Recently, the first ever lattice computation of the $\gamma W$-box radiative correction to the rate of the semileptonic pion decay allowed for a reduction of the theory uncertainty of that rate by a factor of $\sim 3$. A recent dispersion evaluation of the $\gamma W$-box correction on the neutron also led to a significant reduction of the theory uncertainty, but shifted the value of $V_{ud}$ extracted from the neutron and superallowed nuclear $\beta$ decay, resulting in a deficit of the Cabibbo-Kobayashi-Maskawa (CKM) unitarity in the top row. A direct lattice computation of the $\gamma W$-box correction for the neutron decay would provide an independent cross-check for this result but is very challenging. Before those challenges are overcome, we propose a hybrid analysis, converting the lattice calculation on the pion to that on the neutron by a combination of dispersion theory and phenomenological input. The new prediction for the universal radiative correction to free and bound neutron $\beta$-decay reads ${\mathrm{\Delta }}_R^V=0.02477(24)$, in excellent agreement with the dispersion theory result ${\mathrm{\Delta }}_R^V=0.02467(22)$. Combining with other relevant information, the top-row CKM unitarity deficit persists.

We discuss the change of the boundary entropy under an ambient renormalization group flow. We use conformal perturbation theory to calculate the change of the boundary entropy for $d$-dimensional BCFTs between two nearby fixed points. We also use the ${\mathrm{AdS}}_{d+1}/{\mathrm{BCFT}}_d$ model to calculate the boundary entropy. We show that the boundary entropy can increase under the ambient renormalization group flow both in conformal perturbation theory and the ${\mathrm{AdS}}_{d+1}/{\mathrm{BCFT}}_d$ model. In a special case, the change of the boundary entropy in the ${\mathrm{AdS}}_{d+1}/{\mathrm{BCFT}}_d$ model reduces to that of the conformal perturbation theory.

We consider two quantum phase spaces which can be described by two Hopf algebroids linked with the well-known ${\theta }_{\mu \nu }$-deformed $D=4$ Poincaré-Hopf algebra $\mathbb{H}$. The first algebroid describes ${\theta }_{\mu \nu }$-deformed relativistic phase space with canonical NC space-time (constant ${\theta }_{\mu \nu }$ parameters) and the second one incorporates dual to $\mathbb{H}$ quantum ${\theta }_{\mu \nu }$-deformed Poincaré-Hopf group algebra $\mathbb{G}$, which contains noncommutative space-time translations given by $\mathrm{\Lambda }$-dependent ${\mathrm{\Theta }}_{\mu \nu }$ parameters ($\mathrm{\Lambda }\equiv {\mathrm{\Lambda }}_{\mu \nu }$ parametrize classical Lorentz group). The canonical ${\theta }_{\mu \nu }$-deformed space-time algebra and its quantum phase space extension is covariant under the quantum Poincaré transformations described by $\mathbb{G}$. We will also comment on the use of Hopf algebroids for the description of multiparticle structures in quantum phase spaces.

We discuss two types of quantum mechanical models that couple large numbers of Majorana fermions and have orthogonal symmetry groups. In models of vector type, only one of the symmetry groups has a large rank. The large $N$ limit is taken keeping $gN=\lambda$ fixed, where $g$ multiplies the quartic Hamiltonian. We introduce a simple model with $O(N)\times SO(4)$ symmetry, whose energies are expressed in terms of the quadratic Casimirs of the symmetry groups. This model may be deformed so that the symmetry is $O(N)\times O(2{)}^2$, and the Hamiltonian reduces to that studied in [I. R. Klebanov et al., Phys. Rev. D 97, 106023 (2018)]. We find analytic expressions for the large $N$ density of states and free energy. In both vector models, the large $N$ density of states varies approximately as $e^{-|E|/\lambda }$ for a wide range of energies. This gives rise to critical behavior as the temperature approaches the Hagedorn temperature $T_{\mathrm{H}}=\lambda$. In the formal large $N$ limit, the specific heat blows up as $(T_H-T{)}^{-2}$, which implies that $T_H$ is the limiting temperature. However, at any finite $N$, it is possible to reach arbitrarily large temperatures. Thus, the finite $N$ effects smooth out the Hagedorn transition. We also study models of matrix type, which have two $O(N)$ symmetry groups with large rank. An example is provided by the Majorana matrix model with $O(N{)}^2\times O(2)$ symmetry, which was studied in Klebanov et al. In contrast with the vector models, the density of states is smooth and nearly Gaussian near the middle of the spectrum.

We consider the class of higher derivative field equations whose wave operator is a square of another self-adjoint operator of lower order. At the free level, the models of this class are shown to admit a two-parameter series of integrals of motion. The series includes the canonical energy. Every conserved quantity is unbounded in this series. The interactions are included into the equations of motion such that a selected representative in conserved quantity series is preserved at the nonlinear level. The interactions are not necessarily Lagrangian, but they admit the Hamiltonian form of dynamics. The theory is stable if the integral of motion is bounded from below due to the interaction. The motions are finite in the vicinity of the conserved quantity minimum. The equations of motion for fluctuations have the derived form with no resonance. The general constructions are exemplified by the models of the Pais-Uhlenbeck (PU) oscillator with multiple frequency and Podolsky electrodynamics. The example is also considered of stable non-Abelian Yang-Mills theory with higher derivatives.

Continuing our inquiry into the conditions when fluctuation-dissipation relations (FDR) may appear in the context of nonequilibrium dynamics of open quantum systems (over and beyond the conventional FDR from linear response theory) we turn to non-Gaussian systems and consider this issue for an anharmonic quantum oscillator interacting with a scalar quantum field bath. We present the general nonperturbative expressions for the rate of energy (power) exchange between the anharmonic oscillator and its thermal bath. For the cases that a stable final equilibrium state exists, and the nonstationary components of the two-point functions of the anharmonic oscillator have negligible contributions to the power balance, we can show nonperturbatively that equilibration implies an FDR for the anharmonic oscillator. We then use a weakly anharmonic oscillator as an example to illustrate the validity of those two assumptions and show that in the weak anhamonicity limit, they are satisfied according to our first-order perturbative results..

We introduce a functional perturbative method for treating weakly nonlinear systems coupled with a quantum field bath. We demonstrate using this method to obtain the covariance matrix elements and the correlation functions of a quantum anharmonic oscillator interacting with a heat bath. We identify a fluctuation-dissipation relation based on the nonequilibrium dynamics of this nonlinear open quantum system. To establish its connection with dynamical equilibration, we further examine the energy flows between the anharmonic oscillator and the bath field. The vanishing of the net flow is an indication of the existence of an equilibrium state for such an open-system configuration. The results presented here are useful for studying the nonequilibrium physical processes of nonlinear quantum systems such as heat transfer or electron transport.

The general parametrization of a black-hole spacetime in arbitrary metric theories of gravity includes an infinite set of parameters. It is natural to suppose that essential astrophysically observable quantities, such as quasinormal modes, parameters of shadow, electromagnetic radiation and accreting matter in the vicinity of a black hole, must depend mostly on a few of these parameters. Starting from the parametrization for spherically symmetric configurations in the form of an infinite continued fraction, we suggest a compact representation of the asymptotically flat spherically symmetric and slowly rotating black holes in terms of only three and four parameters respectively. A subclass of arbitrarily rotating black holes belonging to the Carter family can also be parametrized by only four parameters. This approximate representation of a black-hole metric should allow one to describe physical observables in the region of strong gravity.

We study the initial value problem for Lovelock and Horndeski theories of gravity. We show that the equations of motion of these theories can be written in a form that, at weak coupling, is strongly hyperbolic and therefore admits a well-posed initial value problem. This is achieved by introducing a new class of “modified harmonic” gauges for general relativity.

We show that a spin-$5/2$ field can be consistently coupled to gravitation without cosmological constant in five-dimensional spacetimes. The fermionic gauge “hypersymmetry” requires the presence of a finite number of additional fields, including a couple of $U(1)$ fields, a spinorial two-form, the dual of the graviton (of mixed (2,1) Young symmetry) and a spin-3 field. The gravitational sector of the action is described by the purely quadratic Gauss-Bonnet term, so that the field equations for the metric are of second order. The local gauge symmetries of the full action principle close, without the need of auxiliary fields, for a suitable extension of the “hyper-Poincaré” algebra. Apart from the Poincaré and spin-$3/2$ generators, it includes a generator of spin 2 and a $U(1)$ central extension. Noteworthy, the algebra admits an invariant trilinear form, and its generators allow us to precisely accommodate the entire field content within a single connection, so that the hypergravity action can be formulated as a gauge theory described by a Chern-Simons form in five dimensions.

We propose that the initial state of the Universe was an isotropic state of maximal entropy. Such a state can be described in terms of a state of closed, interacting, fundamental strings in their high-temperature Hagedorn phase, which constitutes a novel microscopic model for the state of the Universe when it is at the highest sustainable temperature. This state resolves the big-bang singularity by replacing the past of the hot big-bang Universe and sets inflationary initial conditions for the subsequent evolution of the thermal radiation and the semiclassical cosmological geometry. The entropy density in this state is equal to the square root of the energy density in Planck units, while the pressure is positive and equal to the energy density. These relations imply a maximally large entropy density and, therefore, a state that cannot be described by a semiclassical spacetime geometry. If one nevertheless insists on an effective semiclassical description of this state, she can do so by ignoring the entropy. This leads to a partially equivalent description in which the pressure appears to be negative and equal in magnitude to the energy density, as if the energy-momentum tensor was that of a cosmological constant. From this effective perspective, the state describes a period of string-scale inflation of minimal duration. The stringy state ultimately decays, possibly by a process akin to Hawking radiation, and undergoes a transition into a phase of hot radiation. But, from the effective perspective, the same decay corresponds to the heating of the Universe at the end of inflation. Small quantum mechanical fluctuations in the initial state lead to a scale-invariant temperature anisotropies in the hot radiation. The temperature anisotropies are interpreted in the effective description as arising from quantum fluctuations of the curvature and an effective inflaton field. The stringy microscopic description determines the parameters of the model of inflation, as well as the cosmological observables, in terms of the string length scale and coupling strength. In particular, it describes a high-scale model of inflation with a large scalar-to-tensor ratio which is qualitatively compatible with the cosmological observations. Our framework is similar, conceptually, to a recent description of black holes in terms of a maximal entropy state of strings in the Hagedorn phase.

Axion dark matter can resonantly convert into photons in the magnetospheres of neutron stars (NSs). It has recently been shown that radio observations of nearby NSs can therefore provide a highly sensitive probe of the axion parameter space. Here we extend existing calculations by performing the first three-dimensional computation of the photon flux, taking into account the isotropic phase-space distribution of axions and the structure of the NS magnetosphere. In particular, we study the overall magnitude of the flux and its possible time variation. We find that overall signal strength is robust to our more realistic analysis. In addition, we find that the variance of the signal with respect to the NS rotation is washed out by the additional trajectories in our treatment. Nevertheless, we show that SKA observations toward J0806.4-4123 are sensitive to $g_{a\gamma \gamma }\sim 3\times {10}^{-13}{\mathrm{GeV}}^{-1}$ at $m_a\sim 7\times {10}^{-6}\mathrm{eV}$, even when accounting for Doppler broadening. Finally, we provide the necessary code to calculate the photon flux for any given NS system https://github.com/mikaelLEROY/AxionNS_RayTracing.

We present a comprehensive study on oscillation of high-energy neutrinos from two different environments: blue supergiant progenitors that may harbor low-power gamma-ray burst (GRB) jets and neutron star merger ejecta that would be associated with short gamma-ray bursts. We incorporate the radiation constraint that gives a necessary condition for nonthermal neutrino production, and account for the time evolution of the jet, which allows us to treat neutrino oscillation in matter more accurately. For massive star progenitors, neutrino injection inside the star can lead to nonadiabatic oscillation patterns in the early stages between 1 TeV and 10 TeV and is also visible in the flavor ratio. The matter effects predict a ${\nu }_e$ excess in the 10 TeV–100 TeV range. For neutron star merger ejecta, we find a similar behavior in the $100\mathrm{GeV}–10\mathrm{TeV}$ region and the oscillation may result in a ${\nu }_e$ excess around 1 TeV. These features, which enable us to probe the progenitors of long and short GRBs, could be seen by future neutrino detectors with precise flavor ratio measurements. We also discuss potential contributions to the diffuse neutrino flux measured by IceCube, and find parameter sets allowing choked low-power GRB jets to account for the neutrino flux in the 10 TeV–100 TeV range without violating the existing constraints.

This paper presents a non-Hermitian $\mathcal{PT}$-symmetric extension of the Nambu–Jona-Lasinio (NJL) model of quantum chromodynamics in $3+1$ and $1+1$ dimensions. In $3+1$ dimensions, the SU(2)-symmetric NJL Hamiltonian ${\mathcal{H}}_{\mathrm{NJL}}=\overline{\psi }(-i{\gamma }^k{\partial }_k+m_0)\psi -G[(\overline{\psi }\psi {)}^2+(\overline{\psi }i{\gamma }_5\overrightarrow{\tau }\psi {)}^2]$ is extended by the non-Hermitian, $\mathcal{PT}$- and chiral-symmetric bilinear term $ig\overline{\psi }{\gamma }_5{B}_{\mu }{\gamma }^{\mu }\psi$; in $1+1$ dimensions, where ${\mathcal{H}}_{\mathrm{NJL}}$ is a form of the Gross-Neveu model, it is extended by the non-Hermitian $\mathcal{PT}$-symmetric but chiral symmetry breaking term $g\overline{\psi }{\gamma }_5\psi$. In each case, the gap equation is derived, and the effects of the non-Hermitian terms on the generated mass are studied. We have several findings: in previous calculations for the free Dirac equation modified to include non-Hermitian bilinear terms, contrary to expectation, no real mass spectrum can be obtained in the chiral limit. In these cases, a nonzero bare fermion mass is essential for the realization of $\mathcal{PT}$ symmetry in the unbroken regime. Here, in the NJL model, in which four-point interactions are present, we do find real values for the mass spectrum also in the limit of vanishing bare masses in both $3+1$ and $1+1$ dimensions, at least for certain specific values of the non-Hermitian couplings $g$. Thus, the four-point interaction overrides the effects leading to $\mathcal{PT}$ symmetry breaking for these parameter values. Further, we find that in both cases, in $3+1$ and in $1+1$ dimensions, the inclusion of a non-Hermitian bilinear term can contribute to the generated mass. In both models, this contribution can be tuned to be small; we thus fix the fermion mass to its value when $m_0=0$ in the absence of the non-Hermitian term, and then determine the value of the coupling required so as to generate a bare fermion mass. Finally, we find that in both cases, a rich phase structure emerges from the gap equation as a function of the coupling strengths.

The spectrum of excited states observed in the finite volume of lattice QCD is governed by the discrete symmetries of the cubic group. This finite group permits the mixing of orbital angular momentum quanta in the finite volume. As experimental results refer to specific angular momentum in a partial-wave decomposition, a formalism mapping the partial-wave scattering potentials to the finite volume is required. This formalism is developed herein for Hamiltonian effective field theory, an extension of chiral effective field theory incorporating the Lüscher relation linking the energy levels observed in finite volume to the scattering phase shift. The formalism provides an optimal set of rest-frame basis states maximally reducing the dimension of the Hamiltonian, and it should work in any Hamiltonian formalism. As a first example of the formalism’s implementation, lattice QCD results for the spectrum of an isospin-2 $\pi \pi$ scattering system are analyzed to determine the $s$, $d$, and $g$ partial-wave scattering information.

An external Abelian magnetic field excites in the QCD vacuum a tensor supercurrent that represents the tensor polarization of the chiral condensate. This tensor supercurrent can be deduced from the chiral Lagrangian in the presence of anomalies; a similar tensor supercurrent emerges in rotating systems at finite chemical potential. We discuss the microscopic origin of this supercurrent and argue that it screens the instanton–anti-instanton molecules $I\overline{I}$ in the QCD vacuum, similarly to the vector supercurrent screening Abrikosov vortices in a superconductor. A number of possible experimental manifestations of the tensor supercurrent are discussed: (i) spin alignment of axial-vector and vector mesons in heavy ion collisions; (ii) tensor charge of the nucleon; (iii) transversity of quark distributions in polarized nucleons.

Within the effective Lagrangian approach, we study the $p\overline{p}\to \psi \eta$ [$\psi \equiv \psi (3686)$, $J/\psi$] reaction at the low energy where the contributions from nucleon pole and low-lying nucleon resonances, $N(1520)$, $N(1535)$, and $N(1650)$, are considered. All the model parameters are determined with the help of current experimental data on the decay of $\psi \to p\overline{p}\eta$. Within the model parameters, the total and differential cross sections of the $p\overline{p}\to \psi \eta$ reaction are predicted. We show that the relative phases between different amplitudes of different nucleon resonance will change significantly the angular distributions of the $\overline{p}p\to \psi \eta$ reaction. Therefore, we conclude that these reactions are suitable to study experimentally the properties of the low-lying nucleon resonance and the reaction mechanisms. We hope that these theoretical calculations can be tested by future experiments.

In machine learning, likelihood-free inference refers to the task of performing such analysis driven by data instead of an analytical expression. We discuss the application of neural spline flows, a neural density estimation algorithm, to the likelihood-free inference problem of the measurement of neutrino oscillation parameters in long baseline neutrino experiments. A method adapted to physics parameter inference is developed and applied to the case of the disappearance muon neutrino analysis at the T2K experiment.

This paper presents the first combined measurement of the double-differential muon neutrino and antineutrino charged-current cross sections with no pions in the final state on hydrocarbon at the off-axis near detector of the T2K experiment. The data analyzed in this work comprise $5.8\times {10}^{20}$ and $6.3\times {10}^{20}$ protons on target in neutrino and antineutrino mode respectively, at a beam energy peak of 0.6 GeV. Using the two measured cross sections, the sum, difference, and asymmetry were calculated with the aim of better understanding the nuclear effects involved in such interactions. The extracted measurements have been compared with the prediction from different Monte Carlo generators and theoretical models showing that the difference between the two cross sections have interesting sensitivity to nuclear effects.