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One parameter family of exact solutions in General Relativity with a scalar field has been found using the Liouville metric. The scalar field potential has exponential form. This model is interesting, because, in particular, the solution corresponding to the naked singularity provides smooth extension of the Friedmann universe with accelerated expansion through the zero of the scale factor back in time. All geodesics are found explicitly. Their analysis shows that the Liouville solutions are global ones: every geodesic is either continued to infinite value of the canonical parameter in both directions or ends up at the singularity at its finite value., Comment: 25 pages, 12 figures, minor corrections. arXiv admin note: text overlap with arXiv:2405.09422

We study axial algebras, that is, commutative non-associative algebras generated by idempotents whose adjoint actions are semisimple and obey a fusion law. Considering the case, when said adjoint actions having $3$ eigenvalues and the fusion law is the least restrictive, we describe $2$-generated and $3$-generated algebras and prove some of their general properties., Comment: 20 pages

We study the class of idempotent-generated pseudo-composition algebras, which is a subclass of the family of axial algebras. More specifically, we utilise the group-algebra correspondence, natural to the axial framework in order to study some automorphism subgroups of such pseudo-composition algebras., Comment: 16 pages

New one parameter family of exact solutions in General Relativity with a scalar field is found. The metric is of Liouville type which admits complete separation of variables in the geodesic Hamilton-Jacobi equation. This solution exists for the exponential potential for a scalar field and is invariant with respect to global Lorentz transformations. It describes, in particular, evolution of the space-time with the naked singularity. Solutions corresponding to the naked singularity provide accelerating expansion of the homogeneous and isotropic Universe, and can be smoothly continued along geodesics to infinite past without Big Bang., Comment: 8 pages, 2 figures; minor corrections

The effect of the lepton's mass is significantly enhanced when the beam's energy is on the order of the lepton's mass. In the case of electrons, this corresponds to beam momenta on the order of a few MeV and is negligible in higher energy experiments. In this study, we calculate the differential cross section $d\sigma/ d\Omega$ for the helicity-flip meson exchange interference in elastic muon-proton $(\mu p)$ scattering $\mu^- p \rightarrow \mu^- p$. In particular, we examine the $\pi^0$ meson exchange in the $t$-channel for a longitudinally polarized beam and a transversely polarized target. We demonstrate the contribution to be larger for muons due to the lepton mass difference. Then we construct the corresponding beam-target double-spin asymmetries for the target polarized normal and parallel to the momentum transfer in the Breit frame, and then consider the model dependence of the calculation from the estimation of the $\pi^0 \mu \mu$ vertex. The contribution was found to be on the order of $\sim .15\%$ for muons in the kinematic region of the MUSE experiment., Comment: 10 pages, 7 figures

In this work, we examine the extraordinary behavior of polarization and spin angular momentum (AM) density in the vicinity of longitudinal field zeros in three-dimensional monochromatic acoustic fields. We demonstrate that, as governed by the continuity equation, the velocity fields of arbitrary acoustic sources maintain non-diffractive elliptical polarization structures that enclose longitudinal field zeros, despite having divergent transverse spatial profiles of intensity. Furthermore, embedded in these nonparaxial field contours, for infinite distance, are threads of circular polarization singularities. We illuminate these inherent properties in acoustic vortex fields, dipole arrays, and the famous Young's double slit experiment. Our results reveal novel characteristics of vector sound waves that provide a platform for future studies and applications of structured acoustic waves and chiral acoustic phenomena., Comment: 7 pages, 3 figures

The parameterization of the nucleon structure through Generalized Parton Distributions (GPDs) shed a new light on the nucleon internal dynamics. For its direct interpretation, Deeply Virtual Compton Scattering (DVCS) is the golden channel for GPDs investigation. The DVCS process interferes with the Bethe-Heitler (BH) mechanism to constitute the leading order amplitude of the $eN \to eN\gamma$ process. The study of the $ep\gamma$ reaction with polarized positron and electron beams gives a complete set of unique observables to unravel the different contributions to the $ep \gamma$ cross section. This separates the different reaction amplitudes, providing a direct access to their real and imaginary parts which procures crucial constraints on the model dependences and associated systematic uncertainties on GPDs extraction. The real part of the BH-DVCS interference amplitude is particularly sensitive to the $D$-term which parameterizes the Gravitational Form Factors of the nucleon. The separation of the imaginary parts of the interference and DVCS amplitudes provides insights on possible higher-twist effects. We propose to measure the unpolarized and polarized Beam Charge Asymmetries (BCAs) of the $\vec{e}^{\pm}p \to e^{\pm}p \gamma$ process on an unpolarized hydrogen target with {\tt CLAS12}, using polarized positron and electron beams at 10.6 GeV. The azimuthal and $t$-dependences of the unpolarized and polarized BCAs will be measured over a large $(x_B,Q^2)$ phase space using a 100 day run with a luminosity of 0.66$\times 10^{35}$cm$^{-2}\cdot$s$^{-1}$., Comment: Proposal to the Jefferson Lab Program Advisory Committee (PAC51)

Radiative corrections are crucial for modern high-precision physics experiments, and are an area of active research in the experimental and theoretical community. Here we provide an overview of the state of the field of radiative corrections with a focus on several topics: lepton-proton scattering, QED corrections in deep-inelastic scattering, and in radiative light-hadron decays. Particular emphasis is placed on the two-photon exchange, believed to be responsible for the proton form-factor discrepancy, and associated Monte-Carlo codes. We encourage the community to continue developing theoretical techniques to treat radiative corrections, and perform experimental tests of these corrections., Comment: Review article to be submitted to the EPJ A Topical Collection on radiative corrections. 63 pages, 27 figures, 3 tables

This document presents the initial scientific case for upgrading the Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab (JLab) to 22 GeV. It is the result of a community effort, incorporating insights from a series of workshops conducted between March 2022 and April 2023. With a track record of over 25 years in delivering the world's most intense and precise multi-GeV electron beams, CEBAF's potential for a higher energy upgrade presents a unique opportunity for an innovative nuclear physics program, which seamlessly integrates a rich historical background with a promising future. The proposed physics program encompass a diverse range of investigations centered around the nonperturbative dynamics inherent in hadron structure and the exploration of strongly interacting systems. It builds upon the exceptional capabilities of CEBAF in high-luminosity operations, the availability of existing or planned Hall equipment, and recent advancements in accelerator technology. The proposed program cover various scientific topics, including Hadron Spectroscopy, Partonic Structure and Spin, Hadronization and Transverse Momentum, Spatial Structure, Mechanical Properties, Form Factors and Emergent Hadron Mass, Hadron-Quark Transition, and Nuclear Dynamics at Extreme Conditions, as well as QCD Confinement and Fundamental Symmetries. Each topic highlights the key measurements achievable at a 22 GeV CEBAF accelerator. Furthermore, this document outlines the significant physics outcomes and unique aspects of these programs that distinguish them from other existing or planned facilities. In summary, this document provides an exciting rationale for the energy upgrade of CEBAF to 22 GeV, outlining the transformative scientific potential that lies within reach, and the remarkable opportunities it offers for advancing our understanding of hadron physics and related fundamental phenomena., Comment: Updates to the list of authors; Preprint number changed from theory to experiment; Updates to sections 4 and 6, including additional figures

Light from any physical source diffracts over space, as spherical wavefronts grow and energy density is spread out. Diffractive effects pose fundamental limits to light-based technologies, including communications, spectroscopy, and metrology. Polarisation becomes paraxial in the far field limit and, by ignoring longitudinal field components, the rich physics of non-paraxial fields which exist in near-fields or a beam's tight focus are lost. The longitudinal field cannot, however, be ignored when transverse field components vanish (in a transverse field zero) and carry a small non-paraxial region to infinity. We show that a transverse field zero is always accompanied by non-diffracting polarisation structures, whose geometries are independent of the distance to the source, including an enclosing intensity ratio tube, and parallel, non-diverging polarisation singularities. We illustrate these features in multipole radiation and in double slit interference, two examples which have time-fixed transverse field zeros. Non-diffracting structures with changing position are coupled to time-varying zeros, which are present in all far field radiation., Comment: 13 pages, 3 figures; journal version

We study $6$-transposition groups, i.e. groups generated by a normal set of involutions $D$, such that the order of the product of any two elements from $D$ does not exceed $6$. We classify most of the groups generated by $3$ elements from $D$, two of which commute, and prove they are finite., Comment: 12 pages

This White Paper presents the community inputs and scientific conclusions from the Hot and Cold QCD Town Meeting that took place September 23-25, 2022 at MIT, as part of the Nuclear Science Advisory Committee (NSAC) 2023 Long Range Planning process. A total of 424 physicists registered for the meeting. The meeting highlighted progress in Quantum Chromodynamics (QCD) nuclear physics since the 2015 LRP (LRP15) and identified key questions and plausible paths to obtaining answers to those questions, defining priorities for our research over the coming decade. In defining the priority of outstanding physics opportunities for the future, both prospects for the short (~ 5 years) and longer term (5-10 years and beyond) are identified together with the facilities, personnel and other resources needed to maximize the discovery potential and maintain United States leadership in QCD physics worldwide. This White Paper is organized as follows: In the Executive Summary, we detail the Recommendations and Initiatives that were presented and discussed at the Town Meeting, and their supporting rationales. Section 2 highlights major progress and accomplishments of the past seven years. It is followed, in Section 3, by an overview of the physics opportunities for the immediate future, and in relation with the next QCD frontier: the EIC. Section 4 provides an overview of the physics motivations and goals associated with the EIC. Section 5 is devoted to the workforce development and support of diversity, equity and inclusion. This is followed by a dedicated section on computing in Section 6. Section 7 describes the national need for nuclear data science and the relevance to QCD research., Comment: QCD Town Meeting White Paper, as submitted to 2023 NSAC LRP committee on Feb. 28, 2023

In preparation for the 2023 NSAC Long Range Plan (LRP), members of the Nuclear Science community gathered to discuss the current state of, and plans for further leveraging opportunities in, QIST in NP research at the Quantum Information Science for U.S. Nuclear Physics Long Range Planning workshop, held in Santa Fe, New Mexico on January 31 - February 1, 2023. The workshop included 45 in-person participants and 53 remote attendees. The outcome of the workshop identified strategic plans and requirements for the next 5-10 years to advance quantum sensing and quantum simulations within NP, and to develop a diverse quantum-ready workforce. The plans include resolutions endorsed by the participants to address the compelling scientific opportunities at the intersections of NP and QIST. These endorsements are aligned with similar affirmations by the LRP Computational Nuclear Physics and AI/ML Workshop, the Nuclear Structure, Reactions, and Astrophysics LRP Town Hall, and the Fundamental Symmetries, Neutrons, and Neutrinos LRP Town Hall communities., Comment: A white paper for the 2023 nuclear physics long-range planning activity, emerging from the workshop "Quantum Information Science for U.S. Nuclear Physics Long Range Planning'', held in Santa Fe, New Mexico on January 31 - February 1, 2023. 26 pages with 7 figures

The main features of the electron structure function method for calculations of the higher order QED radiative effects to polarized deep-inelastic ep-scattering are presented. A new FORTRAN code ESFRAD based on this method was developed. A detailed quantitative comparison between the results of ESFRAD and other methods implemented in the codes POLRAD and RADGEN for calculation of the higher order radiative corrections is performed., Comment: Contribution to: 17th International Workshop on High-Energy Physics and Quantum Field Theory (QFTHEP 2003), 154-161

The manuscript focuses on the high impact science of the EIC with objective to identify a portion of the science program for QCD precision studies that requires or greatly benefits from high luminosity and low center-of-mass energies. The science topics include (1) Generalized Parton Distributions, 3D imagining and mechanical properties of the nucleon (2) mass and spin of the nucleon (3) Momentum dependence of the nucleon in semi-inclusive deep inelastic scattering (4) Exotic meson spectroscopy (5) Science highlights of nuclei (6) Precision studies of Lattice QCD in the EIC era (7) Science of far-forward particle detection (8) Radiative effects and corrections (9) Artificial Intelligence (10) EIC interaction regions for high impact science program with discovery potential. This paper documents the scientific basis for supporting such a program and helps to define the path toward the realization of the second EIC interaction region., Comment: 103 pages,47 figures

We developed theoretical formalism for generation of optical vortices by phased arrays of atoms. Using Jacobi-Anger expansion, we demonstrate the resulting field topology and determine the least number of array elements necessary for generation of vortices with a given topological charge. Vector vortices were considered, taking into account both spin and orbital angular momenta of electromagnetic fields. It was found that for the vortex field near the phase singularity, the transverse-position dependence of 3D polarization parameters is independent of the distance to the radiation source., Comment: 10 pages, 7 figures

There is an unsettled problem in choosing the correct expressions for the local momentum density and angular momentum density of electromagnetic fields (or indeed, of any non-scalar field). If one only examines plane waves, the problem is moot, as the known possible expressions all give the same result. The momentum and angular momentum density expressions are generally obtained from the energy-momentum tensor, in turn obtained from a Lagrangian. The electrodynamic expressions obtained by the canonical procedure are not the same as the symmetric Belinfante reworking. For the interaction of matter with structured light, for example, twisted photons, this is important; there are drastically different predictions for forces and angular momenta induced on small test objects. We show situations where the two predictions can be checked, with numerical estimates of the size of the effects., Comment: Proceedings version of talk by CEC at the conference on Optical Trapping and Optical Manipulation, SPIE Optics and Photonics, San Diego, 21-25 August 2022. 6 pages, 5 figures

Vector optical vortices exhibit complex polarisation patterns due to the interplay between spin and orbital angular momenta. Here we demonstrate, both analytically and with simulations, that certain polarisation features of optical vortex beams maintain constant transverse spatial dimensions independently of beam divergence due to diffraction. These polarisation features appear in the vicinity of the phase singularity and are associated with the presence of longitudinal electric fields. The predicted effect may prove important in metrology and high resolution imaging applications., Comment: 18 pages, 4 figures; revised text and figures

Spinor fields with a vortex structure in free space that allow them to have arbitrary integer orbital angular momentum along the direction of motion have been studied for some time. Relatively new is the observation in a certain context that the vortex center of this field structure is, unlike a classical whirlpool, not singular. We point out that there are several ways to calculate the local velocity of the spinor field and that all but one show a singular vorticity at the vortex line. That one, using the Dirac bilinear current with no derivatives, is the only one so far (to our knowledge) studied in the literature in this context and we further show how to understand an apparent conflict in the existing results., Comment: 6 pages, no figures

Observation of charge asymmetry by comparing electron and positron, or muon and anti-muon, scattering on a hadronic target presently serves as an experimental tool to study two-photon exchange effects. In addition to two-photon exchange, real photon emission also contributes to the charge asymmetry. We present a theoretical formalism, explicit expressions, and a numerical analysis of hard photon emission for the charge asymmetry in lepton- and antilepton-proton scattering. Different kinematic conditions are considered, namely, either fixed transferred momentum squared or a fixed lepton scattering angle. The infrared divergence from real photon emission is treated by the Bardin-Shumeiko technique and canceled with the soft part of the two-photon exchange contribution extracted and calculated using Tsai approach. All final expressions are obtained beyond the ultrarelativistic approximation with respect to the lepton mass that allows to evaluate numerically of the considered effects not only for ultrarelativistic leptons (JLab) and but for moderately relativistic (MUSE) kinematics, too., Comment: 17 pages, 7 figures

We address a problem of proper definition of momentum density for spatially structured electromagnetic fields. We show that the expressions for the momentum and angular momentum obtained locally are not the same when one uses the canonical energy-momentum tensor instead of the symmetric Belinfante energy-momentum tensor in electrodynamics. This has important consequences for interaction of matter with structured light, for example, twisted photons; and would give drastically different results for forces and angular momenta induced on small test objects. We show, with numerical estimates of the size of the effects, situations where the canonical and symmetrized forms induce very different torques or (superkick) recoil momenta on small objects or atomic rotors, over a broad range of circumstances., Comment: 5 pages, 4 figures

We present SERS-active metal holographic metasurfaces fabricated from metal periodical nanograting deposited on a dielectric substrate. The metasurface consists of a modulated dielectric, which is covered by a thin silver layer. The metasurface operates as an open plasmon resonator. The theory of plasmons excited in the open resonator formed by a metal nanograting is presented. The large local electromagnetic field is predicted for optical frequencies. The excitation of plasmons is experimentally demonstrated in the metasurface designed on a 4-inch Si wafer. The enhancement of the local electric field results in surface-enhanced Raman scattering (SERS). To investigate the SERS effect, the metasurfaces are covered by molecules of 4-mercaptophenylboronic acid, which form covalent bonds with the silver nanolayer and serve as a proof-of-concept. Finally, we obtain a detection limit of 230 nM for molecules of 4-mercaptophenylboronic acid., Comment: 12 pages, 11 figures, 67 references

Structured vortex waves have numerous applications in optics, plasmonics, radio-wave technologies and acoustics. We present a theoretical study of a method for generating vortex states based on coherent superposition of waves from discrete elements of planar phased arrays, given limitations on an element number. Using Jacobi-Anger expansion, we analyze emerging vortex topologies and derive a constraint for the least number of elements needed to generate a vortex with a given leading-order topological charge., Comment: 11 pages, 4 figures; references and discussion added