Fri·Oct 13, 2023Friday·October 13, 2023

1. 01*

   Quantum kinetic equations with flavor and particle-antiparticle coherences for neutrinos

   Kimmo Kainulainen🇫🇮 · Harri Parkkinen🇫🇮

   We develop a formalism to model neutrino evolution encompassing both flavor and particle-antiparticle mixings and decohering collisions. Our results include a quantum kinetic equation (a set of coupled scalar equations) for the generalized neutrino density matrix, valid for arbitrary neutrino masses and kinematics, and a comprehensive set of Feynman rules to compute collision integrals for coherently evolving states. We expose a novel shell structure describing the phase space of mixing neutrinos and show how the prior information on the system can enter into the theory and modify the neutrino flavor evolution. Potential applications of our results include modelling neutrino distributions in hot and dense environments and studies of neutrino mixing effects in colliders and in the early Universe.

   hep-phastro-ph.HEhep-thPoS(2023)·2 citations
2. 02*

   A Dynamical Explanation of the Dark Matter-Baryon Coincidence

   Dawid Brzeminski🇺🇸 · Anson Hook🇺🇸

   The near equality of the dark matter and baryon energy densities is a remarkable coincidence, especially when one realizes that the baryon mass is exponentially sensitive to UV parameters in the form of dimensional transmutation. We explore a new dynamical mechanism, where in the presence of an arbitrary number density of baryons and dark matter, a scalar adjusts the masses of dark matter and baryons until the two energy densities are comparable. In this manner, the coincidence is explained regardless of the microscopic identity of dark matter and how it was produced. This new scalar causes a variety of experimental effects such as a new force and a (dark) matter density-dependent proton mass.

   hep-phPRL(2024)·16 citations
3. 03*

   The statistics and sensitivity of axion wind detection with the homogeneous precession domain of superfluid helium-3

   Joshua W. Foster🇺🇸 · Christina Gao🇺🇸 · William Halperin🇺🇸 · Yonatan Kahn🇺🇸 · Aarav Mande🇺🇸 · Man Nguyen🇺🇸 · Jan Schütte-Engel🇺🇸 · John William Scott🇺🇸

   The homogeneous precession domain (HPD) of superfluid ${}^3$He has recently been identified as a detection medium which might provide sensitivity to the axion-nucleon coupling $g_{aNN}$ competitive with, or surpassing, existing experimental proposals. In this work, we make a detailed study of the statistical and dynamical properties of the HPD system in order to make realistic projections for a full-fledged experimental program. We include the effects of clock error and measurement error in a concrete readout scheme using superconducting qubits and quantum metrology. This work also provides a more general framework to describe the statistics associated with the axion gradient coupling through the treatment of a transient resonance with a non-stationary background in a time-series analysis. Incorporating an optimal data-taking and analysis strategy, we project a sensitivity approaching $g_{aNN}\sim 10^{-12}$ GeV${}^{-1}$ across a decade in axion mass.

   hep-phcond-mat.supr-conhep-exPRD(2024)·11 citations
4. 04*

   Light quark mass dependence of nucleon electromagnetic form factors in dispersively modified chiral perturbation theory

   Fernando Alvarado🇪🇸 · Di An🇸🇪 · Luis Alvarez-Ruso🇪🇸 · Stefan Leupold🇸🇪

   The nucleon isovector electromagnetic form factors are calculated up to next-to-next-to-leading order by combining relativistic chiral perturbation theory (ChPT) of pion, nucleon, and $\Delta$(1232) with dispersion theory. We specifically address the light-quark mass dependence of the form factors, achieving a good description of recent Lattice QCD results over a range of $Q^2<0.6$ GeV${}^2$ and $M_{\pi }<350$ MeV. For the Dirac form factor, the combination of ChPT and dispersion theory outperforms the pure dispersive and pure ChPT descriptions. For the Pauli form factor, the combined calculation leads to results comparable to the purely dispersive ones. The anomalous magnetic moment and the Dirac and Pauli radii are extracted.

   hep-phhep-lathep-thnucl-thPRD(2023)·12 citations
5. 05*

   N${}^3$LO Antenna Functions for Final-State Radiation

   Matteo Marcoli🇨🇭

   We discuss recent progress in the calculation of integrated antenna functions for final-state radiation at N${}^3$LO in QCD. Antenna functions are directly extracted from physical matrix elements for the decay of a colour-singlet state into partons. In order to compute their integrated counterparts, which are necessary ingredients for fixed-order calculations in QCD, each allowed final state has to be individually integrated over the inclusive phase space of the unresolved radiation. We analytically integrated two-, three-, four- and five-particle final-state matrix elements for the decay of a virtual photon and a Higgs boson into partons, considering up to third-order corrections in the strong coupling constant ${\alpha }_s$. The integration over the inclusive phase space is performed relying on well-established reverse unitarity and IBP reduction techniques. We conclude with preliminary comments about the structure of N${}^3$LO subtraction terms in the context of the antenna subtraction method.

   hep-phPoS(2024)·2 citations
6. 06*

   Linearly polarized gluon density at low x

   N.A. Abdulov🇷🇺 · X. Chen🇨🇳 · A.V. Kotikov🇷🇺 · A.V. Lipatov🇷🇺

   Based on a solution of DGLAP evolution equations at small values of Bjorken variable x, a simple analytic approximation for so-called linearly polarized gluon density \tilde{h}_1^{\perp g}(x,k_t^2, Q^2) is obtained at LO of perturbation theory.

   hep-phPisma Zh.Eksp.Teor.Fiz.(2026)·2 citations
7. 07*

   Moving doubly heavy baryon in a strongly coupled plasma from holography

   Xuan Liu🇨🇳 · Jia-Jie Jiang🇨🇳 · Xun Chen🇨🇳 · Mitsutoshi Fujita🇨🇳 · Akira Watanabe🇨🇳

   Gauge/gravity duality is used to study properties of the doubly heavy baryon $(\mathrm{QQq})$ at finite rapidity and temperature in the heavy-ion collision. We investigate the impact of rapidity on string breaking and screening of $\mathrm{QQq}$, and compare these effects with the results for $\mathrm{Q}\bar{\mathrm{Q}}$ in detail. Computations reveal that the string-breaking distances of $\mathrm{QQq}$ and $\mathrm{Q}\bar{\mathrm{Q}}$ are close in the confined state and the effects of rapidity and temperature on the string breaking are not significant. An interesting result shows that $\mathrm{QQq}$ cannot be found at high enough temperatures and rapidities; however, $\mathrm{Q}\bar{\mathrm{Q}}$ can exist under any conditions as long as the separation distance is small enough. Besides, the screening distances of $\mathrm{QQq}$ and $\mathrm{Q}\bar{\mathrm{Q}}$ are also compared at finite rapidity and temperature. Based on the above analysis, we infer that $\mathrm{Q}\bar{\mathrm{Q}}$ is more stable than $\mathrm{QQq}$ at finite rapidity and temperature.

   hep-phCPC(2024)·6 citations
8. 08*

   The QCD Axion: Some Like It Hot

   Federico Bianchini🇺🇸 · Giovanni Grilli di Cortona🇮🇹 · Mauro Valli🇮🇹

   We compare the QCD axion phase-space distribution from unitarized next-to-leading order chiral perturbation theory with the one extracted from pion-scattering data. We derive a robust bound by confronting momentum-dependent Boltzmann equations against up-to-date observations of the Cosmic Microwave Background, of the Baryonic Acoustic Oscillations and of primordial abundances. These datasets imply $m_a\le 0.16$ eV for the 95% credible interval, i.e. $\sim$30% stronger bound than what previously found. We present forecasts using dedicated likelihoods for future cosmological surveys and the sphaleron rate from unquenched lattice QCD.

   hep-phastro-ph.COPRD(2024)·40 citations
9. 09*

   Elimination of QCD Renormalization Scale and Scheme Ambiguities

   Leonardo Di Giustino🇮🇹 · Stanley J. Brodsky🇺🇸 · Philip G. Ratcliffe🇮🇹 · Xing-Gang Wu🇨🇳 · Sheng-Quan Wang🇨🇳

   We present results for the thrust distribution in the electron positron annihilation to the three jet process at NNLO in the perturbative conformal window of QCD, as a function of the number of flavors $N_f$. Given the existence of an infrared interacting fixed point in this region, we can compare the Conventional Scale Setting (CSS) and the Principle of Maximum Conformality (PMC${}_{\infty }$) methods along the entire renormalization group flow from the highest energies to zero energy. We then consider also the QED thrust, obtained as the limit $N_c\to 0$ of the number of colors and we show analogous comparison. QED in the low energy regime develops an infrared non-interacting fixed point. Using these quantum field theory limits as theoretical laboratories, we arrive at interesting results showing new features of the PMC${}_{\infty }$.

   hep-phPoS(2024)·2 citations
10. 10*

    Dual properties of dense quark matter with color superconductivity phenomenon

    T. G. Khunjua🇬🇪 · K. G. Klimenko🇷🇺 · R. N. Zhokhov🇷🇺

    In this paper the massless NJL model extended by the diquark interaction channel is considered. We study its phase structure at zero temperature and in the presence of baryon ${\mu }_B$, isospin ${\mu }_I$, chiral ${\mu }_5$ and chiral isospin ${\mu }_{I5}$ chemical potentials in the mean-field approximation. It is shown that the model thermodynamic potential, which depends on three order parameters, $M$, ${\pi }_1$ and $\Delta$ (where $M$, ${\pi }_1$, and $\Delta$ -- are, respectively, chiral, charged pion and diquark condensates of the model), is symmetric with respect to the (dual) transformation when $M\leftrightarrow {\pi }_1$ and simultaneously ${\mu }_I\leftrightarrow {\mu }_{I5}$. As a result, on the mean-field phase portrait of the model the chiral symmetry breaking (CSB) and charged pion condensation (PC) phases turn out to be dually conjugate with each other, which greatly simplifies the study of the phase portrait of the model. In particular, the duality between CSB and charged PC phases means that in the $({\mu }_I,{\mu }_{I5})$-phase portrait these phases are mirror-symmetrical with respect to the line ${\mu }_I={\mu }_{I5}$, which at the same time is the symmetry axis of the color superconducting (CSC) phase. Moreover, it follows from our analysis that chiral ${\mu }_5$ chemical potential promotes the formation of CSC phase in dense quark matter. And together with ${\mu }_{I5}$ it can generates the charged PC phase even at ${\mu }_I=0$.

    hep-phhep-thPRD(2023)·8 citations
11. 11*

    From QFT to Boltzmann: Freeze-in in the presence of oscillating condensates

    Wen-Yuan Ai🇬🇧 · Ankit Beniwal🇬🇧 · Angelo Maggi🇬🇧 · David J. E. Marsh🇬🇧

    Scalar dark matter (DM), and axions in particular, have an irreducible abundance of particles produced by freeze-in due to portal interactions with the Standard Model plasma in the early Universe. In addition, vacuum misalignment and other mechanisms can lead to the presence of a cold, oscillating condensate. Therefore, generically, the evolution of the DM in both forms, condensate and particles, needs to be studied simultaneously. In non-equilibrium quantum field theory, the condensate and particles are described by one- and two-point functions, respectively. The fundamental coupled equations of motion (EoMs) of these objects are non-local. To simplify the EoMs and bring them into a familiar form for relic abundance calculations, we perform a Markovianization process for a quasi-harmonically oscillating homogeneous condensate, leading to local EoMs for the particle distribution function and the envelope function of condensate oscillation. This reduces the dynamics to a pair of coupled Boltzmann equations, and we derive explicitly the form of the collision operators for all particle and condensate interactions.

    hep-phastro-ph.COhep-thJHEP(2024)·20 citations
12. 12*

    Indirect Probe of Electroweak-Interacting Particles at $\mu$TRISTAN ${\mu }^{+}{\mu }^{+}$ Collider

    Risshin Okabe🇯🇵 · Satoshi Shirai🇯🇵

    Recently, a novel collider, called $\mu$TRISTAN, has been proposed, offering the capability to achieve high-energy collisions of anti-muons. This high-energy collider presents an exceptional opportunity for the discovery of electroweak-interacting massive particles (EWIMPs), which are predicted by various new physics models. In a lepton collider like $\mu$TRISTAN, the potential for discovering EWIMPs extends beyond their direct production. Quantum corrections arising from EWIMP loops can significantly enhance our prospects for discovery by precise measurement of Standard Model processes. This study focuses on the indirect detection method within the $\mu$TRISTAN experiment, with a specific emphasis on TeV-scale EWIMP dark matter scenarios that yield the correct thermal relic density. At collision energies for $\sqrt{s}=O(1-10)$ TeV, these EWIMPs introduce noticeable effects, typically in the range of $O(0.1-1)$\%. Our findings indicate that at $\sqrt{s}=2(10)$ TeV, with an integrated luminosity of 10 ab${}^{-1}$, the $\mu$TRISTAN can detect Higgsino at a mass of 1.3 (3.0) TeV and Wino at a mass of 1.9 (4.4) TeV, assuming an optimistic level of systematic uncertainty in the observation of the Standard Model processes.

    hep-phhep-exPRD(2024)·8 citations
13. 13*

    95 GeV Diphoton and $b\bar{b}$ Excesses in the General Next-to-Minimal Supersymmetric Standard Model

    Junjie Cao🇨🇳 · Xinglong Jia🇨🇳 · Jingwei Lian🇨🇳 · Lei Meng🇨🇳

    The CMS and ATLAS collaborations recently published their results searching for light Higgs bosons, using the complete Run 2 data of the LHC. Both reported an excess in the diphoton invariant mass distribution at $m_{\gamma \gamma }\simeq 95.4\mathrm{GeV}$ with compatible signal strengths. The combined result corresponded to a local significance of $3.1\sigma$. Besides, the mass of the diphoton signal coincided with that of the $b\bar{b}$ excess observed at the LEP. Given the remarkable theoretical advantages of the general Next-to-Minimal Supersymmetric Standard Model, we interpret these excesses by the resonant productions of the singlet-dominated CP-even Higgs boson predicted by the theory. Using both analytic formulae and numerical results, we show that the idea can interpret the excesses by broad parameter space without contradicting current experimental restrictions, including those from the 125~{\rm GeV} Higgs data, the dark matter relic abundance and direct detection experiments, and the collider searches for supersymmetry and extra Higgs bosons. Although the explanations are scarcely affected by present Higgs data and the LHC search for supersymmetry, the dark matter physics may leave footprints on them. We also survey the other signals of the light Higgs boson at the LHC.

    hep-phPRD(2024)·55 citations
14. 14*

    Recycled Dark Matter

    Thomas C. Gehrman🇺🇸 · Barmak Shams Es Haghi🇺🇸 · Kuver Sinha🇺🇸 · Tao Xu🇺🇸

    We outline a new production mechanism for dark matter that we dub "recycling": dark sector particles are kinematically trapped in the false vacuum during a dark phase transition; the false pockets collapse into primordial black holes (PBHs), which ultimately evaporate before Big Bang Nucleosynthesis (BBN) to reproduce the dark sector particles. The requirement that all PBHs evaporate prior to BBN necessitates high scale phase transitions and hence high scale masses for the dark sector particles in the true vacuum. Our mechanism is therefore particularly suited for the production of ultra heavy dark matter (UHDM) with masses above $\sim 10^{12}\mathrm{GeV}$. The correct relic density of UHDM is obtained because of the exponential suppression of the false pocket number density. Recycled UHDM has several novel features: the dark sector today consists of multiple decoupled species that were once in thermal equilibrium and the PBH formation stage has extended mass functions whose shape can be controlled by IR operators coupling the dark and visible sectors.

    hep-phastro-ph.COJCAP(2024)·41 citations
15. 15*

    A Common Origin for the QCD Axion and Sterile Neutrinos from $SU(5)$ Strong Dynamics

    Peter Cox🇦🇺 · Tony Gherghetta🇺🇸 · Arpon Paul🇺🇸

    We identify the QCD axion and right-handed (sterile) neutrinos as bound states of an $SU(5)$ chiral gauge theory with Peccei-Quinn (PQ) symmetry arising as a global symmetry of the strong dynamics. The strong dynamics is assumed to spontaneously break the PQ symmetry, producing a high-quality axion and naturally generating Majorana masses for the right-handed neutrinos at the PQ scale. The composite sterile neutrinos can directly couple to the left-handed (active) neutrinos, realizing a standard see-saw mechanism. Alternatively, the sterile neutrinos can couple to the active neutrinos via a naturally small mass mixing with additional elementary states, leading to light sterile neutrino eigenstates. The $SU(5)$ strong dynamics therefore provides a common origin for a high-quality QCD axion and sterile neutrinos.

    hep-phJHEP(2023)·23 citations
16. 16*

    On probing turbulence in core-collapse supernovae in upcoming neutrino detectors

    Mainak Mukhopadhyay🇺🇸 · Manibrata Sen🇩🇪

    Neutrino propagation through a turbulent medium can be highly non-adiabatic leading to distinct signatures in the survival probabilities. A core-collapse supernova can be host to a number of hydrodynamic instabilities which occur behind the shockfront. Such instabilities between the forward shock and a possible reverse shock can lead to cascades introducing turbulence in the associated matter profile, which can imprint itself in the neutrino signal. In this work, we consider realistic matter profiles and seed in the turbulence using a randomization scheme to study its effects on neutrino propagation in an effective two-flavor framework. We focus on the potential of upcoming neutrino detectors - DUNE and Hyper-Kamiokande to constrain the parameters characterizing turbulence in a supernova. We find that these experiments can effectively constrain the parameter space for the amplitude of the spectra, they will only have mild sensitivity to the spectral index, and cannot inform on deviations from the usual Kolmogorov $5/3$ inverse power law. Furthermore, we also confirm that the double-dip feature, originally predicted in the neutrino spectra associated with forward and reverse shocks, can be completely washed away in the presence of turbulence, leading to total flavor depolarization.

    hep-phastro-ph.HEhep-exJCAP(2024)·4 citations
17. 17*

    Quantum Field Theory of neutrino mixing in spacetimes with torsion

    Antonio Capolupo🇮🇹 · Giuseppe De Maria · Simone Monda🇮🇹 · Aniello Quaranta🇮🇹 · Raoul Serao🇮🇹

    In the framework of quantum field theory, we analyze the neutrino oscillations in the presence of a torsion background. We consider the Einstein-Cartan theory and we study the cases of constant torsion and of linearly time dependent torsion. We derive new neutrino oscillation formulae which are depending on the spin orientation. Indeed the energy splitting induced by the torsion influences oscillation amplitudes and frequencies. This effect is maximal for values of torsion of the same order of the neutrino masses and for very low momenta, and disappears for large values of torsion. Moreover, neutrino oscillation is inhibited for intensities of torsion term much larger than neutrino masses and momentum. The modifications induced by torsion on the $CP$-asymmetry has been also presented. Future experiments, such as PTOLEMY, could provide insights into the effect shown here.

    hep-phgr-qchep-thUniverse(2024)·20 citations
18. 18*

    First steps towards understanding neutrinos

    Francesco Vissani🇮🇹

    We retrace the first steps towards understanding neutrinos, particles predicted by Pauli in 1930 to avoid a supposed violation of time-translation symmetry. Despite the tendency to reduce the whole story to his intuition and the skill of Reines & Cowan, according to history great strides were made in thirties thanks to precious intellectual tools that combined ideas and mathematics. I refer primarily to the contribution of Fermi, who proposed in 1933 a theory in which matter particles can appear and disappear, prototypical of those at the basis of today's particle physics. This theory, despite its limitations, led physicists towards the observation of neutrinos, paved the way for further developments - e.g., it anticipated the characteristic of crossing symmetry - and had an impressive scientific legacy. We reconstruct the chain of arguments in the most accessible terms for a modern reader, emphasising the role of theoretical physics and reflecting on some alternative assessments of Fermi's contribution. A few technical remarks are collected in the appendix.

    ↳ physics.hist-phhep-phhep-th2 citations
19. 19*

    Quintessence in the Weyl-Gauss-Bonnet model

    José Jaime Terente Díaz🇪🇸 · Konstantinos Dimopoulos🇬🇧 · Mindaugas Karčiauskas🇪🇸 · Antonio Racioppi🇪🇪

    Quintessence models have been widely examined in the context of scalar-Gauss-Bonnet gravity, a subclass of Horndeski's theory, and were proposed as viable candidates for Dark Energy. However, the relatively recent observational constraints on the speed of gravitational waves $c_{\text{GW}}$ have resulted in many of those models being ruled out because they predict $c_{\text{GW}}\ne c$ generally. While these were formulated in the metric formalism of gravity, we put forward a new quintessence model with the scalar-Gauss-Bonnet action but in Weyl geometry, where the connection is not metric compatible. We find the fixed points of the dynamical system under some assumptions and determine their stability via linear analysis. The past evolution of the Universe can be reproduced correctly, but the late Universe constraints on $c_{\text{GW}}$ are grossly violated. Moreover, at these later stages tensor modes suffer from the gradient instabilities. We also consider the implications of imposing an additional constraint $c_{\text{GW}}=c$, but this does not lead to evolution that is consistent with cosmological observations

    ↳ gr-qcastro-ph.COhep-phJCAP(2024)·24 citations
20. 20*

    Testing multi-field inflation with LiteBIRD

    Ryusuke Jinno🇯🇵 · Kazunori Kohri🇯🇵 · Takeo Moroi🇯🇵 · Tomo Takahashi🇯🇵 · Masashi Hazumi🇯🇵

    We investigate expected constraints on the primordial tensor power spectrum from the future cosmic microwave background polarization experiment LiteBIRD as a test of multi-field inflation. We argue that the measurements of the tensor-to-scalar ratio and the tensor spectral index, in combination with the constraints on the scalar spectral index from the Planck observation, are useful in testing multi-field inflation models. We also discuss implications for multi-field inflationary model building.

    ↳ astro-ph.COhep-phJCAP(2024)·4 citations
21. 21*

    Terrestrial Very-Long-Baseline Atom Interferometry: Workshop Summary

    Sven Abend · Baptiste Allard · Iván Alonso · John Antoniadis · Henrique Araujo · Gianluigi Arduini · Aidan Arnold · Tobias Aßmann · Nadja Augst · Leonardo Badurina · Antun Balaz · Hannah Banks and 241 other authors

    This document presents a summary of the 2023 Terrestrial Very-Long-Baseline Atom Interferometry Workshop hosted by CERN. The workshop brought together experts from around the world to discuss the exciting developments in large-scale atom interferometer (AI) prototypes and their potential for detecting ultralight dark matter and gravitational waves. The primary objective of the workshop was to lay the groundwork for an international TVLBAI proto-collaboration. This collaboration aims to unite researchers from different institutions to strategize and secure funding for terrestrial large-scale AI projects. The ultimate goal is to create a roadmap detailing the design and technology choices for one or more km-scale detectors, which will be operational in the mid-2030s. The key sections of this report present the physics case and technical challenges, together with a comprehensive overview of the discussions at the workshop together with the main conclusions.

    ↳ hep-exastro-ph.IMgr-qchep-ph+1AVS Quantum Sci.(2024)·69 citations
22. 22*

    Exact evaluation and extrapolation of the divergent expansion for the Heisenberg-Euler Lagrangian I: Alternating Case

    Christian D. Tica · Eric A. Galapon

    We applied the method of finite-part integration [Galapon E.A Proc.R.Soc A 473, 20160567(2017)] to evaluate in closed-form the exact one-loop integral representations of the Heisenberg-Euler Lagrangian from QED for a constant magnetic field and magnetic-like self-dual background. We also devise a prescription based on the finite-part integration of a generalized Stieltjes integral to sum and extrapolate to the strong-field regime the alternating divergent weak-field expansions of the Heisenberg-Euler Lagrangians.

    ↳ math-phhep-phhep-thmath.MP0 citations
23. 23*

    Gravitational form factors of the proton from lattice QCD

    Daniel C. Hackett🇺🇸 · Dimitra A. Pefkou🇺🇸 · Phiala E. Shanahan🇺🇸

    The gravitational form factors (GFFs) of a hadron encode fundamental aspects of its structure, including its shape and size as defined from e.g., its energy density. This work presents a determination of the flavor decomposition of the GFFs of the proton from lattice QCD, in the kinematic region $0\le -t\le 2{\text{GeV}}^2$. The decomposition into up-, down-, strange-quark, and gluon contributions provides first-principles constraints on the role of each constituent in generating key proton structure observables, such as its mechanical radius, mass radius, and $D$-term.

    ↳ hep-lathep-phnucl-thPRL(2024)·154 citations
24. 24*

    The Basso-Dixon Formula and Calabi-Yau Geometry

    Claude Duhr🇩🇪 · Albrecht Klemm🇩🇪 · Florian Loebbert🇩🇪 · Christoph Nega🇩🇪 · Franziska Porkert🇩🇪

    We analyse the family of Calabi-Yau varieties attached to four-point fishnet integrals in two dimensions. We find that the Picard-Fuchs operators for fishnet integrals are exterior powers of the Picard-Fuchs operators for ladder integrals. This implies that the periods of the Calabi-Yau varieties for fishnet integrals can be written as determinants of periods for ladder integrals. The representation theory of the geometric monodromy group plays an important role in this context. We then show how the determinant form of the periods immediately leads to the well-known Basso-Dixon formula for four-point fishnet integrals in two dimensions. Notably, the relation to Calabi-Yau geometry implies that the volume is also expressible via a determinant formula of Basso-Dixon type. Finally, we show how the fishnet integrals can be written in terms of iterated integrals naturally attached to the Calabi-Yau varieties.

    ↳ hep-thhep-phmath-phmath.MPJHEP(2024)·30 citations
25. 25*

    On the Quadratic Phase Quaternion Domain Fourier Transform and on the Clifford algebra of $R^{3,1}$

    Sadataka Furui🇯🇵

    We study application of the Clifford algebra and the Grassmann algebra to image recognitions in $(3+1)D$ using quaternions. Following S.L.Adler, we construct a quaternion-valued wave function model with fermions and bosons of equal degrees of freedom, similar to Cartan's supersymmetric model. The Clifford algebra ${\mathcal{A}}_{3,1}$ is compared with ${\mathcal{A}}_{2,1}$ and the model applied to the $(2+1)D$ non-destructive testing is extended. The fixed point lattice actions are calculated for 7 paths in $(3+1)D$ space with lengths less than or equal to 8 lattice units. Comparison with the quaternion time approach of Ariel, quaternion Fourier transform of Hitzer and the tensor renormalization group approach to classical lattice models are also discussed.

    ↳ math-phhep-lathep-phmath.MP1 citation

* 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.