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Shell Model Calculations for Neutrinoless Double Beta Decay

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Shell Model Calculations for Neutrinoless Double Beta Decay

Sabin Stoica

Horia Hulubei Foundation &

Horia Hulubei National Institute of Physics and Nuclear Engineering

S. Stoica Ischia, May 12-16, 2014

Outline

Introduction: DBD, decay modes, motivation for the study of the neutrinoless double beta decay mode

Th. Challenge: calculation of the nuclear matrix elements

Shell model calculations of the NMEs neutrinoless DBD:

new ShM code, results, discussions

Conclusions

S. Stoica Ischia, May 12-16, 2014

Introduction: Double Beta Decay (DBD)

DBD is a nuclear natural decay by which an e-e nucleus transforms into another e-e nucleus with the same mass but with its nuclear charge changed by two units. It occurs whatever single decay can not occur due to energy reasons or if it is highly forbidden by angular momentum selection rules

(a) and (d) are stable against decay,

but unstable against decay: - -

for (a) and ++ for (d)

35 isotopes decay -- and 6 decay ++

S. Stoica Ischia, May 12-16, 2014

S. Stoica Ischia, May 12-16, 2014

The great interest on 0νββ decay is mainly related to the understanding of the neutrino properties, since neutrino plays a key role in nuclear and particle physics, astrophysics and cosmology.

The interest was also enhanced by the results of the neutrino oscillation experiments that have convincingly showed that neutrinos have mass and oscillate, in contradiction with the initial formulation of the Standard Model (SM).

However, fundamental properties of the neutrinos as their absolute mass, character (are they Dirac or Majorana particles?), mass hierarchy, number of neutrino flavours, etc., are still unknown and their knowledge is of fundamental importance, in understanding, for example, the formation, the structure and the evolution of the Universe and of some of the conservation symmetries in nature.

In this context the neutrinoless DBD mode plays an important role, because it can probe the neutrinos character (Dirac or Majorana) and may give a hint about their absolute mass.

Moreover, information provided by the study of neutrinoless DBD can now be corroborated with information provided by the searching of LNV processes at high energy, particularly at LHC, in order to better constraint neutrino parameters.

S. Stoica Ischia, May 12-16, 2014

ISM– iswell suited todo calculations for DBD. Itincorporates all

types of correlations and uses effective NN interactions which are

checked with other spectroscopic calculations for the nuclei from the

same mass region, the obtained states have the correct no. of p and n

However, for most nuclei the valence spaces do not include enough states; it

faces the problem with large model spaces and associated

computational resources

Issues: i) GT operator needs to be quenched in the case of 2ββ calculations.

Question: should it be quenched as well, for 0ββ calculations?

ii) contribution of higher order nuclear currents: a reduction of 20-30%

Question: how much is this contribution for larger model spaces? Is

this reduction amplified by the equivalent effective operator?

Investigations of these issues imply calculations in increasingly larger model

spaces (for example using 8 major HO shells or more)

improved (fast, efficient) ShM codes which reduce substantially

the computing time of calculation of the TBME of the transition

operators for 0ββ decay

S. Stoica Ischia, May 12-16, 2014

Calculation of the nuclear matrix elements

Horoi, Stoica, PRC81, 024321 (2010)

Neacsu, Stoica, Horoi, PRC 86, 067304 (2012), Neacsu, Stoica, JPG 41, 015201 (2014)

Fast numerical code for computing the TBME

S. Stoica Ischia, May 12-16, 2014

This procedure reduces substantially the CPU time: ~ with a factor of 30 as compared with our older ShM code from ref. PRC81 (2010)

The computing time depends on the n, l quantum numbers of the nucleon orbits

S. Stoica Ischia, May 12-16, 2014

Study of the effect of different nuclear ingredients on NMEs

- their overall effect is to decrease the NME values
- SRC inclusion: J-MS prescription decreases significantly the NME value as compared with softer CCM prescriptions.
- however, NME values calculated with inclusion of only SRC by J-MS prescription, are close (within 10%) to the values calculated with SRC by CCM prescriptions and with the inclusion of other nuclear ingredients (FNS+HOC) a kind a compensation effect
- inclusion of HOC is important correction up to ~ 20%
- tensor component: contribution of (4-9)% (has to be taken with correct sign)
- dependence of NN interactions: up to 17%
- dependence on input nuclear parameters:
- gA quenched/unquenched – (10-14)%; R = r0A1/3 (r0=1.1fm or 1.2fm) ~ 7%
- (A, V) ~ 8%;
- average energy used in closer approx. <E> - negligible

S. Stoica Ischia, May 12-16, 2014

Stoica, Neacsu, arXiv:1405.0517(accepted by AHEP)

S. Stoica Ischia, May 12-16, 2014

Conclusions

- DBD, particularly 0ββ decay mode, continues to be a very interesting nuclear decay process due to the information that it can provide on the neutrino properties and LN conservation
- Challenge: calculation of the NMEs involved
- ShM codes represent a powerful tool for computing NMEs for the DBD. One needs faster computer codes in order to perform calculations in larger model spaces. I presented such a code that reduces substantially the computing time by reducing the computation of the TBMEs to one type of integral (over momentum)
- Systematic study of the effect of nuclear ingredients and input parameters involved in 0ββdecay calculations. One needs a consensus on their use in order to understand and reduce the uncertainties.
- Precise NME and PSF calculations corroborated with the progress in measuring the 0νββ lifetimes, need periodically up-dates of the constraints on neutrino mass parameters
- New opportunity: the searching of LNV processes at LHC; possibility to use information both from low&high energy experiments, to complete our understanding on the neutrino properties.

S. Stoica Ischia, May 12-16, 2014

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