We develop a high-precision model for relativistic observables of the Atomic Clock Ensemble in Space (ACES) experiment on the International Space Station (ISS). We develop all relativistic coordinate transformations that are needed to describe the motion of ACES in Earth orbit and to compute observable quantities. We analyze the accuracy of the required model as it applies to the proper-to-coordinate time transformations, light-time equation, and spacecraft equations of motion. We consider various sources of nongravitational noise and their effects on ACES. We estimate the accuracy of orbit reconstruction that is needed to satisfy the ACES science objectives. Based on our analysis, we derive models for the relativistic observables of ACES, which also account for the contribution of atmospheric drag on the clock rate. We include the Earth’s oblateness coefficient $J_2$ and the effects of major nongravitational forces on the orbit of the ISS. We demonstrate that the ACES reference frame is pseudoinertial at the level of accuracy required by the experiment. We construct a Doppler-canceled science observable representing the gravitational redshift. We derive accuracy requirements for ISS navigation. The improved model is accurate up to $<1\mathrm{ps}$ and $\sim 4\times 10^{-17}$ for time and frequency transfers, correspondingly. These limits are determined by the higher-order harmonics in Earth’s gravitational potential.

We propose the integrable $N$-dimensional Calogero-Coulomb-Stark and two-center Calogero-Coulomb systems and construct their constants of motion via the Dunkl operators. Their Schrödinger equations decouple in parabolic and elliptic coordinates into the set of three differential equations like for the Coulomb-Stark and two-center Coulomb problems. The Calogero term preserves the energy levels, but changes their degrees of degeneracy.

The actions for bosonic fields typically contain terms quadratic in the derivatives of the fields. This is not the case in the Palatini approach to general relativity. The action does not contain any derivatives of the metric and it only contains terms linear in the derivatives of the connection. In general relativity the covariant derivative of the metric vanishes, so it is not possible to include such terms in the action. However, in more general theories this is not the case. In this paper I consider an action which is quadratic in the derivatives of the metric and connection and show that it leads to the coupled Einstein-Maxwell theory or the coupled Einstein-Proca theory with the antisymmetric part of the Ricci tensor playing the role of the electromagnetic field strength.

Binary black hole coalescence has its peak of gravitational-wave generation during the “plunge,” the transition from quasicircular early motion to late quasinormal ringing (QNR). Although advances in numerical relativity have provided plunge waveforms, there is still no intuitive or phenomenological understanding of plunge comparable to that of the early and late stages. Here we make progress in developing such understanding by relying on insights of the linear mathematics of the particle perturbation model for the extreme mass limit. Our analysis, based on the Fourier-domain Green function, and a simple initial model, point to the crucial role played by the kinematics near the “light ring” (the circular photon orbit) in determining the plunge radiation and the excitation of QNR. That insight is then shown to successfully explain results obtained for particle motion in a Schwarzschild background.

Crustal torsional oscillations depend on not only crust properties but also the stellar mass and radius. Thus, one could extract stellar information by identifying the observed frequencies of stellar oscillations with the crustal torsional oscillations. Owing to the confinement of torsional oscillations inside the crust region of neutron stars, we successfully derive an empirical formula for the fundamental crustal torsional oscillations as a function of the stellar mass, radius, the so-called slope parameter of the nuclear symmetry energy, and the angular index of oscillations, with which one can estimate the frequencies with high accuracy. This empirical formula could be valuable in both the astrophysics and nuclear physics communities.

The search for continuous gravitational waves in a wide parameter space at a fixed computing cost is most efficiently done with semicoherent methods, e.g., StackSlide, due to the prohibitive computing cost of the fully coherent search strategies. Prix and Shaltev [Phys. Rev. D 85, 084010 (2012)] have developed a semianalytic method for finding optimal StackSlide parameters at a fixed computing cost under ideal data conditions, i.e., gapless data and a constant noise floor. In this work, we consider more realistic conditions by allowing for gaps in the data and changes in the noise level. We show how the sensitivity optimization can be decoupled from the data selection problem. To find optimal semicoherent search parameters, we apply a numerical optimization using as an example the semicoherent StackSlide search. We also describe three different data selection algorithms. Thus, the outcome of the numerical optimization consists of the optimal search parameters and the selected data set. We first test the numerical optimization procedure under ideal conditions and show that we can reproduce the results of the analytical method. Then we gradually relax the conditions on the data and find that a compact data selection algorithm yields higher sensitivity compared to a greedy data selection procedure.

We introduce new code for stationary and axisymmetric equilibriums, as well as for triaxial quasiequilibrium initial data, of single rotating relativistic stars. The new code is developed as a part of our versatile initial data code for compact objects, Compact Object CALculator (cocal). In computing strong gravitational fields, the waveless formulation is incorporated into the cocal code on top of the previously developed Isenberg-Wilson-Mathews formulation (conformally flat thin-sandwich formulation). Also introduced is a new differential rotation law that contains two parameters to control an angular velocity profile and a transition from uniform to differential rotation. We present convergence tests and solution sequences for both uniformly and differentially rotating equilibriums of stationary axisymmetric compact stars, as well as for quasiequilibrium initial data of uniformly rotating triaxial (nonaxisymmetric) compact stars. We also show comparisons of uniformly rotating axisymmetric solutions computed with three different codes: cocal, lorene, and the RNS code.

We prove that, for a charged spherically symmetric body, twice the radius is always strictly greater than the charge of the body. We also prove that this inequality is sharp. Finally, we discuss the physical implications of this geometrical inequality and present numerical examples that illustrate this theorem.

The center-of-mass energy of two particles can become arbitrarily large if they collide near the event horizon of an extremal Kerr black hole, which is called the Bañados-Silk-West effect. We consider such a high-energy collision of two particles which started from infinity and follow geodesics in the equatorial plane and investigate the energy extraction from such a high-energy particle collision and the production of particles in the equatorial plane. We analytically show that, on the one hand, if the produced particles are as massive as the colliding particles, the energy-extraction efficiency is bounded by 2.19 approximately. On the other hand, if a very massive particle is produced as a result of the high-energy collision, which has negative energy and necessarily falls into the black hole, the upper limit of the energy-extraction efficiency is increased to $(2+\sqrt{3}{)}^2\simeq 13.9$. Thus, higher efficiency of the energy extraction, which is typically as large as 10, provides strong evidence for the production of a heavy particle.

We explore the stopping effect that results from interactions between dark matter and nuclei as the dark matter particles travel underground towards the detector. Although this effect is negligible for heavy dark matter particles, there is parameter phase space where the underground interactions of the dark matter particles with the nuclei can create observable differences in the spectrum. Dark matter particles that arrive on the detector from below can have less energy from the ones arriving from above. These differences can be potentially detectable by upcoming directional detectors. This can unveil a large amount of information regarding the type and strength of interactions between nuclei and light dark matter candidates.

The comparison of the results of direct detection of dark matter, obtained with various target nuclei, requires model-dependent, or even arbitrary, assumptions. Indeed, to draw conclusions either the spin-dependent (SD) or the spin-independent (SI) interaction has to be neglected. In the light of the null results from supersymmetry searches at the LHC, the squark sector is pushed to high masses. We show that for a squark sector at the TeV scale, the framework used to extract constraints from direct detection searches can be redefined as the number of free parameters is reduced. Moreover, the correlation observed between SI and SD proton cross sections constitutes a key issue for the development of the next generation of dark matter detectors.

We investigate properties of low-energy QCD in a finite spatial volume, but with arbitrary temperature. In the limit of small temperature and small cube size compared to the pion Compton wavelength, Leutwyler has shown that the effective theory describing low-energy QCD reduces to that of quantum mechanics on the coset manifold, which is the so-called delta regime of chiral perturbation theory. We solve this quantum mechanics analytically for the case of a $U(1{)}_L\times U(1{)}_R$ subgroup of chiral symmetry, and numerically for the case of $SU(2{)}_L\times SU(2{)}_R$. We utilize the quantum mechanical spectrum to compute the mass gap and chiral condensate, and investigate symmetry restoration in a finite spatial volume as a function of temperature. Because we obtain the spectrum for nonzero values of the quark mass, we are able to interpolate between the rigid rotor limit, which emerges at vanishing quark mass, and the harmonic approximation, which is referred to as the $p$ regime. We find that the applicability of perturbation theory about the rotor limit largely requires lighter-than-physical quarks. As a stringent check of our results, we raise the temperature to that of the inverse cube size. When this condition is met, the quantum mechanics reduces to a matrix model. The condensate we obtain in this limit agrees with that determined analytically in the epsilon regime.

We calculate the properties of excited charm and charm-strange mesons. We use the relativized quark model to calculate their masses and wave functions that are used to calculate radiative transition partial widths and the ${{}^{3}P}_0$ quark-pair-creation model to calculate their strong decay widths. We use these results to make quark model spectroscopic assignments for recently observed charm and charm-strange mesons. In particular, we find that the properties of the $D_J(2550{)}^0$ and $D_J^{*}(2600{)}^0$ are consistent with those of the $2{{}^{1}S}_0(c\overline{u})$ and the $2{{}^{3}S}_1(c\overline{u})$ states respectively, and the $D_1^{*}(2760{)}^0$, $D_3^{*}(2760{)}^{-}$, and $D_J(2750{)}^0$ with those of the $1{{}^{3}D}_1(c\overline{u})$, $1{{}^{3}D}_3(d\overline{c})$, and $1D_2(c\overline{u})$ states respectively. We tentatively identify the $D_J^{*}(3000{)}^0$ as the $1{{}^{3}F}_4(c\overline{u})$ and favor the $D_J(3000{)}^0$ to be the $3{{}^{1}S}_0(c\overline{u})$ although we do not rule out the $1F_3$ and $1F_3^{\prime }$ assignment. For the recently observed charm-strange mesons we identify the $D_{s1}^{*}(2709{)}^{\pm }$, $D_{s1}^{*}(2860{)}^{-}$, and $D_{s3}^{*}(2860{)}^{-}$ as the $2{{}^{3}S}_1(c\overline{s})$, $1{{}^{3}D}_1(s\overline{c})$, and $1{{}^{3}D}_3(s\overline{c})$ states respectively and suggest that the $D_{sJ}(3044{)}^{\pm }$ is most likely the $D_{s1}(2P_1^{\prime })$ or $D_{s1}(2P_1)$ state although it might be the $D_{s2}^{*}(2{{}^{3}P}_2)$ with the $DK$ final state too small to be observed with current statistics. Based on the predicted properties of excited states, that they do not have too large a total width and that they have a reasonable branching ratio to simple final states, we suggest states that should be able to be found in the near future. We expect that the tables of properties summarizing our results will be useful for interpreting future observations of charm and charm-strange mesons.

We discuss massive quark effects in the end-point region $x\to 1$ of inclusive deep inelastic scattering (DIS), where the hadronic final state is collimated and thus represents a jet. In this regime heavy quark pairs are generated via secondary radiation, i.e. due to a gluon splitting in light quark initiated contributions starting at $\mathcal{O}({\alpha }_s^2)$ in the fixed-order expansion. Based on the factorization framework for DIS in the end-point region for massless quarks in soft collinear effective theory (SCET), which we also scrutinize in this work, we construct a variable flavor number scheme that deals with arbitrary hierarchies between the mass scale and the kinematic scales. The scheme exhibits a continuous behavior between the massless limit for very light quarks and the decoupling limit for very heavy quarks. It entails threshold matching corrections, arising from all gauge-invariant factorization components at the mass scale, which are related to each other via consistency conditions. This is explicitly demonstrated by recalculating the known threshold correction for the parton distribution function at $\mathcal{O}({\alpha }_s^2{C}_F{T}_F)$ within SCET. The latter contains large rapidity logarithms $\sim \ln (1-x)$ that can be summed by exponentiation. Their coefficients are universal, which can be used to obtain potentially relevant higher-order results for generic threshold corrections at colliders from computations in DIS. In particular, we extract the $\mathcal{O}({\alpha }_s^3)$ threshold correction multiplied by a single rapidity logarithm from results obtained earlier.

Nucleon-antinucleon optical potential, which explains the experimental data for the processes $e^{+}{e}^{-}\to p\overline{p}$ and $e^{+}{e}^{-}\to \text{pions}$ near the threshold of $p\overline{p}$ pair production, is suggested. To obtain this potential, we have used the available experimental data for $p\overline{p}$ scattering, $p\overline{p}$ pair production in $e^{+}{e}^{-}$ annihilation, and the ratio of electromagnetic form factors of a proton in the timelike region. It turns out that final-state interaction via the optical potential allows one to reproduce the available experimental data with good accuracy. Our results for the cross sections of the $e^{+}{e}^{-}\to 6\pi$ process near the threshold of $p\overline{p}$ pair production are in agreement with the recent experiments.

We report a measurement of the $B^0\to \psi (2S){\pi }^0$ branching fraction based on the full $\mathrm{\Upsilon }(4S)$ data set of $772\times {10}^6$ $B\overline{B}$ pairs collected by the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We obtain $\mathcal{B}(B^0\to \psi (2S){\pi }^0)=(1.17\pm 0.17(\mathrm{stat})\pm 0.08(\mathrm{syst}))\times {10}^{-5}$. The result has a significance of 7.2 standard deviations and is the first observation of the decay $B^0\to \psi (2S){\pi }^0$.

We show how quantum fields can be used to measure the curvature of spacetime. In particular, we find that knowledge of the imprint that spacetime curvature leaves in the correlators of quantum fields suffices, in principle, to reconstruct the metric. We then consider the possibility that the quantum fields obey a natural ultraviolet cutoff, for example, at the Planck scale. We investigate how such a cutoff limits the spatial resolution with which curvature can be deduced from the properties of quantum fields. We find that the metric deduced from the quantum correlator exhibits a peculiar scaling behavior as the scale of the natural UV cutoff is approached.