We present an approach to computing probabilities in quantum field theory for a wide class of source-detector models. The approach works directly with probabilities and not with squared matrix elements, and the resulting probabilities can be written in terms of expectation values of nested commutators and anticommutators. We present results that help in the evaluation of these, including an expression for the vacuum expectation values of general nestings of commutators and anticommutators in scalar field theory. This approach allows one to see clearly how faster-than-light signalling is prevented, because it leads to a diagrammatic expansion in which the retarded propagator plays a prominent role. We illustrate the formalism using the simple case of the much-studied Fermi two-atom problem.

The three-body problem in the framework of a scalar-tensor theory of gravitation is considered. We find that the collinear solution to this problem exists in the presence of the scalar field. Through some numerical examples, we investigate the effects of the scalar field on this solution, the angular velocity of the system and the positions of Lagrange points. We find that while the scalar field’s effects on the Lagrange points of the planets in the Solar System are practically beyond the limits of the current technology, a compact binary with comparable masses will be a good test bed.

We present new spherically symmetric, dyonic soliton and black hole solutions of the $\mathfrak{su}(N)$ Einstein-Yang-Mills equations in four-dimensional asymptotically anti–de Sitter spacetime. The gauge field has nontrivial electric and magnetic components and is described by $N-1$ magnetic gauge field functions and $N-1$ electric gauge field functions. We explore the phase space of solutions in detail for $\mathfrak{su}(2)$ and $\mathfrak{su}(3)$ gauge groups. Combinations of the electric gauge field functions are monotonic and have no zeros; in general the magnetic gauge field functions may have zeros. The phase space of solutions is extremely rich, and we find solutions in which the magnetic gauge field functions have more than fifty zeros. Of particular interest are solutions for which the magnetic gauge field functions have no zeros, which exist when the negative cosmological constant has sufficiently large magnitude. We conjecture that at least some of these nodeless solutions may be stable under linear, spherically symmetric, perturbations.

The effective-one-body theory (EOB) describes the conservative dynamics of compact binary systems in terms of an effective Hamiltonian approach. The Hamiltonian for moderately eccentric motion of two nonspinning compact objects in the extreme mass-ratio limit is given in terms of three potentials: $a(v)$, $\overline{d}(v)$, $q(v)$. By generalizing the first law of mechanics for (nonspinning) black hole binaries to eccentric orbits, [A. Le Tiec, Phys. Rev. D 92, 084021 (2015).] recently obtained new expressions for $\overline{d}(v)$ and $q(v)$ in terms of quantities that can be readily computed using the gravitational self-force approach. Using these expressions we present a new computation of the EOB potential $q(v)$ by combining results from two independent numerical self-force codes. We determine $q(v)$ for inverse binary separations in the range $1/1200\le v\lesssim 1/6$. Our computation thus provides the first-ever strong-field results for $q(v)$. We also obtain $\overline{d}(v)$ in our entire domain to a fractional accuracy of $\gtrsim {10}^{-8}$. We find that our results are compatible with the known post-Newtonian expansions for $\overline{d}(v)$ and $q(v)$ in the weak field, and agree with previous (less accurate) numerical results for $\overline{d}(v)$ in the strong field.

The continued fraction method (also known as Leaver’s method) is one of the most effective techniques used to determine the quasinormal modes of a black hole. For extremal black holes, however, the method does not work (since, in such a case, the event horizon is an irregular singular point of the associated wave equation). Fortunately, there exists a modified version of the method, devised by Onozawa et al. [Phys. Rev. D 53, 7033 (1996)], which works for neutral massless fields around an extremal Reissner-Nordström black hole. In this paper, we generalize the ideas of Onozawa et al. to charged massless perturbations around an extremal Reissner-Nordström black hole and to neutral massless perturbations around an extremal Kerr black hole. In particular, the existence of damped modes is analyzed in detail. Similarities and differences between the results of the original continued fraction method for near extremal black holes and the results of the new continued fraction method for extremal black holes are discussed. Mode stability of extremal black holes is also investigated.

Apart from its debatable correctness, we examine the perturbative stability of the recently proposed cosmology from quantum potential. We find that the proposed quantum corrections invoke additional parameters which apparently introduce perturbative instability to the Universe.

We present a complete phenomenological prospectus for thermal relic neutralinos. Including Sommerfeld enhancements to relic abundance and halo annihilation calculations, we obtain direct, indirect, and collider discovery prospects for all neutralinos with mass parameters $M_1$, $M_2$, $|\mu |<4\mathrm{TeV}$, which freeze out to the observed dark matter abundance, with scalar superpartners decoupled. Much of the relic neutralino sector will be uncovered by the direct detection experiments Xenon1T and LZ, as well as indirect detection with Cerenkov Telescope Array. We emphasize that thermal relic Higgsinos will be found by next-generation direct detection experiments, so long as $M_{1,2}<4\mathrm{TeV}$. Charged tracks at a 100 TeV hadron collider complement indirect searches for relic winos. Thermal relic bino-winos still evade all planned experiments, including disappearing charged-track searches. However, they can be discovered by compressed electroweakino searches at a 100 TeV collider, completing the full coverage of the relic neutralino surface.

Low mechanical loss at low temperatures and a high index of refraction should make silicon optimally suited for thermal noise reduction in highly reflective mirror coatings for gravitational wave detectors. However, due to high optical absorption, amorphous silicon (aSi) is unsuitable for being used as a direct high-index coating material to replace tantala. A possible solution is a multimaterial design, which enables exploitation of the excellent mechanical properties of aSi in the lower coating layers. The possible number of aSi layers increases with absorption reduction. In this work, the optimum heat treatment temperature of aSi deposited via ion-beam sputtering was investigated and found to be $450°\mathrm{C}$. For this temperature, the absorption after deposition of a single layer of aSi at 1064 nm and 1550 nm was reduced by more than 80%.

We investigate the possibility of probing the $CP$-violating $h\overline{t}t$ coupling in the process $e^{+}{e}^{-}\to h\gamma$ at the future high luminosity $e^{+}{e}^{-}$ colliders. Our numerical results show that the cross section for this process can be significantly increased for the allowed $CP$ phase $\xi$ and center of mass energy. For example, the cross section is about 10 times that in the standard model (SM) for $\sqrt{s}=350\mathrm{GeV}$ and $\xi =3\pi /5$ (see text for $\xi$ definition). The simulation for the signal process $e^{+}{e}^{-}\to h\gamma \to b\overline{b}\gamma$ and its backgrounds shows that the signal significance can reach about $5\sigma$ and more than $2.1\sigma$ for $\sqrt{s}=350\mathrm{GeV}$ and 500 GeV, respectively, with the integrated luminosity $\mathcal{L}=3{\mathrm{ab}}^{-1}$ and $\xi \in [\pi /2,3\pi /5]$. For $\mathcal{L}=10{\mathrm{ab}}^{-1}$, the signal significance can be greater than $5\sigma$ for $\sqrt{s}=350\mathrm{GeV}$ and about $4\sigma$ for $\sqrt{s}=500\mathrm{GeV}$ with the $CP$ phase $\xi \in [\pi /2,3\pi /5]$. Besides the cross section enhancement, the $CP$-violating $h\overline{t}t$ coupling will induce a forward-backward asymmetry $A_{FB}$ which is absent in the SM and is a clear signal of new $CP$ violation. Compared with the $A_{FB}$ in the Higgs decay $h\to l^{+}{l}^{-}\gamma$, the $A_{FB}$ can be greatly enhanced in the production process. For example, $A_{FB}$ can reach $-0.55$ for $\xi =\pi /4$ and $\sqrt{s}=500\mathrm{GeV}$. Because of the large backgrounds, the significance of the expected $A_{FB}$ can be observed only at $1.68\sigma$ with $\mathcal{L}=10{\mathrm{ab}}^{-1}$ and $\sqrt{s}=500\mathrm{GeV}$. It is essential to trigger the single photon in the final state to separate the bottom jets arising from scalar or vector bosons, in order to isolate the signal from the backgrounds more efficiently.

This paper reports the first measurement using the NOvA detectors of ${\nu }_{\mu }$ disappearance in a ${\nu }_{\mu }$ beam. The analysis uses a 14 kton-equivalent exposure of $2.74\times {10}^{20}$ protons-on-target from the Fermilab NuMI beam. Assuming the normal neutrino mass hierarchy, we measure $\mathrm{\Delta }{m}_{32}^2=({2.52}_{-0.18}^{+0.20})\times {10}^{-3}{\mathrm{eV}}^2$ and ${\sin }^2{\theta }_{23}$ in the range 0.38–0.65, both at the 68% confidence level, with two statistically degenerate best-fit points at ${\sin }^2{\theta }_{23}=0.43$ and 0.60. Results for the inverted mass hierarchy are also presented.

Recently in Phys. Rev. D 88, 027504 (2013), Yoon has suggested that there may be problems for the nonrelativistic limit of the conformal gravity theory. Here we show that Yoon’s results only hold because of the assumption that gravitational sources can be treated the same way that they are treated in standard Newton-Einstein gravity. Since such an assumption violates the theory’s underlying conformal invariance, Yoon’s conclusions are invalidated.

In the presence of (approximately conserved) axial charge in the QCD plasma at finite temperature, the emitted photons are spin aligned, which is a unique $P$- and $CP$-odd signature of axial charge in the photon emission observables. We compute this “$P$-odd photon emission rate” in a weak coupling regime at a high temperature limit to complete leading order in the QCD coupling constant: the leading log as well as the constant under the log. As in the $P$-even total emission rate in the literature, the computation of the $P$-odd emission rate at leading order consists of three parts: (1) Compton and pair annihilation processes with hard momentum exchange, (2) soft $t$- and $u$-channel contributions with hard thermal loop resummation, (3) Landau-Pomeranchuk-Migdal resummation of collinear bremsstrahlung and pair annihilation. We present analytical and numerical evaluations of these contributions to our $P$-odd photon emission rate observable.

We present a kind of generalized Vaidya solution of a new cubic gravity in five dimensions whose field equations in spherically symmetric spacetime are always second order like the Lovelock gravity. We also study the thermodynamics of its spherically symmetric apparent horizon and get its entropy expression and generalized Misner-Sharp energy. Finally, we present the first law and second law hold in this gravity. Although all the results are analogous to those in Lovelock gravity, we in fact introduce the contribution of a new cubic term in five dimensions where the cubic Lovelock term is just zero.

The usefulness of the Morris-Thorne spatial wormhole motivates a consideration of a generalization to a class of similarly simple spacetime geometries. In this generalization, a “splittable” spacetime can be considered to be built of a parallel stack of identical 3-geometries. Such spacetimes do not have the usual manifestation of gravity, but in Einstein’s theory they will in general have mass-energy density.

We explore the evolutionary behaviors of compact objects in a modified gravitational theory with the help of structure scalars. Particularly, we consider the spherical geometry coupled with heat- and radiation-emitting shearing viscous matter configurations. We construct structure scalars by splitting the Riemann tensor orthogonally in $f(R,T)$ gravity with and without constant $R$ and $T$ constraints, where $R$ is the Ricci scalar and $T$ is the trace of the energy-momentum tensor. We investigate the influence of the modification of gravity on the physical meaning of scalar functions for radiating spherical matter configurations. It is explicitly demonstrated that even in modified gravity, the evolutionary phases of relativistic stellar systems can be analyzed through the set of modified scalar functions.

We present new results through 7PN order on the energy flux from eccentric extreme-mass-ratio binaries. The black hole perturbation calculations are made at very high accuracy (200 decimal places) using a Mathematica code based on the Mano-Suzuki-Takasugi analytic function expansion formalism. All published coefficients in the expansion through 3PN order at lowest order in the mass ratio are confirmed and new analytic and numeric terms are found to high order in powers of $e^2$ at post-Newtonian orders between 3.5PN and 7PN. We also show original work in finding (nearly) arbitrarily accurate expansions for hereditary terms at 1.5PN, 2.5PN, and 3PN orders. An asymptotic analysis is developed that guides an understanding of eccentricity singular factors, which diverge at unit eccentricity and which appear at each PN order. We fit to a model at each PN order that includes these eccentricity singular factors, which allows the flux to be accurately determined out to $e\to 1$.

Constraining cosmology using weak gravitational lensing consists of comparing a measured feature vector of dimension $N_b$ with its simulated counterpart. An accurate estimate of the $N_b\times N_b$ feature covariance matrix $\mathbf{C}$ is essential to obtain accurate parameter confidence intervals. When $\mathbf{C}$ is measured from a set of simulations, an important question is how large this set should be. To answer this question, we construct different ensembles of $N_r$ realizations of the shear field, using a common randomization procedure that recycles the outputs from a smaller number $N_s\le N_r$ of independent ray-tracing $N$-body simulations. We study parameter confidence intervals as a function of ($N_s$, $N_r$) in the range $1\le N_s\le 200$ and $1\le N_r\lesssim {10}^5$. Previous work [S. Dodelson and M. D. Schneider, Phys. Rev. D 88, 063537 (2013)] has shown that Gaussian noise in the feature vectors (from which the covariance is estimated) lead, at quadratic order, to an $O(1/N_r)$ degradation of the parameter confidence intervals. Using a variety of lensing features measured in our simulations, including shear-shear power spectra and peak counts, we show that cubic and quartic covariance fluctuations lead to additional $O(1/N_r^2)$ error degradation that is not negligible when $N_r$ is only a factor of few larger than $N_b$. We study the large $N_r$ limit, and find that a single, $240\mathrm{Mpc}/h$ sized ${512}^3$-particle $N$-body simulation ($N_s=1$) can be repeatedly recycled to produce as many as $N_r=\text{few}\times {10}^4$ shear maps whose power spectra and high-significance peak counts can be treated as statistically independent. As a result, a small number of simulations ($N_s=1$ or 2) is sufficient to forecast parameter confidence intervals at percent accuracy.

The dark matter halos that host galaxies and clusters form out of initial high-density patches, providing a biased tracer of the linear matter density field. In the simplest local bias approximation, the halo field is treated as a perturbative series in the average overdensity of the Lagrangian patch. In more realistic models, however, additional quantities will affect the clustering of halo patches, and this expansion becomes a function of several stochastic variables. In this paper, we present a general multivariate expansion scheme that can parametrize the clustering of any biased Lagrangian tracer, given only the variables involved and their symmetry (in our case rotational invariance). This approach is based on an expansion in the orthonormal polynomials associated with the relevant variables, so that no renormalization of the coefficients ever occurs. We provide an explicit expression for the series coefficients, or Lagrangian bias parameters, in the case of peaks of the linear density field. As an application of our formalism, we present a simple derivation of the original BBKS formula and compute the non-Gaussian bias in the presence of a primordial trispectrum of the local shape.

We study the dimension-6 quark anomalous electroweak couplings in the formulation of linearly realized effective Lagrangian. We investigate the constraints on these anomalous couplings from the $pp\to W^{+}{W}^{-}$ process in detail at the LHC. With additional kinematic cuts, we find that the 14 TeV LHC can provide a test of anomalous couplings of $O(0.1–1){\mathrm{TeV}}^{-2}$. The $pp\to ZZ/Z\gamma /\gamma \gamma$ processes can provide a good complement, as they are sensitive to those anomalous couplings which do not affect the $pp\to W^{+}{W}^{-}$ process. Those processes that only contain anomalous triple vertices, like $pp\to W^{*}\to l{\nu }_l$ or $pp\to {\gamma }^{*}/Z^{*}\to l^{+}{l}^{-}$, can improve the sensitivities to $O(0.01–0.1){\mathrm{TeV}}^{-2}$. We also study the kinematic differences between different anomalous couplings and discuss the potential of the ${\chi }^2$ analysis to distinguish them. Finally, we discuss the detection ability of the possible future 100 TeV proton-proton collider (SPPC) and find that the detection sensitivity is improved by about 1 order of magnitude compared with the LHC.