Given the unique role played by the gravitational form factors (GFFs) in unraveling the internal mechanics of hadrons, we examine the GFFs of ground state pseudoscalar mesons $\pi$, ${\eta }_c$, ${\eta }_b$ and the hypothetical strangeonium ${\eta }_s(s\overline{s})$. We adopt the coupled framework of Dyson-Schwinger and Bethe-Salpeter equations within a contact interaction and employ a novel approach to the dressed amputated meson-meson scattering amplitude, which makes connection with the energy-momentum tensor and with the GFFs. The resulting GFFs fulfill the anticipated symmetry constraints. The corresponding charge and mass radii and the $D$ term are also computed. We show that the $D$ term for the pseudoscalar mesons is bounded within the $(-1,-1/3)$ range; these bounds correspond to the massless (chiral limit) and infinitely massive cases, respectively. Considering the current interest in the GFFs, understanding the $D$ term of pseudoscalar mesons and their GFFs can provide an important first step for future endeavors in the field.

Very strong electromagnetic field can be generated in peripheral relativistic heavy ion collisions. This work is devoted to exploring the interplay between the effects of a constant external electric field and confining potential on heavy-flavor mesons. As the corresponding vector potential linearly depends on one spatial coordinate for a constant electric field, it might be able to overcome the linear confining potential of quantum chromodynamics and induce deconfinement. To perform analytic calculations and for comparison, one and two dimensional systems are studied together with the realistic three dimensional systems. The one dimensional Schrödinger equation can be solved analytically with the help of Airy functions, and deconfinement is indeed realized when the electric field is larger than the string tension. Focus on the confining case, the two and three dimensional Schrödinger equations can be solved analytically in large $r$ limit with the help of elliptic cosine/sine functions, and the wave functions are dominated by the region antiparallel to the electric field. When a more realistic potential is applied, a nonmonotonic feature is found for $\mathrm{\Upsilon }(2S)$ and $\mathrm{\Upsilon }(3S)$-like mesons with increasing electric field.

We address the discovery and characterization of toponium production at the Large Hadron Collider. In the dilepton decay mode, multivariate analyses of spin and color observables could provide evidence that an excess of events present near the $t\overline{t}$ threshold corresponds to a spin-zero color singlet. The semileptonic decay mode may also exhibit an excess near threshold, but is not expected to play any role in the toponium characterization.

We combine the Dyson-Schwinger/Bethe-Salpeter equations framework with modern numerical reconstruction methods to derive the three-dimensional and transverse two-dimensional charge distribution of an array of ground-state pseudoscalar and vector mesons from their elastic electromagnetic form factor in the low-momentum region. The charge radii obtained by averaging over the reconstructed charge distributions have been checked to be consistent with those calculated from the slope of the elastic electromagnetic form factor at zero transferred momentum. The capability of the reconstruction procedure for capturing a reliable low-distance charge distribution is discussed and argued to work down to distances of around 0.1 fm, such that it might be potentially applied to extract, e.g., mass densities from gravitational form factors.

The charged current weak production of $\mathrm{\Delta }(1232)$ from the free proton target induced by the electron/positron in the intermediate energy range corresponding to the beam energy available at JLab and Mainz, has been studied. The results for the differential scattering cross section $\frac{d\sigma }{d{Q}^2}$, the angular distribution $\frac{d\sigma }{d{\mathrm{\Omega }}_{\mathrm{\Delta }}}$, and the total scattering cross section $\sigma (E_e)$ for both the electron and positron induced processes are presented, for the various energies in the range of 0.5–4 GeV. The cross section $\sigma (E_e)$ is found to be of the order of ${10}^{-39}{\mathrm{cm}}^2$ for the electron/positron energies in the few GeV range. The availability of electron/positron beams having well-defined energy and direction with very high luminosity of the order of ${10}^{38}–{10}^{39}{\mathrm{cm}}^{-2}{\sec }^{-1}$, makes it possible to observe the weak charged current production of $\mathrm{\Delta }(1232)$ and determine the axial vector form factors $C_i^A(Q^2);(i=3–5)$. The sensitivity of the differential cross section $\frac{d\sigma }{d{Q}^2}$ to the subdominant form factors $C_3^A(Q^2)$ and $C_4^A(Q^2)$ is found to be strong enough, especially in the low $Q^2$ region, which can be used to determine them phenomenologically and to test the various theoretical models proposed to calculate them.

The experimental data on the helicity amplitudes of charmonium decays allow us to measure entanglement in final state spin correlations and test possible violations of the Bell inequality. We find that the Bell inequality is violated with a significance of $5\sigma$ or more in the decays ${\eta }_c,{\chi }_c^0,J/\psi \to \mathrm{\Lambda }+\overline{\mathrm{\Lambda }}$, $J/\psi \to {\mathrm{\Xi }}^{-}+{\overline{\mathrm{\Xi }}}^{+},{\mathrm{\Xi }}^0+{\overline{\mathrm{\Xi }}}^0,{\mathrm{\Sigma }}^{-}+{\overline{\mathrm{\Sigma }}}^{+},{\mathrm{\Sigma }}^0+{\overline{\mathrm{\Sigma }}}^0$, $\psi (3686)\to {\mathrm{\Xi }}^{-}+{\overline{\mathrm{\Xi }}}^{+},{\mathrm{\Sigma }}^{-}+{\overline{\mathrm{\Sigma }}}^{+},{\mathrm{\Sigma }}^0+{\overline{\mathrm{\Sigma }}}^0$, ${\chi }_c^0,{\chi }_c^1\to \varphi +\varphi$. The decays $\psi (3686)\to \mathrm{\Lambda }+\overline{\mathrm{\Lambda }}$ and ${\mathrm{\Xi }}^0+{\overline{\mathrm{\Xi }}}^0$ show the same violation but with less significance. The decay $\psi (3686)\to {\mathrm{\Omega }}^{-}+{\overline{\mathrm{\Omega }}}^{+}$ displays entanglement. These results firmly establish the presence of entanglement and quantum nonseparability at high energies, in a setting with particles of different spins and interacting through electroweak and strong interactions. In addition, the relatively long lifetime of some of the strange baryons produced in the decays provides a natural probe to test whether quantum spin correlations remain after the particles have interacted with the beam pipe and the first few layers of the detector.

We find that a slowly rotating axion-modified black hole resulting from the backreaction of an axion field on a rotating Kerr black hole can have a $D$-shaped shadow as that for a highly counterrotating Kerr black hole. This is attributed to the fact that the energy exchange between the axion matter and the black hole influences the rotation of the black hole, so the black hole angular momentum first decreases to zero and then starts to rotate to the opposite direction. Further increasing the coupling leads to “human-face-like”-shaped shadows and new lensing due to the chaotic scattering, which are novel and drastically different from those for a Kerr black hole. Our analysis provides the first counterexample to that slowly rotating black hole has nearly circular shadow.

Recently, Pulsar Timing Array (PTA) Collaborations have detected a stochastic gravitational wave background (SGWB) at nano-Hz frequencies, with domain wall networks (DWs) proposed as potential sources. To be cosmologically viable, they must annihilate before dominating the Universe energy budget, thus generating a SGWB. While subhorizon DWs shrink and decay rapidly, causality requires DWs with superhorizon size to continue growing until they reach the Hubble horizon. Those entering the latest can be heavier than a Hubble patch and collapse into primordial black holes (PBHs). We conduct a Bayesian analysis of the PTA signal, interpreting it as an outcome of SGWB from DW networks, with a prior ensuring no PBH overproduction. Our findings indicate that DWs result in the production of solar-mass PBHs. The binary mergers occurring within these PBHs generate a second SGWB in the kilo-Hz domain which could be observable in ongoing or planned Earth-based interferometers.

Massive neutrinos suppress the growth of cosmic structure on nonlinear scales, motivating the use of information beyond the power spectrum to tighten constraints on the neutrino mass, for example by considering cosmic voids. It was recently proposed that constraints on neutrino mass from the halo mass function (HMF) can be improved by considering only the halos that reside within voids—the void-halo mass function (VHMF). We extend this analysis, which made spherical assumptions about the shape of voids, to take into account the nonspherical nature of voids as defined by the Voronoi-tessellation-based void finder, VIDE. In turn, after accounting for one spurious nonspherical void, we find no evidence that the VHMF contains information beyond the HMF. Given this finding, we then introduce a novel summary statistic by splitting halos according to the emptiness of their individual environments, defined by the Voronoi cell volume each halo resides in, and combining the mass functions from each split. We name the corresponding statistic the VorHMF and find that it could provide information regarding neutrino mass beyond the HMF. Our work thus motivates the importance of accounting for the full shape of voids in future analyses, both in terms of removing outliers to achieve robust results and as an additional source of cosmological information.

We present a new paradigm for the production of the dark matter (DM) relic abundance based on the evaporation of early Universe primordial black holes (PBHs) themselves formed from DM particles. As a concrete realization, we consider a minimal model of the dark sector in which a first-order phase transition results in the formation of Fermiball remnants that collapse to PBHs, which then emit DM particles. We show that the regurgitated DM scenario allows for DM in the mass range $\sim 1–{10}^{16}\mathrm{GeV}$, thereby unlocking parameter space considered excluded.

A random matrix model definition of a family of $\mathcal{N}=1$ supersymmetric extensions of the Virasoro minimal string of Collier, Eberhardt, Mühlmann, and Rodriguez is presented. An analysis of the defining string equations shows that the models all naturally have unambiguous nonperturbative completions, which are explicitly supplied by the double-scaled orthogonal polynomial techniques employed. Perturbatively, the multiloop correlation functions of the model define a special supersymmetric class of “quantum volumes,” generalizing the prototype case, some of which are computed.

The model of two dimensional quantum gravity defining the Virasoro minimal string, presented recently by Collier, Eberhardt, Mühlmann, and Rodriguez, was also shown to be perturbatively (in topology) equivalent to a random matrix model. An alternative definition is presented here, in terms of double-scaled orthogonal polynomials, thereby allowing direct access to nonperturbative physics. Already at leading order, the defining string equation’s properties yield valuable information about the nonperturbative fate of the model, confirming that the case $(c=25,\widehat{c}=1)$ (central charges of spacelike and timelike Liouville sectors) is special, by virtue of sharing certain key features of the $\mathcal{N}=1$ supersymmetric JT gravity string equation. Solutions of the full string equation are constructed using a special limit, and the (Cardy) spectral density is completed to all genus and beyond. The distributions of the underlying discrete spectra are readily accessible too, as is the spectral form factor. Some examples of these are exhibited.

Upon introducing a heavy quark in the perturbative regime of the QCD conformal window we precisely determine the associated heavy meson spectrum and wave functions in terms of the number of light flavors and mass. We then compute the conformal Isgur-Wise function which is a central quantity in heavy quark physics. We further determine the impact of the residual low energy confining dynamics on the heavy meson spectrum. As a working framework, we adapt the heavy quark effective theory to the perturbative conformal window dynamics. Our work lays the foundations to systematically go beyond the infinite mass defect approximation in conformal field theories.

We study new classes of metric transformations in the context of scalar-tensor theories, which involve both higher derivatives of the scalar field and derivatives of the metric itself. In general, such transformations are not invertible as they involve derivatives of the metric, which typically leads to instability due to Ostrogradsky ghosts. We show, however, that a certain class of this type of transformations is invertible: We construct new examples of invertible conformal (and also disformal) transformations with higher derivatives. Finally, we make use of these new transformations to construct extended mimetic theories of gravity, and we study their properties in the context of cosmology.

If two initially unbound black holes of masses $M_1$ and $M_2$, total mass $M=M_1+M_2$, reduced mass $\mu =M_1{M}_2/(M_1+M_2)$, and initial relative velocity $v\ll c(4\mu /M)$ in otherwise empty space are captured into a bound orbit by emitting gravitational radiation, the inspiral time to coalescence increases monotonically to infinity as the impact parameter $b$ approaches from below the critical impact parameter $b_c=[340\pi G^7{M}^6\mu /(3c^5{v}^9){]}^{1/7}=[(85\pi /384)(4\mu /M){]}^{1/7}(2GM/c^2)(v/c{)}^{-9/7}$ for capture. Assuming a uniform flux of impinging black holes with $b\le b_c$, the cumulative probability for impact parameters smaller than some value $b$, conditional upon the impact parameter being smaller than $b_c$, is $P=(b/b_c{)}^2$. Then it is shown that the inspiral time for $[M{v}^2/(4\mu c^2){]}^{2/7}\ll P<1$ is $T=(2\pi GM/v^3)P^{21/4}\zeta (3/2,1-P^{7/2})$, and closed-form approximate expressions for the inverse function $P(T/T_0)$ with $T_0=2\pi GM/v^3$ are also given.

Domain wall (DW) networks have a large impact on cosmology and present interesting dynamics that can be controlled by various scaling regimes. In the first stage after spontaneous breaking of the discrete symmetry, the network is seeded with “DW precursors,” the zeros of a tachyonic field. At sufficiently weak coupling, this stage can be quite long. The network is then driven to a nonrelativistic scaling regime; in flat spacetime the correlation length grows like $L\sim t^{\kappa }$ with $\kappa =1/2$. We focus on the precursor regime in cosmology, assuming a power law scale factor $a\propto t^{\alpha }$. We obtain the scaling exponent as a function of the external parameter, $\kappa (\alpha )$, by explicit computation in $1+1$ and $2+1$ dimensions, and find a smooth transition from nonrelativistic scaling with $\kappa \simeq 1/2$ for $\alpha \lesssim 1/2$ to DW gas regime $\kappa \simeq \alpha$ for $\alpha \gtrsim 1/2$, confirming previous arguments. The precise form of the transition $\kappa (\alpha )$ is surprisingly independent of dimension, suggesting that similar results should also be valid in $3+1$ dimensions.

Compact stellar objects like supernovae and neutron stars are believed to cool by emitting axions predominantly via bremsstrahlung ($NN\to NNa$), pion conversion (${\pi }^{-}{p}^{+}\to Na$), and photoproduction ($\gamma N\to Na$). In this paper, we study new contributions to the photoproduction channel pertaining to axions. We first point out the impact of anomaly-induced unavoidable Wess-Zumino-Witten term $\propto {\epsilon }^{\mu \nu \alpha \beta }{F}_{\mu \nu }{\partial }_{\alpha }a{\omega }_{\beta }$ in the photoproduction of such axions. We then perform a complementary data-driven study where the rate of photoproduction can be estimated from low-energy pion photoproduction data. We found that for such heavier axions, i.e., $m_a\sim \mathcal{O}(100)\mathrm{MeV}$, photoproduction processes can be dominant compared to the usual emission processes. In addition, the spectrum of these particles emitted in the process is significantly harder than those originating from bremsstrahlung.

Gauge theories form the basis of our understanding of modern physics—ranging from the description of quarks and gluons to effective models in condensed matter physics. In the nonperturbative regime, gauge theories are conventionally treated discretely as lattice gauge theories. The resulting systems are evaluated with path-integral based Monte Carlo methods. These methods, however, can suffer from the sign problem and do not allow for a direct evaluation of real-time dynamics. In this work, we present a unified and comprehensive framework for gauged Gaussian projected entangled pair states (PEPS), a variational ansatz based on tensor networks. We review the construction of Hamiltonian lattice gauge theories, explain their similarities to PEPS, and detail the construction of the ansatz state. The estimation of ground states is based on a variational Monte Carlo procedure with the PEPS as an ansatz state. This sign-problem-free ansatz can be efficiently evaluated in any dimension with arbitrary gauge groups, and can include dynamical fermionic matter, suggesting new options for the simulation of nonperturbative regimes of gauge theories, including quantum chromodynamics.

The recently revised small-$x$ helicity evolution [J. High Energy Phys. 07 (2022) 095], resumming the double-logarithmic factor, ${\alpha }_{\mathrm{s}}{\ln }^2(1/x)$, allows for the study of helicity distributions of quarks and gluons at small Bjorken $x$, corresponding to high center-of-mass energy. In this work, we calculate the moderate-$x$ initial conditions in the regime, ${\alpha }_{\mathrm{s}}{\ln }^2(1/x)\sim 1$, for the small-$x$ helicity evolution using a light-front valence quark model of the proton, which provides additional physical information about the target. The perturbative emission and absorption of a gluon by the valence quarks are also included. The results, given in Eqs. (35), provide a new set of initial conditions with a significantly reduced number of free parameters than conventional models [Phys. Rev. D 108, 114007 (2023)]. Consequently, the predictive power of small-$x$ helicity evolution is expected to improve once the initial conditions from this work are incorporated.

We develop parametrizations of eight of the lowest Born-Oppenheimer potentials for quarkonium hybrid mesons as functions of the separation $r$ of the static quark and antiquark sources. The parameters are determined by fitting results calculated using pure $SU(3)$ lattice gauge theory. The parametrizations have the correct limiting behavior at small $r$, where the potentials form multiplets associated with gluelumps. They have the correct limiting behavior at large $r$, where the potentials form multiplets associated with excitations of a relativistic string. There is a narrow avoided crossing in the small-$r$ region between two potentials with the same Born-Oppenheimer quantum numbers.