We report an investigation of the mass composition of cosmic rays with energies from 3 to 100 EeV ($1\mathrm{EeV}={10}^{18}\mathrm{eV}$) using the distributions of the depth of shower maximum $X_{\max }$. The analysis relies on $\sim 50,000$ events recorded by the surface detector of the Pierre Auger Observatory and a deep-learning-based reconstruction algorithm. Above energies of 5 EeV, the dataset offers a 10-fold increase in statistics with respect to fluorescence measurements at the Observatory. After cross-calibration using the fluorescence detector, this enables the first measurement of the evolution of the mean and the standard deviation of the $X_{\max }$ distributions up to 100 EeV. Our findings are threefold: (i) The evolution of the mean logarithmic mass toward a heavier composition with increasing energy can be confirmed and is extended to 100 EeV. (ii) The evolution of the fluctuations of $X_{\max }$ toward a heavier and purer composition with increasing energy can be confirmed with high statistics. We report a rather heavy composition and small fluctuations in $X_{\max }$ at the highest energies. (iii) We find indications for a characteristic structure beyond a constant change in the mean logarithmic mass, featuring three breaks that are observed in proximity to the ankle, instep, and suppression features in the energy spectrum.

In the present study, we show the calculation of nonlinear Compton scattering with circularly polarized photons in a cylindrical coordinate using Feynman diagram to calculate photon vortex generation in intermediate states considering conservation of angular momentum. We take two different vortex wave functions based on Bessel function for the emitted photon and the electron after emission of the photon, which are the eigenstate of the $z$ component of the total angular momentum (zTAM) when a particle propagates along the $z$ axis. The result shows that when an electron absorbs $N$ photons a photon vortex with a $\mathrm{zTAM}=N$ is predominantly radiated, but there are still very small contributions of photons with a $\mathrm{zTAM}=(N-1)$ and ($N+1$) due to the spin flip of the initial electron. This means even when an electron absorbs only a single photon, the electron may emit a photon vortex of a zTAM of $2\hslash$. However, the numerical calculations show that the contribution of the spin flip is four orders of magnitude smaller than that of the dominant radiation. We also discuss the circular polarization for the generated photon vortices.

Embedding Feynman integrals in Grassmannians, we can write Feynman integrals as some finite linear combinations of generalized hypergeometric functions. In this paper, we present a general method to obtain Gauss relations among those generalized hypergeometric functions. The hypergeometric expressions of Feynman integral are continued from a connected component to another by the inverse Gauss relations, then continued to the whole domain of definition by the Gauss-Kummer relations. The Laurent series of the Feynman integral around the space-time dimension $D=4$ is obtained by the Gauss adjacent relations, where the coefficient of the term with power of $D-4$ is given as the linear combinations of hypergeometric functions with integer parameters. As examples, we illustrate how to obtain the expressions for the Feynman integrals of the 1-loop self-energy and a 2-loop massless triangle diagram in the domains of definition.

When the quark masses are lighter than those in QCD, the standard lore is that a chiral transition of first order must emerge for three light flavors. Recently, however, numerical simulations on the lattice suggest that the chiral transition is of second order in the chiral limit. Using an extended linear sigma model in the mean field approximation, we study the relation between terms which break the anomalous, $U(1{)}_A$ symmetry and the order of the chiral phase transition, especially how a chiral transition of second order can arise for three massless flavors. We note that in an (unphysical) region of the “Columbia” phase diagram, when the strange quark mass is light and negative, corresponding to topological angle $\theta =\pi$, the $CP$ symmetry is spontaneously broken.

We develop a novel, systematic input scheme for many-boson Hamiltonians in order to solve field theory problems within the light-front Hamiltonian formalism via quantum computing. We present our discussion of this input scheme based on the light-front Hamiltonian of the two-dimensional ${\varphi }^4$ theory. In our input scheme, we employ a set of quantum registers, where each register encodes the occupation of a distinct boson mode as binaries. We squeeze the boson operators of each mode and present the Hamiltonian in terms of unique combinations of the squeezed-boson operators. We design the circuit modules for these unique combinations. Based on these circuit modules, we block encode the many-boson Hamiltonian utilizing the idea of quantum walk. For demonstration purposes, we present the spectral calculations of the Hamiltonian utilizing the hybrid quantum-classical symmetry-adapted quantum Krylov subspace diagonalization algorithm based on our input scheme, where the quantum computations are performed with the IBM qiskit quantum simulator. The results of the hybrid calculations agree with exact results. We can incorporate the input scheme in this work with the input scheme for many-fermion Hamiltonians; they jointly offer new pathways to solving the structure and dynamics of more general field theory problems on future fault-tolerant quantum computers.

For the minimal supersymmetric Standard Model, from the gauge couplings, Yukawa couplings, and the coefficient $\mathit{\mu }$ in the part of the superpotential quadratic in the Higgs superfields, we construct combinations which (for certain renormalization prescriptions) do not depend on the renormalization point in all loops. In other words, these combinations are the renormalization group invariants. Similar invariants are also constructed for the next-to-minimal supersymmetric Standard Model. The derivation is based on the nonrenormalization of the superpotential and the Novikov-Shifman-Vainshtein-Zakharov equations. We argue that the scale invariance of the considered combinations takes place in the class of the higher derivatives$+$minimal subtractions of logarithms scheme. This fact has been verified in the lowest orders, up to and including the one in which the dependence on the renormalization prescription becomes essential. It is also demonstrated that in the $\overline{\mathrm{DR}}$ scheme the renormalization group invariance does not take place starting from the approximation, where the scheme dependence manifests itself.

In this study, we investigate the properties of pseudoscalar and vector charmonia, bottomonia, and $B_c$ mesons using the light-front quark model, focusing on the $M1$ radiative transition. For that purpose, we conduct a variational analysis with a quantum chromodynamics (QCD)-motivated effective Hamiltonian, employing a trial wave function expanded in the harmonic oscillator basis functions up to the $3S$ state. We fit the model parameters to mass spectra and decay constants, obtaining reasonable agreement with experimental data and correctly reflecting the hierarchy of mass spectra and decay constants. In analyzing the $M1$ radiative transition, we consider both good ($\mu =+$) and transverse ($\mu =\perp$) current components with both longitudinal ($h=0$) and transverse $(h=\pm 1)$ polarizations, demonstrating that the results from both components of currents and polarizations are identical. Self-consistency is achieved by substituting $M$ with $M_0$ when computing the operators for decay constants and radiative transitions. We also find that the difference between longitudinal and transverse polarizations of the observables may quantify the anisotropy of the model wave function. Our results on radiative transitions align reasonably well with experimental data, lattice QCD, and theoretical predictions. Furthermore, we also provide predictions for $B_c$ mesons that can be tested in experiments.

Owing to the SU(3) symmetry breaking effect, the axial-vector kaons $K_1(1270)$ and $K_1(1400)$ are established to be mixtures of two P-wave $K_{1A}({{}^{3}P}_1)$ and $K_{1B}({{}^{1}P}_1)$ states. In QCD sum rules, we propose a new construction of the $K_1$ current operators and calculate the two-point correlation functions by including the next-to-leading order four-quark condensates. The mixing angle is determined as $\theta =({46.95}_{-0.23}^{+0.25})°$ by reproducing the masses of $K_1(1270)$ and $K_1(1400)$. We further compose the $K{\overline{K}}_1(1270)$ and $K{\overline{K}}_1(1400)$ interpolating currents with exotic quantum numbers $J^{PC}=1^{-+}$ to investigate the possible molecular interpretation of the recently observed ${\eta }_1(1855)$ state. We calculate the correlation functions and perform the QCD sum rule analyses for these two molecular systems. However, the spectral functions are found to be negative in physical regions so that they are not able to provide reliable investigations of the $K{\overline{K}}_1$ molecular states.

Theoretical predictions of the spectrum of heavy meson-baryon bound states are a fundamental tool for disentangling the nature of the different pentaquark states that have been observed in experimental facilities. Here we explore this spectrum in a phenomenological model that describes the heavy meson-baryon interaction in terms of a contact-range interaction, where the coupling strength is saturated by the exchange of light scalar and vector mesons, i.e., $\sigma$, $\rho$, and $\omega$ exchanges. Saturation determines the couplings modulo an unknown proportionality constant that can be calibrated from a molecular candidate. If we use the $P_{\psi }^N(4312)$ as input, we predict a series of molecular pentaquarks including the $P_{\psi }^N(4440)$ and $P_{\psi }^N(4457)$, the recent $P_{\psi s}^{\mathrm{\Lambda }}(4338)$ and the $P_{\psi s}^{\mathrm{\Lambda }}(4459)$.

We calculate the valence generalized parton distribution functions (GPDs) of pion at zero skewness applying a theoretical approach in which the valence GPDs are related to valence quark distribution functions, directly. To this end, we use the results of modified chiral quark model ($\chi QM$) for the valence quark distributions of pion obtained in our previous work. We also determine the electromagnetic and gravitational form factors of pion and compare the results of our theoretical model for valence GPDs and form factors of pion with the results of some other models and available experimental data.

Two main factors are taken into account when describing the behavior of energetic cosmic rays near black holes: the strong magnetic field and gravity, which determines the geodesic motion of the particles. We draw attention to the third factor: since cosmic ray particles have a nonzero spin, the spin-gravity coupling can play an important role in the ultrarelativistic regime. The reaction of the spinning particle on the gravitomagnetic components of the field of the fast-moving Schwarzschild mass is considered. Some examples and numerical estimations are presented.

Since the discovery of the accelerated expansion of the Universe in 1998, modified gravity (MG) theories have attracted considerable attention as alternatives to dark energy. While distinguishing the effects of MG from those of dark energy using the cosmic expansion alone is difficult, the large-scale structure is expected to differ significantly. Among the plethora of MG models, we are particularly interested in those that introduce a scale dependence in the growth of perturbations; specifically, theories that introduce fifth forces mediated by scalar fields with a finite range accessible to cosmological probes. This is the case with $f(R)$ gravity, which is widely regarded as the most studied model in cosmology. In this work, we utilize, for the first time, the full-shape power spectrum of galaxies to constrain scale-dependent modified gravity theories. By using BOSS DR12 dataset, along with a big bang nucleosynthesis prior on ${\omega }_b$ and a Planck 2018 prior on $n_s$, we obtain an upper bound of $|f_{R0}|<5.89\times {10}^{-6}$ at 68% CL and $<1.53\times {10}^{-5}$ at 95% CL for the Hu-Sawicki ($n=1$) model. We discuss that it is highly unlikely these constraints will be significantly improved by future galaxy spectroscopic catalogs, such as DESI and Euclid.

The KNTW (Keshavarzi-Nomura-Teubner-Wright) data-driven determinations of the hadronic vacuum polarization (HVP) are crucial inputs to previous and future Standard Model (SM) predictions of the muon’s anomalous magnetic moment, $a_{\mu }$. With the muon $g-2$’s new physics case uncertain due to disagreeing HVP evaluations, new SM predictions and experimental measurements of $a_{\mu }$ expected soon, and a complete revamp of the KNTW analysis framework underway, this Letter motivates and describes a blinding scheme for data-driven HVP determinations that has been implemented for future KNTW analyses.

Kaon physics is at an important experimental juncture with respect to the ongoing measurements of several observables. This work will build on the existing status by formulating different phenomenological analyses corresponding to different paths that may lie ahead. Beginning with the golden channels, $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ and $K_L\to {\pi }^0\nu \overline{\nu }$, the paper will eventually cast the spotlight on the importance of a precise measurement of $\mathrm{BR}(K_L\to {\pi }^0\ell \overline{\ell })$. The phenomenological analyses involve sequentially adding kaon physics observables at the projected final precision of their respective measurements to the global fit. More specifically, we consider three different scenarios with different sets of observables assumed at their final precisions. Beginning with $\mathrm{BR}(K^{+}\to {\pi }^{+}\nu \overline{\nu })$ and $\mathrm{BR}(K_L\to {\pi }^0\nu \overline{\nu })$, we sequentially add $\mathrm{BR}(K_L\to {\pi }^{0}e\overline{e})$ and $\mathrm{BR}(K_L\to {\pi }^0\mu \overline{\mu })$ to the global fit. The evolution of the result from one scenario to the next makes a strong case for the consideration of future measurement of $\mathrm{BR}(K_L\to {\pi }^0\ell \overline{\ell })$.

We study supertranslations at spatial and future timelike infinity in the first-order formalism. We relax the Ashtekar-Engle-Sloan boundary conditions to allow supertranslations at the spatial infinity and obtain the precise form of the tetrads and Lorentz connections. Employing the covariant phase space technique we obtain the Hamiltonian charges for the supertranslations at both timelike and spatial infinities. The charges obtained are shown to match the expressions reported adopting the metric-based approach.

Fully nonlinear, plane-symmetric exact solutions of the Einstein equations describing the scattering of gravitational and electromagnetic waves have existed for many years. For these closed-form solutions to be found, idealized wave profiles such as the Dirac delta and Heaviside theta functions must be assumed. Although pathological in that future curvature singularities generically occur, these exact solutions give useful insights into the nonlinear features of the scattering process. Only a limited number of exact solutions exist and this leaves many other physically motivated scattering situations without a nonlinear description. The aim of this paper is to shed light on these unexplored cases. This is achieved through numerical solutions of the Friedrich-Nagy initial boundary value problem for the Einstein equations coupled to the source-free Maxwell equations in plane symmetry. Interesting nonlinear scattering effects are presented for a variety of electromagnetic and gravitational wave profiles not currently described by an exact solution. Implications for electromagnetic wave observations are investigated through analyzing the time-delay and frequency shift imparted on the electromagnetic wave through the nonlinear scattering with a gravitational wave of a given strain. Simple arguments supported by the numerical solutions suggest dramatic effects on the radiation may be observable.

We investigate static, axially symmetric spacetimes without naked singularities that are constructed by patching Weyl class spacetimes with the flat spacetimes. Once the exterior geometry is specified, the junction conditions determine the shape of a thin shell, which is the boundary between the two patched spacetimes, and the distribution of the energy and pressure on this shell, leaving a parameter representing the shell size free. We examine the cases where the exterior of the shell is given by Curzon-Chazy or Zipoy-Voorhees spacetimes. For each case, we find a lower bound on the shell size. Additionally, we find that the weak and null energy conditions are satisfied for any shell size, while the dominant energy condition is satisfied for sufficiently large shells. These results provide concrete examples of nonsingular spacetimes with nonspherically symmetric exteriors that respect the energy conditions.

We report a comprehensive numerical study of the renormalization group flow of marginal couplings in ($3+1$)-dimensional projectable Hořava gravity. First, we classify all fixed points of the flow and analyze their stability matrices. We find that some of the stability matrices possess complex eigenvalues and discuss why this does not contradict unitarity. Next, we scan over the renormalization group trajectories emanating from all asymptotically free fixed points. We identify a unique fixed point giving rise to a set of trajectories spanning the whole range of the kinetic coupling $\lambda$ compatible with unitarity. This includes the region $0<\lambda -1\ll 1$ assumed in previous phenomenological applications. The respective trajectories closely follow a single universal trajectory, differing only by the running of the gravitational coupling. The latter exhibits nonmonotonic behavior along the flow, vanishing both in the ultraviolet and the infrared limits. The requirement that the theory remains weakly coupled along the renormalization group trajectory implies a natural hierarchy between the scale of Lorentz invariance violation and a much larger value of the Planck mass inferred from low-energy interactions.

We obtain a new family of exact vacuum solutions to quadratic gravity that describe pp-waves with two-dimensional wave surfaces that can have any prescribed constant curvature. When the wave surfaces are flat we recover the Peres waves obtained by Madsen, a subset of which forms precisely the vacuum pp-waves of general relativity. If, on the other hand, the wave surfaces have nonvanishing constant curvature then all of our solutions are non-Einstein (i.e. they do not solve Einstein’s equations in vacuum, with or without cosmological constant) and we find that the curvature is linearly related to the value of the cosmological constant. We show that the vacuum field equations reduce to a simple linear biharmonic equation on the curved wave surfaces, and as consequence, the general solution can be written down. We also provide some simple explicit examples.