We consider a simple model of a dark sector with a chiral U(1) gauge symmetry. The anomaly-free condition requires at least five chiral fermions. Some of the fermions acquire masses through a vacuum expectation value of a Higgs field, and they are stable due to an accidental symmetry. This makes them dark matter candidates. If the dark sector was once in thermal equilibrium with the Standard Model and dark radiation constraints are included, two-component dark matter may be needed since the number of massless fermions is restricted. When the Dirac fermion is the main component of dark matter, the kinetic mixing should be around 10 : a larger value is restricted by direct detection limits, while a smaller value prevents thermal freeze-out. If the main dark matter component is a Majorana fermion, the kinetic mixing can be larger. Still, a sub-component of Dirac fermion could produce a detectable signal in future direct detection experiments. We also discuss the possibility of testing an invisible dark photon at future lepton collider experiments, taking into account cosmological constraints.

China

Xiao He

Takaaki Nomura

Norimi Yokozaki

Dark matter and dark radiation from chiral U(1) gauge symmetry

We study a quasi-two-zero neutrino texture based on a type-II seesaw model with modular <inline-formula><tex-math id='TM0002' notation='LaTeX'>$A_4$</tex-math></inline-formula> symmetry to evade the cosmological bound on the sum of neutrino masses while keeping some predictability in the neutrino sector. Working on three fixed points for the modulus, we discuss predictions of the model and show the allowed points satisfying the cosmological bound on neutrino mass from both cosmic microwave background (CMB) and CMB + baryon acoustic oscillation data.

Hiroshi Okada

Quasi-Two-Zero Texture in Type-II Seesaw at Fixed Points from Modular <italic>A</italic> 4 Symmetry

We study a three-loop induced neutrino mass scenario from a non-holomorphic modular $\textit{A}$ $_{4}$ flavor symmetry and obtain the minimum scenario leading to predictions of the lepton masses, mixing angles, and Dirac and Majorana phases, which are shown through chi square analyses. In addition, we discuss the lepton flavor violations, muon anomalous magnetic moment, lepton universality, and relic density of the dark matter candidate. Moreover, we show that our model can be extended to satisfy the observed relic density of dark matter within the limit of perturbation by adding one singlet scalar boson without changing predictions in the neutrino sector.

Neutrino mass model at a three-loop level from a non-holomorphic modular $\textit{A}$ $_{4}$ symmetry * Takaaki Nomura is supported by the Fundamental Research Funds for the Central Universities. Hiroshi Okada is supported by Zhongyuan Talent (Talent Recruitment Series) Foreign Experts Project

We propose a new inverse seesaw model based on hidden local <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> symmetry framework where the inverse seesaw mechanism is induced at one loop level. A Majorana mass term of singlet fermion is forbidden by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> symmetry and it is generated at one-loop level by introducing relevant particle contents to get loop diagram, inducing inverse seesaw mechanism. The same particle contents also contribute to lepton magnetic(electric) dipole moment and lepton flavor violating decays without chiral suppression. We can then obtain sizable muon anomalous magnetic dipole moment that accommodate with deviation from the standard model prediction. The constraints from lepton flavor violating decays and electron magnetic(electric) dipole moment are also discussed to explore testability of the model.

Japan

Radiative inverse seesaw model with hidden <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> gauge symmetry enhancing lepton <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math>

We revisit a supersymmetric flavor model, based on the symmetries of <inline-formula><tex-math id='TM0001' notation='LaTeX'>$SU(2)_L \times A_4 \times Z_3 \times U(1)_R$</tex-math></inline-formula>, which extends the original Altarelli and Feruglio construction by introducing flavon and driving superfields responsible for the spontaneous breaking of the flavor symmetry in order to obtain a nonzero reactor angle. Vacuum alignments of the flavon fields are achieved through the minimization of the scalar potential derived from the superpotential. This setup leads to specific mass matrices for the charged leptons and neutrinos that are consistent with current experimental data, including the measured values of the lepton mixing angles and neutrino mass squared differences. We investigate whether the model can simultaneously accommodate successful thermal leptogenesis. In particular, we analyze the CP asymmetry generated by the decay of heavy Majorana neutrinos, the resulting lepton asymmetry, and its conversion to the baryon asymmetry through the electroweak sphalerons. We find, however, that the CP asymmetry is zero in the leading order of the model since the Dirac neutrino mass matrix has simple texture. Then we consider the next-to-leading order in Yukawa interactions of the Dirac neutrinos. As a result, we can realize the baryon asymmetry of the universe at the present universe. By numerically scanning the parameter space, we identify the regions consistent with both neutrino oscillation data and the observed baryon asymmetry. In the specific case such that one of the couplings for the right-handed Majorana neutrinos is a real parameter, the predicted lightest neutrino mass is at least 5 meV and 15 meV for the normal and inverted neutrino mass hierarchies, respectively. In addition, the range of the Majorana phases may be tested in future experiments.

Yusuke Shimizu

Towa Takahashi

Revisiting the Flavor Model and Leptogenesis

We investigate a radiative seesaw model with two leptoquarks under non-holomorphic modular $\textit{A}$ symmetry. The leptons and quarks belong to non-trivial representations of the modular $\textit{A}$ and the structures of their mass matrices are restricted. Neutrino masses are generated at one-loop level via leptoquark inside loop diagram where structures of relevant Yukawa interactions are determined by the modular $\textit{A}$ symmetry. We scan the free parameters in the model and try to fit all the observed data for both lepton and quark sectors. For allowed parameters, we show some predictions regarding neutrino observables such as sum of neutrino mass and neutrinoless double beta decay.

Xing-Yu Wang

A radiative neutrino mass model with leptoquarks under non-holomorphic modular $\textit{A}$

We propose a new type of lepton seesaw model introducing a modular <italic>A</italic> 4 flavor symmetry in which isospin doublet vector fermions play an important role in constructing seesaw mechanisms for both the charged-lepton mass matrix and the neutrino one. The charged-lepton mass matrix is induced via the Dirac seesaw with a two-by-two block mass matrix. On the other hand, the neutrino mass matrix is generated via a seesaw with four-by-four block mass matrix where the right-handed neutral fermions are also added. Remarkably, the neutral fermion mass matrix provides us with a new type of seesaw formula for the active neutrino mass. Through our chi-squared analysis, we discuss some tendencies of observables, focusing on two fixed points <inline-formula><tex-math id='TM0001' notation='LaTeX'>$\tau =i,\ \omega$</tex-math></inline-formula>.

A New Type of Lepton Seesaw Model in a Modular <italic>A</italic> 4 Symmetry

We investigate TeV scale seesaw scenarios at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>+</mo></msup></math> colliders in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi><mi>TRISTAN</mi></math> (Transposable Ring Intersecting STorage Accelerator in Nippon) experiment. In a minimal type I seesaw scenario, we consider two generations of Standard Model (SM) singlet heavy Majorana–type right-handed neutrinos, which couple with SM-gauge bosons through light-heavy neutrino mixing. We discuss the prospects of probing heavy neutrinos via the processes such as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><mi>ν</mi><msub><mi>N</mi><mi>i</mi></msub><mo stretchy="false">→</mo><msup><mi>e</mi><mo>+</mo></msup><mi>j</mi><mi>j</mi><mi>ν</mi></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>−</mo></msup><mi>j</mi><mi>j</mi><mi>ν</mi></math> for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>346</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>1</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>ab</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math> luminosity. Studying these process, we estimate limits on the light-heavy neutrino mixing angles as a function of heavy neutrino mass, which could be 2 orders of magnitude stronger than electroweak precision data. Further, we study the effect of a doubly charged scalar boson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msup><mi>H</mi><mrow><mo>+</mo><mo>+</mo></mrow></msup><mo stretchy="false">)</mo></math> from the type II seesaw scenario in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>+</mo></msup></math> collision at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>2</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>. In this case, we consider <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msubsup><mo>ℓ</mo><mi>i</mi><mo>+</mo></msubsup><msubsup><mo>ℓ</mo><mi>j</mi><mo>+</mo></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>H</mi><mrow><mo>+</mo><mo>+</mo></mrow></msup><mi>Z</mi><mo>/</mo><mi>γ</mi></math> processes followed by the same-sign dilepton decay of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>H</mi><mrow><mo>+</mo><mo>+</mo></mrow></msup></math>. We find that events involving <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>+</mo></msup></math> among these final states can probe the neutrino mass ordering in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi><mi>TRISTAN</mi></math> experiment at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>5</mn><mi>σ</mi></mrow></math> significance. In addition, we study the production of positively charged triplet fermions in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi><mi>TRISTAN</mi></math> following the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>μ</mi><mo>+</mo></msup><msup><mi mathvariant="normal">Σ</mi><mo>+</mo></msup></math> process, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">Σ</mi><mo>+</mo></msup></math> decays into <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>+</mo></msup><mi>j</mi><mi>j</mi></math> mode through <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson exchange. Considering a triplet at 1 TeV and studying SM backgrounds, we estimate the discovery potential of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>+</mo></msup><mi>j</mi><mi>j</mi></math> signal at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi><mi>TRISTAN</mi></math> with respect to projected luminosity.

Arindam Das

Jinmian Li

South Korea

Sanjoy Mandal

Rao Zhang

Testing tree level TeV scale seesaw scenarios in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi><mi>TRISTAN</mi></math>

We search for predictability of lepton masses and mixing patterns of type-II seesaw scenario in a non-holomorphic modular <math altimg='si1.svg'><msub><mrow><mi>A</mi></mrow><mrow><mn>4</mn></mrow></msub></math> symmetry recently proposed by Qu and Ding. We propose three types of minimum predictive models with different assignments of modular weight, satisfying the neutrino oscillation data in Nufit 5.2. The cosmological bound on the sum of neutrino mass is stringent to our models and CMB bound <math altimg='si2.svg'><mo>&#8721;</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>&#957;</mi></mrow></msub><mo>&#8804;</mo><mn>0.12</mn></math> eV can be satisfied by one of three models playing an important role in discriminating them.

Type-II seesaw of a non-holomorphic modular <italic>A</italic> <inf>4</inf> symmetry

We study a Zee model in a non-holomorphic modular <math altimg='si1.svg'><msub><mrow><mi>A</mi></mrow><mrow><mn>4</mn></mrow></msub></math> flavor symmetry in which we find good predictions in both the cases of normal and inverted hierarchy. Parameter reduction on neutrino sector occurs due to large mass hierarchies between charged-leptons mass eigenvalues and new singly-charged bosons in addition to this flavor symmetry. As a result, we have two complex free parameters including modulus <italic>&#964;</italic>. We show several predictions in terms of verifiable observables such as Dirac CP, Majorana phases, sum of the neutrino masses, and the effective mass for neutrino double beta decay in addition to demonstrating allowed regions for our input parameters.