We study carefully the problem of the bootstrap on the half-line. We show why one needs the full set of constraints derived from the Stieltjes theorem on the moment problem by reexamining previous results on the hydrogen atom. We also study the hydrogen atom at continuous angular momentum. We show that the constraints on the moment problem alone do not fix the boundary conditions in all cases and at least one of the positive matrices needs to be slightly enlarged to remove unphysical branches. We explain how to solve the more general problem of the bootstrap for Robin boundary conditions. The recursion relations that are usually used receive additional anomalous contributions. These corrections are necessary to compute the moments of the measure. We apply these to the linear potential and we show how the bootstrap matches the analytical results, based on the Airy function, for this example.

Although the Wald entropy is commonly suitable for the first law of black hole thermodynamics, whether it satisfies the second law has not been examined sufficiently. For any high-order curvature gravity, the Wald entropy has been shown not to obey the linearized second law, and the general expression of entropy of black holes that always satisfies the linearized second law is further obtained. For gravity with nonminimal coupling matter fields, however, whether the Wald entropy of black holes satisfies the second law has not been studied enough. Recently, a general second-order scalar-tensor gravitational theory has been proposed. The Lagrangian of the gravitational theory is a linear combination of four components, and the Wald entropy can also be written as four parts. We should investigate each part of the expression separately to examine whether the Wald entropy satisfies the linearized second law. For the first and fourth parts contributed by two nonminimal coupling terms in Lagrangian contained in Horndeski gravity and Gauss-Bonnet gravity, the entropy of black holes is not expressed as the Wald entropy because the entropy in Gauss-Bonnet gravity is Jacobson-Myers entropy. The third part contributed by the Lagrangian in Einstein-Hilbert action is Bekenstein-Hawking entropy, which obeys the second law automatically. Therefore, to obtain the entropy of black holes that meets the linearized second law, we only need to study the second part of the Wald entropy. According to the null energy condition and the Raychaudhuri equation, one can show that the second part of the Wald entropy with correction terms will increase monotonically constrained by the null energy condition during the perturbation process. The second part of the Wald entropy should be modified to satisfy the linearized second law, and the expression of the entropy of black holes, which always obeys the linearized second law, is obtained in the general second-order scalar-tensor gravity.

We present robust, model-marginalized limits on both the total neutrino mass ($\sum m_{\nu }$) and abundances ($N_{\mathrm{eff}}$) to minimize the role of parametrizations, priors and models when extracting neutrino properties from cosmology. The cosmological observations we consider are cosmic microwave background temperature fluctuation and polarization measurements, supernovae Ia luminosity distances, baryon acoustic oscillation observations and determinations of the growth rate parameter from the Data Release 16 of the Sloan Digital Sky Survey IV. The degenerate neutrino mass spectrum (which implies the prior $\sum m_{\nu }>0$) is weakly or moderately preferred over the normal and inverted hierarchy possibilities, which imply the priors $\sum m_{\nu }>0.06$ and $\sum m_{\nu }>0.1\mathrm{eV}$ respectively. Concerning the underlying cosmological model, the $\mathrm{\Lambda }\mathrm{CDM}$ minimal scenario is almost always strongly preferred over the possible extensions explored here. The most constraining 95% CL bound on the total neutrino mass in the $\mathrm{\Lambda }\mathrm{CDM}+\sum m_{\nu }$ picture is $\sum m_{\nu }<0.087\mathrm{eV}$. The parameter $N_{\mathrm{eff}}$ is restricted to $3.08\pm 0.17$ (68% CL) in the $\mathrm{\Lambda }\mathrm{CDM}+N_{\mathrm{eff}}$ model. These limits barely change when considering the $\mathrm{\Lambda }\mathrm{CDM}+\sum m_{\nu }+N_{\mathrm{eff}}$ scenario. Given the robustness and the strong constraining power of the cosmological measurements employed here, the model-marginalized posteriors obtained considering a large spectra of nonminimal cosmologies are very close to the previous bounds, obtained within the $\mathrm{\Lambda }\mathrm{CDM}$ framework in the degenerate neutrino mass spectrum. Future cosmological measurements may improve the current Bayesian evidence favoring the degenerate neutrino mass spectra, challenging therefore the consistency between cosmological neutrino mass bounds and oscillation neutrino measurements, and potentially suggesting a more complicated cosmological model and/or neutrino sector.

Several recent numerical studies have examined the effects of neutrino neutral-current scattering on fast flavor conversion (FFC). Those studies are in apparent conflict, with some finding enhancement of flavor conversion and others finding suppression. The ones that report enhancement all use homogeneous models, and we discuss in detail the self-consistency issues that they face as a result. We reproduce scattering-enhanced FFC in our own homogeneous calculations, showing that it occurs for both neutral- and charged-current scattering and that it is due to isotropization of the angular distributions over time. Because this is the very feature of the calculations that is not self-consistent, we conclude that the enhancement effect is of unclear astrophysical relevance and may not occur in natural environments.

The current knowledge on the $D^{*}$ mesons is still inadequate. Encouraged by the positive development prospects of high-luminosity and high-precision experiments, the Cabibbo-favored nonleptonic $D^{*}\to \overline{K}{\pi }^{+}$, ${\overline{K}}^{*}{\pi }^{+}$, $\overline{K}{\rho }^{+}$ weak decays are studied with the naive factorization approach. It is found that branching ratios of these processes can reach up to $\mathcal{O}({10}^{-10})$ or more, and can be accessible at STCF, CEPC, FCC-ee, and LHCb@HL-LHC experiments in the future. It might even be possible to search for the $D^{*0}\to K^{*-}{\pi }^{+}$ and $K^{-}{\rho }^{+}$ decays at the running SuperKEKB experiments.

In the usual quantum field theoretical approach, neutrino oscillations are studied diagonalizing either the mass or matter Hamiltonians. In this paper we analyze the problem from an on-shell amplitude perspective, where Lagrangians or Hamiltonians are not available. We start by studying in detail how flavor enters in the amplitudes and how the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix emerges. We then analyze the elastic amplitude of two neutrinos and two charged leptons that induce matter effects and propose a strategy to obtain the known results of the standard oscillation theory without Hamiltonians. Finally, we extend the previously proposed procedure and use the most general elastic 4-point amplitude to study beyond the Standard Model effects on oscillations.

In this work the spontaneous symmetry breaking in certain nonlinear theories with second-class constraints is explored. Using the Dirac’s method we perform an analysis of the constraints and the counting of the degrees of freedom. The corresponding effective Hamiltonian is constructed explicitly. It is shown that on the surfaces where the effective Hamiltonian takes critical values the symplectic structure becomes degenerate. In particular, we demonstrate that under the condition of spontaneous symmetry breaking, which implies nontrivial vacuum surfaces, second-class constraints behave as first-class ones on certain regions of the phase space, leading to undefined Dirac’s brackets and to the modification of the number of degrees of freedom. As a physical consequence, these models can suffer from certain pathologies such as the existence of modes with an acausal propagation. Concrete examples where this phenomena occurs are described in detail.

In the presence of transition magnetic moments between active and sterile neutrinos, the search for a Primakoff upscattering process at coherent elastic neutrino-nucleus scattering ($\mathrm{CE}\nu \mathrm{NS}$) experiments can provide stringent constraints on the neutrino magnetic moment. We show that a radiative upscattering process with an emitted photon in the final state can induce a novel coincidence signal at $\mathrm{CE}\nu \mathrm{NS}$ experiments that can also probe neutrino transition magnetic moments beyond existing limits. Furthermore, the differential distributions for such a radiative mode can also potentially be sensitive to the Dirac vs Majorana nature of the sterile state mediating the process. This can provide valuable insights into the nature and mass generation mechanism of the light active neutrinos.

Given a statistical ensemble of quantum states, the corresponding Page curve quantifies the average entanglement entropy associated with each possible spatial bipartition of the system. In this work, we study a natural extension in the presence of a conservation law and introduce the symmetry-resolved Page curves, characterizing average bipartite symmetry-resolved entanglement entropies. We derive explicit analytic formulas for two important statistical ensembles with a $U(1)$-symmetry: Haar-random pure states and random fermionic Gaussian states. In the former case, the symmetry-resolved Page curves can be obtained in an elementary way from the knowledge of the standard one. This is not true for random fermionic Gaussian states. In this case, we derive an analytic result in the thermodynamic limit based on a combination of techniques from random-matrix and large-deviation theories. We test our predictions against numerical calculations and discuss the subleading finite-size corrections.

In this work we outline the general analytic characteristics satisfied by scalar correlation functions at finite temperature in local quantum field theory. We demonstrate that the locality of the fields in particular imposes significant constraints on the spectral structure of the theory, and that this enables the nonperturbative effects experienced by thermal particle states to be directly calculated from Euclidean correlation functions, avoiding the inverse problem.

We study the critical collapse of a massive complex scalar field coupled minimally to gravity. Taking as initial data a simple Gaussian pulse with a shape similar to the harmonic ansatz for boson stars, we obtain critical collapse of type I and II when varying the Gaussian width $\sigma$. For $\sigma \le 0.5$ we find collapse of type II with a critical exponent $\gamma =0.38\pm 0.01$ and an echoing period $\mathrm{\Delta }=3.4\pm 0.1$. These values are very similar to the well-known results for a real massless scalar field. On the other hand, for $\sigma \ge 2.5$ we obtain the collapse of type I. In this case we find that the critical solutions turn out to be an unstable boson stars in the ground state: all the data obtained from our simulations can be contrasted with the characteristic values for unstable boson stars and their corresponding Lyapunov exponents.

We discuss the importance of multiring images in the optical appearance of a horizonless spherically symmetric compact object, when illuminated by an optically thin accretion disk. Such an object corresponds to a subcase of an analytically tractable extension of the Kerr solution dubbed as the “eye of the storm” by Simpson and Visser in [J. Cosmol. Astropart. Phys. 03 (2022) 011], which merits in removing curvature singularities via an asymptotically Minkowski core, while harboring both a critical curve and an infinite potential barrier at the center for null geodesics. This multiring structure is induced by light rays winding several times around the object, and whose luminosity is significantly boosted as compared to the Schwarzschild solution by the modified shape of the potential. Using three toy profiles for the emission of an infinitely thin disk, truncated at its inner edge (taking its maximum value there) and having different decays with the distance, we discuss the image created by up to eight rings superimposed on top of the direct emission of the disk as its edge is moved closer to the center of the object. Our results point to the existence of multiring images with a non-negligible luminosity in shadow observations when one allows for the existence of other compact objects in the cosmic zoo beyond the Schwarzschild solution. Such multiring images could be detectable within the future projects on very long baseline interferometry.

Inspirals of stellar-mass compact objects into massive black holes, known as extreme mass ratio inspirals (EMRIs), are one of the key targets for upcoming space-based gravitational-wave detectors. In this paper we take the first steps needed to systematically incorporate the effect of external gravitating matter on EMRIs. We model the inspiral as taking place in the field of a Schwarzschild black hole perturbed by the gravitational field of a far axisymmetric distribution of mass enclosing the system. We take into account the redshift, frame-dragging, and quadrupolar tide caused by the enclosing matter, thus incorporating all effects to inverse third order of the characteristic distance of the enclosing mass. Then, we use canonical perturbation theory to obtain the action-angle coordinates and Hamiltonian for mildly eccentric precessing test-particle orbits in this background. Finally, we use this to efficiently compute mildly eccentric inspirals in this field and document their properties. This work shows the advantages of canonical perturbation theory for the modeling EMRIs, especially in the cases when the background deviates from the standard black hole fields.

The geometric optics approximation provides an interpretation for eikonal correspondence that, in black-hole-containing spacetimes, connects high-frequency black hole quasinormal modes with closed photon orbits around said black hole. This correspondence has been identified explicitly for Schwarzschild, Reissner-Nordström, Kerr, and Kerr-Newman black holes, the violation of which can be a potential hint toward physics beyond General Relativity. Notably, the aforementioned black hole spacetimes have sufficient symmetries such that both the geodesic equations and the master wave equations are separable. The identification of the correspondence seems to largely rely on these symmetries. One naturally asks how the eikonal correspondence would appear if the spacetime were less symmetric. For a pioneering work in this direction, we consider in this paper a deformed Schwarzschild spacetime retaining only axisymmetry and stationarity. We show that up to the first order of spacetime deformations the eikonal correspondence manifests through the definition of the averaged radius of trapped photon orbits along their one period. This averaged radius overlaps the potential peak in the master wave equation, which can be defined up to the first order of spacetime deformations, allowing the explicit identification of the eikonal correspondence.

In this paper we study scenarios of the super-Eddington accretion onto black holes at high redshifts $z>10$, which are expected to be seeds to evolve to supermassive black holes until redshift $z\sim 7$. For a initial mass, $M_{\mathrm{BH},\mathrm{ini}}\lesssim 2\times {10}^3{M}_{\odot }$ of a seed black hole (BH), we definitely need the super-Eddington accretion, which can be applicable to both astrophysical and primordial origins. Such an accretion disk inevitably emitted high-energy photons which had heated the cosmological plasma of the inter-galactic medium continuously from high redshifts. In this case, cosmic history of cosmological gas temperature is modified, by which the absorption feature of the cosmological 21-cm lines are suppressed. By comparing theoretical predictions of the 21-cm line absorption with the observational data at $z\sim 17$, we obtain a cosmological upper bound on the mass-accretion rate as a function of the seed BH masses. In order to realize $M_{\mathrm{BH}}\sim {10}^9{M}_{\odot }$ at $z\sim 7$ by a continuous mass accretion on to a seed BH, to be consistent with the cosmological 21-cm line absorption at $z\sim 17$, we obtained an severe upper bound on the initial mass of the seed BH to be $M_{\mathrm{BH},\mathrm{ini}}\lesssim {10}^2{M}_{\odot }$ ($M_{\mathrm{BH},\mathrm{ini}}\lesssim {10}^6{M}_{\odot }$) when we assume a seed BH with its comoving number density $n_{\mathrm{seed},0}\sim {10}^{-3}{\mathrm{Mpc}}^{-3}$ ($n_{\mathrm{seed},0}\sim {10}^{-7}{\mathrm{Mpc}}^{-3}$). We also discuss some implications for application to primordial black holes as the seed black holes.

We perform an analysis of leptogenesis in the context of a simple extension of the Standard Model with two fermions, one charged ($\chi$) and one neutral ($\psi$), in addition to three right-handed neutrinos, interacting through a charged gauge singlet scalar $S$. The dark sector ($\chi$ and $\psi$) interacts feebly and produces a relic density consistent with the existing data. The right-handed neutrinos decay into the charged scalar $S$ and a lepton, providing, along with the virtual exchange of $S$ in the standard decay channel, an additional source of $CP$ asymmetry. The advantage of this scenario is that it can generate naturally the observed baryon asymmetry of the Universe, even for right-handed neutrino masses in 10 TeV region, without requiring neutrinos to be degenerate.

It is known that neutrinos from supernova (SN) bursts can potentially give rise to nuclear recoil (NR) signals arising from the neutral current (NC) process of coherent elastic neutrino-nucleus scattering ($\mathrm{CE}\nu \mathrm{NS}$) interactions of the neutrinos with xenon nuclei in future, large (multiton scale) liquid xenon (LXe) detectors employed for dark matter searches, depending on the SN progenitor mass and distance to the SN. In this paper, we show that the same detectors will also be sensitive to inelastic charged-current (CC) interactions of the SN electron neutrinos (${\nu }_e\mathrm{CC}$) with xenon nuclei. Such interactions, while creating an electron in the final state, also leave the postinteraction target nucleus in an excited state, the subsequent deexcitation of which produces, among other particles, $\gamma$ rays and neutrons. The electron and deexcitation $\gamma$ rays will give “electron recoil” (ER) type signals, while the deexcitation neutrons—the so-called “neutrino-induced neutrons” (${\nu }_e\mathrm{In}$)—produce, through their multiple scattering on the xenon nuclei, further xenon nuclear recoils that will also give NR signals (in addition to those produced through the $\mathrm{CE}\nu \mathrm{NS}$ interactions). We discuss the observable scintillation and ionization signals associated with SN neutrino-induced $\mathrm{CE}\nu \mathrm{NS}$ and ${\nu }_e\mathrm{CC}$ events in a generic LXe detector and argue that upcoming, sufficiently large LXe detectors should be able to detect both these types of events due to neutrinos from reasonably close-by SN bursts. We also note that since the total CC-induced ER and NR signals receive contributions predominantly from ${\nu }_e\mathrm{CC}$ interactions while the $\mathrm{CE}\nu \mathrm{NS}$ contribution comes from NC interactions of all six species of neutrinos, identification of the ${\nu }_e\mathrm{CC}$ and $\mathrm{CE}\nu \mathrm{NS}$ origin events may offer the possibility of extracting useful information about the distribution of the total SN explosion energy going into different neutrino flavors.

We discuss the gauge symmetry breaking of six-dimensional theories in flux compactification with a magnetic flux background and a constant vacuum expectation value (VEV) for the scalar fields, which are zero modes of extra spatial components of the gauge field. Although the effective potential for the scalar fields are known not to be generated classically and radiatively in a magnetic flux background only, the one-loop effective potential is shown to be generated by the effects of the nonzero constant VEV. As illustrations, we calculate the one-loop effective potential in SU(2) and SU(3) Yang-Mills theories. In both cases, we expect that the potential minimum is located at nonzero VEV and the gauge symmetry breaking takes place.

We show that one can explain the neutral and charged anomalies in $B$-meson decays in the minimal theory for quark-lepton unification. The implications for flavor violating processes are discussed in detail. Strikingly, experimental observations suggest that the unification of quarks and leptons could be realized at the $\mathcal{O}({10}^2)\mathrm{TeV}$ scale.

In this work, we discuss the electromagnetic properties of the $S$-wave ${\mathrm{\Sigma }}_c^{(*)}{D}^{(*)}$-type doubly charmed molecular pentaquarks, which have close relation to their inner structures. Both the $S-D$ wave mixing effect and the coupled channel effect are taken into account. We analyze the magnetic moments for the $S$-wave ${\mathrm{\Sigma }}_c^{(*)}{D}^{(*)}$ molecular states, and extend our theoretical framework to study the transition magnetic moments and the radiative decay widths between the $S$-wave ${\mathrm{\Sigma }}_c^{(*)}{D}^{(*)}$ molecules. We discuss the relations between the magnetic moments and the transition magnetic moments for the $S$-wave ${\mathrm{\Sigma }}_c^{(*)}{D}^{(*)}$-type doubly charmed molecular pentaquarks, which can be regarded as an indirect way to measure their magnetic moments experimentally. The present study may inspire the experimentalist’s interest in measuring the electromagnetic properties of the hadronic molecular states.