Our recently developed variant of variationally optimized perturbation, in particular consistently incorporating renormalization group properties, is adapted to the calculation of the QCD spectral density of the Dirac operator and the related chiral quark condensate $⟨\overline{q}q⟩$ in the chiral limit, for $n_f=2$ and $n_f=3$ massless quarks. The results of successive sequences of approximations at two-, three-, and four-loop orders of this modified perturbation exhibit a remarkable stability. We obtain $⟨\overline{q}q{⟩}_{n_f=2}^{1/3}(2\mathrm{GeV})=-(0.833–0.845){\overline{\mathrm{\Lambda }}}_2$, and $⟨\overline{q}q{⟩}_{n_f=3}^{1/3}(2\mathrm{GeV})=-(0.814–0.838){\overline{\mathrm{\Lambda }}}_3$ where the range spanned by the first and second numbers (respectively, four- and three-loop order results) defines our theoretical error, and ${\overline{\mathrm{\Lambda }}}_{n_f}$ is the basic QCD scale in the $\overline{\mathrm{MS}}$ scheme. We obtain a moderate suppression of the chiral condensate when going from $n_f=2$ to $n_f=3$. We compare these results with some other recent determinations from other nonperturbative methods (mainly lattice and spectral sum rules).

The NEMO-3 detector, which had been operating in the Modane Underground Laboratory from 2003 to 2010, was designed to search for neutrinoless double-$\beta$ ($0\nu \beta \beta$) decay. We report the final results of a search for $0\nu \beta \beta$ decays with 6.914 kg of ${}^{100}\mathrm{Mo}$ using the entire NEMO-3 data set with a detector live time of 4.96 yr, which corresponds to an exposure of $34.3\mathrm{kg}·\mathrm{yr}$. We perform a detailed study of the expected background in the $0\nu \beta \beta$ signal region and find no evidence of $0\nu \beta \beta$ decays in the data. The level of observed background in the $0\nu \beta \beta$ signal region [2.8–3.2] MeV is $0.44\pm 0.13\mathrm{counts}/\mathrm{yr}/\mathrm{kg}$, and no events are observed in the interval [3.2–10] MeV. We therefore derive a lower limit on the half-life of $0\nu \beta \beta$ decays in ${}^{100}\mathrm{Mo}$ of $T_{1/2}(0\nu \beta \beta )>1.1\times 10^{24}\mathrm{yr}$ at the 90% confidence level, under the hypothesis of decay kinematics similar to that for light Majorana neutrino exchange. Depending on the model used for calculating nuclear matrix elements, the limit for the effective Majorana neutrino mass lies in the range $⟨m_{\nu }⟩<0.33–0.62\mathrm{eV}$. We also report constraints on other lepton-number violating mechanisms for $0\nu \beta \beta$ decays.

Using the canonical Arnowitt–Deser–Misner Hamiltonian formalism, a “first law of mechanics” is established for binary systems of point masses moving along generic stable bound (eccentric) orbits. This relationship is checked to hold within the post-Newtonian approximation to general relativity, up to third order. Several applications are discussed, including the use of gravitational self-force results to inform post-Newtonian theory and the effective one-body model for eccentric-orbit compact binaries.

A measurement of primordial non-Gaussianity will be of paramount importance to distinguish between different models of inflation. Cosmic microwave background (CMB) anisotropy observations have set unprecedented bounds on the non-Gaussianity parameter $f_{\mathrm{NL}}$ but the interesting regime $f_{\mathrm{NL}}\lesssim 1$ is beyond their reach. Brightness-temperature fluctuations in the 21-cm line during the dark ages ($z\sim 30–100$) are a promising successor to CMB studies, giving access to a much larger number of modes. They are, however, intrinsically nonlinear, which results in secondary non-gaussianities orders of magnitude larger than the sought-after primordial signal. In this paper we carefully compute the primary and secondary bispectra of 21-cm fluctuations on small scales. We use the flat-sky formalism, which greatly simplifies the analysis, while still being very accurate on small angular scales. We show that the secondary bispectrum is highly degenerate with the primordial one, and argue that even percent-level uncertainties in the amplitude of the former lead to a bias of order $\mathrm{\Delta }{f}_{\mathrm{NL}}\sim 10$. To tackle this problem we carry out a detailed Fisher analysis, marginalizing over the amplitudes of a few smooth redshift-dependent coefficients characterizing the secondary bispectrum. We find that the signal-to-noise ratio for a single redshift slice is reduced by a factor of $\sim 5$ in comparison to a case without secondary non-gaussianities. Setting aside foreground contamination, we forecast that a cosmic-variance-limited experiment observing 21-cm fluctuations over $30\le z\le 100$ with a 0.1-MHz bandwidth and 0.1 arc min angular resolution could achieve a sensitivity of order $f_{\mathrm{NL}}^{\text{local}}\sim 0.03$, $f_{\mathrm{NL}}^{\text{equil}}\sim 0.04$ and $f_{\mathrm{NL}}^{\text{ortho}}\sim 0.03$.

We study the behavior of the tree-level S-matrix of a variety of theories as two particles become soft. By analogy with the recently found subleading soft theorems for gravitons and gluons, we explore subleading terms in double soft emissions. We first consider double soft scalar emissions and find subleading terms that are controlled by the angular momentum operator acting on hard particles. The order of the subleading theorems depends on the presence or not of color structures. Next we obtain a compact formula for the leading term in a double soft photon emission. The theories studied are a special Galileon, Dirac–Born–Infeld, Einstein–Maxwell–Scalar, nonlinear sigma model and Yang–Mills–Scalar. We use the recently found Cachazo–He–Yuan representation of these theories in order to give a simple proof of the leading order part of all these theorems.

Planetary ephemerides are a very powerful tool to constrain deviations from the theory of general relativity (GR) using orbital dynamics. The effective field theory framework called the Standard-Model Extension (SME) has been developed in order to systematically parametrize hypothetical violations of Lorentz symmetry (in the Standard Model and in the gravitational sector). In this communication, we use the latest determinations of the supplementary advances of the perihelia and of the nodes obtained by planetary ephemerides analysis to constrain SME coefficients from the pure gravity sector and also from gravity-matter couplings. Our results do not show any deviation from GR and they improve current constraints. Moreover, combinations with existing constraints from Lunar Laser Ranging and from atom interferometry gravimetry allow us to disentangle contributions from the pure gravity sector from the gravity-matter couplings.

We present the first numerical calculation of the (local) metric perturbation produced by a small compact object moving on an eccentric equatorial geodesic around a Kerr black hole, accurate to first order in the mass ratio. The procedure starts by first solving the Teukolsky equation to obtain the Weyl scalar ${\psi }_4$ using semianalytical methods. The metric perturbation is then reconstructed from ${\psi }_4$ in an (outgoing) radiation gauge, adding the appropriate nonradiative contributions arising from the shifts in mass and angular momentum of the spacetime. As a demonstration we calculate the generalized redshift $U$ as a function of the orbital frequencies ${\mathrm{\Omega }}_r$ and ${\mathrm{\Omega }}_{\varphi }$ to linear order in the mass ratio, a gauge invariant measure of the conservative corrections to the orbit due to self-interactions. In Schwarzschild, the results surpass the existing result in the literature in accuracy, and we find new estimates for some of the unknown 4PN and 5PN terms in the post-Newtonian expansion of $U$. In Kerr, we provide completely novel values of $U$ for eccentric equatorial orbits. Calculation of the full self-force will appear in a forthcoming paper.

We report a measurement of the branching fraction of $B^{+}\to {\tau }^{+}{\nu }_{\tau }$ decays using a data sample of $772\times {10}^{6}B\overline{B}$ pairs, collected at the $\mathrm{\Upsilon }(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We reconstruct the accompanying $B$ meson in a semileptonic decay and detect the recoiling $B$ candidate in the decay channel $B^{+}\to {\tau }^{+}{\nu }_{\tau }$. We obtain a branching fraction of $\mathcal{B}(B^{+}\to {\tau }^{+}{\nu }_{\tau })=[1.25\pm 0.28(\text{stat}.)\pm 0.27(\text{syst}.)]\times {10}^{-4}$. This result is in good agreement with previous measurements and the expectation from the calculation based on the Standard Model.

We investigate the stability of an inhomogeneous chiral condensed phase against low energy fluctuations about a spatially modulated order parameter. This phase corresponds to the so-called dual chiral density wave in the context of quark matter, where the chiral condensate is spatially modulated with a finite wave vector in a single direction. From the symmetry viewpoint, the phase realizes a locking of flavor and translational symmetries. Starting with a Landau-Ginzburg-Wilson effective Lagrangian, we find that the associated Nambu-Goldstone modes, whose dispersion relations are spatially anisotropic and soft in the direction normal to the wave vector of the modulation, wash out the long-range order at finite temperatures, but support algebraically decaying long-range correlations. This implies that the phase can exhibit a quasi-one-dimensional order as in liquid crystals.

A future holographic screen is a hypersurface of indefinite signature, foliated by marginally trapped surfaces with area $A(r)$. We prove that $A(r)$ grows strictly monotonically. Future holographic screens arise in gravitational collapse. Past holographic screens exist in our own Universe; they obey an analogous area law. Both exist more broadly than event horizons or dynamical horizons. Working within classical general relativity, we assume the null curvature condition and certain generiticity conditions. We establish several nontrivial intermediate results. If a surface $\sigma$ divides a Cauchy surface into two disjoint regions, then a null hypersurface $N$ that contains $\sigma$ splits the entire spacetime into two disjoint portions: the future-and-interior, $K^{+}$; and the past-and-exterior, $K^{-}$. If a family of surfaces $\sigma (r)$ foliate a hypersurface, while flowing everywhere to the past or exterior, then the future-and-interior $K^{+}(r)$ grows monotonically under inclusion. If the surfaces $\sigma (r)$ are marginally trapped, we prove that the evolution must be everywhere to the past or exterior, and the area theorem follows. A thermodynamic interpretation as a second law is suggested by the Bousso bound, which relates $A(r)$ to the entropy on the null slices $N(r)$ foliating the spacetime. In a companion letter, we summarize the proof and discuss further implications.

We report an improved geoneutrino measurement with Borexino from 2056 days of data taking. The present exposure is $(5.5\pm 0.3)\times {10}^{31}\mathrm{proton}\times \mathrm{yr}$. Assuming a chondritic Th/U mass ratio of 3.9, we obtain ${23.7}_{-5.7}^{+6.5}(\text{stat}{)}_{-0.6}^{+0.9}(\text{sys})$ geoneutrino events. The null observation of geoneutrinos with Borexino alone has a probability of $3.6\times {10}^{-9}$ ($5.9\sigma$). A geoneutrino signal from the mantle is obtained at 98% C.L. The radiogenic heat production for U and Th from the present best-fit result is restricted to the range 23–36 TW, taking into account the uncertainty on the distribution of heat producing elements inside the Earth.

It is now possible to compute linear in mass-ratio terms in the post-Newtonian (PN) expansion for compact binaries to very high orders using linear black hole perturbation theory applied to various invariants. For instance, a computation of the redshift invariant of a point particle in a circular orbit about a black hole in linear perturbation theory gives the linear-in-mass-ratio portion of the binding energy of a circular binary with an arbitrary mass ratio. This binding energy, in turn, encodes the system’s conservative dynamics. We give a method for extracting the analytic forms of these post-Newtonian coefficients from high-accuracy numerical data using experimental mathematics techniques, notably an integer relation algorithm. Such methods should be particularly important when the calculations progress to the considerably more difficult case of perturbations of the Kerr metric. As an example, we apply this method to the redshift invariant in the Schwarzschild metric. Here, we obtain analytic coefficients to 12.5PN order and higher-order terms in mixed analytic-numerical form to 21.5PN, including analytic forms for the complete 13.5PN coefficient and all the logarithmic terms at 13PN. We have computed the individual modes to over 5000 digits, of which we use at most 1240 in the present calculation. At these high orders, an individual coefficient can have over 30 terms, including a wide variety of transcendental numbers, when written out in full. We are still able to obtain analytic forms for such coefficients from the numerical data through a careful study of the structure of the expansion. The structure we find also allows us to predict certain “leading logarithm”-type contributions to all orders. The additional terms in the expansion we obtain improve the accuracy of the PN series for the redshift observable, even in the very strong-field regime inside the innermost stable circular orbit, particularly when combined with exponential resummation.

A sterile neutrino of $\sim \mathrm{keV}$ mass is a well-motivated dark matter candidate. Its decay generates an x-ray line that offers a unique target for x-ray telescopes. For the first time, we use the Gamma-ray Burst Monitor (GBM) onboard the Fermi Gamma-Ray Space Telescope to search for sterile neutrino decay lines; our analysis covers the energy range 10–25 keV (sterile neutrino mass 20–50 keV), which is inaccessible to x-ray and gamma-ray satellites such as Chandra, Suzaku, XMM-Newton, and INTEGRAL. The extremely wide field of view of the GBM enables a large fraction of the Milky Way dark matter halo to be probed. After implementing careful data cuts, we obtain $\sim 53$ days of full-sky observational data. We observe an excess of photons towards the Galactic center, as expected from astrophysical emission. We search for sterile neutrino decay lines in the energy spectrum, and find no significant signal. From this, we obtain upper limits on the sterile neutrino mixing angle as a function of mass. In the sterile neutrino mass range 25–40 keV, we improve upon previous upper limits by approximately an order of magnitude. Better understanding of detector and astrophysical backgrounds, as well as detector response, will further improve the sensitivity of a search with the GBM.

Weak gravitational lensing allows one to reconstruct the spatial distribution of the projected mass density across the sky. These “mass maps” provide a powerful tool for studying cosmology as they probe both luminous and dark matter. In this paper, we present a weak lensing mass map reconstructed from shear measurements in a $139{\mathrm{deg}}^2$ area from the Dark Energy Survey (DES) science verification data. We compare the distribution of mass with that of the foreground distribution of galaxies and clusters. The overdensities in the reconstructed map correlate well with the distribution of optically detected clusters. We demonstrate that candidate superclusters and voids along the line of sight can be identified, exploiting the tight scatter of the cluster photometric redshifts. We cross-correlate the mass map with a foreground magnitude-limited galaxy sample from the same data. Our measurement gives results consistent with mock catalogs from $N$-body simulations that include the primary sources of statistical uncertainties in the galaxy, lensing, and photo-$z$ catalogs. The statistical significance of the cross-correlation is at the $6.8\sigma$ level with 20 arcminute smoothing. We find that the contribution of systematics to the lensing mass maps is generally within measurement uncertainties. In this work, we analyze less than 3% of the final area that will be mapped by the DES; the tools and analysis techniques developed in this paper can be applied to forthcoming larger data sets from the survey.

We propose a new class of dark matter models with unusual phenomenology. What is ordinary about our models is that dark matter particles are weakly interacting massive particles; they are weakly coupled to the standard model and have weak scale masses. What is unusual is that they come in multiplets of a new dark non-Abelian gauge group with milliweak coupling. The massless dark gluons of this dark gauge group contribute to the energy density of the Universe as a form of weakly self-interacting dark radiation. In this paper we explore the consequences of having (i) dark matter in multiplets, (ii) self-interacting dark radiation, and (iii) dark matter which is weakly coupled to dark radiation. We find that (i) dark matter cross sections are modified by multiplicity factors which have significant consequences for collider searches and indirect detection, and (ii) dark gluons have thermal abundances which affect the cosmic microwave background (CMB) as dark radiation. Unlike additional massless neutrino species the dark gluons are interacting and have vanishing viscosity and (iii) the coupling of dark radiation to dark matter represents a new mechanism for damping the large scale structure power spectrum. A combination of additional radiation and slightly damped structure is interesting because it can remove tensions between global $\mathrm{\Lambda }\mathrm{CDM}$ fits from the CMB and direct measurements of the Hubble expansion rate ($H_0$) and large scale structure (${\sigma }_8$).

Accretion disks around black holes radiate a significant fraction of the rest mass of the accreting material in the form of thermal radiation from within a few gravitational radii of the black hole ($r\lesssim 20GM/c^2$). In addition, the accreting matter may also be illuminated by hard x rays from the surrounding plasma which adds fluorescent transition lines to the emission. This radiation is emitted by matter moving along geodesics in the metric; therefore the strong Doppler and gravitational redshifts observed in the emission encode information about the strong gravitational field around the black hole. In this paper the possibility of using the x-ray emission as a strong field test of general relativity is explored by calculating the spectra for both the transition line and thermal emission from a thin accretion disk in a series of parametrically deformed Kerr metrics. In addition the possibility of constraining a number of known black hole spacetimes in alternative theories of gravity is also considered.

We study the analytic structure of partial-wave amplitudes derived from $u$- and $t$-channel exchange processes. The latter plays a crucial role in dispersion-theory approaches to coupled-channel systems that model final state interactions in QCD. A general spectral representation is established that is valid in the presence of anomalous thresholds, decaying particles or overlapping left-hand and right-hand cut structures as it occurs frequently in hadron physics. The results are illustrated at hand of ten specific processes.

We renormalize six-dimensional ${\varphi }^3$ theory in the modified minimal subtraction ($\overline{\mathrm{MS}}$) scheme at four loops. From the resulting $\beta$-function, anomalous dimension, and mass anomalous dimension, we compute four loop critical exponents relevant to the Lee–Yang edge singularity and percolation problems. Using resummation methods and information on the exponents of the relevant two-dimensional conformal field theory, we obtain estimates for exponents in dimensions 3, 4, and 5 which are in reasonable agreement with other techniques for these two problems. The renormalization group functions for the more general theory with an $O(N)$ symmetry are also computed in order to obtain estimates of exponents at various fixed points in five dimensions. Included in this $O(N)$ analysis is the full evaluation of the mass operator mixing matrix of anomalous dimensions at four loops. We show that its eigenexponents are in agreement with the mass exponents computed at $O(1/N^2)$ in the nonperturbative large $N$ expansion.

We systematically performed numerical-relativity simulations for black hole-neutron star (BH-NS) binary mergers with a variety of the BH spin orientation and nuclear-theory-based equations of state (EOS) of the NS. The initial misalignment angles of the BH spin measured from the direction of the orbital angular momentum are chosen in the range of $i_{\text{tilt},0}\approx 30°-90°$. We employed four models of nuclear-theory-based zero-temperature EOS for the NS in which the compactness of the NS is in the range of $\mathcal{C}=M_{\mathrm{NS}}/R_{\mathrm{NS}}=0.138-0.180$, where $M_{\mathrm{NS}}$ and $R_{\mathrm{NS}}$ are the mass and the radius of the NS, respectively. The mass ratio of the BH to the NS, $Q=M_{\mathrm{BH}}/M_{\mathrm{NS}}$, and the dimensionless spin parameter of the BH, $\chi$, are chosen to be $Q=5$ and $\chi =0.75$, together with $M_{\mathrm{NS}}=1.35M_{\odot }$ so that the BH spin misalignment has a significant effect on tidal disruption of the NS. We obtain the following results: (i) The inclination angles of $i_{\text{tilt},0}<70°$ and $i_{\text{tilt},0}<50°$ are required for the formation of a remnant disk with its mass larger than $0.1M_{\odot }$ for the cases $\mathcal{C}=0.140$ and $\mathcal{C}=0.160$, respectively, while the disk mass is always smaller than $0.1M_{\odot }$ for $\mathcal{C}\gtrsim 0.175$. The ejecta with its mass larger than $0.01M_{\odot }$ is obtained for $i_{\text{tilt},0}<85°$ with $\mathcal{C}=0.140$, for $i_{\text{tilt},0}<65°$ with $\mathcal{C}=0.160$, and for $i_{\text{tilt},0}<30°$ with $\mathcal{C}=0.175$. (ii) The rotational axis of the dense part of the remnant disk with its rest-mass density larger than ${10}^9\mathrm{g}/{\mathrm{cm}}^3$ is approximately aligned with the remnant BH spin for $i_{\text{tilt},0}\approx 30°$. On the other hand, the disk axis is misaligned initially with $\sim 30°$ for $i_{\text{tilt},0}\approx 60°$, and the alignment with the remnant BH spin is achieved at $\sim 50–60\mathrm{ms}$ after the onset of merger. The accretion time scale of the remnant disk is typically $\sim 100\mathrm{ms}$ and depends only weakly on the misalignment angle and the EOS. (iii) The ejecta velocity is typically $\sim 0.2–0.3c$ and depends only weakly on the misalignment angle and the EOS of the NS, while the morphology of the ejecta depends on its mass. (iv) The gravitational-wave spectra contains the information of the NS compactness in the cutoff frequency for $i_{\text{tilt},0}\lesssim 60°$.

We systematically calculate the relativistic corrections to the polarization variables of prompt $J/\psi$ photoproduction and hadroproduction using the factorization formalism of nonrelativistic QCD. Specifically, we include the ${{}^{3}S}_1^{[1]}$ and ${{}^{3}P}_J^{[1]}$ color-singlet and the ${{}^{3}S}_1^{[8]}$, ${{}^{1}S}_0^{[8]}$, and ${{}^{3}P}_J^{[8]}$ color-octet channels as well as the effects due to the mixing between the ${{}^{3}S}_1^{[8]}$ and ${{}^{3}D}_1^{[8]}$ channels. We provide all the squared hard-scattering amplitudes in analytic form. Assuming the nonrelativistic-QCD long-distance matrix elements to satisfy the velocity scaling rules, we find the relativistic corrections to be appreciable, especially at small transverse momentum $p_T$ and large inelasticity $z$. The results obtained here and in our previous work on the unpolarized yield [Phys. Rev. D 90, 014045 (2014)] will help to render global analyses of prompt $J/\psi$ production data more complete and hopefully to shed light on the $J/\psi$ polarization puzzle.