Excited State Transitions in Double Beta Decay : A brief Review

Neutrinoless double beta decays requires lepton number violation and provide an important probe for physics beyond the Standard Model. Nuclear matrix elements (NME) are needed to connect the half-life of the decay with the neutrino mass. The calculation of these NME depends on nuclear models and is subject to large uncertainties. 0νββ and 2νββ decays can also occur into excited states. Especially the 2νββ excited state transitions are accessible in current experiments and together with the ground state transitions provide an important cross check for nuclear model calculations. This contribution will present the current experimental status of excited state transitions in double beta decay isotopes.


Introduction
Double beta decays are second order weak nuclear decays.Their observation is only feasible in nuclear configurations where two consecutive single beta decays are energetically forbidden or otherwise strongly suppressed.The two-neutrino double beta (2νββ) decay is a Standard Model process which has been observed in 13 isotopes with half-lives around 10 18−21 yr.The neutrino-less double beta (0νββ) decay is lepton number violating (LNV) and requires massive neutrino mass eigenstates and the Majorana nature of neutrinos: The experimental signature is the energy of two e − which show a continues spectrum up to the Q-value for the 2νββ mode and a discrete electron sum energy in case of the 0νββ mode.The 0νββ decay has not been observed and the calculation of the half-life requires two model dependent assumptions: (1) the LNV process and (2) a nuclear model describing the nuclear matrix element (NME).The standard interpretation of (1) is the light Majorana neutrino exchange.In this interpretation, T 0ν 1/2 is proportional to the square of the inverse Majorana neutrino mass |m ee | −2 .Instead, the calculation of the 2νββ half-life requires only the knowledge of the NME: Here, G 2/0ν is the phase space factor (PSF) and M 2/0ν the NME of the decay mode.The calculation of the PSF is relatively straight forward.As a leading term approximation, a e-mail: bjoern.lehnert@tu-dresden.de G 2ν is proportional to E 11 whereas G 0ν is proportional to E 5 .Current calculations considering nuclear and atomic corrections are performed e.g. in [1].states.Typically, the first excited state in the daughter is a 2 + state.Excited 0 + states cannot directly decay into the 0 + g.s. and cascade via the 2 + state while emitting two gammas.This is illustrated for the case of 76 Ge in Fig. 1.The properties of the most prominent DBD isotopes are listed in Tab. 1 showing the Q-value, the excitation level of 0 + 1 as well as the most prominent γ-lines for experimental searches.

Experimental Considerations
A number of past review articles contain experimental and theoretical data on excited state transitions.A complete list up to 2002 is published in [15]  state results up to 2007 is published in [16].A combination of half-lifes from multiple measurements of the same isotope up to 2010 is presented in [17].A few new experimental results were achieved since then and will be briefly described here.
The experimental search for DBD excited state transitions can be distinguished into two approaches: (1) with gamma spectroscopy of a DBD target using HPGe detectors or (2) as secondary analysis in large scale 0νββ decay experiments.
The first approach is a dedicated search for de-excitation γ-lines and cannot distinguish between the 2νββ and the 0νββ mode Recently, first limits in 110 Pd were obtained with gamma spectroscopy.A 0.8 kg palladium sample was investigated in the Felsenkeller low-level underground laboratory in Dresden, Germany [20] and in the HADES underground facility of IRMM Mol, Belgium [21].The best half-life limit was found to be > 2.0 • 10 20 yr (95 % C.L.).
The second approach profits from the low background infrastructure and large target materials in 0νββ experiments.Many of these experiments are segmented in individual detectors and use anti-coincidence vetoes between these segments to distinguish background from 0νββ events; the electrons of a 0νββ decay deposit their energy in a small volume whereas γ-background often results in distributed energy depositions due to scattering.The anti-coincidence vetoes for 0νββ can be used searching for coincides between ββ and γ energies of excited state transitions.In homogeneous DBD experiments as e.g.LXe in EXO-200 or NEXT, pulse shapes can be used to distinguish between single-site and multi-site energy depositions.New experimental results are available using current 0νββ experiments: CUORICINO uses 11.3 kg TeO 2 in 62 bolometer crystals at LNGS and found a new best limit for 2νββ 0 + 1 in 130 Te as T1 /2 >1.3•10 23 yr (90% CL) [22].CUORICINO is a prototype tower of the CUORE detector which will have 19 similar towers with a target mass of 204 kg 130 Te and a total segmentation of 988.CUORE will be able to strongly improve the sensitivity for this decay mode in the near future.Another recent results comes from the EXO-200 experiment investigating 136 Xe with a LXe TPC in the WIPP near Carlsbad, New Mexico.A large fiducial target mass of 80 kg enriched LXe is achieved; however, nonsegmentation and poor energy resolution increase the difficulty to identify the excited state event topologies.A pulse shape quantifier is used to investigate multi-site events.A fit is performed over a wide energy range resulting in a new best limit for 2νββ 0 + 1 in 136 Xe of T1 /2 >1.2•10 23 yr (90% CL) is obtained [23].

Theoretical Considerations
The half-life for excited state transitions can be calculated directly via Eq. 3. Various direct calculations have been performed in the past which are, however, largely older than 10 years.An alternative is to use the ratio of NMEs and PSFs for the 0 + 1 and 0 + g.s.transition and scale that ratio with the 0 + g.s.half-life: The ratio of NMEs has the advantage than some theoretical uncertainty cancel out and the excited state half-life prediction becomes more reliable.This approach can be used with a systematical and intra-comparable calculation of NMEs as is e.g.performed with IBM-2 model [24].Tab. 2 shows the experimental half-lives and half-life limits for the 2νββ 0 + g.s. and 0 + 1 transitions for prominent DBD isotopes.The third and fourth column show a list of direct calculations for 0 + 1 using QRPA.The prediction in the last column is calculated using the ration in Eq. 5 with NMEs from [24], PSFs from [1] and T g.s.
1/2 from column 2. The theoretical predictions from QRPA and IBM-2 often disagree strongly.The tendency is that IBM-2 predicts longer half-lives.Many of the older QRPA predictions Table 2. Current data for excited state transitions.Shown are observed half-lives or half-life limits of the ground state and 0 + 1 transitions.The last three columns show theoretical predictions: two direct calculations from QRPA and a calculated half-life ratio between 0 + 1 and 0 + g.s.scaled with the measured 0 + g.s.half-life as described in the text.a world average values b corrected in [38] are ruled out by recent experimental limit.Most IBM-2 predictions are still below the current experimental sensitivity.However, it is particular interesting to look at the two cases of 100 Mo and 150 Nd in which the experimental 0 + g.s. and 0 + 1 half-life values can be directly compared to the models.The IBM-2 half-lives as discussed above do not describe the experimental observation.In fact the prediction is a factor of 37 ( 100 Mo) and 14 ( 150 Nd) larger than the observed half-life.A recent idea to explain this deficiency are intermediate scissor states.Those could potentially increase the rate of 0 + 1 over 0 + g.s.transition as shown for 154 Gd [25].Further conclusions are expected soon also for 150 Nd.

Conclusion
After the observation of many 2νββ ground state transitions with half-life between 10 18−21 yr, 2νββ 0 + 1 transitions have been observed in 100 Mo and 150 Nd with T1 /2 = (7.5 ± 1.2) • 10 20 yr and T1 /2 = (1.33 +0.63  −0.36 ) • 10 20 yr respectively.The discovery of 0 + 1 transitions in more isotopes is around the corner with the current generation of 0νββ experiments.In the near future excited state transitions will help to validate and tune NME calculations for 0νββ.

Figure 1 .
Figure 1.Decay scheme of 76 Ge serving as an example for a typical configuration of double beta decays into excited states.

Table 1 .
. A collection of excited DOI: 10.1051/ C Owned by the authors, published by EDP Sciences, 2015 Excited state structure in important DBD isotopes.The columns denote: nuclide and transition, Q-value of the decay, energy level of first excited 0 + state and the observable γ-lines in the experimental signature.γ-lines are ordered as 0 + 1 − 2 + 1 , 2 + 1 − 0 + g.s.transition.For 130 Te there are multiple decay branches going via two 2 + states.The branches are ordered with decreasing probability.All information from [2] if not otherwise noted.