Erratum: Assessment of uncertainties in QRPA $0νββ$-decay nuclear matrix elements [Nucl. Phys. A 766, 107 (2006)]
This is an erratum to our previously published paper.
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arXiv subjects
Petr Vogel
Publications and source records attributed to Petr Vogel.
Neutrinoless double beta decay
The status of the search for neutrinoless double beta decay is reviewed. The effort to reach the sensitivity needed to cover the effective Majorana neutrino mass corresponding to the degenerate and inverted mass hierarchy is described. Various issues concerning the theory (and phenomenology) of the relation between the $0νββ$ decay rate and the absolute neutrino mass scale are discussed, in particular the issue of mechanism of the $0νββ$ decay. Finally, the relation between the neutrino magnetic moments and the charge conjugation property (Dirac vs. Majorana) is described.
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Towards absolute neutrino masses
Various ways of determining the absolute neutrino masses are briefly reviewed and their sensitivities compared. The apparent tension between the announced but unconfirmed observation of the $0νββ$ decay and the neutrino mass upper limit based on observational cosmology is used as an example of what could happen eventually. The possibility of a ``nonstandard'' mechanism of the $0νββ$ decay is stressed and the ways of deciding which of the possible mechanisms is actually operational are described. The importance of the $0νββ$ nuclear matrix elements is discussed and their uncertainty estimated.
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Model Independent Naturalness Bounds on Magnetic Moments of Majorana Neutrinos
We analyze the implications of neutrino masses for the magnitude of neutrino magnetic moments. By considering electroweak radiative corrections to the neutrino mass, we derive model-independent naturalness upper bounds on neutrino magnetic moments, generated by physics above the electroweak scale. For Majorana neutrinos, these bounds are weaker than present experimental limits if $μ_ν$ if generated by new physics at $\sim$ 1 TeV, and surpass current experimental sensitivity only for new physics scales $>$ 10 -- 100 TeV. The discovery of a neutrino magnetic moment near present limits would thus signify that neutrinos are Majorana particles.
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Model Independent Bounds on Magnetic Moments of Majorana Neutrinos
We analyze the implications of neutrino masses for the magnitude of neutrino magnetic moments. By considering electroweak radiative corrections to the neutrino mass, we derive model-independent naturalness upper bounds on neutrino magnetic moments, $μ_ν$, generated by physics above the electroweak scale. For Dirac neutrinos, the bound is several orders of magnitude more stringent than present experimental limits. However, for Majorana neutrinos the magnetic moment contribution to the mass is Yukawa suppressed. The bounds we derive for magnetic moments of Majorana neutrinos are weaker than present experimental limits if $μ_ν$ is generated by new physics at ~ 1 TeV, and surpass current experimental sensitivity only for new physics scales > 10 -- 100 TeV. The discovery of a neutrino magnetic moment near present limits would thus signify that neutrinos are Majorana particles.
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Muon capture on nuclei: random phase approximation evaluation versus data for 6 $\le$ Z $\le$ 94 nuclei
We use the random phase approximation to systematically describe the total muon capture rates on all nuclei where they have been measured. We reproduce the experimental values on these nuclei to better than 15% accuracy using the free nucleon weak form factors and residual interactions with a mild $A$ dependency. The isospin dependence and the effects associated with shell closures are fairly well reproduced as well. However, the calculated rates for the same residual interactions would be significantly lower than the data if the in-medium quenching of the axial-vector coupling constant is employed to other than the true Gamow-Teller amplitudes. Our calculation thus suggests that no quenching is needed in the description of semileptonic weak processes involving higher multipole transitions and momentum transfer $\sim m_μ$, with obvious importance to analogous weak processes.
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Uncertainties in the $0νββ$--decay nuclear matrix elements
The nuclear matrix elements $M^{0ν}$ of the neutrinoless double beta decay ($0νββ$) of most nuclei with known $2νββ$-decay rates are systematically evaluated using the Quasiparticle Random Phase Approximation (QRPA) and Renormalized QRPA (RQRPA). The experimental $2νββ$-decay rate is used to adjust the most relevant parameter, the strength of the particle-particle interaction. With such procedure the $M^{0ν}$ values become essentially independent on single-particle basis size, the axial vector quenching factor, etc. Theoretical arguments in favor of the adopted way of determining the interaction parameters are presented. It is suggested that most of the spread among the published $M^{0ν}$'s can be ascribed to the choices of implicit and explicit parameters, inherent to the QRPA method.
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How Magnetic is the Dirac Neutrino?
We derive model-independent, "naturalness" upper bounds on the magnetic moments μ_νof Dirac neutrinos generated by physics above the scale of electroweak symmetry breaking. In the absence of fine-tuning of effective operator coefficients, we find that current information on neutrino mass implies that |μ_ν| < 10^(-14) Bohr magnetons. This bound is several orders of magnitude stronger than those obtained from analyses of solar and reactor neutrino data and astrophysical observations.
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Assessment of uncertainties in QRPA $0νββ$-decay nuclear matrix elements
The nuclear matrix elements $M^{0ν}$ of the neutrinoless double beta decay ($0νββ$) of most nuclei with known $2νββ$-decay rates are systematically evaluated using the Quasiparticle Random Phase Approximation (QRPA) and Renormalized QRPA (RQRPA). The experimental $2νββ$-decay rate is used to adjust the most relevant parameter, the strength of the particle-particle interaction. New results confirm that with such procedure the $M^{0ν}$ values become essentially independent on the size of the single-particle basis. Furthermore, the matrix elements are shown to be also rather stable with respect to the possible quenching of the axial vector strength parametrized by reducing the coupling constant $g_A$, as well as to the uncertainties of parameters describing the short range nucleon correlations. Theoretical arguments in favor of the adopted way of determining the interaction parameters are presented. Furthermore, a discussion of other implicit and explicit parameters, inherent to the QRPA method, is presented. Comparison is made of the ways these factors are chosen by different authors. It is suggested that most of the spread among the published $0νββ$ decay nuclear matrix elements can be ascribed to these choices.
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Neutrinoless double beta decay and direct searches for neutrino mass
Study of the neutrinoless double beta decay and searches for the manifestation of the neutrino mass in ordinary beta decay are the main sources of information about the absolute neutrino mass scale, and the only practical source of information about the charge conjugation properties of the neutrinos. Thus, these studies have a unique role in the plans for better understanding of the whole fast expanding field of neutrino physics.
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New contribution to WIMP-nucleus scattering
A weakly-interacting massive particle (WIMP) is perhaps the most promising candidate for the dark matter in the Galactic halo. The WIMP detection rate in laboratory searches is fixed by the cross section for elastic WIMP-nucleus scattering. Here we calculate the contribution to this cross section from two-nucleon currents from pion exchange in the nucleus, and show that it may in some cases be comparable to the one-nucleon current that has been considered in prior work, and perhaps help resolve the discrepancies between the various direct dark-matter search experiments. We provide simple expressions that allow these new contributions to be included in current calculations.
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Neutrinoless double-beta decay and effective field theory
We analyze neutrinoless double $β$-decay ($\nbb$-decay) mediated by heavy particles from the standpoint of effective field theory. We show how symmetries of the $\nbb$-decay quark operators arising in a given particle physics model determine the form of the corresponding effective, hadronic operators. We classify the latter according to their symmetry transformation properties as well as the order at which they appear in a derivative expansion. We apply this framework to several particle physics models, including R-parity violating supersymmetry (RPV SUSY) and the left-right symmetric model (LRSM) with mixing and a right-handed Majorana neutrino. We show that, in general, the pion exchange contributions to $\nbb$-decay dominate over the short-range four-nucleon operators. This confirms previously published RPV SUSY results and allows us to derive new constraints on the masses in the LRSM. In particular, we show how a non-zero mixing angle $ζ$ in the left-right symmetry model produces a new potentially dominant contribution to $\nbb$-decay that substantially modifies previous limits on the masses of the right-handed neutrino and boson stemming from constraints from $\nbb$-decay and vacuum stability requirements.
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Supernova Neutrinos
I describe how the signals corresponding to the supernova $ν_e$ and $\barν_e$ (charged current reactions) as well as all active neutrinos (neutral current reactions) can be separately observed in various existing detectors. These observations would make it possible to determine the flux and average energy (or temperature) for each of these three neutrino signal components. I argue that all these quantities are needed in order to understand the interplay between the so far poorly known supernova neutrino emission process and the neutrino oscillations.
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On the uncertainty in the $0νββ$ decay nuclear matrix elements
The nuclear matrix elements $M^{0ν}$ of the neutrinoless double beta decay ($0νββ$) are evaluated for $^{76}$Ge,$^{100}$Mo, $^{130}$Te, and $^{136}$Xe within the Renormalized Quasiparticle Random Phase Approximation (RQRPA) and the simple QRPA. Three sets of single particle level schemes are used, ranging in size from 9 to 23 orbits. When the strength of the particle-particle interaction is adjusted so that the $2νββ$ decay rate is correctly reproduced, the resulting $M^{0ν}$ values become essentially independent on the size of the basis, and on the form of different realistic nucleon-nucleon potentials. Thus, one of the main reasons for variability of the calculated $M^{0ν}$ within these methods is eliminated.
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Constraints on Two-Body Axial Currents from Reactor Antineutrino-Deuteron Breakup Reactions
We discuss how to reduce theoretical uncertainties in the neutrino-deuteron breakup cross-sections crucial to the Sudbury Neutrino Observatory's efforts to measure the solar neutrino flux. In effective field theory, the dominant uncertainties in all neutrino-deuteron reactions can be expressed through a single, common, isovector axial two-body current parameterized by $L_{1,A}$. After briefly reviewing the status of fixing $L_{1,A}$ experimentally, we present a constraint on $L_{1,A}$ imposed by existing reactor antineutrino-deuteron breakup data. This constraint alone leads to an uncertainty of 6-7% at 7 MeV neutrino energy in the cross-sections relevant to the Sudbury Neutrino Observatory. However, more significantly for the Sudbury experiment, the constraint implies an uncertainty of only 0.7% in the ratio of charged to neutral current cross-sections used to verify the existence of neutrino oscillations, at the same energy. This is the only direct experimental constraint from the two-body system, to date, of the uncertainty in these cross-sections.
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Detection of Supernova Neutrinos by Neutrino-Proton Elastic Scattering
We propose that neutrino-proton elastic scattering, $ν+ p \to ν+ p$, can be used for the detection of supernova neutrinos in scintillator detectors. Though the proton recoil kinetic energy spectrum is soft, with $T_p \simeq 2 E_ν^2/M_p$, and the scintillation light output from slow, heavily ionizing protons is quenched, the yield above a realistic threshold is nearly as large as that from $\barν_e + p \to e^+ + n$. In addition, the measured proton spectrum is related to the incident neutrino spectrum, which solves a long-standing problem of how to separately measure the total energy and temperature of $ν_μ$, $ν_τ$, $\barν_μ$, and $\barν_τ$. The ability to detect this signal would give detectors like KamLAND and Borexino a crucial and unique role in the quest to detect supernova neutrinos.
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Double Beta Decay
The motivation, present status, and future plans of the search for the neutrinoless double beta decay are reviewed. It is argued that, motivated by the recent observations of neutrino oscillations, there is a reasonable hope that neutrinoless double beta decay corresponding to the neutrino mass scale suggested by oscillations, of about 50 meV, actually exists. The challenges to achieve the sensitivity corresponding to this mass scale, and plans to overcome them, are described.
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Reactor-based Neutrino Oscillation Experiments
The status of neutrino oscillation searches employing nuclear reactors as sources is reviewed. This technique, a direct continuation of the experiments that proved the existence of neutrinos, is today an essential tool in investigating the indications of oscillations found in studying neutrinos produced in the sun and in the earth's atmosphere. The low-energy of the reactor \nuebar makes them an ideal tool to explore oscillations with small mass differences and relatively large mixing angles. In the last several years the determination of the reactor anti-neutrino flux and spectrum has reached a high degree of accuracy. Hence measurements of these quantities at a given distance L can be readily compared with the expectation at L = 0, thus testing \nuebar disappearance. While two experiments, Chooz and Palo Verde, with baselines of about 1 km and thus sensitive to the neutrino mass differences associated with the atmospheric neutrino anomaly, have collected data and published results recently, an ambitious project with a baseline of more than 100 km, Kamland, is preparing to take data. This ultimate reactor experiment will have a sensitivity sufficient to explore part of the oscillation phase space relevant to solar neutrino scenarios. It is the only envisioned experiment with a terrestrial source of neutrinos capable of addressing the solar neutrino puzzle.
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