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The wave equation is an important physical partial differential equation, and in recent years, deep learning has shown promise in accelerating or replacing traditional numerical methods for solving it. However, existing deep learning methods suffer from high data acquisition costs, low training efficiency, and insufficient generalization capability for boundary conditions. To address these issues, this paper proposes an unsupervised learning method for the wave equation based on finite difference residual constraints. We construct a novel finite difference residual constraint based on structured grids and finite difference methods, as well as an unsupervised training strategy, enabling convolutional neural networks to train without data and predict the forward propagation process of waves. Experimental results show that finite difference residual constraints have advantages over physics-informed neural networks (PINNs) type physical information constraints, such as easier fitting, lower computational costs, and stronger source term generalization capability, making our method more efficient in training and potent in application., Comment: in Chinese language

Cavity magnomechanics has shown great potential in studying macroscopic quantum effects, especially for quantum entanglement, which is a key resource for quantum information science. Here we propose to realize magnon mediated nonreciprocal photon-phonon entanglement, which exhibits asymmetry when opposite magnetic or driving fields are respectively applied to the magnons with the Kerr effect or the photons with the Sagnac effect. We find that the mean magnon number can selectively exhibit nonreciprocal linear or nonlinear (bistable) behavior with the strength of the strong driving field on the cavity. Assisted by this driving field, the magnon-phonon coupling is greatly enhanced, leading to the nonreciprocal photon-phonon entanglement via the swapping interaction between the magnons and photons. This nonreciprocal entanglement can be significantly enhanced with the magnon Kerr and Sagnac effects. Given the available parameters, the nonreciprocal photon-phonon entanglement can be preserved at $\sim3$ K, showing remarkable resilience against the bath temperature. The result reveals that our paper holds promise in developing various nonreciprocal devices with both the magnon Kerr and Sagnac effects in cavity magnomechanics., Comment: 9 pages, 7 figures

We study the nonlinear $\sigma$-model in ${(d+1)}$-dimensional spacetime with connected target space $K$ and show that, at energy scales below singular field configurations (such as vortices), it has an emergent non-invertible higher symmetry. The symmetry defects of the emergent symmetry are described by the $d$-representations of a discrete $d$-group $\mathbb{G}^{(d)}$ (i.e. the emergent symmetry is the dual of the invertible $d$-group $\mathbb{G}^{(d)}$ symmetry). The $d$-group $\mathbb{G}^{(d)}$ is determined such that its classifying space $B\mathbb{G}^{(d)}$ is given by the $d$-th Postnikov stage of $K$. In $(2+1)$D and for finite $\mathbb{G}^{(2)}$, this symmetry is always holo-equivalent to an invertible ${0}$-form (ordinary) symmetry with potential 't Hooft anomaly. The singularity-free disordered phase of the nonlinear $\sigma$-model spontaneously breaks this symmetry, and when $\mathbb{G}^{(d)}$ is finite, it is described by the deconfined phase of $\mathbb{G}^{(d)}$ higher gauge theory. We consider examples of such disordered phases. We focus on a singularity-free $S^2$ nonlinear $\sigma$-model in ${(3+1)}$D and show that it has an emergent non-invertible higher symmetry. As a result, its disordered phase is described by axion electrodynamics and has two gapless modes corresponding to a photon and a massless axion. Notably, this non-perturbative result is different from the results obtained using the $S^N$ and $\mathbb{C}P^{N-1}$ nonlinear $\sigma$-models in the large-$N$ limit., Comment: 13+12 pages, 1+2 figures. v2: published version

A generalized symmetry (defined by the algebra of local symmetric operators) can go beyond group or higher group description. A theory of generalized symmetry (up to holo-equivalence) was developed in terms of symmetry-TO -- a bosonic topological order (TO) with gappable boundary in one higher dimension. We propose a general method to compute the 2+1D symmetry-TO from the local symmetric operators in 1+1D systems. Our theory is based on the commutant patch operators, which are extended operators constructed as products and sums of local symmetric operators. A commutant patch operator commutes with all local symmetric operators away from its boundary. We argue that topological invariants associated with anyon diagrams in 2+1D can be computed as contracted products of commutant patch operators in 1+1D. In particular, we give concrete formulae for several topological invariants in terms of commutant patch operators. Topological invariants computed from patch operators include those beyond modular data, such as the link invariants associated with the Borromean rings and the Whitehead link. These results suggest that the algebra of commutant patch operators is described by 2+1D symmetry-TO. Based on our analysis, we also argue briefly that the commutant patch operators would serve as order parameters for gapped phases with finite symmetries., Comment: 18 pages

The BESIII collaboration has recently reported the first time measurement of the decay asymmetry $\alpha(\Lambda_c^+ \to \Xi^0 K^+) = 0.01 \pm 0.16(stat.) \pm 0.03(syst.)$ and also a sizable phase shift of $\delta_P-\delta_S = -1.55 \pm 0.25$ or $1.59\pm 0.25$ between S- and P-wave amplitudes. This implies significant strong phase shifts in the decay amplitudes. The strong phases indicate the existence of rescattering or loop effects, which are challenging to calculate due to non-perturbative effects. By employing the flavor $SU(3)_F$ symmetry and applying the K\"orner-Pati-Woo theorem to reduce the number of parameters, we find that the current data already allow us to obtain, for the first time, model-independent decay amplitudes and their strong phases. The establishment of the existence of sizable strong phases opens a window for future investigations into CP violation. In our fit, a notable discrepancy emerges in the branching ratio of $\Xi_c^0 \to \Xi^- \pi^+$. The direct relationship between $\Gamma (\Lambda_c^+ \to \Lambda e^+\nu_e)$ and $\Gamma (\Xi_c^0 \to \Xi^- e^+\nu_e)$, along with newly discovered $SU(3)_F$ relations, collectively suggests an underestimation of $\mathcal{B}(\Xi_c^0 \to \Xi^- \pi^+)$ in experimental findings., Comment: 6 pages, new references added

Belle II has recently reported the new measurement ${\cal B}(B^+\to K^+\nu\bar\nu)=(2.3\pm0.7)\times 10^{-5}$ \cite{Belle-II:2023esi} which is two times larger than their previous result (although consistent within errors) and about $2.7\,\sigma$ higher than the SM prediction. We re-examine new physics scenarios we have discussed previously which can enhance this rate to determine if they can accommodate the higher value reported in the new measurement. We use consistency with existing bounds on $B\to K^*\nu\bar\nu$, $b\to s \ell^+\ell^-$, $B\to D^{(*)}\ell\bar\nu$ and $B_s$ mixing to limit possible explanations for the excess. For the case of LFV neutrino couplings, we find that only two leptoquarks remain viable requiring a large $C_{9^\prime}^{\tau\tau}=-C_{10^\prime}^{\tau\tau}$. For models with different types of light dark matter particle pairs (scalar, fermion, or vector), the preliminary $q^2$ distribution from Belle II, which shows that the excess appears mostly for bins with $3\leq q^2\leq7$ GeV$^2$ \cite{Belle-II:2023esi}, implies only the vector current operators with scalar or vector dark matter particles with masses in the hundreds of MeV can match the anomaly., Comment: Correct two typos

It is known that $n$-degenerate Landau levels with the same spin-valley quantum number can be realized by $n$-layer graphene with rhombohedral stacking under magnetic field $B$. We find that the wave functions of degenerate Landau levels are concentrated at the surface layers of the multi-layer graphene if the dimensionless ratio $\eta = \gamma_1/(v_F\sqrt{2e\hbar B/c}) \approx 9/\sqrt{B[\text{Tesla}]} \gg 1$, where $\gamma_1$ is the interlayer hopping energy and $v_F$ the Fermi velocity of single-layer graphene. This allows us to suggest that: 1) filling fraction $\nu=\frac12$ (or $\nu_n = 5\frac12$) non-Abelian state with Ising anyon can be realized in three-layer graphene for magnetic field $ B \in [ 2 , 9] $ Tesla; 2) filling fraction $\nu=\frac23$ (or $\nu_n = 7\frac13$) non-Abelian state with Fibonacci anyon can be realized in four-layer graphene for magnetic field $ B \in [ 5 , 9] $ Tesla. Here, $\nu$ is the total filling fraction in the degenerate Landau levels, and $\nu_n$ is the filling fraction measured from charge neutrality point which determines the measured Hall conductance. We have assumed the following conditions to obtain the above results: the exchange effect of Coulomb interaction polarizes the $SU(4)$ spin-valley quantum number in the degenerate Landau levels and effective dielectric constant $\epsilon \gtrsim 10$ to reduce the Coulomb interaction. The high density of states of multi-layer graphene helps to reduce the Coulomb interaction via screening., Comment: 5 pages, 2 figure

We use the computer algebraic system GAP to classify modular data up to rank 11, and integral modular data up to rank 12. This extends the previously obtained classification of modular data up to rank 6. Our classification includes all the modular data from modular tensor categories up to rank 11. But our list also contains a few potential unitary modular data at ranks 9, 10 and 11, which are not known to correspond to any unitary modular tensor categories (such as those from Kac-Moody algebra, twisted quantum doubles of finite group, as well as their Abelian anyon condensations). It remains to be shown if those potential modular data can be realized by modular tensor categories or not, although we provide some evidence that all but one may be constructed from centers of near-group categories. The classification of modular data corresponds to a classification of modular tensor categories (up to modular isotopes which are not expected to be present at low ranks). The classification of modular tensor categories leads to a classification of gapped quantum phases of matter in 2-dimensional space for bosonic lattice systems with no symmetry, as well as a classification of generalized symmetries in 1-dimensional space., Comment: 443 pages (main text 64 pages), 1 figure

We propose a unified point cloud video self-supervised learning framework for object-centric and scene-centric data. Previous methods commonly conduct representation learning at the clip or frame level and cannot well capture fine-grained semantics. Instead of contrasting the representations of clips or frames, in this paper, we propose a unified self-supervised framework by conducting contrastive learning at the point level. Moreover, we introduce a new pretext task by achieving semantic alignment of superpoints, which further facilitates the representations to capture semantic cues at multiple scales. In addition, due to the high redundancy in the temporal dimension of dynamic point clouds, directly conducting contrastive learning at the point level usually leads to massive undesired negatives and insufficient modeling of positive representations. To remedy this, we propose a selection strategy to retain proper negatives and make use of high-similarity samples from other instances as positive supplements. Extensive experiments show that our method outperforms supervised counterparts on a wide range of downstream tasks and demonstrates the superior transferability of the learned representations., Comment: Accepted by ICCV 2023

Adversarial attacks can compromise the robustness of real-world detection models. However, evaluating these models under real-world conditions poses challenges due to resource-intensive experiments. Virtual simulations offer an alternative, but the absence of standardized benchmarks hampers progress. Addressing this, we propose an innovative instant-level data generation pipeline using the CARLA simulator. Through this pipeline, we establish the Discrete and Continuous Instant-level (DCI) dataset, enabling comprehensive experiments involving three detection models and three physical adversarial attacks. Our findings highlight diverse model performances under adversarial conditions. Yolo v6 demonstrates remarkable resilience, experiencing just a marginal 6.59% average drop in average precision (AP). In contrast, the ASA attack yields a substantial 14.51% average AP reduction, twice the effect of other algorithms. We also note that static scenes yield higher recognition AP values, and outcomes remain relatively consistent across varying weather conditions. Intriguingly, our study suggests that advancements in adversarial attack algorithms may be approaching its ``limitation''.In summary, our work underscores the significance of adversarial attacks in real-world contexts and introduces the DCI dataset as a versatile benchmark. Our findings provide valuable insights for enhancing the robustness of detection models and offer guidance for future research endeavors in the realm of adversarial attacks.

Due to finite masses and mixing, for neutrinos propagation in space-time, there is a chiral oscillation between left- and right- chiral neutrinos, besides the usual oscillation between different generations. The probability of chiral oscillation is suppressed by a factor of $m^2/E^2$ making the effect small for relativistic neutrinos. However, for non-relativistic neutrinos, this effect can be significant. In matter, the equation of motion is modified. When neutrinos produced in weak interaction pass through the matter, the eigen-energies are split into two different ones depending on the helicity of the neutrino. This results in different oscillation behavior for neutrinos with different helicity, in particular there is a new resonant effect related to the helicity state of neutrino different than the usual MSW effect. For Majorana neutrinos, chiral oscillation also depends on Majorana phases., Comment: 7 pages, 3 figures, published version

To enable the practical use of skyrmion-based devices, it is essential to achieve a balance between energy efficiency and thermal stability, while also ensuring reliable electrical detection against noise. Understanding how a skyrmion interacts with material disorder and external perturbations is thus essential. Here we investigate the electronic noise of a single skyrmion under the influence of thermal fluctuations and spin currents in a magnetic thin film. We detect the thermally induced noise with a 1/f signature in the strong pinning regime but a random telegraph noise in the intermediate pinning regime. Both the thermally dominated and current-induced telegraph-like signals are detected in the weak pinning regime. Our results provide a comprehensive electronic noise picture of a single skyrmion, demonstrating the potential of noise fluctuation as a valuable tool for characterizing the pinning condition of a skyrmion. These insights could also aid in the development of low-noise and reliable skyrmion-based devices.

The gauged $U(1)_{L_\mu - L_\tau}$ model is a candidate model for explaining the muon g-2 anomaly because the $Z'$ in the model has a natural normal coupling to muon. Due to other experimental data constraints the viable mass range for the usual $Z'$ is constrained to be lower than a few hundred MeV. It has been shown that if the $Z'$ has a maximal off-diagonal mixing, $(\bar \mu \gamma^\mu \tau + \bar \tau \gamma^\mu \mu) Z'_\mu$, a large mass for $Z'$ is possible. This class of models has a very interesting signature for detection, such as $\mu^-\mu^+ \to \tau^- \tau^+$ pair, $\mu^- \mu^+ \to \mu^\pm\mu^\pm \tau^\mp \tau^\mp$ at a muon collider. In this work we study in detail these processes. We find that the in the parameter space solving the muon g-2 anomaly, t-channel $\tau^- \tau^+$ pair production can easily be distinguished at more than 5$\sigma$ level from the s-channel production as that predicted in the standard model. The smoking gun signature of doubly same sign $\mu^\pm \mu^\pm + \tau^\mp\tau^\mp$ pairs production can have a 5$\sigma$ sensitivity, at a muon collider of 3 TeV with $\mathcal{O}$($fb^{-1}$) luminosity., Comment: 10 pages, 7 figures

Spin textures such as magnetic domain walls and skyrmions have the potential to revolutionize electronic devices by encoding information bits. Although recent advancements in ferromagnetic films have led to promising device prototypes, their widespread implementation has been hindered by the material-related drawbacks. Antiferromagnetic spin textures, however, offer a solution to many of these limitations, paving the way for faster, smaller, more energy-efficient, and more robust electronics. The functionality of synthetic antiferromagnets, comprised of two or more magnetic layers separated by spacers, may be easily manipulated by making use of different materials as well as interface engineering. In this Perspective article, we examine the challenges and opportunities presented by spin textures in synthetic antiferromagnets and propose possible directions and prospects for future research in this burgeoning field.

A large amount of data on hadronic two body weak decays of anti-triplet charmed baryons $T_{c\bar 3}$ to an octet baryon $T_8$ and an octet or singlet pseudoscalar meson $P$, $T_{c \bar 3} \to T_8 P$, have been measured. The SU(3) flavor symmetry has been applied to study these decays to obtain insights about weak interactions for charm physics. However not all such decays needed to determine the SU(3) irreducible amplitudes have been measured forbidding a complete global analysis. Previously, it has been shown that data from measured decays can be used to do a global fit to determine all except one parity violating and one parity conserving amplitudes of the relevant SU(3) irreducible amplitudes causing 8 hadronic two body weak decay channels involving $\Xi^0_c$ to $\eta$ or $\eta'$ transitions undetermined. It is important to obtain information about these decays in order to guide experimental searches. In this work using newly measured decay modes by BESIII and Belle in 2022, we carry out a global analysis and parameterize the unknown amplitudes to provide the ranges for the branching ratios of the 8 undetermined decays. Our results indicate that the SU(3) flavor symmetry can explain the measured data exceptionally well, with a remarkable minimal $\chi^2/d.o.f.$ of 1.21 and predict 80 observables in 45 decays for future experimental data to test. We then vary the unknown SU(3) amplitudes to obtain the allowed range of branching ratios for the 8 undetermined decays. We find that some of them are within reach of near future experimental capabilities. We urge our experimental colleagues to carry out related searches., Comment: 9pages, 2 figures, 3 tables

We present a new self-supervised paradigm on point cloud sequence understanding. Inspired by the discriminative and generative self-supervised methods, we design two tasks, namely point cloud sequence based Contrastive Prediction and Reconstruction (CPR), to collaboratively learn more comprehensive spatiotemporal representations. Specifically, dense point cloud segments are first input into an encoder to extract embeddings. All but the last ones are then aggregated by a context-aware autoregressor to make predictions for the last target segment. Towards the goal of modeling multi-granularity structures, local and global contrastive learning are performed between predictions and targets. To further improve the generalization of representations, the predictions are also utilized to reconstruct raw point cloud sequences by a decoder, where point cloud colorization is employed to discriminate against different frames. By combining classic contrast and reconstruction paradigms, it makes the learned representations with both global discrimination and local perception. We conduct experiments on four point cloud sequence benchmarks, and report the results on action recognition and gesture recognition under multiple experimental settings. The performances are comparable with supervised methods and show powerful transferability., Comment: Accepted by AAAI2023

Cavity optomechanics, a promising platform to investigate macroscopic quantum effects, has been widely used to study nonreciprocal entanglement with Sagnec effect. Here we propose an alternative way to realize nonreciprocal entanglemment among magnons, photons, and phonons in a hybrid cavity-magnon optomechanics, where magnon Kerr effect is used. We show that the Kerr effect gives rise to a magnon frequency shift and an additional two-magnon effect. Both of them can be tuned from positive to negative via tuning the magectic field direction, leading to nonreciprocity. By tuning system parameters such as magnon frequency detuning or the coefficient of the two-magnon effect, bipartite and tripartite entanglements can be nonreciprocally enhanced. By further studying the defined bidirectional contrast ratio, we find that nonreciprocity in our system can be switch on and off, and can be engineered by the bath temperature. Our proposal not only provides a potential path to demonstrate nonreciprocal entanglement with the magnon Kerr effect, but also opens a direction to engineer and design diverse nonreciprocal devices in hybrid cavity-magnon optomechanics with nonlinear effects., Comment: 8 pages,4 figures

Chiral field theories describe large classes of matter, from the edges of Quantum Hall systems to the electroweak sector of the Standard Model, but defining them on the lattice has been an ongoing challenge due to a no-go theorem precluding free local models, the potential of symmetry anomalies, and sign problems. Some approaches define a $1+1$d chiral field theory as the edge of a $2+1$d system and argue that the edge decouples from the bulk, but this can be difficult to verify due to finite size effects and strong interactions. On the other hand, recent work has shown how to define the $2+1$d bulk theory as an exactly solvable model with zero correlation length, in which case the edge theory may be extracted exactly. We use these techniques to derive a lattice field theory on a $1+1$d spacetime lattice which carries an anomalous chiral $U(1)$ symmetry with zero chiral central charge. The lattice theory with anomalous chiral $U(1)$ symmetry is always gapless, regardless of lattice interactions. We demonstrate the chiral anomaly by coupling to a background gauge field, develop a field theory which demonstrates the chiral behavior, and show how to assemble a chiral, anomaly-free theory where the gauge field may be taken to be dynamical., Comment: 5 pages, 1 figure. arXiv admin note: text overlap with arXiv:2203.01427

Hyperon nonleptonic decays that change strangeness by two units, such as $\Xi\to N\pi$ and $\Omega^-\to nK^-,\Lambda\pi^-,\Sigma^{(*)}\pi$, are highly suppressed in the standard model. Only a few of them have been searched for to date, leading to experimental upper bounds which are many orders of magnitude above the expectations of the standard model. This leaves ample opportunity to look for indications of new physics in these processes. At the same time, most, but not all, $\Delta S=2$ interactions beyond the standard model are severely constrained by kaon-mixing data. We present two scenarios where new physics satisfying the kaon-mixing constraints can enhance the hyperon decay rates to levels that can be probed in future quests by BESIII and LHCb and at the proposed Super Tau-Charm Factory. Both scenarios require significant fine-tuning., Comment: 25 pages, 5 figures, slightly expanded, in line with journal version

Although condensed matter systems usually do not have higher-form symmetries, we show that, unlike 0-form symmetry, higher-form symmetries can emerge as exact symmetries at low energies and long distances. In particular, emergent higher-form symmetries at zero temperature are robust to arbitrary local UV perturbations in the thermodynamic limit. This result is true for both invertible and non-invertible higher-form symmetries. Therefore, emergent higher-form symmetries are exact emergent symmetries: they are not UV symmetries but constrain low-energy dynamics as if they were. Since phases of matter are defined in the thermodynamic limit, this implies that a UV theory without higher-form symmetries can have phases characterized by exact emergent higher-form symmetries. We demonstrate this in three lattice models, the quantum clock model and emergent $\mathbb{Z}_N$ and $U(1)$ ${p}$-gauge theory, finding regions of parameter space with exact emergent (anomalous) higher-form symmetries. Furthermore, we perform a generalized Landau analysis of a 2+1D lattice model that gives rise to $\mathbb{Z}_2$ gauge theory. Using exact emergent 1-form symmetries accompanied by their own energy/length scales, we show that the transition between the deconfined and Higgs/confined phases is continuous and equivalent to the spontaneous symmetry-breaking transition of a $\mathbb{Z}_2$ symmetry, even though the lattice model has no symmetry. Also, we show that this transition line must always contain two parts separated by multi-critical points or other phase transitions. We discuss the physical consequences of exact emergent higher-form symmetries and contrast them to emergent 0-form symmetries. Lastly, we show that emergent 1-form symmetries are no longer exact at finite temperatures, but emergent $p$-form symmetries with $p\geq 2$ are., Comment: 22 + 15 pages, 16 figures, 3 appendices. v2: minor changes throughout, added references, updated Sections 3 and 4, and added section 5 on finite temperature effects. v3: made manuscript shorter with minor changes to content. v4: minor changes and added a section on the Fradkin-Shenker model

A characteristic property of a gapless liquid state is its emergent symmetry and dual symmetry, associated with the conservation laws of symmetry charges and symmetry defects respectively. These conservation laws, considered on an equal footing, can't be described simply by the representation theory of a group (or a higher group). They are best described in terms of a topological order (TO) with gappable boundary in one higher dimension; we call this the symTO of the gapless state. The symTO can thus be considered a fingerprint of the gapless state. We propose that a largely complete characterization of a gapless state, up to local-low-energy equivalence, can be obtained in terms of its maximal emergent symTO. In this paper, we review the symmetry/topological-order (Symm/TO) correspondence and propose a precise definition of maximal symTO. We discuss various examples to illustrate these ideas. We find that the 1+1D Ising critical point has a maximal symTO described by the 2+1D double-Ising topological order. We provide a derivation of this result using symmetry twists in an exactly solvable model of the Ising critical point. The critical point in the 3-state Potts model has a maximal symTO of double (6,5)-minimal-model topological order. As an example of a noninvertible symmetry in 1+1D, we study the possible gapless states of a Fibonacci anyon chain with emergent double-Fibonacci symTO. We find the Fibonacci-anyon chain without translation symmetry has a critical point with unbroken double-Fibonacci symTO. In fact, such a critical theory has a maximal symTO of double (5,4)-minimal-model topological order. We argue that, in the presence of translation symmetry, the above critical point becomes a stable gapless phase with no symmetric relevant operator., Comment: 41 pages, 21 figures; it includes a review on Symmetry/Topological Order correspondence

We put forward complementary relations of entanglement, coherence, steering inequality violation, and Bell nonlocality for arbitrary three-qubit states. We show that two families of genuinely entangled three-qubit pure states with single parameter exist, and they exhibit maximum coherence and steering inequality violation for a fixed amount of negativity, respectively. It is found that the negativity is exactly equal to the geometric mean of bipartite concurrences for the three-qubit pure states, although the negativity is always less than or equal to the latter for three-qubit mixed states. Moreover, the complementary relation between negativity and first-order coherence for tripartite entanglement states are established. Furthermore, we investigate the close relation between the negativity and the maximum steering inequality violation. In addition, the complementary relation between negativity and the maximum Bell-inequality violation for arbitrary three-qubit states is obtained. The results provide reliable evidence of fundamental connections among entanglement, coherence, steering inequality violation, and Bell nonlocality., Comment: 11 pages, 5 figures

Motivated by flavour symmetry models, we construct theories based on a low-energy limit featuring lepton flavour triality that have the flavour-violating decays $\tau^\pm \to \mu^\pm \mu^\pm e^\mp$ and $\tau^\pm \to e^\pm e^\pm \mu^\mp$ as the main phenomenological signatures of physics beyond the standard model. These decay modes are expected to be probed in the near future with increased sensitivity by the Belle II experiment at the SuperKEKB collider. The simple standard model extensions featured have doubly-charged scalars as the mediators of the above decay processes. The phenomenology of these extensions is studied here in detail., Comment: 24 pages, 4 figures Additional references and neutrino mass discussion added. Matches version accepted for publication in Physical Review D