A scotogenic model can radiatively generate the observed neutrino mass, provide a dark matter candidate, and lead to rare lepton flavor-violating processes. We aim to extend the model to establish a potential connection to the quark flavor-related processes within the framework of scotogenesis, enhancing the unexpectedly large branching ratio (BR) of <math><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><mi>ν</mi><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> observed by the Belle II Collaboration. Meanwhile, the model can address tensions between some experimental measurements and standard model (SM) predictions in flavor physics, such as the muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> excess and the higher BR of <math><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>→</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math>. In the model, we introduce the following dark particles: a neutral singlet Dirac-type lepton (<math><mi>N</mi></math>); two inert Higgs doublets (<math><msub><mi>η</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math>), with one carrying a lepton number; a charged singlet dark scalar <math><mo>(</mo><msup><mi>χ</mi><mo>+</mo></msup><mo>)</mo></math>; and a singlet vectorlike up-type dark quark (<math><mi>T</mi></math>). The first two entities are responsible for the radiative neutrino mass, and <math><msup><mi>χ</mi><mo>+</mo></msup></math> couples to right-handed quarks and leptons and can resolve the tensions existing in muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> and <math><msub><mi>B</mi><mi>s</mi></msub><mo>→</mo><msup><mi>μ</mi><mo>−</mo></msup><msup><mi>μ</mi><mo>+</mo></msup></math>. Furthermore, the BR of <math><msup><mi>B</mi><mo>+</mo></msup><mo>→</mo><msup><mi>K</mi><mo>+</mo></msup><mi>ν</mi><mover><mi>ν</mi><mo>¯</mo></mover></math> can be enhanced up to a factor of 2 compared to the SM prediction through the mediations of the dark <math><mi>T</mi></math> and the charged scalars. In addition, we also study the impacts on the <math><mi>K</mi><mo>→</mo><mi>π</mi><mi>ν</mi><mover><mi>ν</mi><mo>¯</mo></mover></math> decays.

Taiwan

Chuan-Hung Chen

Cheng-Wei Chiang

Rare <math><mi>B</mi></math> and <math><mi>K</mi></math> decays in a scotogenic model

In addition to anomalies associated with the muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> and the branching ratio (BR) of <math><mrow><mi>B</mi><mo>→</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup><mi>τ</mi><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math>, Belle II recently observed an unexpectedly large BR in the <math><msup><mi>B</mi><mo>+</mo></msup><mo>→</mo><msup><mi>K</mi><mo>+</mo></msup><mi>ν</mi><mover><mi>ν</mi><mo>¯</mo></mover></math> decay. To resolve the anomalous excesses in these observables, we propose a framework involving a leptoquark, denoted by <math><msub><mi>S</mi><mn>1</mn></msub></math>, which has the feature that down-type quarks merely couple to neutrinos but not the charged leptons, avoiding the strict constraint from the <math><msub><mi>B</mi><mi>s</mi></msub><mo>→</mo><msup><mi>μ</mi><mo>−</mo></msup><msup><mi>μ</mi><mo>+</mo></msup></math> decay. With the introduction of the <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></mrow></msub></math> gauge symmetry, the <math><msup><mi>Z</mi><mo>′</mo></msup></math> with light mass not only resolves the muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> anomaly, but also ensures that <math><msub><mi>S</mi><mn>1</mn></msub></math> couples exclusively to the third-generation leptons so that only <math><mi>τ</mi><msub><mover><mi>ν</mi><mo>¯</mo></mover><mi>τ</mi></msub></math> and <math><mi>τ</mi></math>-neutrino modes are involved in the processes <math><mi>b</mi><mo>→</mo><mi>c</mi><mo>ℓ</mo><mover><mi>ν</mi><mo>¯</mo></mover></math> and <math><mi>b</mi><mo>→</mo><mi>s</mi><mi>ν</mi><mover><mi>ν</mi><mo>¯</mo></mover></math>, respectively. Under the dominant constraints from <math><mo>|</mo><mi>Δ</mi><mi>F</mi><mo>|</mo><mo>=</mo><mn>2</mn></math> processes, we find that the <math><msub><mi>S</mi><mn>1</mn></msub></math> contributions to the BRs of <math><mi>B</mi><mo>→</mo><msup><mi>K</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup><mi>ν</mi><mover><mi>ν</mi><mo>¯</mo></mover></math> and <math><msub><mi>K</mi><mi>L</mi></msub><mo>→</mo><msup><mi>π</mi><mn>0</mn></msup><mi>ν</mi><mover><mi>ν</mi><mo>¯</mo></mover></math> can be factorized into the same multiplicative factor multiplying the standard model predictions, and the enhancement can be up to a factor of 2. In particular, <math><mi>B</mi><mo>(</mo><msup><mi>K</mi><mo>+</mo></msup><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><mi>ν</mi><mover><mi>ν</mi><mo>¯</mo></mover><mo>)</mo></math> can reach the upper <math><mn>1</mn><mi>σ</mi></math> error of the experimental value, i.e., <math><mo>≃</mo><mn>15.4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>11</mn></mrow></msup></math>. We also show that the model can fit the new world averages of <math><mi>R</mi><mo>(</mo><msup><mi>D</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup><mo>)</mo></math> and contribute significantly to the <math><mi>τ</mi></math> polarization in the <math><mi>B</mi><mo>→</mo><mi>D</mi><mi>τ</mi><mover><mi>ν</mi><mo>¯</mo></mover></math> decay and <math><mi>B</mi><mo>(</mo><msub><mi>B</mi><mi>c</mi></msub><mo>→</mo><mi>τ</mi><mover><mi>ν</mi><mo>¯</mo></mover><mo>)</mo></math>.

Flavor anomalies in leptoquark model with gauged <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></mrow></msub></math>

A <math><msup><mi>Z</mi><mo>′</mo></msup></math> gauge boson with sub-GeV mass has acquired a significant interest in phenomenology, particularly in view of the muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> anomaly and coherent elastic neutrino-nucleon scattering. The latter is challenged by the nuclear recoil energy of a few tens of keV but has been observed by the COHERENT experiment. To further reconcile the observed excesses in <math><mi>R</mi><mo>(</mo><msup><mi>D</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup><mo>)</mo></math> from semileptonic charmful <math><mi>B</mi></math> decays and in the <math><mi>W</mi></math> boson mass, we investigate a model with a gauged <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></mrow></msub></math> symmetry and a scalar leptoquark. In contrast to the mechanism that involves kinetic mixing between the gauge bosons of <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><mi>em</mi></mrow></msub></math> and <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></mrow></msub></math>, we adopt a dynamical symmetry breaking of <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></mrow></msub></math> by incorporating an additional Higgs doublet. Through mixing with the <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></mrow></msub></math>-charged Higgs doublet, new Higgs decay channels <math><mi>h</mi><mo>→</mo><msub><mi>Z</mi><mn>1</mn></msub><msub><mi>Z</mi><mn>1</mn></msub><mo>/</mo><msub><mi>Z</mi><mn>1</mn></msub><msub><mi>Z</mi><mn>2</mn></msub></math> occur at percent-level branching ratios, which could be accessible at the LHC. The <math><mi>W</mi></math>-mass anomaly observed by CDF II can be potentially resolved through the enhancement in the oblique parameter <math><mi>T</mi></math>. Due to the flavored gauge symmetry, the introduced scalar leptoquark <math><msup><mi>S</mi><mfrac><mn>1</mn><mn>3</mn></mfrac></msup><mo>=</mo><mo>(</mo><mover><mn>3</mn><mo>¯</mo></mover><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>/</mo><mn>3</mn><mo>)</mo></math> exhibits a unique coupling to the <math><mi>τ</mi></math> lepton, offering an explanation for the excesses observed in <math><mi>R</mi><mo>(</mo><msup><mi>D</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup><mo>)</mo></math>. Moreover, <math><mi>τ</mi><mo>→</mo><mi>μ</mi><mo>(</mo><msub><mi>Z</mi><mn>1</mn></msub><mo>→</mo><mo>)</mo><msup><mi>e</mi><mo>−</mo></msup><msup><mi>e</mi><mo>+</mo></msup></math> via the resonant light gauge boson decay can reach the sensitivity of Belle II at an integrated luminosity of <math><mrow><mn>50</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>ab</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math>.

Chun-Wei Su

Phenomenological study of a gauged <math><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></math> model with a scalar leptoquark

Abstract The open N = 2 string theory is defined on the 4D space-time with the split signature (+, +, −, −). The string field theory action of the open N = 2 string theory is described by the 4D Wess–Zumino–Witten (WZW$_{4}$) model. The equation of motion of the WZW$_{4}$ model is the Yang equation, which is equivalent to the anti-self-dual Yang–Mills equation. In this paper, we study soliton-type classical solutions of the WZW$_{4}$ model in the split signature by calculating the action density of the WZW$_{4}$ model. We find that the action density of the one-soliton solutions is localized on a 3D hyperplane. This shows that there would be codimension-one-solitonic objects, or equivalently some kind of three-branes in the open N = 2 string theory. We also prove that, in the asymptotic region of the space-time, the action density of the n-soliton solutions is a “non-linear superposition” of n one-solitons. This suggests the existence of n intersecting three-branes in the N = 2 strings. Finally we make a reduction to a (1 + 2)D real space-time to calculate the energy densities of the soliton solutions. We can successfully evaluate the energy distribution for the two-soliton solutions and find that there is no singularity in the interacting region. This implies the existence of smooth intersecting codimension-one branes in the whole region. Soliton solutions in the Euclidean signature are also discussed.

Japan

Masashi Hamanaka

Shan-Chi Huang

Hiroaki Kanno

Solitons in open = 2 String Theory Kahler-Chen-Simons theory A tour through N=2 strings On soliton solutions of the anti-self-dual Yang-Mills equations from the perspective of integrable systems Soliton solutions in an integrable chiral model in 2+1 dimensions On the space-time monopole equation A review on tachyon condensation in open string field theories Soliton equations as dynamical systems on infinite dimensional Grassmann manifold

Flavor-changing neutral current (FCNC) top-quark decays are highly suppressed due to the Glashow-Iliopoulos-Maiani mechanism in the standard model (SM). If <math><mi>t</mi><mo>→</mo><mi>q</mi><mi>h</mi><mo>,</mo><mi>q</mi><mi>V</mi></math> with <math><mi>V</mi><mo>=</mo><mi>g</mi></math>, <math><mrow><mi>γ</mi></mrow></math>, <math><mrow><mi>Z</mi></mrow></math> are all induced via quantum loop levels, then we investigate the effect that can enhance the top-FCNC up to the sensitivity designed at the high-luminosity (HL) LHC. Inspired by the mechanism of the scotogenic neutrino mass, we extend the SM by including <math><msub><mi>Z</mi><mn>2</mn></msub></math>-odd colored fermions when a <math><msub><mi>Z</mi><mn>2</mn></msub></math> discrete is imposed. The results show that by taking <math><mi>BR</mi><mo>(</mo><mi>t</mi><mo>→</mo><mi>u</mi><mi>g</mi><mo>)</mo><mo>≲</mo><mn>0.61</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math> recently measured by ATLAS as an input, <math><mi>t</mi><mo>→</mo><mi>q</mi><mi>γ</mi></math> can be indirectly bounded to be <math><mi>BR</mi><mo>(</mo><mi>t</mi><mo>→</mo><mi>q</mi><mi>γ</mi><mo>)</mo><mo>≲</mo><mn>3.2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></math>, which is below the expected sensitivity at the HL LHC. After taking potential constraints from various experiments into account, the obtained branching ratios for the loop-induced <math><mi>t</mi><mo>→</mo><mi>q</mi><mi>h</mi></math> and <math><mi>t</mi><mo>→</mo><mi>q</mi><mi>Z</mi></math> decays can be <math><mi>O</mi><mo>(</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup><mo>)</mo></math>, which falls within the sensitivity at the HL LHC.

China

Takaaki Nomura

Scotogenic top-quark FCNC decays

We construct a scotogenic Majorana neutrino mass model in a gauged U(1) X  extension of the standard model, where the mass of the gauge boson and the unbroken gauge symmetry, which leads to a stable dark matter (DM), can be achieved through the Stueckelberg mechanism. It is found that the simplest version of the extended model consists of the two inert-Higgs doublets and one vector-like singlet fermion. In addition to the Majorana neutrino mass, we study the lepton flavor violation (LFV) processes, such as ℓ  i  → ℓ  j  γ, ℓ  i  → 3ℓ  j , μ − e conversion rate in nucleus, and muonium-antimuonium oscillation. We show that the sensitivities of μ → 3e and μ − e conversion rate designed in Mu3e and COMET/Mu2e experiments make both decays the most severe constraints on the μ → e LFV processes. It is found that τ → μγ and τ → 3μ can reach the designed significance level of Belle II. In addition to explaining the DM relic density, we also show that the DM-nucleon scattering cross section can satisfy the currently experimental limit of DM direct detection.

Lepton flavor violation and scotogenic Majorana neutrino mass in a Stueckelberg U(1) X  model

A unique characteristic of exponentially growing scattering amplitude arises in an anomalous Abelian effective field theory when an extremely light Dirac neutrino mass is introduced to break the symmetry. We show that the low energy effective Lagrangian can be made explicitly gauge invariant with the help of a nonlinear representation of the Goldstone or Stueckelberg field. We study the peculiar feature of exponential growth in the ultra-high-energy neutrino-nucleon inelastic scattering. It is found that the inelastic scattering cross section is highly sensitive to the ratio of gauge coupling to the gauge boson mass, <math><msub><mrow><mi>g</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>/</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>X</mi></mrow></msub></math>. When the IceCube measurement of ultra-high-energy neutrinos, which is consistent with the standard model prediction up to <math><msub><mrow><mi>E</mi></mrow><mrow><mi>ν</mi></mrow></msub><mo>∼</mo><mn>6</mn></math> PeV, is taken into account, the inferred constraint on <math><msub><mrow><mi>g</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>/</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>X</mi></mrow></msub></math> is more severe than that obtained from the events of mono-lepton+missing transverse energy at the LHC. A muon collider with a collision energy of 10 TeV can be a good environment other than hadron colliders to probe the novel effect.

Ultra-high-energy neutrino scattering in an anomalous (1) Effective Field Theory

The quartic scalar coupling λ 5 term, which violates the lepton-number by two units in the Ma-model, is phenomenologically small when the model is applied to the lepton-flavor violation (LFV) processes. In order to dynamically generate the λ 5 parameter through quantum loop effects and retain the dark matter (DM) candidate, we extend the Ma-model by adding a Z 2-odd vector-like lepton doublet and a Z 2-even Majorana singlet. With the new couplings to the Higgs and gauge bosons, the observed DM relic density can be explained when the upper limits from the DM-nucleon scattering cross sections are satisfied. In addition to the neutrino data and LFV constraints, it is found that the DM relic density can significantly exclude the free parameter space. Nevertheless, the resulting muon g − 2 mediated by the inert charged-Higgs can fit the 4.2σ deviation between the experimental measurement and the SM result, and the branching ratio for τ → μγ can be as large as the current upper limit when the rare μ → (eγ, 3e) decays are suppressed. In addition, it is found that the resulting BR(τ → μρ) can reach the sensitivity of Belle II with an integrated luminosity of 50 ab  −1.

South Korea

Two-loop radiative seesaw, muon g − 2, and τ-lepton-flavor violation with DM constraints

We study the two-Higgs-doublet model with a type-II seesaw mechanism. In view of constraints from the Higgs data, we consider the aligned two-Higgs-doublet scheme and its effects on muon anomalous magnetic dipole moment, <math><msub><mi>a</mi><mi>μ</mi></msub></math>, including both one-loop and two-loop Barr-Zee type diagrams. Thanks to a sizable trilinear scalar coupling, the Barr-Zee type diagrams mediated by the Higgs triplet fields have a dominant effect on <math><msub><mi>a</mi><mi>μ</mi></msub></math>. In particular, unlike the usual two-Higgs-doublet models that require exotic Higgs bosons light in mass, the masses of the corresponding particles in the model are of <math><mrow><mi>O</mi><mo>(</mo><mn>100</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>. The doubly charged Higgs boson presents a different decay pattern from the usual Higgs triplet model and thus calls for a new collider search strategy, such as multi-<math><mi>τ</mi></math> searches at the LHC.

Muon <math><mrow><mi>g</mi><mo>−</mo><mn>2</mn></mrow></math> in a two-Higgs-doublet model with a type-II seesaw mechanism

A nonconventional <math><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>e</mi><mo>−</mo><mi>μ</mi></mrow></msub></math> gauge model is proposed to explain the observed neutrino masses and the unexpected anomalous magnetic moments of the electron and muon (lepton <math><mi>g</mi><mo>−</mo><mn>2</mn></math>), where for suppressing the neutrino coupling to <math><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></math> gauge boson, only the right-handed electron and muon in the standard model carry the <math><mi>U</mi><msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>e</mi><mo>−</mo><mi>μ</mi></mrow></msub></math> charge. Although the light lepton masses are suppressed when the gauge symmetry is spontaneously broken, they can be generated through the Yukawa couplings to newly introduced particles, such as vector-like lepton doublets and singlets, and scalar singlets. It is found that the same Yukawa couplings combined with the new scalar couplings to the Higgs can induce the radiative lepton-flavor violation processes <math><msup><mrow><mi>ℓ</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>→</mo><mi>ℓ</mi><mi>γ</mi></math> and lepton <math><mi>g</mi><mo>−</mo><mn>2</mn></math>, where the lepton <math><mi>g</mi><mo>−</mo><mn>2</mn></math> is proportional to <math><msub><mrow><mi>m</mi></mrow><mrow><mi>ℓ</mi></mrow></msub></math>. When Majorana fermions and a scalar singlet are further added into the model, the active neutrinos can obtain masses via the radiative seesaw mechanism. When the bounds from the <math><msub><mrow><mi>m</mi></mrow><mrow><mi>e</mi></mrow></msub></math> and <math><msub><mrow><mi>m</mi></mrow><mrow><mi>μ</mi></mrow></msub></math> and the neutrino data are satisfied, we find that the electron <math><mi>g</mi><mo>−</mo><mn>2</mn></math> can reach an order of <math><mo>−</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>12</mn></mrow></msup></math>, and the muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> can be an order of <math><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>9</mn></mrow></msup></math>. In addition, when the <math><mi>μ</mi><mo>→</mo><mi>e</mi><mi>γ</mi></math> decay is suppressed, the resulting branching ratio for <math><mi>τ</mi><mo>→</mo><mi>e</mi><mi>γ</mi></math> can be of <math><mi>O</mi><mo>(</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>8</mn></mrow></msup><mo>)</mo></math>, and that for <math><mi>τ</mi><mo>→</mo><mi>μ</mi><mi>γ</mi></math> can be as large as the current upper limit.