Bolometric Double Beta Decay Experiments: Review and Prospects

This review aims to cover the history and recent developments on cryogenic bolometers for neutrinoless double beta decay (0ν2β) searches. A 0ν2β decay observation would confirm the total lepton charge non-conservation, which is related to a global U(1)LC symmetry. This discovery would also provide essential information on neutrino masses and nature, opening the door to new physics beyond the Standard Model. The bolometric technology shows good prospects for future ton-scale experiments that aim to fully investigate the inverted ordering region of neutrino masses. The big advantage of bolometers is the high energy resolution and the possibility of particle identification, as well as various methods of additional background rejection. The CUORE experiment has proved the feasibility of ton-scale cryogenic experiments, setting the most stringent limit on 130Te 0ν2β decay. Two CUPID demonstrators (CUPID-0 and CUPID-Mo) have set the most stringent limits on 82Se and 100Mo isotopes, respectively, with compatibly low exposures. Several experiments are developing new methods to improve the background in the region of interest with bolometric detectors. CUPID and AMoRE experiments aim to cover the inverted hierarchy region, using scintillating bolometers with hundreds of kg of 100Mo. We review all of these efforts here, with a focus on the different types of radioactive background and the measures put in place to mitigate them.

Texture One Zero Model Based on A4 Flavor Symmetry and its Implications to Neutrinoless Double Beta Decay

Neutrinos are perhaps the most elusive particles in our Universe. Neutrino physics could be counted as a benchmark for various new theories in elementary particle physics and also for the better understanding of the evolution of the Universe. To complete the neutrino picture, the missing information whether it is about their mass or their nature that the neutrinos are Majorana particles could be provided by the observation of a process called neutrinoless double beta (0νββ) decay. Neutrinoless double beta decay is a hypothesised nuclear process in which two neutrons simultaneously decay into protons with no neutrino emission. In this paper we proposed a neutrino mass model based on A4 symmetry group and studied its implications to 0νββ decay. We obtained a lower limit on |Mee| for inverted hierarchy and which can be probed in 0νββ experiments like SuperNEMO and KamLAND-Zen.

GERDA and LEGEND: Probing the Neutrino Nature and Mass at 100 meV and beyond

The Gerda (GERmanium Detector Array) project, located at Laboratori Nazionali del Gran Sasso (LNGS), was started in 2005, a few years after the claim of evidence for the neutrinoless double beta decay (0νββ) of 76Ge to the ground state of 76Se: it is an ultra-rare process whose detection would directly establish the Majorana nature of the neutrino and provide a measurement of its mass and mass hierarchy. The aim of Gerda was to confirm or disprove the claim by an increased sensitivity experiment. After establishing the new technology of Ge detectors operated bare in liquid Argon and since 2011, Gerda efficiently collected data searching for 0νββ of 76Ge, first deploying the 76Ge-enriched detectors from two former experiments and later new detectors with enhanced signal-to-background rejection, produced from freshly 76Ge-enriched material. Since then, the Gerda setup has been upgraded twice, first in 2013–2015 and later in 2018. The period before 2013 is Phase I and that after 2015 is Phase II. Both the Gerda setup and the analysis tools evolved along the project lifetime, allowing to achieve the remarkable average energy resolution of ∼3.6 and ∼2.6 keV for Coaxial Germanium (Coax) detectors and for Broad Energy Germanium (BEGe), respectively, and the background index of 5.2−1.3+1.6 · 10−4 cts/(keV·kg·yr) in a 230 keV net range centered at Qββ. No evidence of the 0νββ decay at Qββ = 2039.1 keV has been found, hence the limit of 1.8·1026 yr on the half-life (T1/20ν) at 90% C.L. was set with the exposure of 127.2 kg·yr. The corresponding limit range for the effective Majorana neutrino mass mee has been set to 79–180 meV. The Gerda performances in terms of background index, energy resolution and exposure are the best achieved so far by 76Ge double beta decay experiments. In Phase II, Gerda succeeded in operating in a background free regime and set a world record. In 2017, the Legend Collaboration was born from the merging of the Gerda and Majorana Collaborations and resources with the aim to further improve the Gerda sensitivity. First, the Legend200 project, with a mass of up to 200 kg of 76Ge-enriched detectors, aims to further improve the background index down to <0.6 · 10−3 cts/(keV·kg·yr) to explore the Inverted Hierarchy region of the neutrino mass ordering, then the Legend1000 (1 ton of 76Ge-enriched) will probe the Normal Hierarchy. In this paper, we describe the Gerda experiment, its evolution, the data analysis flow, a selection of its results and technological achievements, and finally the design, features and challenges of Legend, the Gerda prosecutor.

Neutrino mass, leptogenesis and sterile neutrino dark matter in inverse seesaw framework

We study [Formula: see text] flavor symmetric inverse seesaw model which has the possibility of simultaneously addressing neutrino phenomenology, dark matter (DM) and baryon asymmetry of the universe (BAU) through leptogenesis. The model is the extension of the standard model by the addition of two (RH) neutrinos and three sterile fermions leading to a keV scale sterile neutrino DM and two pairs of quasi-Dirac states. The CP violating decay of the lightest quasi-Dirac pair present in the model generates lepton asymmetry which then converts to BAU. Thus, this model can provide a simultaneous solution for nonzero neutrino mass, DM content of the universes and the observed baryon asymmetry. The [Formula: see text] flavor symmetry in this model is augmented by additional [Formula: see text] symmetry to constrain the Yukawa Lagrangian. A detailed numerical analysis has been carried out to obtain DM mass, DM-active mixing as well as BAU both for normal hierarchy as well as inverted hierarchy. We try to correlate the two cosmological observables and found a common parameter space satisfying the DM phenomenology and BAU. The parameter space of the model is further constrained from the latest cosmological bounds on the observables.

Towards unification of quark and lepton flavors in $$A_4$$ modular invariance

We study quark and lepton mass matrices in the $$A_4$$ A 4 modular symmetry towards the unification of the quark and lepton flavors. We adopt modular forms of weights 2 and 6 for quarks and charged leptons, while we use modular forms of weight 4 for the neutrino mass matrix which is generated by the Weinberg operator. We obtain the successful quark mass matrices, in which the down-type quark mass matrix is constructed by modular forms of weight 2, but the up-type quark mass matrix is constructed by modular forms of weight 6. The viable region of $$\tau $$ τ is close to $$\tau =i$$ τ = i . Lepton mass matrices also work well at nearby $$\tau =i$$ τ = i , which overlaps with the one of the quark sector, for the normal hierarchy of neutrino masses. In the common $$\tau $$ τ region for quarks and leptons, the predicted sum of neutrino masses is 87–120 meV taking account of its cosmological bound. Since both the Dirac CP phase $$\delta _{CP}^\ell $$ δ CP ℓ and $$\sin ^2\theta _{23}$$ sin 2 θ 23 are correlated with the sum of neutrino masses, improving its cosmological bound provides crucial tests for our scheme as well as the precise measurement of $$\sin ^2\theta _{23}$$ sin 2 θ 23 and $$\delta _{CP}^\ell $$ δ CP ℓ . The effective neutrino mass of the $$0\nu \beta \beta $$ 0 ν β β decay is $$\langle m_{ee}\rangle =15$$ ⟨ m ee ⟩ = 15 –31 meV. It is remarked that the modulus $$\tau $$ τ is fixed at nearby $$\tau =i$$ τ = i in the fundamental domain of SL(2, Z), which suggests the residual symmetry $$Z_2$$ Z 2 in the quark and lepton mass matrices. The inverted hierarchy of neutrino masses is excluded by the cosmological bound of the sum of neutrino masses.

Phenomenology of keV sterile neutrino in minimal extended seesaw

We explore the possibility of a single generation of keV scale sterile neutrino [Formula: see text] as a dark matter candidate within the minimal extended seesaw (MES) framework and its influence in neutrinoless double beta decay [Formula: see text] study. Three hierarchical right-handed neutrinos were considered to explain neutrino mass. We also address baryogenesis via the mechanism of thermal leptogenesis considering the decay of the lightest RH neutrino to a lepton and Higgs doublet. A generic model based on [Formula: see text] flavor symmetry is constructed to explain both normal and inverted hierarchy mass pattern of neutrinos. Significant results on effective neutrino masses are observed in presence of sterile mass [Formula: see text] and active-sterile mixing [Formula: see text] in [Formula: see text]. Results from [Formula: see text] give stringent upper bounds on the active-sterile mixing matrix element. To establish sterile neutrino as dark matter within this model, we checked decay width and relic abundance of the sterile neutrino, which restricted sterile mass [Formula: see text] within some definite bounds. Constrained regions on the CP phases and Yukawa couplings are obtained from [Formula: see text] and baryogenesis results. Co-relations among these observable are also established and discussed within this framework.

$$U(1)_{B-L}$$ extension of the standard model with $$S_3$$ symmetry

We propose a renormalizable $$B-L$$B-L Standard Model (SM) extension based on $$S_3$$S3 symmetry which successfully accommodates the observed fermion mass spectra and flavor mixing patterns as well as the CP violating phases. The small masses for the light active neutrinos are generated through a type I seesaw mechanism. The obtained physical parameters in the lepton sector are well consistent with the global fit of neutrino oscillations (Esteban et al. in J High Energy Phys 01:106, 2019) for both normal and inverted neutrino mass orderings. The model also predicts effective neutrino mass parameters of $${\langle m_{ee}\rangle }= {1.02\times 10^{-2}}\,{\mathrm {eV}},\, m_{\beta }= {1.25}\times 10^{-2}\,{\mathrm {eV}}$$⟨mee⟩=1.02×10-2eV,mβ=1.25×10-2eV for normal hierarchy (NH) and $${\langle m_{ee}\rangle } ={5.03}\times 10^{-2}\, {\mathrm {eV}},\, m_{\beta } ={5.05}\times 10^{-2}\, {\mathrm {eV}}$$⟨mee⟩=5.03×10-2eV,mβ=5.05×10-2eV for inverted hierarchy (IH) which are all well consistent with the future large and ultra-low background liquid scintillator detectors which has been discussed in Ref. (Zhao et al. in Chin Phys C 41(5):053001, 2017) or the limit of the effective neutrino mass can be reached by the planning of future experiments. The model results are consistent with and successfully accommodate the recent experimental values of the physical observables of the quark sector, including the six quark masses, the quark mixing angles and the CP violating phase in the quark sector.

CP violations in a predictive A4 symmetry model

We will investigate numerically a seesaw model with $A_4$ flavor symmetry to find allowed regions satisfying the current experimental neutrino oscillation data, then use them to predict physical consequences. Namely, the lightest active neutrino mass is of the order of $\mathcal{O}(10^{-2})$ eV. The effective neutrino mass $|\langle m\rangle|$ associated with neutrinoless double beta decay is in the range $[0.002 \,\mathrm{eV},0.038\,\mathrm{eV}]$ and $[0.048\,\mathrm{eV},0.058\,\mathrm{eV}]$, corresponding to the normal and the inverted hierarchy schemes, respectively. Other relations among relevant physical quantities are shown, so that they can be determined if some of them are confirmed experimentally. The recent data of the baryon asymmetry of the Universe ($\eta_B$) can be explained via leptogenesis caused by the effect of the renormalization group evolution on the Dirac Yukawa couplings, provided the right-handed neutrino mass scale $M_0$ ranges from $\mathcal{O}(10^8)$ GeV to $\mathcal{O}(10^{12})$ GeV for $\tan\beta =3$. This allowed $M_0$ range is different from the scale of $\mathcal{O}(10^{13})$ GeV for other effects that also generate a consistent $\eta_B$ from leptogenesis. The branching ratio of the decay $ \mu \rightarrow\,e\gamma$ may reach future experimental sensitivity for very light values of $M_0$. Hence, it will be inconsistent with the $M_0$ range predicted from the $\eta_B$ data whenever this decay is detected experimentally.

Fermion mass and mixing in an extension of the standard model with D5 symmetry

We suggest a renormalizable standard model (SM) extension based on [Formula: see text] symmetry which accommodates leptonic mass and mixing parameters with nonzero [Formula: see text] and Dirac CP violating phase. Both normal and inverted neutrino mass ordering as well as the smallness of the active neutrino masses are generated at leading order through type-I seesaw mechanism in which the obtained physical parameters are well consistent with the global fit of neutrino oscillation data [P. F. de Salas et al., Phys. Lett. B 782, 633 (2018)], while the quark masses are in good agreement with the recent experimental data [Particle Data Group (M. Tanabashi et al.), Phys. Rev. D 98, 030001 (2018)]. The model also predicts an effective Majorana neutrino mass parameter of [Formula: see text] for normal hierarchy and [Formula: see text] for inverted hierarchy which are all well below the most current upper limit given [P. F. de Salas et al., Front. Astron. Space Sci. 5, 36 (2018); CUORE Collab. (C. Alduino et al.), Phys. Rev. Lett. 120, 132501 (2018)] and beyond the reach of the present [Formula: see text] decay experiments.

Orthodoxy – the symbolic language of the drama July by Ivan Vyrypaev

Aim. The aim of the paper is to interpret and analyse Orthodox symbols through the prism of the Orthodox theology. Methods. The senses of the Orthodox symbolism as proposed by the artist are not always compliant with Orthodox doctrine. Therefore, in order to fully understand the sense of Ivan Vyrypaev’s drama, it is necessary to first decode the Orthodox symbols that make up the language of the work discussed. For this reason, the major Orthodox symbols occurring in July will be listed at the very beginning of the paper. Then, they will be discussed in the context of the Orthodox theology as well as the artist’s own words. This task will contribute to the decoding of the language of I. Vyrypaev’s work. Results. According to I. Vyrypaev, the cruelty of a patient of the Smolensk madhouse is an inverted hierarchy of values which at the same time serves as his path of inquiry. On the other hand, the superficial attitudes, such as good, culture, humanitarianism, liberal values or democracy are obstacles (demons) which he has to overcome in order to find himself and God. The Orthodox symbols in July are allegories by means of which the author wants to show the main hero’s path to the truth. Furthermore, a justification for this way of thinking is one of the mottos that I. Vyrypaev included in July. Conclusions. In the drama July, I. Vyrypaev utilised the following sacral symbols: the theological significance of the Church in the Orthodox faith, the idea of communality, the concept of Orthodox humility as well as the idea of deification and martyrdom. The threads of the Orthodox symbolism used by I. Vyrypaev are superficial and should not be interpreted literally. The author consciously inverts the hierarchy of the Orthodox symbols in his work in order to show the bewilderment and corruption of the modern society. In the drama July I. Vyrypaev is more focused on being inspired by the Orthodox culture than on closely reflecting its senses. The symbolism of the altar and the ideas of martyrdom as applied in July are similar to the Christian symbols in the Roman Catholic approach.