Weak pion production off the nucleon at low energies has been systematically investigated in manifestly relativistic baryon chiral perturbation theory with explicit inclusion of the $\mathrm{\Delta }(1232)$ resonance. Most of the involved low-energy constants have been previously determined in other processes such as pion-nucleon elastic scattering and electromagnetic pion production off the nucleon. For numerical estimates, the few remaining constants are set to be of natural size. As a result, the total cross sections for single pion production on neutrons and protons, induced either by neutrino or antineutrino, are predicted. Our results are consistent with the scarce existing experimental data except in the ${\nu }_{\mu }n\to {\mu }^{-}n{\pi }^{+}$ channel, where higher-order contributions might still be significant. The $\mathrm{\Delta }$ resonance mechanisms lead to sizeable contributions in all channels, especially in ${\nu }_{\mu }p\to {\mu }^{-}p{\pi }^{+}$, even though the considered energies are close to the production threshold. The present study provides a well-founded low-energy benchmark for phenomenological models aimed at the description of weak pion production processes in the broad kinematic range of interest for current and future neutrino-oscillation experiments.

We explore a general framework to treat coupled-channel systems in the presence of overlapping left- and right-hand cuts as well as anomalous thresholds. Such systems are studied in terms of a generalized potential, where we exploit the known analytic structure of $t$- and $u$-channel forces as the exchange masses approach their physical values. Given an approximate generalized potential the coupled-channel reaction amplitudes are defined in terms of nonlinear systems of integral equations. For large exchange masses, where there are no anomalous thresholds present, conventional $N/D$ methods are applicable to derive numerical solutions to the latter. At a formal level a generalization to the anomalous case is readily formulated by use of suitable contour integrations with amplitudes to be evaluated at complex energies. However, it is a considerable challenge to find numerical solutions to anomalous systems set up on a set of complex contours. By suitable deformations of left-hand and right-hand cut lines we manage to establish a framework of linear integral equations defined for real energies. Explicit expressions are derived for the driving terms that hold for an arbitrary number of channels. Our approach is illustrated in terms of schematic three-channel systems. It is demonstrated that despite the presence of anomalous thresholds the scattering amplitude can be represented in terms of three phase shifts and three inelasticity parameters, as one would expect from the coupled-channel unitarity condition.

In $\mathrm{SU}(N)$ gauge-Higgs theories, with a single Higgs field in the fundamental representation, there exists in addition to the local gauge symmetry a global SU(2) symmetry, at $N=2$, and a global U(1) symmetry, for $N\ne 2$. We construct a gauge-invariant order parameter for the breaking of these global symmetries in the Higgs sector and calculate numerically the transition lines, in coupling-constant space, for SU(2) and SU(3) gauge theories with unimodular Higgs fields. The order parameter is nonlocal, and, therefore, its nonanalyticity does not violate the theorem proved by Osterwalder and Seiler. We then show that there exists a transition, in gauge-Higgs theories, between two types of confinement: ordinary color neutrality in the Higgs region and a stronger condition, which we have called “separation-of-charge confinement”, in the confinement region. We conjecture that the symmetry-breaking transition coincides with the transition between these two physically different types of confinement.

We study the ground-state properties of a class of ${\mathbb{Z}}_n$ lattice gauge theories in $1+1$ dimensions, in which the gauge fields are coupled to spinless fermionic matter. These models, stemming from discrete representations of the Weyl commutator for the U(1) group, preserve the unitary character of the minimal coupling and have, therefore, the property of formally approximating lattice quantum electrodynamics in one spatial dimension in the large-$n$ limit. The numerical study of such approximated theories is important to determine their effectiveness in reproducing the main features and phenomenology of the target theory, in view of implementations of cold-atom quantum simulators of QED. In this paper, we study the cases $n=2÷8$ by means of a DMRG code that exactly implements Gauss’s law. We perform a careful scaling analysis and show that, in absence of a background field, all ${\mathbb{Z}}_n$ models exhibit a phase transition which falls in the Ising universality class, with spontaneous symmetry breaking of the $CP$ symmetry. We then perform the large-$n$ limit and find that the asymptotic values of the critical parameters approach the ones obtained for the known phase transition of the zero-charge sector of the massive Schwinger model, which occurs at negative mass.

Recent data from LHC13 by the TOTEM Collaboration indicate an unexpected decrease in the value of the $\rho$ parameter and a ${\sigma }_{\mathrm{tot}}$ value in agreement with the trend of previous measurements at 7 and 8 TeV. These data at 13 TeV are not simultaneously described by the predictions from Pomeron models selected by the COMPETE Collaboration but show agreement with the maximal Odderon dominance, as recently demonstrated by Martynov and Nicolescu. Here, we present a detailed analysis on the applicability of Pomeron dominance by means of a general class of forward scattering amplitude, consisting of even-under-crossing leading contributions associated with single, double, and triple poles in the complex angular momentum plane and subleading even and odd Regge contributions. The analytic connection between ${\sigma }_{\mathrm{tot}}$ and $\rho$ is obtained by means of singly subtracted dispersion relations, and we carry out fits to $pp$ and $\overline{p}p$ data in the interval 5 GeV–13 TeV. The data set comprises all the accelerator data below 7 TeV, and we consider two independent ensembles by adding either only the TOTEM data or the TOTEM and ATLAS data at the LHC energy region. In the data reductions to each ensemble, the uncertainty regions are evaluated with both one and two standard deviations ($\sim 68\%$ and $\sim 95\%\mathrm{CL}$, respectively). Besides the general analytic model, we investigate four particular cases of interest, three of them typical of outstanding models in the literature. We conclude that, within the experimental and theoretical uncertainties and both ensembles, the general model and three particular cases are not able to describe the ${\sigma }_{\mathrm{tot}}$ and $\rho$ data at 13 TeV simultaneously. However, if the discrepancies between the TOTEM and ATLAS data are not resolved, one Pomeron model, associated with double and triple poles and with only 7 free parameters, seems not to be excluded by the complete set of experimental information presently available.

The study of pion production in nuclei is important for signal and background determinations in current and future neutrino oscillation experiments. The first step, however, is to understand the pion production reactions at the free nucleon level. We present an exhaustive study of the charged-current and neutral-current neutrino and antineutrino pion production off nucleons, paying special attention to the angular distributions of the outgoing pion. We show, using general arguments, that parity violation and time-reversal odd correlations in the weak differential cross sections are generated from the interference between different contributions to the hadronic current that are not relatively real. Next, we present a detailed comparison of three state-of-the-art, microscopic models for electroweak pion production off nucleons, and we also confront their predictions with polarized electron data, as a test of the vector content of these models. We also illustrate the importance of carrying out a comprehensive test at the level of outgoing pion angular distributions, going beyond comparisons done for partially integrated cross sections, where model differences cancel to a certain extent. Finally, we observe that all charged and neutral current distributions show sizable anisotropies, and identify channels for which parity-violating effects are clearly visible. Based on the above results, we conclude that the use of isotropic distributions for the pions in the center of mass of the final pion-nucleon system, as assumed by some of the Monte Carlo event generators, needs to be improved by incorporating the findings of microscopic calculations.

We analyze a quantum version of the weak equivalence principle, in which we compare the response of a static particle detector crossed by an accelerated cavity with the response of an accelerated detector crossing a static cavity in ($1+1$)-dimensional flat spacetime. We show, for both massive and massless scalar fields, that the nonlocality of the field is enough for the detector to distinguish the two scenarios. We find this result holds for vacuum and excited field states of different kinds and we clarify the role of field mass in this setup.

We address the issue of fermionic particle creation in cosmological bouncing models governed by general relativity, but where the bounce itself takes place due to quantum effects. If the energy scale of the bounce is not very close to the Planck energy, the Wheeler-DeWitt approach can be used to furnish sensible singularity-free background models with a contracting phase preceding an expanding phase in which the fermions evolve. The fermionic fields considered are massive, neutral and minimally coupled to gravity. We are particularly interested in neutrinos, neutrons and heavy neutrinos motivated by theories beyond the standard model of particle physics. We perform a numerical analysis for a bouncing model containing radiation and a pressureless fluid. The results reveal that the fermionic production depends on the ratio between the quantum bounce length scale and the Compton wavelength of the particle, and it is very small, with no back-reaction, unless the fermions are very heavy with masses up to $10^9\mathrm{GeV}$. Hence, investigations concerning baryogenesis in such bouncing models should either go beyond the minimal coupling between gravity and the fermionic fields considered here, or assume the existence of such heavy fermions as a starting point.

Inclusive ${\chi }_{cJ}$ ($J=0$, 1, 2) production from $\mathrm{\Upsilon }(1S)$ decay is studied within the framework of nonrelativistic QCD (NRQCD) factorization at leading order in $v_Q^2$, which includes the contributions of $b\overline{b}({{}^{3}S}_1^{[1]})\to c\overline{c}({{}^{3}P}_J^{[1]})+X$ and $b\overline{b}({{}^{3}S}_1^{[1]})\to c\overline{c}({{}^{3}S}_1^{[8]})+X$. For both channels, the short-distance coefficients are calculated through $\mathcal{O}({\alpha }_s^5)$, which is next-to-leading order for the second one. By fitting to the measured $\mathrm{\Upsilon }(1S)$ branching fractions to ${\chi }_{c1}$ and ${\chi }_{c2}$, we obtain the color-octet long-distance matrix element (LDME) $⟨{\mathcal{O}}^{{\chi }_{c0}}({{}^{3}S}_1^{[8]})⟩=(4.04\pm 0.47_{-0.34}^{+0.67})\times {10}^{-3}{\mathrm{GeV}}^3$, where the first error is experimental and the second one due to the renormalization scale dependence, if we use as input $⟨{\mathcal{O}}^{{\chi }_{c0}}({{}^{3}P}_0^{[1]})⟩=0.107{\mathrm{GeV}}^5$ as obtained via potential-model analysis. Previous LDME sets, extracted from data of prompt ${\chi }_{cJ}$ hadroproduction, yield theoretical predictions that systematically undershoot or mildly overshoot the experimental values of $\mathcal{B}(\mathrm{\Upsilon }\to {\chi }_{cJ}+X)$.

We report on a fully differential next-to-next-to-leading order (NNLO) calculation of $s$-channel single top (anti)quark production with a semileptonic decay at the LHC, neglecting the color correlation between the light and heavy quark lines and in the narrow width approximation. The NNLO corrections can increase the cross section by about 10% in the low transverse momentum region of the top quark and reduce scale variation uncertainty. In order to compare with experimental results without unfolding procedures, we also present theoretical predictions with fiducial cuts, including total cross sections and distributions of observables used in the experimental multivariate analysis. The NNLO corrections are found to be about $-8\%$ for fiducial cross sections.

We show that one can reduce the coupled system of seven field equations of the ($3+1$)-dimensional gauged Skyrme model to the Heun equation (which, for suitable choices of the parameters, can be further reduced to the Whittaker-Hill equation) in two nontrivial topological sectors. Hence, one can get a complete analytic description of gauged solitons in ($3+1$) dimensions living within a finite volume in terms of classic results in the theory of differential equations and Kummer’s confluent functions. We consider here two types of gauged solitons: gauged Skyrmions and gauged time crystals (namely, gauged solitons periodic in time, whose time period is protected by a winding number). The dependence of the energy of the gauged Skyrmions on the baryon charge can be determined explicitly. The theory of Kummer’s confluent functions leads to a quantization condition for the period of the time crystals. Likewise, the theory of Sturm-Liouville operators gives rise to a quantization condition for the volume occupied by the gauged Skyrmions. The present analysis also discloses that resurgent techniques are very well suited to deal with the gauged Skyrme model as well. In particular, we discuss a very nice relation between the electromagnetic perturbations of the gauged Skyrmions and the Mathieu equation which allows to use many of the modern resurgence techniques to determine the behavior of the spectrum of these perturbations.

We consider the many-body system of neutrinos interacting with each other through neutral current weak force. Emerging many-body effects in such a system could play important roles in some astrophysical sites such as the core collapse supernovae. In the literature this many-body system is usually treated within the mean field approximation which is an effective one-body description based on omitting entangled neutrino states. In this paper, we consider the original many-body system in an effective two flavor mixing scenario under the single angle approximation and present a solution without using the mean field approximation. Our solution is formulated around a special class of many-body eigenstates which do not undergo any level crossings as the neutrino self-interaction rate decreases while the neutrinos radiate from the supernova. In particular, an initial state which consists of electron neutrinos and antineutrinos of an orthogonal flavor can be entirely decomposed in terms of those eigenstates. Assuming that the conditions are perfectly adiabatic so that the evolution of these eigenstates follow their variation with the interaction rate, we show that this initial state develops a spectral split at exactly the same energy predicted by the mean field formulation.

The problem of thundercloud electrification is one of the most difficult ones in atmospheric physics. The structure of electric fields in clouds escapes from the detailed in situ measurements; few balloon flights reveal these rather complicated structures. To gain insight into the problem of the charge structure of a thundercloud, we use new key evidence—the fluxes of particles from a thundercloud, the so-called thunderstorm ground enhancements—TGEs. TGEs originate from electron acceleration and multiplication processes in the strong electric fields in the thundercloud, and the intensity and energy spectra of electrons and gamma rays as observed on the Earth’s surface are directly connected with the atmospheric electric field. Discovery of long-lasing TGEs poses new challenges for revealing structures in the thundercloud responsible for hours-extending gamma ray fluxes. In the presented paper, we demonstrate that experimentally measured intensities and energy spectra of the “thundercloud particles” give clues for understanding charge structures embedded in the atmosphere. A rather short “runaway” process above the detector site, which is consistent with the tripole structure of the cloud electrification, is changing to a much less energetic emission that lasts for hours. Measurements of enhanced particle fluxes are accompanied by the simulation experiments with corsika and geant4 codes.

Pfaffian diagrams are formulated to represent gluon amplitudes computed from the Cachazo-He-Yuan (CHY) formula. They may be regarded as a systematic regrouping of Feynman diagrams after internal momenta are expanded and products of vertex factors are evaluated. This reprocessing enables gluon amplitudes expressed in Pfaffian diagrams to contain fewer terms. For example, there are 19 terms for the four-point amplitude in Pfaffian diagrams and 35 terms in Feynman diagrams. Gauge invariance is simpler and more explicit in Pfaffian diagrams, in that the subset of diagrams with the same root configuration is already gauge invariant in all lines but two. In getting to these results, several technical difficulties must be overcome. Double poles must be converted to simple poles, integrations must be carried out directly and formulated into simple rules, and the three Möbius constant lines must be suitably chosen to minimize the number of terms present.

The implementation of the heavy quark spin symmetry in possible molecular states at the mixed bottom-charm threshold is somewhat different from that at the open charm or bottom thresholds. In particular it depends on two parameters describing separately the symmetry for the bottom and for charmed quarks. The corresponding spin structures of the $S$-wave molecular states of the meson pairs $B^{(*)}{D}^{(*)}$ are discussed as well as their consequences for properties of possible near-threshold resonances, analogs of the known charmoniumlike and bottomoniumlike $X$ and $Z$ states.

It has been suggested that the production of a heavy quarkonium near threshold in electron-proton scattering can shed light on the origin of the proton mass via the QCD trace anomaly. We study the photoproduction of $J/\psi$ off the proton using gauge/string duality and demonstrate that the $t$ dependence of the differential cross section $d\sigma /dt$ at small $t$ is a sensitive probe of the trace anomaly.

We report the measurement of $\gamma \gamma \to {\eta }_c(1S),{\eta }_c(2S)\to {\eta }^{\prime }{\pi }^{+}{\pi }^{-}$ with ${\eta }^{\prime }$ decays to $\gamma \rho$ and $\eta {\pi }^{+}{\pi }^{-}$ using $941{\mathrm{fb}}^{-1}$ of data collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. The ${\eta }_c(1S)$ mass and width are measured to be $M=[2984.6\pm 0.7(\mathrm{stat})\pm 2.2(\mathrm{syst})\pm 0.3(\mathrm{model})]\mathrm{MeV}/c^2$ and $\mathrm{\Gamma }=[30.8_{-2.2}^{+2.3}(\mathrm{stat})\pm 2.5(\mathrm{syst})\pm 1.4(\mathrm{model})]\mathrm{MeV}$, respectively. First observation of ${\eta }_c(2S)\to {\eta }^{\prime }{\pi }^{+}{\pi }^{-}$ with a significance of $5.5\sigma$ including systematic error is obtained, and the ${\eta }_c(2S)$ mass is measured to be $M=[3635.1\pm 3.7(\mathrm{stat})\pm 2.9(\mathrm{syst})\pm 0.4(\mathrm{model})]\mathrm{MeV}/c^2$. The products of the two-photon decay width and branching fraction ($\mathcal{B}$) of decays to ${\eta }^{\prime }{\pi }^{+}{\pi }^{-}$ are determined to be ${\mathrm{\Gamma }}_{\gamma \gamma }$${\mathrm{\Gamma }}_{\gamma \gamma }\mathcal{B}=[65.4\pm 2.6(\mathrm{stat})\pm 7.8(\mathrm{syst})]\mathrm{eV}$ for ${\eta }_c(1S)$ and $[{5.6}_{-1.1}^{+1.2}(\mathrm{stat})\pm 1.1(\mathrm{syst})]\mathrm{eV}$ for ${\eta }_c(2S)$. The cross sections for $\gamma \gamma \to {\eta }^{\prime }{\pi }^{+}{\pi }^{-}$ and ${\eta }^{\prime }{f}_2(1270)$ are measured for the first time.

We apply the idea of using a matter-time gauge in quantum gravity to quantum cosmology. For a Friedmann-Lemaître-Robertson-Walker (FLRW) universe with dust and a cosmological constant $\mathrm{\Lambda }$, we show that the dynamics maps exactly to the simple harmonic oscillator in the dust-time gauge. For $\mathrm{\Lambda }>0$ the oscillator frequency is imaginary, for $\mathrm{\Lambda }<0$ it is real, and for $\mathrm{\Lambda }=0$ the universe is a free particle. This result provides (i) a simple and general demonstration of nonperturbative singularity avoidance in FLRW quantum cosmology for all $\mathrm{\Lambda }$, (ii) an exact Lorentzian Hartle-Hawking wave function, and (iii) the present age of the universe as the characteristic decay time of the propagator.