Results from the experiments like LSND, and MiniBooNE hint towards the possible presence of an extra eV-scale sterile neutrino. The addition of such a neutrino will significantly impact the standard three-flavor neutrino oscillations; in particular, it can give rise to additional degeneracies due to new sterile parameters. In our work, we investigate how the sensitivity to determine the octant of the neutrino mixing angle ${\theta }_{23}$ is affected by introducing a sterile neutrino to the standard three generation framework. We compute the oscillation probabilities analytically in the presence of a sterile neutrino, using the approximation that ${\mathrm{\Delta }}_{21}$, the smallest mass squared difference, is zero. We use these probabilities to understand the degeneracies analytically at different baselines. We present our results of the sensitivity to octant of ${\theta }_{23}$ for beam neutrinos using a liquid argon time projection chamber (LArTPC). We also obtain octant sensitivity using atmospheric neutrinos using the same LArTPC detector. For the latter, we present our results assuming (i) no charge identification capability, and (ii) partial charge identification capability using the charge tagging ability of muon capture in argon. In addition, we include the charge tagging capability of muon capture in argon which allows one to differentiate between muon neutrino and antineutrino events. The combined sensitivity of beam and atmospheric neutrinos in a similar experimental setup is also delineated. We observe that by combining simulated data from the beam and atmospheric neutrinos (including charge-id for muons), the sensitivity to the octant of ${\theta }_{23}$ for true values of ${\theta }_{23}=41°(49°)$ exceeds $4\sigma (3\sigma )$ for more than 50% values of true ${\delta }_{13}$.

Recent lattice QCD results for the low-lying odd-parity excitations of the nucleon near the $N^{*}(1535)$ and $N^{*}(1650)$ resonance positions have revealed that the lattice QCD states have magnetic moments consistent with predictions from a constituent quark model. Using Hamiltonian effective field theory (HEFT) to describe pion-nucleon scattering in the $I(J^P)=\frac{1}{2}({\frac{1}{2}}^{-})$ channel, we represent these two quark-model-like states as two single-particle bare basis states, dressed and mixed by meson-baryon scattering channels. By constraining the free parameters of the Hamiltonian with $S_{11}$ pion-nucleon scattering data, we perform the first calculation of the finite-volume spectrum using two bare-baryon basis states. By comparing this spectrum to contemporary lattice QCD results at three lattice volumes, we analyze the eigenvectors of the Hamiltonian to gain insight into the structure and composition of these two low-lying resonances. We find that an interpretation of the two low-lying nucleon resonances as quark-model-like states dressed by meson-baryon interactions is consistent with both the $S_{11}$ scattering data and lattice QCD. We introduce a novel HEFT formalism for estimating scattering-state contaminations in lattice QCD correlation functions constructed with standard three-quark operators. Not only are historical lattice QCD results described with excellent accuracy, but correlation functions with large scattering-state contaminations are identified.

Understanding the dynamics of bound state formation is one of the fundamental questions in confining quantum field theories such as Quantum Chromodynamics (QCD). One hadronization mechanism that has garnered significant attention is the breaking of a string initially connecting a fermion and an antifermion. Deepening our understanding of real-time string-breaking dynamics with simpler, lower dimensional models like the Schwinger model can improve our understanding of the hadronization process in QCD and other confining systems found in condensed matter and statistical systems. In this paper, we consider the string-breaking dynamics within the Schwinger model and investigate its modification inside a thermal medium, treating the Schwinger model as an open quantum system coupled to a thermal environment. Within the regime of weak coupling between the system and environment, the real-time evolution of the system can be described by a Lindblad evolution equation. We analyze the Liouvillian gaps of this Lindblad equation and the time dependence of the system’s von Neumann entropy. We observe that the late-time relaxation rate decreases as the environment correlation length increases. Moreover, when the environment correlation length is infinite, the system exhibits two steady states, one in each of the sectors with definite charge-conjugation-parity ($CP$) quantum numbers. For parameter regimes where an initial string breaks in vacuum, we observe a delay of the string breaking in the medium, due to kinetic dissipation effects. Conversely, in regimes where an initial string remains intact in vacuum time evolution, we observe string breaking (melting) in the thermal medium. We further discuss how the Liouvillian dynamics of the open Schwinger model can be simulated on quantum computers and provide an estimate of the associated Trotter errors.

We present a lattice calculation of the $K\to \pi \pi$ matrix elements and amplitudes with both the $\mathrm{\Delta }I=3/2$ and $1/2$ channels and ${ϵ}^{\prime }$, the measure of direct $CP$ violation. We use periodic boundary conditions (PBC), where the correct kinematics of $K\to \pi \pi$ can be achieved via an excited two-pion final state. To overcome the difficulty associated with the extraction of excited states, our previous work [Z. Bai et al., Standard Model prediction for direct $CP$ violation in $K\to \pi \pi$ decay, Phys. Rev. Lett. 115, 212001 (2015); R. Abbott et al., Direct $CP$ violation and the $\mathrm{\Delta }I=1/2$ rule in $K\to \pi \pi$ decay from the Standard Model, Phys. Rev. D 102, 054509 (2020).] successfully employed G-parity boundary conditions, where pions are forced to have nonzero momentum enabling the $I=0$ two-pion ground state to express the on shell kinematics of the $K\to \pi \pi$ decay. Here instead we overcome the problem using the variational method which allows us to resolve the two-pion spectrum and matrix elements up to the relevant energy where the decay amplitude is on shell. In this paper we report an exploratory calculation of $K\to \pi \pi$ decay amplitudes and ${ϵ}^{\prime }$ using PBC on a coarser lattice size of ${24}^3\times 64$ with inverse lattice spacing $a^{-1}=1.023\mathrm{GeV}$ and the physical pion and kaon masses. The results are promising enough to motivate us to continue our measurements on finer lattice ensembles in order to improve the precision in the near future.

Inspired by the recent observation of $e^{+}{e}^{-}\to \omega X(3872)$ by the BESIII Collaboration, in this work we study the production of the charmonium ${\chi }_{cJ}(2P)$ by $e^{+}{e}^{-}$ annihilation. We find that the $e^{+}{e}^{-}\to \omega {\chi }_{c0}(2P)$ and $e^{+}{e}^{-}\to \omega {\chi }_{c2}(2P)$ have sizable production rates, when taking the cross section data from $e^{+}{e}^{-}\to \omega X(3872)$ as the scaling point and treating the $X(3872)$ as the charmonium ${\chi }_{c1}(2P)$. Considering that the dominant decay modes of ${\chi }_{c0}$ and ${\chi }_{c2}(2P)$ involve $D\overline{D}$ final states, we propose that $e^{+}{e}^{-}\to \omega D\overline{D}$ is an ideal process to identify ${\chi }_{c0}(2P)$ and ${\chi }_{c2}(2P)$, which is similar to the situation that happens in the $D\overline{D}$ invariant mass spectrum of the $\gamma \gamma \to D\overline{D}$ and $B^{+}\to D^{+}{D}^{-}{K}^{+}$ processes. With the continued accumulation of experimental data, these proposed production processes offer a promising avenue for exploration by the BESIII and Belle II collaborations.

Inspired by the recent observation of new ${\mathrm{\Omega }}_c^0$ states by the LHCb Collaboration, we explore the excited ${\mathrm{\Omega }}_c$ states from the pentaquark perspective in the quark delocalization color screening model. Our results indicate that the ${\mathrm{\Omega }}_c(3185)$ can be well interpreted as a molecular $\mathrm{\Xi }D$ predominated resonance state with $J^P=1/2^{-}$. The ${\mathrm{\Omega }}_c(3120)$ can also be interpreted as a molecular ${\mathrm{\Xi }}_c^{*}\overline{K}$ state with $J^P=3/2^{-}$ and a new molecular state ${\mathrm{\Xi }}_c^{*}{\overline{K}}^{*}$ with $J^P=5/2^{-}$ and a mass of 3526 MeV is predicted, which is worth searching in the future. Other reported ${\mathrm{\Omega }}_c$ states cannot be well described in the framework of pentaquark systems in the present work. The three-quark excited state or the unquenched picture may be a good explanation, which is worth further exploration.

We consider electroweak gauge boson corrections to the masses of pseudoscalar mesons to next to leading order in ${\alpha }_s$ and $1/N_C$. The pion mass shift induced by the $Z$ boson is shown to be $m_{{\pi }^{\pm }}-m_{{\pi }^0}=-0.00201(12)\mathrm{MeV}$. While being small compared to the electromagnetic mass shift, the prediction lies about a factor of $\sim 4$ above the precision of the current experimental measurement and a factor $O(10)$ below the precision of current lattice calculations. This motivates future implementations of these electroweak gauge boson effects on the lattice. Finally, we consider beyond standard model contributions to the pion mass difference.

In this study, we investigate the nonleptonic decays of the charmed-baryon ${\mathrm{\Xi }}_c^0$ induced by the $c\to u(d\overline{d})/(s\overline{s})$ transition. Utilizing the factorization assumption, we decompose the decay amplitudes in terms of transition form factors which are then calculated within the light-front quark model. We employ helicity amplitudes to analyze the nonleptonic decay modes of the charmed-baryons ${\mathrm{\Xi }}_c^0$ and derive benchmark results for decay widths and branching fractions. Our calculations suggest that the branching fractions for some of these rare nonleptonic decays are at the order of ${10}^{-5}–{10}^{-4}$, which are likely to be detectable at experiments such as LHCb, Belle-II, etc. The potential data accumulated in the future may help to further our understanding of the decay mechanism in the presence of charm quarks.

This paper reports the study of $D_s^{+}\to {\tau }^{+}\nu$ via ${\tau }^{+}\to {\pi }^{+}{\overline{\nu }}_{\tau }$ using a boosted decision tree method, with $7.33{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ collision data collected by the BESIII detector at center-of-mass energies between 4.128 and 4.226 GeV. The branching fraction of $D_s^{+}\to {\tau }^{+}{\nu }_{\tau }$ is determined to be $(5.44\pm 0.17_{\mathrm{stat}}\pm 0.13_{\mathrm{syst}})\%$. The product of the $D_s^{+}$ decay constant $f_{D_s^{+}}$ and the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ is $f_{D_s^{+}}|V_{cs}|=(248.3\pm {3.9}_{\mathrm{stat}}\pm {3.1}_{\mathrm{syst}}\pm {1.0}_{\text{input}})\mathrm{MeV}$. Combining with the $|V_{cs}|$ value obtained from the Standard Model global fit or the $f_{D_s^{+}}$ from the lattice quantum chromodynamics, we determine $|V_{cs}|=0.993\pm 0.015_{\mathrm{stat}}\pm 0.012_{\mathrm{syst}}\pm 0.004_{\text{input}}$ and $f_{D_s^{+}}=(255.0\pm {4.0}_{\mathrm{stat}}\pm {3.2}_{\mathrm{syst}}\pm {1.0}_{\text{input}})\mathrm{MeV}$. The first uncertainty is statistical, the second one is systematic and the third one is due to the input parameters, mainly the lifetime of $D_s^{+}$. All results obtained in this work supersede the BESIII previous results based on $6.32{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ collision data taken at center-of-mass energies between 4.178 and 4.226 GeV.

Out-of-time-order correlators are widely used as an indicator of quantum chaos but give false-positive quantum Lyapunov exponents for integrable systems with isolated saddle points. We propose an alternative indicator that fixes this drawback and retains all advantages of out-of-time-order correlators. In particular, the new indicator correctly predicts the average Lyapunov exponent and the Ehrenfest time in the semiclassical limit, can be calculated analytically using the replica trick, and satisfies the bound on chaos.

Motivated by the existence of two-body hadronic molecules composed of $\mathrm{\Omega }\mathrm{\Omega }$, ${\mathrm{\Omega }}_{ccc}{\mathrm{\Omega }}_{ccc}$, and ${\mathrm{\Omega }}_{bbb}{\mathrm{\Omega }}_{bbb}$ predicted by lattice QCD simulations, we use the Gaussian expansion method to investigate whether three-body systems composed of $\mathrm{\Omega }\mathrm{\Omega }\mathrm{\Omega }$, ${\mathrm{\Omega }}_{ccc}{\mathrm{\Omega }}_{ccc}{\mathrm{\Omega }}_{ccc}$, and ${\mathrm{\Omega }}_{bbb}{\mathrm{\Omega }}_{bbb}{\mathrm{\Omega }}_{bbb}$ can bind with the two-body ${}^1{S}_0$ interactions provided by lattice QCD. Our results show that none of the three-body systems bind. On the other hand, we find that with the one-boson exchange potentials the $\mathrm{\Omega }\mathrm{\Omega }\mathrm{\Omega }$ system develops a bound state, for which the ${}^5{S}_2$ interaction plays an important role. Our studies support the existence of the ${\frac{3}{2}}^{+}$ $\mathrm{\Omega }\mathrm{\Omega }\mathrm{\Omega }$ bound state and the nonexistence of the ${\frac{3}{2}}^{+}$ ${\mathrm{\Omega }}_{ccc}{\mathrm{\Omega }}_{ccc}{\mathrm{\Omega }}_{ccc}$ and ${\mathrm{\Omega }}_{bbb}{\mathrm{\Omega }}_{bbb}{\mathrm{\Omega }}_{bbb}$ bound states, due to the suppressed ${}^5{S}_2$ interactions in heavier systems.

We analyze newly expanded and refined data from lattice studies of an $SU(3)$ gauge theory with eight Dirac fermions in the fundamental representation. We focus on the light composite states emerging from these studies, consisting of a set of pseudoscalars and a single light scalar. We first consider the view that this theory is just outside the conformal window. In this case, the pseudoscalars arise from spontaneous breaking of chiral symmetry. Identifying the scalar in this case as an approximate dilaton, we fit the lattice data to a dilaton effective field theory, finding that it yields a good fit even at lowest order. For comparison, we then consider the possibility that the theory is inside the conformal window. The fermion mass provides a deformation, triggering confinement. We employ simple scaling laws to fit the lattice data and find that it is of lesser quality.

An analysis is given of the local phase space of gravity coupled to matter to second order in perturbation theory. Working in local regions with boundaries at finite distance, we identify matter, Coulomb, and additional boundary modes. The boundary modes take the role of reference frames for both diffeomorphisms and internal Lorentz rotations. Passing to the quantum level, we identify the constraints that link the bulk and boundary modes. The constraints take the form of a multifingered Schrödinger equation, which determines the relational evolution of the quantum states in the bulk with respect to the quantum reference fields for the local gravitational symmetries at the boundary. Taking the boundary to infinity, we obtain quantum reference frames for asymptotic symmetries.

The addition of mass terms in general breaks gauge symmetries which can be recovered usually via Stueckelberg fields. The massive BF model describes massive spin-1 particles while preserving the $U(1)$ symmetry without Stueckelberg fields. Replacing the spin-1 curvature (field strength) by the Riemann tensor one can define its spin-2 analog (massive“BR” model). Here we investigate the canonical structure of the free mBR model in terms of gauge invariants in arbitrary dimensions and compare with the massive BF model. We also investigate nonlinear completions of the mBR model in arbitrary dimensions. In $D=3$ we find a nonlinear completion in the form of a bimetric model which is a subcase of a new class of bimetric models whose decoupling limit is ghost free at leading order. Their spectrum consists only of massive spin-2 particles. In arbitrary dimensions $D\ge 3$ we show that the consistency of a possible single metric completion of the mBR model is related with the consistency of a higher rank description of massless spin-1 particles in arbitrary backgrounds.

In this work we present analytical and numerical evidence that classical integrable models possessing infinitely many degrees of freedom unexpectedly exhibit some features that are typical of chaotic systems. By studying how the conserved charges change under a small deformation of the initial conditions, we conclude that the inverse scattering map is responsible for the presence of these features, in spite of the system being integrable. We investigate this phenomenon in the explicit examples of the Korteweg–de Vries equation and the sine-Gordon model and further provide general arguments supporting this statement.

We suggest a new indicator of quantum chaos based on the logarithmic out-of-time-order correlator. On the one hand, this indicator correctly reproduces the average classical Lyapunov exponent in the semiclassical limit and directly links the definitions of quantum chaos and classical K system. On the other hand, it can be analytically calculated using the replica trick and the Schwinger-Keldysh diagram technique on a $2n$-fold Keldysh contour. To illustrate this approach, we consider several one-dimensional systems, including the quantum cat map, and three paradigmatic large-$N$ models, including the Sachdev-Ye-Kitaev model. Furthermore, we find that correlations between replicas can reduce the magnitude of the Lyapunov exponent compared to estimates based on conventional out-of-time-order correlators.

We consider some classes of Horndeski theories in four dimensions for which a certain combination of the Einstein equations within a spherical ansatz splits into two distinct branches. Recently, for these theories, some integrability and compatibility conditions have been established which have made it possible to obtain black hole solutions depending on a single integration constant identified as the mass. Here, we will show that these compatibility conditions can be generalized to accommodate a time dependence by promoting the constant mass to an arbitrary function of the retarded (advanced) time. As a direct consequence, we prove that all the static black hole solutions can be naturally promoted to nonstatic Vaidya-like solutions. We extend this study in arbitrary higher dimensions where the pure gravity part is now described by the Lovelock theory and, where the scalar field action enjoyed the conformal invariance. For these theories, the splitting in two branches is also effective, and we show that their known static black hole solutions can as well be promoted to Vaidya-like solutions.

This paper proposes physical processes to use a Schwarzschild black hole as a rechargeable battery and nuclear reactor. As a rechargeable battery, it can at most transform 25% of input mass into available electric energy in a controllable and slow way. We study its internal resistance, efficiency of discharging, maximum output power, cycle life, and totally available energy. As a nuclear reactor, it realizes an effective nuclear reaction “$\alpha$ $\mathrm{particles}+\text{black hole}\to \mathrm{positrons}+\text{black hole}$” and can transform 25% mass of $\alpha$ particle into the kinetic energy of positrons. This process amplifies the available kinetic energy of natural decay hundreds of times. Since some tiny-sized primordial black holes are suspected to have an appreciable density in dark matter, the result of this paper implies that such black-hole-originated dark matter can be used as reactors to supply energy.

The gravitational induced interference is studied here in the framework of teleparallel gravity. We derive the gravitational phase difference and we apply the result to the case of a Kerr spacetime. Afterwards, we compute the fringe shifts in an interference experiment of particles and discuss how to increase their values by changing the given parameters that include the area in between the paths, the energy of the particles, the distance from the black hole, the mass, and the spin of the black hole. It turns out that it is more difficult to detect the fringe shifts for massless particles than for massive particles. As a further application, we show how the mass of the black hole and its angular momentum can be obtained from the measurement of the fringe shifts. Finally, we compare the phase difference derived in teleparallel gravity with a previous work in general relativity.

Isolated horizons that admit the Hopf bundle structure $H\to S^2$ are investigated; however, the null direction is allowed to be not tangent to the bundle fibers. The horizons are assumed to be axisymmetric. The geometry of such horizons is characterized by an axially symmetric dataset on a topological two-dimensional sphere: a metric tensor with a conical singularity at its poles, and a regular rotation scalar, in a nonextremal case. In the extremal horizon case one more regular function is needed. The horizon equations induced by Einstein’s equations are imposed. The existence of regular extremal horizons satisfying the vacuum (with cosmological constant) equation of extremality, obtained from singular solutions on the sphere, is pointed out. All horizons of the assumed topology and symmetry satisfying the $\mathrm{\Lambda }$-vacuum Type D equation are derived. They are compared to the Killing horizons contained in the accelerated Kerr-Newman-Unti-Tamburino (NUT)–(anti–)de Sitter spacetimes. If the cosmological constant takes special values determined by the other parameters, the bundle fibers become tangent to the null direction. As an additional but also important result, spacetimes of the topology $H\times \mathbb{R}$ locally isometric to the accelerated Kerr-NUT–(anti–)de Sitter spacetimes are constructed for every value of the mass, Kerr, NUT parameters, the cosmological constant, and the acceleration. When the acceleration parameter is not zero, the conical singularity can be removed whenever the NUT parameter does not vanish either.