Δ Jπ = 2- =>

..)()()1()(2 5 chxjxxG

H e +−= μνμβ

β ψγγψ

)().1()( kvrkix +=νψ

⎟⎠⎞

⎜⎝⎛ +−−= )..

31.(),()ˆ.

21(),()()( 1

00 rprpEZFirZiEZFpuxe γγγγαψ

plane wave expansion - rkie .

s wave p wave

s1/2 wave p1/2 wave p3/2 wave

Rhenium beta decay

Δ Jπ = 2- => leptons have to take

Amplitude = e (s1/2) & ν(p) + e(p3/2) & ν(s)

2/11 − + 2/11 +

Δ L = 2

e (p1/2) & ν(p) => no change of parity

( )),(),(31

02

122 EZFkEZFpR +×

2200

23

22

)()(2 νπ

mEEEEpEMVGdEd udF −−−=Γ

Rhenium beta decay

first unique transition

for allowed trans. only F0 survives = s waves of both leptons

2

1872

1872

2 Re||)(3

4||12

>⊗<+

= ∑ +

nnn

nn

i

A YRrOs

JgM στπ

Rhenium beta decayelectron kinetic energy spectrum normalized to unity

0523.0||)(3

4||10*35.4 210

2/1 =>⊗<⇒= ∑n

innn

f JYRrJyT σπ

Rhenium beta decay

2200

223

22

)()(6 νπ

mEEEEpERMVGdEd udF −−−=Γ ( )),(),( 0

21

2 EZFkEZFp +

dEd

dEd

dEd SP Γ

+Γ

=Γ 410027.1/ −×=ΓΓ PS

electron P wave is dominant => important

Rhenium beta decay

plane wave limit => neglecting the Coulomb interaction 1),(

1),(

1

0

→→

EZFEZF

keVk 47.2max = keVp 50max ≅

kinematics is enhancing the P wave

Rhenium beta decay

νmQTe −=maxQ - highest electron kinetic energyto obtain in case of zero neutrino mass

S and P wave contributions near the endpoint

maxee TTY −=

Rhenium beta decay

- negligible

The goal is that we can define (similar as for tritium)

- almost constant due to small Q value in comparison with me

220

2 )( νmEEk e −−=

),(),(

0

12

e

e

EZFEZFp

Rhenium beta decay

Kurie plot properly scaled is the same for 3H & 187Re

42

0

2

0Re )(1)(/)(

eee EE

mEEBEK−

−−≅ ν

ee EEy −= max Arnaboldi, PRL 96, 042503 (2006)

experimenttheory

Conclusions

• Exact relativistic treatment of 3H beta decay including recoil

• Dominance of P wave of electron in 187Re first unique decay

• Linearity of Kurie plot in 187Re decay under discussion with Milano group