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A theoretical investigation of electron-D2 resonant collisions - via the low lying and the Rydberg states of D2- - is presented for vibrational excitation, dissociative electron attachment and dissociative excitation processes by using the local-complex-potential approach. Full sets of vibrationally resolved cross sections, involving the ground electronic state - X 1{\Sigma}+g - and the first two electronic excited states - b 3{\Sigma}+u and B 1{\Sigma}+ u - of the D2 molecule, are given for fusion plasma applications in their technologically relevant partially dissociated, detached divertor regimes. In particular, transitions between electronic excited states are also considered. Comparisons are made with cross sections present in the literature, where available

A full set of vibrationally-resolved cross sections for electron impact excitation of NO(X2{\Pi}, v) molecules is calculated from ab initio molecular dynamics, in the framework of the local-complex-potential approach. Electron-vibration energy exchanges in non-equilibrium thermodynamic conditions are studied from a state-to-state model accounting for all electron impact excitation and de-excitation processes of the nitric oxide vibration manifold, and it is shown that the calculated vibration relaxation times are in good agreement with the experimental data. The new vibrational excitation cross sections are used in a complete electron impact cross section set in order to obtain non-equilibrium electron energy distributions functions and to calculate electron transport parameters in NO. It is verified that the new cross sections bring a significant improvement between simulations and experimental swarm data, providing an additional validation of the calculations, when used within the complete set of cross sections investigated in this work.

We study the time-momentum representation of the kernel needed to compute hadronic vacuum polarization contributions to the muon $g$-$2$ in the space-like region at next-to-leading order. For small values of the time, we present analytical series expansions; for large values of the time, we present numerical series expansions which overcome the problems showed by na\"ive asymptotic expansions. These results are to be employed in lattice QCD determinations of hadronic vacuum polarization contributions to the muon $g$-$2$ at next-to-leading order., Comment: 11 pages, 3 figures v2: published version

Multichannel quantum defect theory is applied in the treatment of the dissociative recombination and vibrational excitation processes for the BeD$^+$ ion in the twenty four vibrational levels of its ground electronic state ($\textrm{X}\,{^{1}\Sigma^{+}},v_{i}^{+}=0\ldots 23$). Three electronic symmetries of BeD$^{**}$ states (\ensuremath{^{2}\Pi}, \ensuremath{^{2}\Sigma^{+}}, and \ensuremath{^{2}\Delta}), are considered in the calculation of cross sections and the corresponding rate coefficients. The incident electron energy range is $10^{-5}$--2.7 eV and the electron temperature range is 100--5000~K. The vibrational dependence of these collisional processes is highlighted. The resulting data are useful in magnetic confinement fusion edge plasma modelling and spectroscopy, in devices with beryllium based main chamber materials, such as ITER and JET, and operating with the deuterium-tritium fuel mix. An extensive rate coefficients database is presented in graphical form and also by analytic fit functions whose parameters are tabulated in the supplementary material., Comment: 7 pages, 5 figures, 3 tables

We present a complete reevaluation of the irreducible two-loop vacuum-polarization correction to the photon propagator in quantum electrodynamics, i.e. with an electron-positron pair in the fermion propagators. The integration is carried out by reducing the integrations to a limited set of master integrals, which are calculated using integration-by-parts identities. Dimensional regularization is used in D = 4-2*epsilon dimensions, and on-mass shell renormalization is employed. The one-loop effect is given to order epsilon, to be combined with the 1/epsilon divergence of the two-loop amplitude. Master integrals are given. Final evaluations of two-loop energy shifts for 1S, 2S, and 2P states are done analytically, and results are presented, with an emphasis on muonic hydrogen. For relativistic Dirac-Coulomb reference states, higher-order coefficients are obtained for the Zalpha-expansion. We compare the results obtained to the existing literature., Comment: 17 pages; RevTeX; see Physical Review D for Supplementary Material

Our previous studies of dissociative recombination, and vibrational excitation/de-excitation of the BeH$^+$ ion, based on the multichannel quantum defect theory, are extended to collision energies above the dissociation threshold, taking into account the vibrational continua of the BeH$^+$ ion and, consequently, its dissociative excitation. We have also significantly increased the number of dissociative states of $^2{\Pi}$, $^2{\Sigma}^+$ and $^2\Delta$ symmetry included in our cross section calculations, generating the most excited-ones by using appropriate scaling laws. Our results are suitable for modeling the kinetics of BeH+ in edge fusion plasmas for collision energies up to 12 eV., Comment: 9 pages, 9 figures

We exploit the properties of a sequence of functions that approximate the divisor functions and combine them with an analytical formula of a delta-like sequence to give a new proof of a theorem of Gronwall on the asymptotic of the divisor functions.

Within our program of physical characterization of trans-Neptunian objects and centaurs, we predicted a stellar occultation by the centaur (54598) Bienor to occur on January 11, 2019, with good observability potential. We obtained high accuracy astrometric data to refine the prediction, resulting in a shadow path favorable for the Iberian Peninsula. This encouraged us to carry out an occultation observation campaign that resulted in five positive detections from four observing sites. This is the fourth centaur for which a multichord (more than two chords) stellar occultation has been observed so far, the other three being (2060) Chiron, (10199) Chariklo, and (95626) 2002 GZ$_{32}$. From the analysis of the occultation chords, combined with the rotational light curve obtained shortly after the occultation, we determined that Bienor has an area-equivalent diameter of $150\pm20$ km. This diameter is $\sim30$ km smaller than the one obtained from thermal measurements. The position angle of the short axis of the best fitting ellipse obtained through the analysis of the stellar occultation does not match that of the spin axis derived from long-term photometric models. We also detected a strong irregularity in one of the minima of the rotational light curve that is present no matter the aspect angle at which the observations were done. We present different scenarios to reconcile the results from the different techniques. We did not detect secondary drops related to potential rings or satellites. Nonetheless, similar rings in size to that of Chariklo's cannot be discarded due to low data accuracy., Comment: Accepted for publication in A\&A

A celebrated theorem of Delange gives a sufficient condition for an arithmetic function to be the sum of the associated Ramanujan expansion with the coefficients provided by a previous result of Wintner. By applying the Delange theorem to the correlation of the von Mangoldt function with its incomplete form, we deduce an inequality involving the counting function of the prime numbers in arithmetic progressions. A remarkable aspect is that such an inequality is equivalent to the famous conjectural formula by Hardy and Littlewood for the twin primes.

Rate coefficients for the dissociative recombination, vibrational excitation and vibrational de-excitation of the BeT$^{+}$ ion for all vibrational levels of its ground electronic state ($ X\ensuremath{^{1}\Sigma^{+}},v_{i}^{+}=0,\dots,27$) are reported, including in the calculation the contribution of super-excited states of the BeT complex pertaining to three electronic symmetries - $^{2}\Pi$, $^{2}\Sigma^{+}$, and $^{2}\Delta$. These data are suitable for the kinetic modeling of beryllium and tritium containing plasma, as encountered in magnetic fusion devices with beryllium walls (JET, ITER). In the present study we restrict ourselves to incident electron energies from 10$^{-3}$ up to $2.7$ eV, and to electron temperatures between $100$ and $5000$ K, respectively. Together with our earlier and closely related studies on the BeH$^{+}$ and BeD$^{+}$ systems, this present work completes the isotopic coverage for the beryllium monohydride ions. The vibrational energy (rather than the vibrational quantum state) is identified as a proper isotopic similarity parameter, e.g., for reduced but still isotopically correct plasma chemistry models., Comment: 27 pages, 7 figures, 15 tables

We describe the major low-energy electron-impact processes involving H$^+_2$ and HD$^+$, relevant for the astrochemistry of the early Universe: Dissociative recombination, elastic, inelastic and superelastic scattering. We report cross sections and Maxwellian rate coefficients of both rotational and vibrational transitions, and outline several important features, like isotopic, rotational and resonant effects., Comment: 5 pages, 4 figures

Cross sections and thermal rate coefficients are computed for electron-impact dissociative recombination and vibrational excitation/de-excitation of the N$^+_2$ molecular ion in its lowest six vibrational levels, for collision energies/temperatures up to 2.3 eV/5000 K., Comment: 9 pages, 4 figures, 3 tables

The mini-proceedings of the STRONG2020 Virtual Workshop "Space-like and Time-like determination of the Hadronic Leading Order contribution to the Muon $g-2$", November 24--26 2021, are presented. This is the first workshop of the STRONG2020 WP21: JRA3-PrecisionSM: Precision Tests of the Standard Model (http://www.strong-2020.eu/joint-research-activity/jra3-precisionsm.html). The workshop was devoted to review of the working group activitity on: $(\it i)$ Radiative Corrections and Monte Carlo tools for low-energy hadronic cross sections in $e^+ e^-$ collisions; $(\it ii)$ Annotated database for $e^+e^-$ into hadrons processes at low energy; $(\it iii)$ Radiative Corrections and Monte Carlo tools for $\mu$-$e$ elastic scattering., Comment: 43 pages, 21 contributions. Editors: A. Kup\'s\'c and G. Venanzoni

We present simple analytic expressions to compute the hadronic vacuum polarization contribution to the muon $g$-2 in the space-like region up to next-to-next-to-leading order. These results can be employed in lattice QCD calculations of this contribution as well as in space-like determinations based on scattering data, like that expected from the proposed MUonE experiment at CERN., Comment: 14 pages, 6 figures. v2: NNLO results presented. v3: minor changes

We report on the design and whole characterization of low-noise and affordable-cost Yb-doped double-clad fiber amplifiers operating at room temperature in the near-infrared spectral region at pulse repetition rate of 160 MHz. Two different experimental configurations are discussed. In the first one, a broadband seed radiation with a transform limited pulse duration of 71 fs, an optical spectrum of 20 nm wide at around 1040 nm, and 20 mW average power is adopted. In the second configuration, the seed radiation is constituted by stretched pulses with a time duration as long as 170 ps, with a 5-nm narrow pulse spectrum centered at 1029 nm and 2 mW average input power. In both cases we obtained transform limited pulse trains with an amplified output power exceeding 2 W. Furthermore, relative intensity noise measurements show that no significant noise degradation occurs during the amplification process.

This study investigates the potential of deep learning methods to identify individuals with suspected COVID-19 infection using remotely collected heart-rate data. The study utilises data from the ongoing EU IMI RADAR-CNS research project that is investigating the feasibility of wearable devices and smart phones to monitor individuals with multiple sclerosis (MS), depression or epilepsy. Aspart of the project protocol, heart-rate data was collected from participants using a Fitbit wristband. The presence of COVID-19 in the cohort in this work was either confirmed through a positive swab test, or inferred through the self-reporting of a combination of symptoms including fever, respiratory symptoms, loss of smell or taste, tiredness and gastrointestinal symptoms. Experimental results indicate that our proposed contrastive convolutional auto-encoder (contrastive CAE), i. e., a combined architecture of an auto-encoder and contrastive loss, outperforms a conventional convolutional neural network (CNN), as well as a convolutional auto-encoder (CAE) without using contrastive loss. Our final contrastive CAE achieves 95.3% unweighted average recall, 86.4% precision, anF1 measure of 88.2%, a sensitivity of 100% and a specificity of 90.6% on a testset of 19 participants with MS who reported symptoms of COVID-19. Each of these participants was paired with a participant with MS with no COVID-19 symptoms., Comment: 34pages, 4figures

A recently introduced approach to the classical gravitational dynamics of binary systems involves intricate integrals (linked to a combination of nonlocal-in-time interactions with iterated $\frac1r$-potential scattering) which have so far resisted attempts at their analytical evaluation. By using computing techniques developed for the evaluation of multi-loop Feynman integrals (notably Harmonic Polylogarithms and Mellin transform) we show how to analytically compute all the integrals entering the nonlocal-in-time contribution to the classical scattering angle at the sixth post-Newtonian accuracy, and at the seventh order in Newton's constant, $G$ (corresponding to six-loop graphs in the diagrammatic representation of the classical scattering angle)., Comment: This paper is a significantly extended version of our previous, separate arxiv submission "Gravitational dynamics at O(G^6): perturbative gravitational scattering meets experimental mathematics" e-Print: 2008.09389 [gr-qc]. The most significant extension is that we now present results at the 7th order in G. 24 pages; revtex macros used; 1 ancillary file

A recently introduced approach to the gravitational dynamics of binary systems involves intricate integrals, linked to nonlocal-in-time interactions arising at the 5-loop level of classical gravitational scattering. We complete the analytical evaluation of classical gravitational scattering at the sixth order in Newton's constant, $G$, and at the sixth post-Newtonian accuracy. We use computing techniques developed for the evaluation of multi-loop Feynman integrals to obtain our results in two ways: high-precision arithmetic, yielding reconstructed analytic expressions, and direct integration {\it via} Harmonic Polylogarithms. The analytic expression of the tail contribution to the scattering involve transcendental constants up to weight four., Comment: 9 pages, no figures, one ancillary text file

We present a detailed description of the recent idea for a direct decomposition of Feynman integrals onto a basis of master integrals by projections, as well as a direct derivation of the differential equations satisfied by the master integrals, employing multivariate intersection numbers. We discuss a recursive algorithm for the computation of multivariate intersection numbers and provide three different approaches for a direct decomposition of Feynman integrals, which we dub the straight decomposition, the bottom-up decomposition, and the top-down decomposition. These algorithms exploit the unitarity structure of Feynman integrals by computing intersection numbers supported on cuts, in various orders, thus showing the synthesis of the intersection-theory concepts with unitarity-based methods and integrand decomposition. We perform explicit computations to exemplify all of these approaches applied to Feynman integrals, paving a way towards potential applications to generic multi-loop integrals., Comment: 53 Pages, references added; matches published version

Ultrafast nanophotonics is an emerging research field aimed at the development of nanodevices capable of light modulation with unprecedented speed. A promising approach exploits the optical nonlinearity of nanostructured materials (either metallic or dielectric) to modulate their effective permittivity via interaction with intense ultrashort laser pulses. While the ultrafast temporal dynamics of such nanostructures following photoexcitation has been studied in depth, sub-ps transient spatial inhomogeneities taking place at the nanoscale have been so far almost ignored. Here we theoretically predict and experimentally demonstrate that the inhomogeneous space-time distribution of photogenerated hot carriers induces a transient symmetry breaking in a plasmonic metasurface made of highly symmetric metaatoms. The process is fully reversible, and results in a broadband transient dichroic optical response with a recovery of the initial isotropic state in less than 1 picosecond, overcoming the speed bottleneck caused by slower relaxation processes, such as electron-phonon and phonon-phonon scattering. Our results pave the way to the development of ultrafast dichroic devices, capable of Tera bit/s modulation of light polarization.

Frequency combs have triggered an impressive evolution of optical metrology across diverse regions of the electromagnetic spectrum, from the ultraviolet to the terahertz frequencies. An unexplored territory, however, remains in the region of vibrational bending modes, mostly due to the lack of single-mode lasers in the long-wavelength (LW) part of the mid-infrared (MIR) spectrum. We fill this gap through a purely MIR-based nonlinear laser source with tunability from 12.1 to 14.8 $\mu$m, optical power up to 110 $\mu$W, MHz-level linewidth and comb calibration. This enables the first example of bending modes metrology in this region, with the assessment of several CO$_2$-based frequency benchmarks with uncertainties down to 30 kHz, and the accurate study of the $\nu_{11}$ band of benzene, which is a significant testbed for the resolution of the spectrometer. These achievements pave the way for LW-MIR metrology, rotationally-resolved studies and astronomic observations of large molecules, such as aromatic hydrocarbons., Comment: 36 pages including Supplementary Materials, 4 figures (paper), 3 figures (SM)

Motivated by the huge need of data for non-equilibrium plasma modeling, a theoretical investigation of dissociative electron attachment to the NO molecule is performed. The calculations presented here are based on the Local-Complex-Potential approach, taking into account five NO$^-$ resonances. Three specific channels of the process are studied, including the production of excited nitrogen atoms $\mathrm{N}(^2\mathrm{D})$ and of its anions N$^-$. Interpretation of the existing experimental data and their comparison with our theoretical result are given. A full set of ro-vibrationally-resolved cross sections and the corresponding rate coefficients are reported. In particular, a relatively notably large cross section of N$^-$ ion formation at low energy of the incident electron and for vibrationally excited NO target is predicted. Finally, molecular rotation effects are discussed., Comment: 7 pages, 7 figures

A celebrated conjecture of Hardy and Littlewood provides with an asymptotic formula for the counting function of the twin primes. We give an unconditional proof of such a formula by means of a finite Ramanujan expansion of the counting function expressed in terms of the von Mangoldt function and its incomplete form. In a completely analogous way, we solve the conjugate conjecture on the representations of any even integer as the sum of two prime numbers., Comment: Lemma 1 is wrong

We review the current status of the theory predictions for elastic $\mu$-$e$ scattering, describing the recent activities and future plans of the theory initiative related to the proposed MUonE experiment., Comment: 23 pages, 14 figures. Invited review for EPJ-C, identical to published version

A theoretical investigation of the dissociative excitation by electron impact on the NO molecule is presented, aiming to make up for the lack of data for this process in the literature. A full set of vibrationally-resolved cross sections and corresponding rate coefficients are calculated using the Local-Complex-Potential approach and five resonant states of NO^-., Comment: 5 pages, 3 figures

The 4-loop QED mass and wave function renormalization constants $Z_2$ and $Z_m$ have been evaluated in the on-shell subtraction scheme with 1100 digits of precision. We also worked out the coefficients of the five color structures of the QCD renormalization constants $Z_2^{OS}$ and $Z_m^{OS}$ which can obtained from QED-like diagrams. The results agree with lower precision results available in the literature. Analytical fits were also obtained for all these quantities., Comment: 12 pages, 1 table and 1 figure; v2: revised version accepted by Physics Letters B; v3: added the missing definition of the constant t_{63}

The famous Miller-Urey experiment, which provides essential information on the prebiotic synthesis of the molecules of life, still has many obscure points. In this paper, we want to suggest a way of possible future progress, which consists in framing the experience of Miller and Urey in the context of the kinetics of ionized gas, or plasma. In this framework, extremely effective and versatile theoretical tools, based on quantum mechanics and chemical kinetics, make it possible to look, in a new way, at the elementary processes that lead to the formation of excited species and ions, at the base of the cascade of subsequent reactions.

We have evaluated with 1100 digits of precision the contribution of all the 891 mass-independent four-loop Feynman diagrams contributing to the slope of the Dirac form factor in QED. The total 4-loop contribution is $ m^2 F_1^{(4)'}(0) = 0.886545673946443145836821730610315359390424032660064745... \left(\frac{\alpha}{\pi}\right)^4$. We have fit a semi-analytical expression to the numerical value. The expression contains harmonic polylogarithms of argument $e^{\frac{i\pi}{3}}$, $e^{\frac{2i\pi}{3}}$, $e^{\frac{i\pi}{2}}$, one-dimensional integrals of products of complete elliptic integrals and six finite parts of master integrals, evaluated up to 4800 digits. I show the correction on the shift of the energy levels of the hydrogen atom due to the slope., Comment: 12 pages, 3 figures and 3 tables; v2: a few misprints corrected, version formatted to be published on Physics Letters B