-Nucleus Interactions

Double-beta Decay and

Cristina VOLPEInstitut de Physique Nucléaire Orsay, France

2b-Decay: Status andFuture

PLAN

Intense -sources

-Nucleus: Link to 2-decay

Conclusions and Pespectives

: Majorana or Dirac particles?

Dirac Majorana

=

?

How do we search for the -nature?

Beyond the Standard Model(e.g. exchange of massive Majorana neutrinos)

20: 2n 2p + 2e-

Lepton-violating process

22: 2n 2p + 2e- + 2e

20: 2n 2p + 2e-

Within the Standard Model(V-A theory)

76Ge

76As

76Se(0)

Haxton and Stevenson, Prog. Part. Nucl. Phys., 1984; Suhonen and Civitarese, Phys. Rep., 1998;Faessler and Simkovic, J. Phys. G, 1998; Elliott and Vogel, Ann. Rev. Nucl. Part. Sci. 2002; H.Ejiri, Phys. Rep.; Elliott and Engel, J. Phys. G, 2004;….

Klapdor et al., 2001

> 1.9 1025 y (90% C.L.)< m> < 0.3 – 1.0 eV

20: 2n 2p + 2e-

The present best limit(Heidelberg-Moscow,IGEX).

T0

2/1

76Ge76As

76Se(0)

The experimental search

22: 2n 2p + 2e- + 2e

Observed in various nuclei:48Ca, 76Ge, 82Se, 96Zr, 100Mo, 116Cd, 128Te, 130Te, 136Xe, 150Nd.

The half-lives vary in the range:T1/2(150Nd) = 4.2 1019 y toT1/2(128Te) = 7.2 1024 y

A RECENT CLAIM forEVIDENCE by KLAPDOR et al., PLB (2004).

Present and FutureThe only presently running experiment is NEMO3 (Modane, France).

T1/2 = 7.3 ±0.0025(stat)±0.7(syst) 1018 y

100Mo

CUORE and GERDA will confirm or refute Klapdor’s claim.

A large number of experiments (Majorana, MOON, COBRA, XMASS, SuperNEMO, etc…) are now under investigation. The aim is to reach about 50meV sensitivity.

Theoretical Aspects

: phase space factorM : nuclear matrix elements<m> : effective neutrino mass

T0

2/1 ( ) M2 <m>2Q5

1=

This has important implications: e.g. _ it translates in an uncertainty on the -mass; _ it can prevent getting the hierarchy; _ it renders difficult to choose the best candidate.

REDUCING THE UNCERTAINTIES: A MAJOR CHALLENGE.

Several efforts to understand the sensitivity of the calculations(e.g. interaction, spaces) and to better constrain the predictions.

Theoretical predictions (mainly performed within Shell Model and QRPA) exhibit significant variations of the neutrinoless double-beta decay half-lives for the same candidate emitter.

ex: Rodin, Faessler, Simkovic, Vogel, PRC68 (2003).

The 2(2) T1/2 22: 2n 2p + 2e- + 2e

GAMOW-TELLER STATES CONTRIBUTE.

Using second-order perturbation theory and

j(H) 1.,

The 2 half-life 20: 2n 2p + 2e-

76Ge

Bobyk,Kaminski,Simkovic,PRC2001

MANY STATES ARE INVOLVED.

Exchange of a massive Majorana neutrino

e-

e-

n

n

p

p

Little experimental information on such states.

Several processes have been considered to constrain the nuclear matrix elements, in particular beta-decay, muon capture, 2(2), charge-exchange reactions.

48Ti48Ca

48Sc

(0)

Constraints

ee

C.Volpe, hep-ph/0501233.What about using neutrino-nucleus interactions ?

: only a few energy levelsMuto,Bender,Klapdor, Z.Phys.A 1989; Aunola, Suhonen, 1996; Civitarese, Suhonen; …

charge-exchange reactions : a very good tool, high resolutionBernabeu et al., 1988; Akimune et al., 1997; Ejiri, Phys. Rep.; S. Rakers et al, PRC 2004; …

capture : states up to 100 MeV, only one branchKortelainen and Suhonen, Europhys. Lett. 2002; Phys. Atom. 2004.

: only 1+ (GT) statesMuto, Bender, Klapdor, 1993; Faessler et al., 1987; Rodin et al. PRC 2003; …

Neutrinoless Double-beta Decay e-

e-

n

n

p

p

Using second-order perturbation theory, the matrix elementsinvolved in the half-lives are of the type :

j(H) 1.,

The excited states are called isospin (Fermi)and spin-isospin modes (Gamow-Teller).

f|O12|i>= <f|1 x 2 V(|r1-r2|)|i> where O12 is a two-body operator and V(|r1-r2|) is the neutrino propagator which describes the exchange of the neutrino between the two decay vertices («neutrino potential»).

By making a multipole expansion of the neutrino potential :

V(|r1-r2|)~dqq2v(q)[jL(qr1)YL(r1)][jL(qr2)YL(r2)]

and inserting a number of intermediate states :

m<f| jL(qr1)YL(r1)]1.1|m><m|[jL(qr2)YL(r2)]2.|i>

2+

48Ti

48Ca

48Sc(0)

1-

1+

3-

-Nucleus : a new constraint for 2(0)? C.Volpe, hep-ph/0501233.

The effective V-A interaction Hamiltonian :

The nuclear transition probabilities are the key quantities :

THE SAME STATES AS IN (0) 2 ARE EXCITED.

Applying the Foldy-Wouthuysen transformation and using perturbation theory :

-Nucleus Interactions C

N

ee

C.Volpe, hep-ph/0501233.

e + 48Ca 48Sc + e-

<E >=60 MeV

An example

48Ti

48Ca

48Sc(0)

e 1-

1+2+

3-

e

Results of a microscopic calculation(QRPA).

C.Volpe, hep-ph/0501233.

<E >=30 MeV

e + 48Ca 48Sc + e-

e + 48Ti 48Sc + e+

<E >=60 MeV

An example

48Ti

48Ca

48Sc(0)

e 1-

1+2+

3-

e

Results of a microscopic calculation(QRPA).

C.Volpe, hep-ph/0501233.

THESE STUDIES COULD GIVE A SUPPLEMENTARY CONSTRAIN TO 2(0) DECAY PREDICTIONS.

<E >=30 MeV

e + 48Ti 48Sc + e+

Future intense -sources :conventional & low-energy beta-beams.

INTENSE -SOURCES

Neutrino beams can be produced with:

ee

SnS, Oak Ridge (USA), JHP (Japan),Multi-MW proton driver (Europe)

THE BETA-BEAM CONCEPT:

Zucchelli, PLB 2002

Lorentz boost

1/high

Low-Energy BETA-BEAMS

6He 6He

CONVENTIONAL METHODS:

6He 6Li + e- + e

Pure neutrino beams produced by boostingions which decay through beta-decay.

H.Ejiri NIMA, 503, 278(2003).

THE PROPOSAL

C. Volpe, Journ. Phys. G. 30 (2004), hep-ph/0303222.

Neutrino properties, like the magnetic moment.

Low-energy Beta-beams

To exploit the beta-beam concept to produce intense and pure low energy neutrino beams.

A BETA-BEAM FACILITY FOR LOW ENERGY NEUTRINOS.

PHYSICS POTENTIAL

Neutrino-nucleus interaction studies.

boost

6He 6He

6He

…

closedetector

PS

SPS

EURISOL

Beta-beam baseline at CERN

Storage Ring

…or at one of the laboratories that willproduce intense radioactive beams inthe future (need of ion acceleration toGeV energy and of a storage ring).

Neutrino-nucleus measurements

TWO POSSIBLE SCENARIOS.

d

length of thestraight sections

L total length

Two options studied :- Large ring- Small Ring

Serreau and Volpe, hep-ph/0403293, PRC70 (2004).

POSSIBLE SITES

-Nucleus Interaction Rates

INTERESTING INTERACTION RATES CAN BE OBTAINED.

Neutrino Fluxes

<E~2Q/2The unique feature that the -energy can be easily varied.

Serreau and Volpe, hep-ph/0403293, PRC70 (2004).

Small Ring : d = 150 m, L= 450m Large Ring :d = 2.5 km, L =7.5 km

Small Ring Large Ring

25779 1956e + D

e + DEventsper year

1942494

m=35 tons

1802363

Conclusions and Perspectives

The search for the neutrinoless double-beta decay is crucial. Future experiments will reach the tensof meV sensitivity.

Conventional sources and low-energy beta-beams could offer theopportunity to perform such studies.

Neutrino-nucleus interactions : a new constraintfor the calculation of the half-lives.

Constraining the theoretical predictions represents a major challenge.