Limits of Majorana neutrino mass from combined analysis of data from <Superscript>76</Superscript>Ge and <Superscript>136</Superscript>Xe neutrinoless double beta decay experiments

We present effective Majorana neutrino mass limits <m _ββ> obtained from the joint analysis of the recently published results of ⁷⁶Ge and ¹³⁶Xe neutrinoless double beta decay (0νββ) experiments, which was carried out by using the Bayesian calculations. Nuclear matrix elements (NMEs) used for the analysis are taken from the works, in which NMEs of ⁷⁶Ge and ¹³⁶Xe were simultaneously calculated. This reduced systematic errors connected with NME calculation techniques. The new effective Majorana neutrino mass limits <m _ββ> less than [85.4–197.0] meV are much closer to the inverse neutrino mass hierarchy region.     

Towards the meV limit of the effective neutrino mass in neutrinoless double-beta decays

We emphasize that it is extremely important for future neutrinoless double-beta(0νββ)decay experiments to reach the sensitivity to the effective neutrino mass|mββ|≈1 meV.With such a sensitivity,it is highly possible to discover the signals of 0νββ decays.If no signal is observed at this sensitivity level,then either neutrinos are Dirac particles or stringent constraints can be placed on their Majorana masses.In this paper,assuming the sensitivity of|mββ|≈1 meV for future 0νββ decay experiments and the precisions on neutrion oscillation parameters after the JUNO experiment,we fully explore the constrained regions of the lightest neutrino mass m1 and two Majorana-type CP-violating phases{ρ,σ}.Several important conclusions in the case of normal neutrino mass ordering can be made.First,the lightest neutrino mass is severely constrained to a narrow range m1∈[0.7,8]meV,which together with the precision measurements of neutrino mass-squared differences from oscillation experiments completely determines the neutrino mass spectrum m2∈[8.6,11.7]meV ing phases is limited to ρ∈[130°,230°],which cannot be obtained from any other realistic experiments.Third,the sum of three neutrino masses is found to beΣ≡m1+m2+m3∈[59.2,72.6]meV,while the effective neutrino mass for beta decays turns out to be mβ≡(|Ue1|2m1^2+|Ue2|2m2^2+|Ue3|2m3^2)1/2∈[8.9,12.6]meV.These observations clearly set up the roadmap for future non-oscillation neutrino experiments aiming to solve the fundamental problems in neutrino physics.     

Calculation of double beta decay rates and the neutrino mass

Predictions for 2v and 0v double beta decay rates are given for all nuclei with A ⩾ 70, for which double beta decay is energetically allowed. These predictions are based on detailed nuclear structure studies of the beta strength distribution and replace earlier estimates basing mostly on phase space considerations. New and more stringent limits on the Majorana neutrino mass are deduced from existing double beta decay experiments. Since the collective effects arising from spin-isospin as well as quadrupole-quadrupole forces are found to lead to a strong reduction of the nuclear matrix elements for two-neutrino double beta decay, but to have only minor influence on the matrix elements M^0v for the neutrinoless decay mode, the smaller limits for m_v result mainly from the fact that the widely used scaling procedure underestimates the 0_v matrix elements. It is further discussed to what extent interference between different neutrinos affects the obtained mass limits.     

Direct neutrino mass measurements

The determination of the neutrino rest mass plays an important role at the intersections of cosmology, particle physics and astroparticle physics. This topic is currently being addressed by two complementary approaches in laboratory experiments. Neutrinoless double beta decay experiments probe whether neutrinos are Majorana particles and determine an effective neutrino mass value. Single beta decay experiments such as KATRIN and MARE investigate the spectral shape of β-decay electrons close to their kinematic endpoint in order to determine the neutrino rest mass with a model-independent method. Owing to neutrino flavour mixing, the neutrino mass parameter appears as an average of all neutrino mass eigenstates contributing to the electron neutrino. The KArlsruhe TRItium Neutrino experiment (KATRIN) is currently the experiment in the most advanced status of commissioning. Applying an ultra-luminous molecular windowless gaseous tritium source and an integrating high-resolution spectrometer of MAC-E filter type, it allows β-spectroscopy close to the T ₂ end-point with unprecedented precision and will reach a sensitivity of 200 meV/c ² (90% C.L.) on the neutrino rest mass.     

Status of neutrinoless double beta decay searches

Neutrinoless double beta decay is one of the most sensitive tools in non-accelerator particle physics to probe the regime of physics beyond the standard model. It can provide in fact fundamental informations on the character of neutrinos and their absolute mass scale. The present status of experiments searching for neutrinoless double-beta decay (ββ(0ν)) is reviewed and the most relevant results discussed. Phenomenological aspects of ββ(0ν) are introduced. Given the observation of neutrino oscillations and the present knowledge of neutrino masses and mixing parameters, a possibility to observe ββ(0ν) at a neutrino mass scale m _ν in the range 10–50 meV could actually exist. The achievement of the required experimental sensitivity is a real challenge faced by a number of new proposed projects. A review of the various proposed experiments in the context of their figure-of-merit parameters is given. The most important parameters contributing to the experimental sensitivity are finally outlined. A short discussion on nuclear matrix element calculations is also given.     

Study of the production of Λb0 and B0 hadrons in pp collisions and first measurement of the Λb0→J/ψpK- branching fraction

The product of the Λ_b⁰(B⁰) di erential production cross-section and the branching fraction of the decay Λ_b⁰→J/ψpK^- (B⁰→J/ψpK^*(892)⁰) is measured as a function of the beauty hadron transverse momentum, pT, and rapidity, y. The kinematic region of the measurements is p_T <20 GeV/c and 2.0< y< 4.5. The measurements use a data sample corresponding to an integrated luminosity of 3fb^-1 collected by the LHCb detector in pp collisions at centre-of-mass energies √s= 7 TeV in 2011 and √s= 8 TeV in 2012. Based on previous LHCb results of the fragmentation fraction ratio, f_Λb⁰/f_d, the branching fraction of the decay Λ_b⁰→J/ψpK^- is measured to be
B(Λ_b⁰→J/ψpK^-)=(3.17±0.04±0.07±0.34_-0.28^+0.45)×10^-4,
where the rst uncertainty is statistical, the second is systematic, the third is due to the uncertainty on the branching fraction of the decay B⁰→J/ψpK^*(892)⁰, and the fourth is due to the knowledge of f_Λb⁰/f_d. The sum of the asymmetries in the production and decay between Λ_b⁰ and Λ_b⁰ is also measured as a function of p_T and y. The previously published branching fraction of Λ_b⁰→J/ψpπ^-, relative to that of Λ_b⁰→J/ψpK^-, is updated. The branching fractions of Λ_b⁰→P_c⁺(→J/ψp)K^- are determined.     

Search for finite-mass neutrinos in the decay π+→μ+vμ

If neutrinos possess non-zero mass, pion decay might have small decay branches to neutrino states with large masses. We have searched for such branches in the decay of pions produced at the Indiana University Cyclotron. The energy spectrum of decay muons shows no evidence for such neutrino branches and if these decays do exist, their branching ratios must be less than 10^?2 to 10^?3 for neutrino masses in the ranFge 7–33 MeV.     

Measurement of the absolute branching fraction of D+→K0e+ve via K0→π0π0

By analyzing 2.93 fb^-1 data collected at the center-of-mass energy √s=3.773 GeV with the BESIII detector, we measure the absolute branching fraction of the semileptonic decay D⁺→K⁰e⁺v_e to be B(D⁺→K⁰e⁺v_e)=(8.59±0.14±0.21)% using K⁰→K_S⁰→π⁰π⁰, where the first uncertainty is statistical and the second systematic. Our result is consistent with previous measurements within uncertainties..     

Cherenkov effect in the weak interactions generated by the neutrinos and new approach for estimation of neutrino mass

It is shown that if weak interactions can generate masses and polarize matter, then the Cherenkov effect induced by these interactions at v _v > c/n appears. The effect of (resonance) enhancement of neutrino oscillations in matter (v _v < c/n) and the Cherenkov (v _v > c/n) effect are competitive processes and at definite neutrino energies the effect of (resonance) enhancement of neutrino oscillations in matter will change to the Cherenkov effect. Then neutrino vacuum oscillations will regenerate and we obtain an excellent possibility of estimating neutrino masses. And knowing estimation of mass for one (electron) neutrino we can obtain masses of the rest neutrinos by using the values for mass differences for neutrinos obtained in oscillation experiments.     

A xenon solar neutrino detector

The neutrino capture reaction by ¹³¹Xe with the threshold of 352 keV is suggested for solar neutrinos detection. The most important feature of this process is its high sensitivity to beryllium neutrinos, that contribute approximately 40% to the total capture rate predicted in the Standard Solar Model (45 SNU). The expected counting rate of the xenon detector from the main solar neutrino sources predicted by the Standard Solar Model is ≈ 1500 events/yr.     

Nuclear structure effects on the neutrinoless double beta decay

The nuclear matrix elements of the 0ν ββ decay of⁷⁶Ge,⁸²Se,¹⁰⁰Mo,^128,130Te,¹³⁶Xe and¹⁵⁰Nd are calculated in the proton-neutron quasiparticle RPA with theG-matrix of the Paris potential. It is shown that the matrix elements are not sensitive to details of nuclear structure, in contrast to the 2ν ββ decay. We investigate effects of ground-state correlations and those of short-range correlations on the suppression of the nuclear matrix elements. We also discuss effective values of the neutrino mass which are deduced from experimental 0ν ββ decay half-lives.     

Statistical theory of nuclear neutrino capture: (II). Inclusion of first-forbidden transitions

The statistical theory of nuclear neutrino capture is extended to include first-forbidden transitions. A comparison with the theory of Bahcall and Frautschi is made. It is found that the present theory predicts neutrino capture cross sections which are smaller than those of Bahcall and Frautschi by a factor 2–3 for neutrino energies less than 50 MeV when first-forbidden transitions are dominant. Calculation of the cross section is made for the process in which ³⁷Cl nuclei capture electron neutrinos that are emitted in muon decay. The present calculation gives a cross section which is around one half of that of Donnelly and Haxton. Finally the contributions of the highly excited states in ³⁷Ar to the neutrino capture cross section are evaluated. It is shown that the contributions from the highly excited states (E > 6.02 MeV) to the neutrino capture cross section amount to 60% for E_v = 50 MeV.     

Status of the Sudbury Neutrino Observatory

Solar neutrinos from the decay of ⁸B have been detected at the Sudbury Neutrino Observatory via the charged-current (CC) and neutral-current (NC) reactions on deuterium and by the elastic scattering (ES) of electrons. The CCr eaction is sensitive exclusively to electron neutrinos, the NCr eaction is sensitive to all neutrino species, and the ES reaction also has a small sensitivity to muon and tau neutrinos. These measurements provided strong evidence that neutrinos change flavor as they propagate from the center of the Sun to the Earth at the 5.3σ level. It will also be shown that a global solar neutrino analysis of matter-enhanced neutrino oscillations of two active flavors strongly favors the large mixing angle solution.     

Geometry of the effective Majorana neutrino mass in the 0νββ decay

The neutrinoless double-beta (0νββ) decay is a unique process used to identify the Majorana nature of massive neutrinos, and its rate depends on the size of the effective Majorana neutrino mass <m>_ee. We put forward a novel ‘coupling-rod’ diagram to describe <m>_ee in the complex plane, by which the effects of the neutrino mass ordering and CP-violating phases on <m>_ee are intuitively understood. We show that this geometric language allows us to easily obtain the maximum and minimum of |<m>_ee|. It remains usable even if there is a kind of new physics contributing to <m>_ee, and it can also be extended to describe the effective Majorana masses <m>_eμ, <m>_eτ, <m>_μμ, <m>_μτ and <m>_ττ which may appear in some other lepton-number violating processes.     

Majorana neutrinos, <Emphasis Type="Italic">CP</Emphasis> violation,neutrinoless double beta and tritium beta decays

If the present or upcoming searches for neutrinoless double beta ((ββ)_0ν) decay give a positive result, the Majorana nature of massive neutrinos will be established. From the determination of the value of the (ββ)_0ν-decay effective Majorana mass parameter (|〈m〉|), it would be possible to obtain information on the type of neutrino mass spectrum. Assuming 3-ν mixing and massive Majorana neutrinos, we discuss the information that a measurement of, or an upper bound on, |〈m〉| can provide on the value of the lightest neutrino mass m₁. With additional data on the neutrino masses obtained in ³H β-decay experiments, it might be possible to establish whether the CP symmetry is violated in the lepton sector. This would require very high precision measurements. If CP invariance holds, the allowed patterns of the relative CP parities of the massive Majorana neutrinos would be determined.     

Double beta decay

Double beta decay is a rare nuclear process changing the nuclear charge by two units leaving atomic number unchanged. The detection of the neutrino accompanied mode (A,Z)→(A,Z + 2) + 2e^? + &;2v^? ₂ with half-lives around 10²⁰ years is among the rarest decays ever observed. Of outmost importance for particle physics and especially neutrino physics, is the neutrinoless mode (A,Z)→(A,Z + 2) + 2e^?. This process is violating lepton number by two units and requires massive Majorana neutrinos, i.e. neutrino and antineutrino are identical. The current experimental status is reviewed and an outlook towards future activities is given.     

Neutrino masses as a second-order effect in Higgs coupling

It is suggested that in the usual type of gauge theory all fermions, including neutrinos, have right-handed components. The smallness or vanishing of the observed neutrino masses is explained by the fact that the appropriate neutral Higgs boson does not develop a non-zero vacuum expectation value. In the case when the neutrino masses do not vanish they are finite, of order G_Fm³, where m is the mass of the charged lepton. Non-conservation of lepton flavor gives rise to an instability of all neutrinos except v_e and to μ→e+γ decay, but at a very low level.     

On non-unitary lepton mixing and neutrino mass observables

There are three observables related to neutrino mass, namely the kinematic mass in direct searches, the effective mass in neutrino-less double beta decay, and the sum of neutrino masses in cosmology. In the limit of exactly degenerate neutrinos there are very simple relations between those observables, and we calculate corrections due to non-zero mass splitting. We discuss how the possible non-unitarity of the lepton mixing matrix may modify these relations and find in particular that corrections due to non-unitarity can exceed the corrections due to mass splitting. We furthermore investigate constraints from neutrino-less double beta decay on mass and mixing parameters of heavy neutrinos in the type I see-saw mechanism. There are constraints from assuming that heavy neutrinos are exchanged, and constraints from assuming light neutrino exchange, which arise from an exact see-saw relation. The latter has its origin in the unitarity violation arising in see-saw scenarios. We illustrate that the limits from the latter approach are much stronger. The drastic impact of the new limit on inverse neutrino-less double beta decay (e⁻e⁻→W⁻W⁻)$(e^{-}{e}^{-}\to W^{-}{W}^{-})$ is studied. We furthermore discuss neutrino mixing in case there is one or more light sterile neutrinos. Neutrino oscillation probabilities for long baseline neutrino oscillation experiments are considered, and the analogy to general non-unitarity phenomenology, such as zero-distance effects, is pointed out.     

A search for decays of heavy neutrinos in the mass range 0.5–2.8 GeV

A search for decays of heavy neutrinos was conducted by the CHARM Collaboration in a prompt neutrino beam produced by dumping 400 GeV protons in a Cu target, and in the CERN wide-band neutrino beam produced by 400 GeV primary protons. No candidate event was found. In the beam-dump experiment heavy neutrinos have been assumed to be produced by mixing in charmed D meson decays. Neutrinos decaying into e⁺e⁻v_e, μ⁺e⁻v_μ, and μ⁺μ⁻v_μ were searched for. Limits of |U_ei|², |U_μi|² < 10⁻⁷ were obtained for neutrino masses around 1.5 GeV. In the wide-band experiment heavy neutrinos were assumed to be produced by neutral-current neutrino interactions in the CHARM calorimeter. Here a search was made for neutrinos decaying into a μ and hadrons. This experiment is sensitive to decays of neutrinos with mass in the range 0.5–2.8 GeV with limits of |U_μi|² < 3 × 10⁻⁴ for masses around 2.5 GeV. These measurements extend our previous results in the mass range 10–400 MeV.