We calculate finite-$N_{\mathrm{c}}$ corrections to the next-to-leading order (NLO) Balitsky-Kovchegov (BK) equation. We find analytical expressions for the necessary correlators of six Wilson lines in terms of the two-point function using the Gaussian approximation. In a suitable basis, the problem reduces from the diagonalization of a six-by-six matrix to the diagonalization of a three-by-three matrix, which can easily be done analytically. We study numerically the effects of these finite-$N_{\mathrm{c}}$ corrections on the NLO BK equation. In general, we find that the finite-$N_{\mathrm{c}}$ corrections are smaller than the expected $1/N_{\mathrm{c}}^2\sim 10\%$. The corrections may be large for individual correlators, but have less of an influence on the shape of the amplitude as a function of the dipole size. They have an even smaller effect on the evolution speed as a function of rapidity.

We report results from searches for new physics with low-energy electronic recoil data recorded with the XENON1T detector. With an exposure of 0.65 tonne-years and an unprecedentedly low background rate of $76\pm 2_{\mathrm{stat}}\mathrm{events}/(\mathrm{tonne}\times \mathrm{year}\times \mathrm{keV})$ between 1 and 30 keV, the data enable one of the most sensitive searches for solar axions, an enhanced neutrino magnetic moment using solar neutrinos, and bosonic dark matter. An excess over known backgrounds is observed at low energies and most prominent between 2 and 3 keV. The solar axion model has a $3.4\sigma$ significance, and a three-dimensional 90% confidence surface is reported for axion couplings to electrons, photons, and nucleons. This surface is inscribed in the cuboid defined by $g_{\mathrm{ae}}<3.8\times {10}^{-12}$, $g_{\mathrm{ae}}{g}_{\mathrm{an}}^{\mathrm{eff}}<4.8\times {10}^{-18}$, and $g_{\mathrm{ae}}{g}_{\mathrm{a}\mathrm{\gamma }}<7.7\times {10}^{-22}{\mathrm{GeV}}^{-1}$, and excludes either $g_{\mathrm{ae}}=0$ or $g_{\mathrm{ae}}{g}_{\mathrm{a}\mathrm{\gamma }}=g_{\mathrm{ae}}{g}_{\mathrm{an}}^{\mathrm{eff}}=0$. The neutrino magnetic moment signal is similarly favored over background at $3.2\sigma$, and a confidence interval of ${\mu }_{\nu }\in (1.4,2.9)\times {10}^{-11}{\mu }_B$ (90% C.L.) is reported. Both results are in strong tension with stellar constraints. The excess can also be explained by $\beta$ decays of tritium at $3.2\sigma$ significance with a corresponding tritium concentration in xenon of $(6.2\pm 2.0)\times {10}^{-25}\mathrm{mol}/\mathrm{mol}$. Such a trace amount can neither be confirmed nor excluded with current knowledge of its production and reduction mechanisms. The significances of the solar axion and neutrino magnetic moment hypotheses are decreased to $2.0\sigma$ and $0.9\sigma$, respectively, if an unconstrained tritium component is included in the fitting. With respect to bosonic dark matter, the excess favors a monoenergetic peak at $(2.3\pm 0.2)\mathrm{keV}$ (68% C.L.) with a $3.0\sigma$ global ($4.0\sigma$ local) significance over background. This analysis sets the most restrictive direct constraints to date on pseudoscalar and vector bosonic dark matter for most masses between 1 and $210\mathrm{keV}/{\mathrm{c}}^2$. We also consider the possibility that ${}^{37}\mathrm{Ar}$ may be present in the detector, yielding a 2.82 keV peak from electron capture. Contrary to tritium, the ${}^{37}\mathrm{Ar}$ concentration can be tightly constrained and is found to be negligible.

Primordial black holes (PBH), produced through a variety of processes in the early universe, could fill galactic halos accounting for a fraction or the totality of the dark matter. In particular, PBH with substellar masses could be captured by stars, start to swallow their material, and eventually turn them into BH, hence originating a peculiar new type of stellar catastrophic event. Here we revisit this process in the most favorable case of PBH capture by neutron stars. We detail a number of novel features in the capture phase, during the settling within the star and mass growth of the PBH, and illustrate some phenomenological consequences. In particular, we point out that in the subsonic regime the PBH drag takes the form of a Bondi accretion. As a result, the onset of the final transmutation of the NS into a stellar sized BH is expected with the PBH seed in slight off-center position. We also compute the gravitational wave energy-loss and signals associated to different phases of the PBH-stellar interaction. In particular, the emission associated to the accretion phase is periodic with a few kHz frequency; in the rare case of a nearby Galactic event and for light PBH, it could constitute a warning of the forthcoming transmutation.

We present a search for anisotropic cosmic birefringence in $500{\mathrm{deg}}^2$ of southern sky observed at 150 GHz with the SPTpol camera on the South Pole Telescope. We reconstruct a map of cosmic polarization rotation anisotropies using higher-order correlations between the observed cosmic microwave background (CMB) $E$ and $B$ fields. We then measure the angular power spectrum of this map, which is found to be consistent with zero. The nondetection is translated into an upper limit on the amplitude of the scale-invariant cosmic rotation power spectrum, $L(L+1)C_L^{\alpha \alpha }/2\pi <0.10\times {10}^{-4}{\mathrm{rad}}^2$ ($0.033{\mathrm{deg}}^2$, 95% C.L.). This upper limit can be used to place constraints on the strength of primordial magnetic fields, $B_{1\mathrm{Mpc}}<17\mathrm{nG}$ (95% C.L.), and on the coupling constant of the Chern-Simons electromagnetic term $g_{a\gamma }<4.0\times {10}^{-2}/H_I$ (95% C.L.), where $H_I$ is the inflationary Hubble scale. For the first time, we also cross-correlate the CMB temperature fluctuations with the reconstructed rotation angle map, a signal expected to be nonvanishing in certain theoretical scenarios, and find no detectable signal. We perform a suite of systematics and consistency checks and find no evidence for contamination.

We report in detail on searches for eV-scale sterile neutrinos, in the context of a $3+1$ model, using eight years of data from the IceCube Neutrino Telescope. By analyzing the reconstructed energies and zenith angles of 305,735 atmospheric ${\nu }_{\mu }$ and ${\overline{\nu }}_{\mu }$ events we construct confidence intervals in two analysis spaces: ${\sin }^2(2{\theta }_{24})$ vs $\mathrm{\Delta }{m}_{41}^2$ under the conservative assumption ${\theta }_{34}=0$; and ${\sin }^2(2{\theta }_{24})$ vs ${\sin }^2(2{\theta }_{34})$ given sufficiently large $\mathrm{\Delta }{m}_{41}^2$ that fast oscillation features are unresolvable. Detailed discussions of the event selection, systematic uncertainties, and fitting procedures are presented. No strong evidence for sterile neutrinos is found, and the best-fit likelihood is consistent with the no sterile neutrino hypothesis with a $p$ value of 8% in the first analysis space and 19% in the second.

We define the “kink transform” as a one-sided boost of bulk initial data about the Ryu-Takayanagi surface of a boundary cut. For a flat cut, we conjecture that the resulting Wheeler-DeWitt patch is the bulk dual to the boundary state obtained by the Connes cocycle (CC) flow across the cut. The bulk patch is glued to a precursor slice related to the original boundary slice by a one-sided boost. This evades ultraviolet divergences and distinguishes our construction from a one-sided modular flow. We verify that the kink transform is consistent with known properties of operator expectation values and subregion entropies under CC flow. CC flow generates a stress tensor shock at the cut, controlled by a shape derivative of the entropy; the kink transform reproduces this shock holographically by creating a bulk Weyl tensor shock. We also go beyond known properties of CC flow by deriving novel shock components from the kink transform.

The gravitomagnetic tidal Love number of a slowly rotating body was calculated previously under the assumption that the velocity perturbation created by the tidal field consists of an induction piece proportional to the vector potential, and a rotational piece that scales with $\mathrm{\Omega }$, the body’s angular velocity. The second part of this assumption is wrong: the rotational piece of the velocity perturbation scales in fact like ${\mathrm{\Omega }}^0=1$. The previous calculations are therefore incorrect, and the purpose of this paper is to repair the mistake. To keep the technical difficulties to a minimum, the treatment here is restricted to a post-Newtonian expansion carried out to leading order—previous calculations of the gravitomagnetic Love number were performed in full general relativity. On the other hand, the computation presented here is not restricted to a stationary tidal field. I show that the correct scaling of the velocity perturbation with $\mathrm{\Omega }$ leads to the promotion of the Love number to a Love tensor ${k_{jk}}^{pq}$, a four-index object that relates the body’s current quadrupole moment $S_{jk}$ to the gravitomagnetic tidal moment ${\mathcal{B}}_{pq}$. The tensorial nature of this quantity has to do with the fact that each $e^{im\varphi }$ piece of the tidal force gives rise to an $m$-specific velocity perturbation and therefore to a Love number that depends on $m$. The collection of these $m$-specific Love numbers makes up the Love tensor ${k_{jk}}^{pq}$.

We present a lattice QCD calculation of the $\mathrm{\Delta }I=1/2$, $K\to \pi \pi$ decay amplitude $A_0$ and ${ϵ}^{\prime }$, the measure of direct $CP$ violation in $K\to \pi \pi$ decay, improving our 2015 calculation [1] of these quantities. Both calculations were performed with physical kinematics on a ${32}^3\times 64$ lattice with an inverse lattice spacing of $a^{-1}=1.3784(68)\mathrm{GeV}$. However, the current calculation includes nearly 4 times the statistics and numerous technical improvements allowing us to more reliably isolate the $\pi \pi$ ground state and more accurately relate the lattice operators to those defined in the standard model. We find $\mathrm{Re}(A_0)=2.99(0.32)(0.59)\times {10}^{-7}\mathrm{GeV}$ and $\mathrm{Im}(A_0)=-6.98(0.62)(1.44)\times {10}^{-11}\mathrm{GeV}$, where the errors are statistical and systematic, respectively. The former agrees well with the experimental result $\mathrm{Re}(A_0)=3.3201(18)\times {10}^{-7}\mathrm{GeV}$. These results for $A_0$ can be combined with our earlier lattice calculation of $A_2$ [2] to obtain $\mathrm{Re}({ϵ}^{\prime }/ϵ)=21.7(2.6)(6.2)(5.0)\times {10}^{-4}$, where the third error represents omitted isospin breaking effects, and $\mathrm{Re}(A_0)/\mathrm{Re}(A_2)=19.9(2.3)(4.4)$. The first agrees well with the experimental result of $\mathrm{Re}({ϵ}^{\prime }/ϵ)=16.6(2.3)\times {10}^{-4}$. A comparison of the second with the observed ratio $\mathrm{Re}(A_0)/\mathrm{Re}(A_2)=22.45(6)$, demonstrates the standard model origin of this “$\mathrm{\Delta }I=1/2$ rule” enhancement.

We report a measurement of the energy spectrum of cosmic rays for energies above $2.5\times {10}^{18}\mathrm{eV}$ based on 215,030 events recorded with zenith angles below 60°. A key feature of the work is that the estimates of the energies are independent of assumptions about the unknown hadronic physics or of the primary mass composition. The measurement is the most precise made hitherto with the accumulated exposure being so large that the measurements of the flux are dominated by systematic uncertainties except at energies above $5\times {10}^{19}\mathrm{eV}$. The principal conclusions are

(1) The flattening of the spectrum near $5\times {10}^{18}\mathrm{eV}$, the so-called “ankle,” is confirmed.

(2) The steepening of the spectrum at around $5\times {10}^{19}\mathrm{eV}$ is confirmed.

(3) A new feature has been identified in the spectrum: in the region above the ankle the spectral index $\gamma$ of the particle flux ($\propto E^{-\gamma }$) changes from $2.51\pm 0.03(\mathrm{stat})\pm 0.05(\mathrm{syst})$ to $3.05\pm 0.05(\mathrm{stat})\pm 0.10(\mathrm{syst})$ before changing sharply to $5.1\pm 0.3(\mathrm{stat})\pm 0.1(\mathrm{syst})$ above $5\times {10}^{19}\mathrm{eV}$.

(4) No evidence for any dependence of the spectrum on declination has been found other than a mild excess from the Southern Hemisphere that is consistent with the anisotropy observed above $8\times {10}^{18}\mathrm{eV}$.

The stochastic cosmological gravitational-wave background (CGWB) provides a direct window to study early universe phenomena and fundamental physics. With the proposed third-generation ground-based gravitational wave detectors, Einstein Telescope (ET) and Cosmic Explorer (CE), we might be able to detect evidence of a CGWB. However, to dig out these prime signals would be a difficult quest as the dominance of the astrophysical foreground from compact-binary coalescence (CBC) will mask this CGWB. In this paper, we study a subtraction-noise projection method, making it possible to reduce the residuals left after subtraction of the astrophysical foreground of CBCs, greatly improving our chances to detect a cosmological background. We carried out our analysis based on simulations of ET and CE and using posterior sampling for the parameter estimation of binary black-hole mergers. We demonstrate the sensitivity improvement of stochastic gravitational-wave searches and conclude that the ultimate sensitivity of these searches will not be limited by residuals left when subtracting the estimated BBH foreground, but by the fraction of the astrophysical foreground that cannot be detected even with third-generation instruments, or possibly by other signals not included in our analysis. We also resolve previous misconceptions of residual noise in the context of Gaussian parameter estimation.

We report the observation of gravitational waves from a binary-black-hole coalescence during the first two weeks of LIGO’s and Virgo’s third observing run. The signal was recorded on April 12, 2019 at 05∶30∶44 UTC with a network signal-to-noise ratio of 19. The binary is different from observations during the first two observing runs most notably due to its asymmetric masses: a $\sim 30M_{\odot }$ black hole merged with a $\sim 8M_{\odot }$ black hole companion. The more massive black hole rotated with a dimensionless spin magnitude between 0.22 and 0.60 (90% probability). Asymmetric systems are predicted to emit gravitational waves with stronger contributions from higher multipoles, and indeed we find strong evidence for gravitational radiation beyond the leading quadrupolar order in the observed signal. A suite of tests performed on GW190412 indicates consistency with Einstein’s general theory of relativity. While the mass ratio of this system differs from all previous detections, we show that it is consistent with the population model of stellar binary black holes inferred from the first two observing runs.

In this paper we have considered the 3D Ising model perturbed with the energy operator coupled with a nonuniform harmonic potential acting as a trap, showing that this system satisfies the trap-size scaling behavior. Eventually, we have computed the correlators $⟨\sigma (z)\sigma (0)⟩$, $⟨\epsilon (z)\epsilon (0)⟩$ and $⟨\sigma (z)\epsilon (0)⟩$ near the critical point by means of conformal perturbation theory. Combining this result with Monte Carlo simulations, we have been able to estimate the OPE coefficients $C_{\sigma \epsilon }^{\sigma }$, $C_{\sigma \sigma }^{\epsilon }$ and $C_{\epsilon \epsilon }^{\epsilon }$, finding a good agreement with the values obtained in [G. Costagliola, Phys. Rev. D 93, 066008 (2016), F. Kos, D. Poland, D. Simmons-Duffin, and A. Vichi, J. High Energy Phys. 08 (2016) 036].

Current cosmological data exhibit a tension between inferences of the Hubble constant, $H_0$, derived from early and late-Universe measurements. One proposed solution is to introduce a new component in the early Universe, which initially acts as “early dark energy” (EDE), thus decreasing the physical size of the sound horizon imprinted in the cosmic microwave background (CMB) and increasing the inferred $H_0$. Previous EDE analyses have shown this model can relax the $H_0$ tension, but the CMB-preferred value of the density fluctuation amplitude, ${\sigma }_8$, increases in EDE as compared to $\mathrm{\Lambda }$ cold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$), increasing tension with large-scale structure (LSS) data. We show that the EDE model fit to CMB and SH0ES data yields scale-dependent changes in the matter power spectrum compared to $\mathrm{\Lambda }\mathrm{CDM}$, including 10% more power at $k=1\mathrm{h}/\mathrm{Mpc}$. Motivated by this observation, we reanalyze the EDE scenario, considering LSS data in detail. We also update previous analyses by including Planck 2018 CMB likelihoods, and perform the first search for EDE in Planck data alone, which yields no evidence for EDE. We consider several data set combinations involving the primary CMB, CMB lensing, supernovae, baryon acoustic oscillations, redshift-space distortions, weak lensing, galaxy clustering, and local distance-ladder data (SH0ES). While the EDE component is weakly detected ($3\sigma$) when including the SH0ES data and excluding most LSS data, this drops below $2\sigma$ when further LSS data are included. Further, this result is in tension with strong constraints imposed on EDE by CMB and LSS data without SH0ES, which show no evidence for this model. We also show that physical priors on the fundamental scalar field parameters further weaken evidence for EDE. We conclude that the EDE scenario is, at best, no more likely to be concordant with all current cosmological data sets than $\mathrm{\Lambda }\mathrm{CDM}$, and appears unlikely to resolve the $H_0$ tension.

We analyze the evolution of hydrodynamic fluctuations for QCD matter below $T_c$ in the chiral limit, where the pions (the Goldstone modes) must be treated as additional non-Abelian superfluid degrees of freedom, reflecting the broken $S{U}_L(2)\times S{U}_R(2)$ symmetry of the theory. In the presence of a finite pion mass $m_{\pi }$, the hydrodynamic theory is ordinary hydrodynamics at long distances, and superfluidlike at short distances. The presence of the superfluid degrees of freedom then gives specific contributions to the bulk viscosity, the shear viscosity, and diffusion coefficients of the ordinary theory at long distances which we compute. This determines, in some cases, the leading dependence of the transport parameters of QCD on the pion mass. We analyze the predictions of this computation, as the system approaches the $O(4)$ critical point.

We study superpotentials from worldsheet instantons in heterotic Calabi-Yau compactifications for vector bundles constructed from line bundle sums, monads, and extensions. Within a certain class of manifolds and for certain second homology classes, we derive simple necessary conditions for a nonvanishing instanton superpotential. These show that nonvanishing instanton superpotentials are rare and require a specific pattern for the bundle construction. For the class of monad and extension bundles with this pattern, we derive a sufficient criterion for nonvanishing instanton superpotentials based on an affine Hilbert function. This criterion shows that a nonzero instanton superpotential is common within this class. The criterion can be checked using commutative algebra methods only and depends on the topological data defining the Calabi-Yau $X$ and the vector bundle $V$.

We present results of the first lattice QCD calculations of $B_c\to B_s$ and $B_c\to B_d$ weak matrix elements. Form factors across the entire physical $q^2$ range are then extracted and extrapolated to the physical-continuum limit before combining with Cabbibo-Kobayashi-Maskawa (CKM) matrix elements to predict the semileptonic decay rates $\mathrm{\Gamma }(B_c^{+}\to B_s^0\overline{\ell }{\nu }_{\ell })=52.4(2.5)\times {10}^9{\mathrm{s}}^{-1}$ and $\mathrm{\Gamma }(B_c^{+}\to B^0\overline{\ell }{\nu }_{\ell })=3.10(21)\times {10}^9{\mathrm{s}}^{-1}$. The lattice QCD uncertainty is comparable to the CKM uncertainty here. Results are derived from correlation functions computed on MILC Collaboration gauge configurations with a range of lattice spacings including $2+1+1$ flavors of dynamical sea quarks in the highly improved staggered quark (HISQ) formalism. HISQ is also used for the propagators of the valence light, strange, and charm quarks. Two different formalisms are employed for the bottom quark: nonrelativistic QCD (NRQCD) and heavy-HISQ. Checking agreement between these two approaches is an important test of our strategies for heavy quarks on the lattice. From chained fits of NRQCD and heavy-HISQ data, we obtain the differential decay rates $d\mathrm{\Gamma }/d{q}^2$ as well as integrated values for comparison to future experimental results.

Astrometric weak gravitational lensing is a powerful probe of the distribution of matter on sub-Galactic scales, which harbor important information about the fundamental nature of dark matter. We propose a novel method that utilizes angular power spectra to search for the correlated pattern of apparent motions of celestial objects induced from time-dependent lensing by a population of Galactic subhalos. Application of this method to upcoming astrometric datasets will allow for the direct measurement of the properties of Galactic substructure, with implications for the underlying particle physics. We show that, with near-future astrometric observations, it may be possible to statistically detect populations of cold dark matter subhalos, compact objects, as well as density fluctuations sourced by scalar field dark matter. Currently unconstrained parameter space will already be accessible using upcoming data from the ongoing Gaia mission.

Using the new methodology introduced in a recent paper [D. Bini, T. Damour, and A. Geralico, Phys. Rev. Lett. 123, 231104 (2019)], we present the details of the computation of the conservative dynamics of gravitationally interacting binary systems at the fifth post-Newtonian (5PN) level, together with its extension at the fifth-and-a-half post-Newtonian level. We present also the sixth post-Newtonian (6PN) contribution to the third-post-Minkowskian (3PM) dynamics. Our strategy combines several theoretical formalisms: post-Newtonian, post-Minkowskian, multipolar-post-Minkowskian, gravitational self-force, effective one-body, and Delaunay averaging. We determine the full functional structure of the 5PN Hamiltonian (which involves 95 nonzero numerical coefficients), except for two undetermined coefficients proportional to the cube of the symmetric mass ratio, and to the fifth and sixth power of the gravitational constant, $G$. We present not only the 5PN-accurate, 3PM contribution to the scattering angle but also its 6PN-accurate generalization. Both results agree with the corresponding truncations of the recent 3PM result of Bern et al. [Z. Bern, C. Cheung, R. Roiban, C. H. Shen, M. P. Solon, and M. Zeng, Phys. Rev. Lett. 122, 201603 (2019)]. We also compute the 5PN-accurate, fourth-post-Minkowskian (4PM) contribution to the scattering angle, including its nonlocal contribution, thereby offering checks for future 4PM calculations. We point out a remarkable hidden simplicity of the gauge-invariant functional relation between the radial action and the effective-one-body energy and angular momentum.

Using a recently introduced method [D. Bini, T. Damour, and A. Geralico, Phys. Rev. Lett. 123, 231104 (2019)], which splits the conservative dynamics of gravitationally interacting binary systems into a nonlocal-in-time part and a local-in-time one, we compute the local part of the dynamics at the sixth post-Newtonian (6PN) accuracy. Our strategy combines several theoretical formalisms: post-Newtonian, post-Minkowskian, multipolar-post-Minkowskian, effective-field-theory, gravitational self-force, effective one-body, and Delaunay averaging. The full functional structure of the local 6PN Hamiltonian (which involves 151 numerical coefficients) is derived, but contains four undetermined numerical coefficients. Our 6PN-accurate results are complete at orders $G^3$ and $G^4$, and the derived $O(G^3)$ scattering angle agrees, within our 6PN accuracy, with the computation of [Z. Bern, C. Cheung, R. Roiban, C. H. Shen, M. P. Solon, and M. Zeng, Phys. Rev. Lett. 122, 201603 (2019)]. All our results are expressed in several different gauge-invariant ways. We highlight, and make a crucial use of, several aspects of the hidden simplicity of the mass-ratio dependence of the two-body dynamics.

New structural properties of post-Minkowskian (PM) gravity are derived, notably within its effective one body (EOB) formulation. Our results concern both the mass dependence, and the high-energy behavior, of the classical scattering angle. We generalize our previous work by deriving, up to the fourth post-Minkowskian (4PM) level included, the explicit links between the scattering angle and the two types of potentials entering the Hamiltonian description of PM dynamics within EOB theory. We compute the scattering amplitude derived from quantizing the third post-Minkowskian (3PM) EOB radial potential (including the contributions coming from the Born iterations), and point out various subtleties in the relation between perturbative amplitudes and classical dynamics. We highlight an apparent tension between the classical 3PM dynamics derived by Bern et al. [Phys. Rev. Lett. 122, 201603 (2019)], and previous high-energy self-force results [Phys. Rev. D 86, 104041 (2012)], and propose several possible resolutions of this tension. We point out that linear-in-mass-ratio self-force computations can give access to the exact 3PM and 4PM dynamics.