Mon·Aug 21, 2023Monday·August 21, 2023

1. 01*

   Phenomenological profile of scotogenic fermionic dark matter

   Anirban Karan🇪🇸 · Soumya Sadhukhan🇮🇳 · José W. F. Valle🇪🇸

   We consider the possibility that neutrino masses arise from the exchange of dark matter states. We examine in detail the phenomenology of fermionic dark matter in the singlet-triplet scotogenic reference model. We explore the case of singlet-like fermionic dark matter, taking into account all co-annihilation effects relevant for determining its relic abundance, such as fermion-fermion and scalar-fermion co-annihilation. Although this in principle allows for dark matter below 60 GeV, the latter is in conflict with charged lepton flavour violation (cLFV) and/or collider physics constraints. We examine the prospects for direct dark matter detection in upcoming experiments up to 10 TeV. Fermion-scalar coannihilation is needed to obtain viable fermionic dark matter in the 60-100 GeV mass range. Fermion-fermion and fermion-scalar coannihilation play complementary roles in different parameter regions above 100 GeV.

   hep-phJHEP(2023)·15 citations
2. 02*

   Early Universe hypercharge breaking and neutrino mass generation

   Sergio López-Zurdo🇪🇸 · Álvaro Lozano-Onrubia🇪🇸 · Luca Merlo🇪🇸 · José Miguel No🇪🇸

   We show that the conditions allowing for a spontaneous breaking of the $U(1{)}_Y$ hypercharge gauge symmetry of the Standard Model (SM) in the early Universe are generically present in extensions of the SM addressing the generation of light neutrino masses via radiative contributions. In such scenarios, the breaking of (hyper)charge at high-temperatures yields new possibilities for explaining the observed matter-antimatter asymmetry of the Universe. Considering for concreteness the Zee-Babu radiative neutrino mass generation model, we show that a period of hypercharge breaking prior to the electroweak phase transition could allow for successful baryogenesis via a non-conventional leptogenesis mechanism, based on the presence of charge-breaking masses for the SM leptons in the early Universe.

   hep-phPRL(2025)·0 citations
3. 03*

   Off-shellness in generalized parton distributions and form factors of the pion

   Vanamali Shastry🇵🇱 · Wojciech Broniowski🇵🇱 · Enrique Ruiz Arriola🇪🇸

   We study the effects of off-shellness in the generalized parton distributions of the pion. On general grounds, these distributions exhibit a richer structure than in the on-shell case due to absence of the crossing symmetry. In particular, their moments involve additional terms odd in the skewness parameter, associated with new form factors. We bring up relations between the off-shell charge and gravitational form factors, as well as the pion form factor, and discuss their derivations based on the Ward-Takahashi identities. We illustrate the features at the (leading-$N_c$) one-quark-loop level with the help of the spectral quark model of the pion, constructed to embed the vector meson dominance. Simple analytic expressions for the form factors and the distributions follow. Thus obtained off-shell generalized parton distributions are evolved from the quark model scale to higher scales with the LO DGLAP equations. We evaluate the corresponding Compton amplitudes which enter the cross-section for the electroproduction of the pion off the proton (the Sullivan process). It is found in our model that the effects of off-shellness in the generalized parton distribution are substantial, however, they can be largely canceled by the corresponding off-shell corrections to the pion propagator. In particular, this is the case of the Compton form factors entering the deeply virtual Compton scattering amplitude. As a result, we expect small off-shellness effects in electroproduction reactions, such as the Sullivan process.

   hep-phPRD(2023)·5 citations
4. 04*

   Color symmetry and confinement as an underlying superconformal structure in holographic QCD

   Guy F. de Teramond🇨🇷 · Stanley J. Brodsky🇺🇸

   Dedicated to the memory of our colleague, Harald Fritzsch, who, together with Murray Gell-Mann, introduced the color quantum number as the exact symmetry responsible for the strong interaction, thus establishing quantum chromodynamics (QCD) as a fundamental non-Abelian gauge theory. A basic understanding of hadron properties, however, such as confinement and the emergence of a mass scale, from first principles QCD has remained elusive: Hadronic characteristics are not explicit properties of the QCD Lagrangian and perturbative QCD, so successful in the large transverse momentum domain, is not applicable at large distances. In this article, we shall examine how this daunting obstacle is overcome in holographic QCD with the introduction of a superconformal symmetry in anti de Sitter (AdS) space which is responsible for confinement and the introduction of a mass scale within the superconformal group. When mapped to light-front coordinates in physical spacetime, this approach incorporates supersymmetric relations between the Regge trajectories of meson, baryon and tetraquark states which can be visualized in terms of specific $SU(3{)}_C$ color representations of quarks. We will also briefly discuss here the implications of holographic models for QCD color transparency in view of the present experimental interest. Based on the invited contribution to the book dedicated to the memory of Harald Fritzsch.

   hep-phInt.J.Mod.Phys.A(2024)·5 citations
5. 05*

   Proton number cumulants in a modified van der Waals hadron resonance gas

   Kshitish Kumar Pradhan🇮🇳 · Ronald Scaria🇮🇳 · Dushmanta Sahu🇮🇳 · Raghunath Sahoo🇮🇳

   An estimate of the proton number cumulants in the hadronic matter is presented considering a van der Waals-type interaction between the constituent particles. We argue that the attractive and repulsive parameters in the VDW hadron resonance gas (VDWHRG) model change as functions of baryochemical potential (${\mu }_B$) and temperature ($T$). This, in turn, affects the estimation of thermodynamic properties and, consequently, the conserved charge fluctuations. We employ a simple parametrization to bring in the center-of-mass energy ($\sqrt{s_{\mathrm{NN}}}$) dependence on temperature and baryochemical potential and then estimate the proton number cumulants with the modified approach. The modified van der Waals hadron resonance gas model (MVDWHRG) explains the existing experimental data very well.

   hep-phhep-exnucl-exnucl-th5 citations
6. 06*

   $K^{+}N$ elastic scatterings for estimation of in-medium quark condensate with strange quarks

   Yutaro Iizawa🇯🇵 · Daisuke Jido🇯🇵 · Stephan Hübsch🇯🇵

   We revisit the low-energy $K^{+}N$ elastic scatterings in the context of the in-medium quark condensate with strange quarks. The chiral ward identity connects the in-medium quark condensate to the soft limit value of the pseudoscalar correlation function evaluated in nuclear matter. The in-medium correlation function of the psuedoscalar fields with strangeness describes in-medium kaon propagation and is obtained by kaon-nucleon scattering amplitudes in the low density approximation. We construct the kaon-nucleon scattering amplitudes in chiral perturbation theory up to the next-to-leading order and add some terms of the next-to-next-to-leading order with the strange quark mass to improve expansion of the strange quark sector. We also consider the effect of a possible broad resonance state around $P_{\mathrm{lab}}=600$ MeV/c for $I=0$ reported in the previous study. The low energy constants are determined by existent $K^{+}N$ scattering data. We obtain good reproduction of the $K^{+}p$ scattering amplitude by chiral perturbation theory, while the description of the $KN$ amplitude with $I=0$ is not so satisfactory due to the lack of low energy data. Performing analytic continuation of the scattering amplitudes obtained by chiral perturbation theory to the soft limit, we estimate the in-medium strange quark condensate.

   hep-phnucl-exnucl-thPTEP(2024)·5 citations
7. 07*

   Deeply-virtual and photoproduction of mesons at higher-order and higher-twist

   K. Passek-K.🇭🇷

   Both deeply-virtual and photoproduction of mesons offer promising access to generalized parton distributions and complementary description of different kinematical regions. The higher-order contributions offer stabilizing effect with respect to the dependence on renormalization scales, while higher-twist effects have been identified as especially important in the case of the production of pseudo-scalar mesons. This was confirmed by recent evaluation of the complete twist-3 contribution to $\pi$ and $\eta$/${\eta }^{\prime }$ photoproduction and its confrontation with experimental data.

   hep-phActa Phys.Polon.Supp.(2023)·1 citation
8. 08*

   Two-loop radiative corrections to $e^{+}{e}^{-}\to \gamma {\gamma }^{\ast }$ cross section

   V.S. Fadin🇷🇺 · R.N. Lee🇷🇺

   The increasing accuracy of current and planned experiments to measure the anomalous magnetic moment of the muon requires more precision and reliability of its theoretical calculation. For this purpose, we calculate the differential cross section for the process of annihilation of an electron-positron pair into two photons, one of which is virtual, accompanied by the emission of soft photons, taking into account radiative corrections of the order ${\alpha }^2$. The results obtained can be used to improve the accuracy of calculating the contribution of the hadron vacuum polarization to the muon anomalous moment. It is shown that all logarithmically amplified two-loop corrections can be easily found using modern theorems of soft and collinear factorizations and available one-loop results.

   hep-phJHEP(2023)·17 citations
9. 09*

   Cabibbo angle anomalies and a global fit to vector-like quarks

   Matthew Kirk🇪🇸

   The most recent determinations of $V_{ud}$ from superallowed beta decays lead to a discrepancy when compared to the value implied by mesonic CKM measurements combined with CKM unitarity. On top of this, improved precision in lattice QCD calculations have revealed another discrepancy between the $V_{us}$ determinations from kaon and pion semi-leptonic decays. The combination of these can be referred to as the Cabibbo angle anomaly, which we find has a significance of around $3\sigma$. After summarising the current state of these issues, I will talk about new physics models that modify semi-leptonic decays as potential explanations, and why vector-like quarks in particular appear the most promising candidates. I will then discuss the results of a global fit to various vector-like quark models, and how other constraints are important in determining the most likely explanation. Finally I will touch on future experiments that could shed further light on the situation.

   hep-phhep-exPoS·4 citations
10. 10*

    A Hybrid Type I + III Inverse Seesaw Mechanism in $U(1{)}_{R-L}$-symmetric MSSM

    Cem Murat Ayber🇨🇦 · Seyda Ipek🇨🇦

    We show that, in a $U(1{)}_{R-L}$-symmetric supersymmetric model, the pseudo-Dirac bino and wino can give rise to three light neutrino masses through effective operators, generated at the messenger scale between a SUSY breaking hidden sector and the visible sector. The neutrino-bino/wino mixing follows a hybrid type I+III inverse seesaw pattern. The light neutrino masses are governed by the ratio of the $U(1{)}_{R-L}$-breaking gravitino mass, $m_{3/2}$, and the messenger scale ${\Lambda }_M$. The charged component of the $SU(2{)}_L$-triplet, here the lightest charginos, mix with the charged leptons and generate flavor-changing neutral currents at tree level. We find that resulting lepton flavor violating observables yield a lower bound on the messenger scale, ${\Lambda }_M\gtrsim (500-1000)\mathrm{TeV}$ for a simplified hybrid mixing scenario. We identify interesting mixing structures for certain $U(1{)}_{R-L}$-breaking singlino/tripletino Majorana masses. For example, in some parameter regimes, bino or wino has no mixing with the electron neutrino. We also describe the rich collider phenomenology expected in this neutrino-mass generation mechanism.

    hep-phJHEP(2023)·1 citation
11. 11*

    A Survey of Neutrino Flavor Models and the Neutrinoless Double Beta Decay Funnel

    Peter B. Denton🇺🇸 · Julia Gehrlein🇺🇸

    The neutrinoless double beta decay experimental effort continues to make tremendous progress with hopes of covering the inverted neutrino mass hierarchy in coming years and pushing from the quasi-degenerate hierarchy into the normal hierarchy. As neutrino oscillation data is starting to suggest that the mass ordering may be normal, we may well be faced with staring down the funnel of death: a region of parameter space in the normal ordering where -- for a particular cancellation among the absolute neutrino mass scale, the Majorana phases, and the oscillation parameters -- the neutrinoless double beta decay rate may be vanishingly small. To answer the question of whether this region of parameter space is theoretically preferred, we survey five broad categories of flavor model structures which make various different predictions for parameters relevant for neutrinoless double beta decay to determine how likely it is that the rate may be in this funnel region. We find that a non-negligible fraction of predictions surveyed are at least partially in the funnel region. Our results can guide model builders and experimentalists alike in focusing their efforts on theoretically motivated regions of parameter space.

    hep-phPRD(2024)·31 citations
12. 12*

    How to measure the spin of invisible states in $e^{+}{e}^{-}\to \gamma +X$

    Martin Bauer🇬🇧 · Sofie Nordahl Erner🇬🇧

    We examine the production of an invisible state $X$ together with a photon, $e^{+}{e}^{-}\to \gamma +X$, at electron positron colliders and present measurement strategies that can detect the spin of the invisible state as well as the underlying production mechanism, based on the angular distribution of the final state photon, the cross sections for polarized initial states and the photon polarization. Our measurement strategy can be used to identify whether the invisible state is a hidden photon or an axion. The results are compared with a detailed analysis of the Standard Model background and we calculate the sensitivity reach for searches for axions and hidden photons at Belle II.

    hep-phPRD(2023)·4 citations
13. 13*

    Pre-equilibrium photons from the early stages of heavy-ion collisions

    Oscar Garcia-Montero🇩🇪 · Aleksas Mazeliauskas🇩🇪 · Philip Plaschke🇩🇪 · Sören Schlichting🇩🇪

    We use QCD kinetic theory to compute photon production in the chemically equilibrating Quark-Gluon Plasma created in the early stages of high-energy heavy-ion collisions. We do a detailed comparison of pre-equilibrium photon rates to the thermal photon production. We show that the photon spectrum radiated from a hydrodynamic attractor evolution satisfies a simple scaling form in terms of the specific shear viscosity $\eta /s$ and entropy density $dS/d\zeta \sim {{\left(T{\tau }^{1/3}\right)}^{3/2}}_{\infty }$. We confirm the analytical predictions with numerical kinetic theory simulations. We use the extracted scaling function to compute the pre-equilibrium photon contribution in $\sqrt{s_{NN}}=2.76\text{TeV}$ 0-20\% PbPb collisions. We demonstrate that our matching procedure allows for a smooth switching from pre-equilibrium kinetic to thermal hydrodynamic photon production. Finally, our publicly available implementation can be straightforwardly added to existing heavy ion models.

    hep-phnucl-thJHEP(2024)·37 citations
14. 14*

    Scalar induced gravity waves from ultra slow-roll Galileon inflation

    Sayantan Choudhury🇮🇳 · Ahaskar Karde🇮🇳 · Sudhakar Panda🇮🇳 · M. Sami🇮🇳

    We consider the production of secondary gravity waves in Galileon inflation with an ultra-slow roll (USR) phase and show that the spectrum of scalar-induced gravitational waves (SIGWs) in this case is consistent with the recent NANOGrav 15-year data and with sensitivities of other ground and space-based missions, LISA, BBO, DECIGO, CE, ET, HLVK (consists of aLIGO, aVirgo, and KAGRA), and HLV(03). Thanks to the non-renormalization property of Galileon theory, the amplitude of the large fluctuation is controllable at the sharp transitions between SR and USR regions. We show that the behaviour of the GW spectrum, when one-loop effects are included in the scalar power spectrum, is preserved under a shift of the sharp transition scale with peak amplitude ${\Omega }_{\mathrm{GW}}{h}^2\sim \mathcal{O}(10^{-6})$, and hence it can cover a wide range of frequencies within $\mathcal{O}(10^{-9}\mathrm{Hz}-10^7\mathrm{Hz})$. An analysis of the allowed mass range for primordial black holes (PBHs) is also performed, where we find that mass values ranging from $\mathcal{O}(1M_{\odot }-10^{-18}{M}_{\odot })$ can be generated over the corresponding allowed range of low and high frequencies.

    ↳ astro-ph.COgr-qchep-phhep-thNPB(2024)·88 citations
15. 15*

    Mass and infinite dimensional geometry

    Puskar Mondal🇺🇸

    I unravel an elegant geometric meaning of the mass of the lowest energy excited state of a renormalizable quantized field theory by studying the weighted geometry of the classical configuration space of the theory. A suitably defined regularized Bakry-Emery Ricci curvature of these infinite dimensional spaces controls the spectra of the corresponding quantum Hamiltonians. The Ricci curvature part of the full Bakry-Emery Ricci curvature appears to be purely quantum in nature. This geometric contribution to the spectra in the context of quantum field theory has not been studied previously to my knowledge. Assuming the existence of rigorous quantization, I present a few problems starting from massive free particles to the non-abelian Yang-Mills theory. A remarkable property is observed in the large $N$ Yang-Mills theory, where a non-trivial mass gap is preserved. This occurs due to the fact that the regularized Bakry-Emery Ricci curvature that is responsible for the gap of the configuration space scales as $g_{YM}^{2}N=\lambda$ ('t Hooft coupling) that remains invariant.

    ↳ hep-thhep-ph3 citations
16. 16*

    Scattering Amplitudes of Fermions on Monopoles

    Valentin V. Khoze🇬🇧

    We consider scattering processes involving massless fermions and 't Hooft-Polyakov magnetic monopoles in a minimal SU(2) model and in the Grand Unified SU(5) theory. We construct expressions for on-shell amplitudes for these processes in the $J=0$ partial wave using the spinor helicity basis consisting of single-particle and pairwise helicities. These processes are unsuppressed and are relevant for the monopole catalysis of proton decay. The amplitudes for the minimal processes involving a single fermion scattering on a monopole in the initial state and half-fermion solitons in the final state are presented for the first time and are used to obtain the amplitudes for processes involving more fermions in the initial state and integer fermion numbers in the final state. A number of such anomalous and non-anomalous processes, along with their amplitude expressions, are written down for the $SU(5)$ GUT model.

    ↳ hep-thhep-phJHEP(2023)·13 citations
17. 17*

    Design and performance of the ENUBET monitored neutrino beam

    F. Acerbi🇮🇹 · I. Angelis🇬🇷 · L. Bomben🇮🇹 · M. Bonesini🇮🇹 · F. Bramati🇮🇹 · A. Branca🇮🇹 · C. Brizzolari🇮🇹 · G. Brunetti🇮🇹 · M. Calviani🇨🇭 · S. Capelli🇮🇹 · S. Carturan🇮🇹 · M.G. Catanesi🇮🇹 and 60 other authors

    The ENUBET project is aimed at designing and experimentally demonstrating the concept of monitored neutrino beams. These novel beams are enhanced by an instrumented decay tunnel, whose detectors reconstruct large-angle charged leptons produced in the tunnel and give a direct estimate of the neutrino flux at the source. These facilities are thus the ideal tool for high-precision neutrino cross-section measurements at the GeV scale because they offer superior control of beam systematics with respect to existing facilities. In this paper, we present the first end-to-end design of a monitored neutrino beam capable of monitoring lepton production at the single particle level. This goal is achieved by a new focusing system without magnetic horns, a 20 m normal-conducting transfer line for charge and momentum selection, and a 40 m tunnel instrumented with cost-effective particle detectors. Employing such a design, we show that percent precision in cross-section measurements can be achieved at the CERN SPS complex with existing neutrino detectors.

    ↳ hep-exhep-phphysics.acc-phphysics.ins-detEPJC(2023)·25 citations
18. 18*

    Reconstructing $S$-matrix Phases with Machine Learning

    Aurélien Dersy🇺🇸 · Matthew D. Schwartz🇺🇸 · Alexander Zhiboedov🇨🇭

    An important element of the $S$-matrix bootstrap program is the relationship between the modulus of an $S$-matrix element and its phase. Unitarity relates them by an integral equation. Even in the simplest case of elastic scattering, this integral equation cannot be solved analytically and numerical approaches are required. We apply modern machine learning techniques to studying the unitarity constraint. We find that for a given modulus, when a phase exists it can generally be reconstructed to good accuracy with machine learning. Moreover, the loss of the reconstruction algorithm provides a good proxy for whether a given modulus can be consistent with unitarity at all. In addition, we study the question of whether multiple phases can be consistent with a single modulus, finding novel phase-ambiguous solutions. In particular, we find a new phase-ambiguous solution which pushes the known limit on such solutions significantly beyond the previous bound.

    ↳ hep-thcs.LGhep-phJHEP(2024)·19 citations
19. 19*

    Sequential decays of the triple strange process $\bar{p}p\to {\bar{\Omega }}^{+}{\Omega }^{-}\to K^{+}\bar{\Lambda }{K}^{-}\Lambda \to K^{+}\bar{p}{\pi }^{+}{K}^{-}p{\pi }^{-}$: a model-independent approach

    Deepak Pachattu🇮🇳

    A model-independent irreducible tensor formalism is developed to analyse $\bar{\Omega }\Omega$ production in $\bar{p}p$ collisions and its subsequent decay via the triple-strange decay process, ${\bar{\Omega }}^{+}{\Omega }^{-}\to K^{+}\bar{\Lambda }{K}^{-}\Lambda \to K^{+}\bar{p}{\pi }^{+}{K}^{-}p{\pi }^{-}$. These processes are relevant for the upcoming experiments at PANDA. We not only provide expressions for the density matrix of the $\Omega \bar{\Omega }$ system but also for the products at each stage of the decay. The Fano statistical tensors so obtained not only completely characterize the relevant final systems but also provide expressions for joint angular distributions. Finally, we show which of the Fano statistical tensors characterizing the $\bar{\Omega }\Omega$ system can be inferred from the Fano statistical tensors characterizing the final $\bar{p}p$ system, wherein we also obtain the relation between the production cross sections for $\Omega \bar{\Omega }$ and the final $p\bar{p}$ system.

    ↳ nucl-thhep-phnucl-exNPA(2024)·1 citation
20. 20*

    Subhalo effective density slope measurements from HST strong lensing data with neural likelihood-ratio estimation

    Gemma Zhang · Atınç Çağan Şengül🇺🇸 · Cora Dvorkin🇺🇸

    Examining the properties of subhalos with strong gravitational lensing images can shed light on the nature of dark matter. From upcoming large-scale surveys, we expect to discover orders of magnitude more strong lens systems that can be used for subhalo studies. To optimally extract information from a large number of strong lensing images, machine learning provides promising avenues for efficient analysis that is unachievable with traditional analysis methods, but application of machine learning techniques to real observations is still limited. We build upon previous work, which uses a neural likelihood-ratio estimator, to constrain the effective density slopes of subhalos and demonstrate the feasibility of this method on real strong lensing observations. To do this, we implement significant improvements to the forward simulation pipeline and undertake careful model evaluation using simulated images. Ultimately, we use our trained model to predict the effective subhalo density slope from combining a set of strong lensing images taken by the \textit{Hubble Space Telescope}. We found the subhalo slope measurement of this set of observations to be steeper than the slope predictions of cold dark matter subhalos. Our result adds to several previous works that also measured high subhalo slopes in observations. Although a possible explanation for this is that subhalos with steeper slopes are easier to detect due to selection effects and thus contribute to statistical bias, our result nevertheless points to the need for careful analysis of more strong lensing observations from future surveys.

    ↳ astro-ph.COhep-phMNRAS(2023)·22 citations
21. 21*

    TAMBO: Searching for Tau Neutrinos in the Peruvian Andes

    William G. Thompson (for the TAMBO Collaboration)🇺🇸

    The detection of high-energy astrophysical neutrinos by IceCube has opened a new window on our Universe. While IceCube has measured the flux of these neutrinos at energies up to several PeV, much remains to be discovered regarding their origin and nature. Currently, measurements are limited by the small sample size of astrophysical neutrinos and by the difficulty of discriminating between electron and tau neutrinos. TAMBO is a next-generation neutrino observatory specifically designed to detect tau neutrinos in the 1-100 PeV energy range, enabling tests of neutrino physics at high energies and the characterization of astrophysical neutrino sources. The observatory will comprise an array of water Cherenkov and plastic scintillator detectors deployed on the face of the Colca Canyon in the Peruvian Andes. This unique geometry will facilitate a high-purity measurement of astrophysical tau neutrino properties. In this talk, I will present the prospects of TAMBO in the context of next-generation neutrino observatories and provide an overview of its current status.

    ↳ astro-ph.HEhep-exhep-ph12 citations
22. 22*

    A Regularized $(XP{)}^2$ Model

    Yu-Qi Chen🇨🇳 · Zhao-Feng Ge🇨🇳

    We investigate a dynamic model described by the classical Hamiltonian $H(x,p)=(x^2+a^2)(p^2+a^2)$, where $a^2>0$, in classical, semi-classical, and quantum mechanics. In the high-energy $E$ limit, the phase path resembles that of the $(XP{)}^2$ model. However, the non-zero value of $a$ acts as a regulator, removing the singularities that appear in the region where $x,p\sim 0$, resulting in a discrete spectrum characterized by a logarithmic increase in state density. Classical solutions are described by elliptic functions, with the period being determined by elliptic integrals. In semi-classical approximation, we speculate that the asymptotic Riemann-Siegel formula may be interpreted as summing over contributions from multiply phase paths. We present three different forms of quantized Hamiltonians, and reformulate them into the standard Schrödinger equation with $\cosh 2x$-like potentials. Numerical evaluations of the spectra for these forms are carried out and reveal minor differences in energy levels. Among them, one interesting form possesses Hamiltonian in the Schrödinger equation that is identical to its classical version. In such scenarios, the eigenvalue equations can be expressed as the vanishing of the Mathieu functions' value at $i\infty$ points, and furthermore, the Mathieu functions can be represented as the wave functions.

    ↳ quant-phhep-phhep-thmath-ph+1Phys.Scripta(2024)·0 citations

* Reconstructed cohort: no mailing for this day survives in the archive. Papers are grouped by their submission times and arXiv's announcement cut-off, assuming announcement without delay; positions follow identifier order. Validated at ~91% exact-day agreement against the archived era.