As measurements of neutrino mixing angles continue to become more precise, it is increasingly likely that in the very near future a realistic neutrino mixing model will be required to precisely reproduce their best-fit values. In this study, a modified TM <inline-formula><tex-math id='TM0002' notation='LaTeX'>$_2$</tex-math></inline-formula> mixing model that reproduces the best-fit values of all three neutrino mixing angles is proposed. The model reproduces the correct mixing angles within 1 <inline-formula><tex-math id='TM0003' notation='LaTeX'>$\sigma$</tex-math></inline-formula> of the current best-fit values and is robust against any future changes of the best-fit values.

Japan

Michael Fodroci

Teruyuki Kitabayashi

Modified TM <sub>2</sub> for Reproducing All Best-Fit Values of Neutrino Mixing Angles

Although the hybrid natural inflation is a successful inflation model, the symmetry breaking scale in the model should be large for a negative value of the running of the scalar spectral index. This study proposed a generalized hybrid natural inflation model that can realize a low-scale inflation with a negative value of the running of the scalar spectral index.

Generalized hybrid natural inflation

Magic textures are successful candidates of the correct texture for Majorana neutrinos. In this study, we demonstrate that several types of magic textures of Majorana neutrinos are approximately immanent in the flavor mass matrix of Dirac neutrinos. In addition, the normal mass ordering of Dirac neutrino masses is slightly preferable to inverted mass ordering in the context of magic textures.

Yuta Hyodo

Is the magic texture of Majorana neutrinos immanent in Dirac nature?

Abstract Because primordial black holes (PBHs) evaporate into all particle species in nature, PBHs may emit several dark matter (DM) particle species with specific mass spectra. We assume that PBHs are the only source of DMs, and DMs only interact with the standard model particles gravitationally. We show a relation between the number of DM particle species N$_{DM}$ and initial PBH density β and mass . β– curves for different N$_{DM}$ tend to overlap with each other for heavy initial PBHs. We also show the allowed region of DM masses for multiple DMs.

Primordial black holes and dark matter mass spectra SciPost Phys

Abstract We show that if the lepton flavor-violating μ → eγ process is observed in the MEG II experiment, the initial density of primordial black holes (PBHs) can be constrained with scotogenic dark matter. As a benchmark case, if PBH evaporation occurs in the radiation-dominated era, the initial density may be 2 × 10$^{−17}$ ≲ β ≲ 3 × 10$^{−16}$ for the (TeV)-scale dark sector in the scotogenic model, where β is the ratio of the PBH density ρ$_{PBH}$ to the radiation density ρ$_{rad}$ at the time of PBH formation. As another benchmark case, if PBHs evaporate in the PBH-dominated era, the initial density may be 1 × 10$^{−8}$ ≲ β ≲ 3 × 10$^{−7}$ for (GeV)-scale dark matter, with other (TeV)-scale particles in the scotogenic model.

Primordial black holes and lepton flavor violation with scotogenic dark matter

Abstract The magic texture is one of the successful textures of the flavor neutrino mass matrix for Majorana neutrinos. In this paper, it turns out that two new types of magic textures are also consistent with neutrino oscillation experiments, observation of cosmic microwave background radiation, and neutrinoless double beta decay experiments. The connection between these new magic textures and the leptogenesis scenario for the origin of the baryon asymmetry of the Universe is also discussed.

New magic textures of Majorana neutrinos and the baryon asymmetry of the Universe

One- and two-zero textures for the flavor neutrino mass matrix have been successful in explaining mixing in the neutrino sector. Conservatively, six cases of one-zero textures and seven cases of two-zero textures are compatible with observations. We show that one case may be the most natural in the one- and two-zero textures schemes if tiny neutrino masses are generated by the type-II seesaw mechanism in triplet Higgs models.

Texture zeros flavor neutrino mass matrix and triplet Higgs models

Abstract We study the capability of generating the correct flavor neutrino mass matrix in a scalar clockwork model. First, we assume that the flavor structure is controlled by the Yukawa couplings as in the standard model. In this case, the correct flavor neutrino mass matrix could be obtained by appropriate Yukawa couplings  where . Next, we assume that the Yukawa couplings are extremely democratic: . In this case, the model parameters of the scalar clockwork sector, such as the site number of a clockwork gear in a clockwork chain, should have the flavor indices  and/or  to generate the correct flavor neutrino mass matrix. We show some examples of assignments of the flavor indices which can yield the correct flavor neutrino mass matrix.

Scalar clockwork and flavor neutrino mass matrix

An <math><mi>O</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> spinor, Φ, as a doublet denoted by <math><msub><mrow><mn>2</mn></mrow><mrow><mi>D</mi></mrow></msub></math> consists of an <math><mi>S</mi><mi>O</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> spinor, ϕ, and its complex conjugate, <math><msup><mrow><mi>ϕ</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math>, which form <math><mi>Φ</mi><mo>=</mo><msup><mrow><mo>(</mo><mi>ϕ</mi><mo>,</mo><msup><mrow><mi>ϕ</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>)</mo></mrow><mrow><mi>T</mi></mrow></msup></math> to be identified with a Majorana-type spinor of <math><mi>O</mi><mo>(</mo><mn>4</mn><mo>)</mo></math>. The four gamma matrices <math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>μ</mi></mrow></msub></math> (<math><mi>μ</mi><mo>=</mo><mn>1</mn><mo>∼</mo><mn>4</mn></math>) are given by <math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mtext>diag.</mtext><mrow><mo>(</mo><msub><mrow><mi>τ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msubsup><mrow><mi>τ</mi></mrow><mrow><mi>i</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>)</mo></mrow></math> (<math><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></math>) and <math><msub><mrow><mi>Γ</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>=</mo><mo>−</mo><msub><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>⊗</mo><msub><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msub></math>, where <math><msub><mrow><mi>τ</mi></mrow><mrow><mi>i</mi></mrow></msub></math> denote the Pauli matrices. The rotations and axis-reflections of <math><mi>O</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> are, respectively, generated by <math><msub><mrow><mi>Σ</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub></math> and <math><msub><mrow><mi>Σ</mi></mrow><mrow><mi>i</mi><mn>4</mn></mrow></msub></math>, where <math><msub><mrow><mi>Σ</mi></mrow><mrow><mi>μ</mi><mi>ν</mi></mrow></msub><mo>=</mo><mo>[</mo><msub><mrow><mi>Γ</mi></mrow><mrow><mi>μ</mi></mrow></msub><mo>,</mo><msub><mrow><mi>Γ</mi></mrow><mrow><mi>ν</mi></mrow></msub><mo>]</mo><mo>/</mo><mn>2</mn><mi>i</mi></math>. While Φ is regarded as a scalar, a fermionic <math><mi>O</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> spinor is constructed out of an <math><mi>S</mi><mi>O</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> doublet Dirac spinor and its charge conjugate. These <math><mi>O</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> spinors are restricted to be neutral and cannot carry the standard model quantum numbers because they contain particles and antiparticles. Our <math><mi>O</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> spinors serve as candidates of dark matter. The <math><mi>O</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> symmetry in particle physics is visible when the invariance of interactions is considered by explicitly including their complex conjugates. It is possible to introduce a dark gauge symmetry based on <math><mi>S</mi><mi>O</mi><mo>(</mo><mn>3</mn><mo>)</mo><mo>×</mo><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math> equivalent to <math><mi>O</mi><mo>(</mo><mn>3</mn><mo>)</mo></math>, where the <math><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math> parity is described by a <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> charge giving 1 for a particle and −1 for an antiparticle. The <math><mi>S</mi><mi>O</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> and <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> gauge bosons turn out to transform as the axial vector of <math><mi>O</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> and the pseudoscalar of <math><mi>O</mi><mo>(</mo><mn>3</mn><mo>)</mo></math>, respectively. This property is related to the consistent definition of the nonabelian field strength tensor of <math><mi>O</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> or of the U(1) charge of the O(3)-transformed spinor. To see the feasibility of our dark matter models, we discuss scalar dark matter phenomenology based on the dark <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> gauge model.

Masaki Yasuè

Spinorial structure of (3) and Application to Dark Matter

The clockwork mechanism provides a natural way to obtain hierarchical masses and couplings in a theory. We propose a clockwork model that has nine clockwork generations. In this model, the candidates of the origin of the neutrino mixings are nine Yukawa mass matrix elements <math><msup><mi>Y</mi><mrow><mi>a</mi><mi>β</mi></mrow></msup></math> that connect neutrinos and clockwork fermions, nine clockwork mass ratios <math><msub><mi>q</mi><mrow><mi>a</mi><mi>β</mi></mrow></msub></math>, and nine numbers of clockwork fermions <math><msub><mi>n</mi><mrow><mi>a</mi><mi>β</mi></mrow></msub></math>, where <math><mrow><mi>a</mi></mrow></math>, <math><mrow><mi>β</mi><mo>=</mo><mn>1</mn></mrow></math>, 2, 3. Assuming <math><mo>|</mo><msup><mi>Y</mi><mrow><mi>a</mi><mi>β</mi></mrow></msup><mo>|</mo><mo>=</mo><mn>1</mn></math>, the neutrino mixings originate from the pure clockwork sector. We show that the observed neutrino mixings are exactly obtained from a clockwork model in the case of the <math><msub><mi>q</mi><mrow><mi>a</mi><mi>β</mi></mrow></msub></math> origin scenario. In the <math><msub><mi>n</mi><mrow><mi>a</mi><mi>β</mi></mrow></msub></math> origin scenario, the correct order of magnitude of the observed neutrino mixings is obtained from a clockwork model.