We revisit a double-scaled limit of the superconformal index of $\mathcal{N}=2$ superconformal field theories (SCFTs) which generalizes the Schur index. The resulting partition function, $\widehat{\mathcal{Z}}(q,\alpha )$, has a standard $q$-expansion with coefficients depending on a continuous parameter $\alpha$. The Schur index is a special case with $\alpha =1$. Through explicit computations we argue that this partition function is an invariant of certain mass deformations and vacuum expectation value (vev) deformations of the SCFT. In particular, two SCFTs residing in different corners of the same Coulomb branch, satisfying certain restrictive conditions, have the same partition function with a nontrivial map of the parameters, ${\widehat{\mathcal{Z}}}_1(q,{\alpha }_1)={\widehat{\mathcal{Z}}}_2(q,{\alpha }_2({\alpha }_1))$. For example, we show that the Schur index of all the SCFTs in the Deligne-Cvitanović series is given by special values of $\alpha$ of the partition function of the $\mathrm{SU}(2)N_f=4$ $\mathcal{N}=2$ SQCD.

Baryon acoustic oscillation (BAO) measurements play a key role in ruling out postrecombination solutions to the Hubble tension. However, because the data compression leading to these measurements assumes a fiducial $\mathrm{\Lambda }\mathrm{CDM}$ cosmology, their reliability in testing late-time modifications to $\mathrm{\Lambda }\mathrm{CDM}$ has at times been called into question. We play devil’s advocate and posit that fiducial cosmology assumptions do indeed affect BAO measurements in such a way that low-redshift acoustic angular scales (proportional to the Hubble constant $H_0$) are biased low and test whether such a rescaling can rescue postrecombination solutions. The answer is no. First, strong constraints on the shape of the $z\lesssim 2$ expansion history from unanchored Type Ia Supernovae (SNeIa) prevent large deviations from $\mathrm{\Lambda }\mathrm{CDM}$. In addition, unless ${\mathrm{\Omega }}_m$ is significantly lower than 0.3, the rescaled BAO measurements would be in strong tension with geometrical information from the cosmic microwave background. We demonstrate this explicitly on several dark energy (DE) models ($w\mathrm{CDM}$, CPL DE, phenomenologically emergent DE, holographic DE, ${\mathrm{\Lambda }}_s\mathrm{CDM}$, and the negative cosmological constant model), finding that none can address the Hubble tension once unanchored SNeIa are included. We argue that the ${\mathrm{\Lambda }}_s\mathrm{CDM}$ sign-switching cosmological constant model possesses interesting features which make it the least unpromising one among those tested. Our results demonstrate that possible fiducial cosmology-induced BAO biases cannot be invoked as loopholes to the Hubble tension “no-go theorem”, and highlight the extremely important but so far underappreciated role of unanchored SNeIa in ruling out postrecombination solutions.

We investigate the impact of residual annihilation from sub-GeV mass thermal relic dark matter candidates during big bang nucleosynthesis (BBN). Focusing on candidates with $p$-wave annihilation channels, we show that the hadronic injection of pions and kaons beyond freeze-out, and their subsequent interaction with protons and neutrons prior to the deuterium bottleneck, provides a sensitivity to annihilation that surpasses that of the cosmic microwave background (CMB) and indirect detection in the galaxy.

We compute the classical one-loop gravitational Compton amplitude describing the scattering of a graviton off a massive spinning compact object at the second post-Minkowskian order, including terms through the quartic order in spin. Our analysis includes spin-induced finite-size effects up to the hexadecapolar order and extends recent results obtained for minimal couplings at the quadratic order in spin. From the amplitude, we determine the scattering phase in momentum space, applicable in both the eikonal and wave regimes. In the eikonal limit, we then isolate the spin-independent contribution of the graviton field, explicitly linking it to the dynamics of a massless scalar probe in a Kerr background. This constitutes the first complete description of classical one-loop Compton scattering for generic spinning compact objects at the second post-Minkowskian and hexadecapolar orders.

We construct an exact analytic solution of the revised small-$x$ helicity evolution equations from Borden, Kovchegov, and Li [Helicity evolution at small x: Quark to gluon and gluon to quark transition operators, J. High Energy Phys. 09 (2024) 037], where the contributions of the quark-to-gluon and gluon-to-quark transition operators were newly included. These evolution equations are written in the large-$N_c$ and -$N_f$ limit and are double-logarithmic, resumming powers of ${\alpha }_s{\ln }^2(1/x)$. Here $N_c$ and $N_f$ are the numbers of quark colors and flavors, respectively, while ${\alpha }_s$ is the strong coupling constant and $x$ is the Bjorken-$x$ variable. Using our solution, we obtain analytic, small-$x$, large-$N_c$ and -$N_f$ expressions for the flavor singlet quark and gluon helicity parton distribution functions (PDFs) and for the $g_1$ structure function as double-inverse Laplace transforms. We also extract analytic expressions for the eigenvalues of the matrix of polarized Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) anomalous dimensions and, subsequently, analytic expressions for each of the four individual polarized anomalous dimensions themselves ($\mathrm{\Delta }{\gamma }_{qq},\mathrm{\Delta }{\gamma }_{qG},\mathrm{\Delta }{\gamma }_{Gq}$, and $\mathrm{\Delta }{\gamma }_{GG}$): these expressions resum powers of ${\alpha }_s/{\omega }^2$ to all orders at large $N_c$ and $N_f$ (with $\omega$ the Mellin moment variable). We extract the leading small-$x$ asymptotic power-law growth of the helicity distributions, given by $\mathrm{\Delta }\mathrm{\Sigma }(x,Q^2)\sim \mathrm{\Delta }G(x,Q^2)\sim g_1(x,Q^2)\sim {(\frac{1}{x})}^{{\alpha }_h}$, where the intercept ${\alpha }_h$ satisfies an algebraic equation. Although the algebraic complexity of the equation prevented us from obtaining a general analytic expression for ${\alpha }_h$, we determine ${\alpha }_h$ numerically for various values of $N_c$ and $N_f$ (and, for the special case of $N_f=2N_c$, we determine ${\alpha }_h$ analytically). We further obtain the explicit asymptotic expressions for the helicity distributions, which yield numerical values for the ratio of the gluon helicity PDF to the flavor singlet quark helicity PDF in the small-$x$ asymptotic limit (for different $N_f/N_c$). Just as for the analytic solution to small-$x$ helicity evolution equations in the large-$N_c$ limit constructed in Borden and Kovchegov [Analytic solution for the revised helicity evolution at small x and large ${\mathrm{N}}_c$: New resummed gluon-gluon polarized anomalous dimension and intercept, Phys. Rev. D 108, 014001 (2023)] and for the iterative solution to the large-$N_c$ and -$N_f$ helicity evolution equations constructed in Borden, Kovchegov, and Li [Helicity evolution at small x: Quark to gluon and gluon to quark transition operators, J. High Energy Phys. 09 (2024) 037], we again find that all our predictions for polarized DGLAP anomalous dimensions are fully consistent with the existing finite-order calculations. Similar to the large-$N_c$ case [Borden and Kovchegov, Analytic solution for the revised helicity evolution at small x and large ${\mathrm{N}}_c$: New resummed gluon-gluon polarized anomalous dimension and intercept, Phys. Rev. D 108, 014001 (2023)], our intercept ${\alpha }_h$ (evaluated at various $N_c$ and $N_f$ values) exhibits a very slight disagreement with the predictions made within the infrared evolution equations framework in Bartels et al. [Flavor singlet contribution to the structure function G(1) at small x, Z. Phys. C 72, 627 (1996)], Blümlein and Vogt [The singlet contribution to the structure function $g_1(x,Q^2)$ at small $x$, Phys. Lett. B 386, 350 (1996)], Boussarie et al. [Proton spin structure at small-$x$, Phys. Lett. B 797, 134817 (2019)].

We review lattice results related to pion, kaon, $D$-meson, $B$-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $f_{+}(0)$ arising in the semileptonic $K\to \pi$ transition at zero momentum transfer, as well as the decay-constant ratio $f_K/f_{\pi }$ and its consequences for the Cabibbo–Kobayashi–Maskawa (CKM) matrix elements $V_{us}$ and $V_{ud}$. We review the determination of the $B_K$ parameter of neutral kaon mixing as well as the additional four $B$ parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $m_c$ and $m_b$ as well as those for the decay constants, form factors, and mixing parameters of charmed and bottom mesons and baryons. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant ${\alpha }_s$. We review the determinations of nucleon charges from the matrix elements of both isovector and flavor-diagonal axial, scalar and tensor local quark bilinears, and momentum fraction, helicity moment and the transversity moment from one-link quark bilinears. We also review determinations of scale-setting quantities. Finally, in this review we have added a new section on the general definition of the low-energy limit of the Standard Model.

This paper reports world averages of measurements of $b$-hadron, $c$-hadron, and $\tau$-lepton properties obtained by the Heavy Flavor Averaging Group using results available before October 2023. In rare cases, significant results obtained several months later are also used. For the averaging, common input parameters used in the various analyses are adjusted (rescaled) to common values, and known correlations are taken into account. The averages include branching fractions, lifetimes, neutral meson mixing parameters, $CP$ violation parameters, parameters of semileptonic decays, and Cabibbo-Kobayashi-Maskawa matrix elements.

We study the dynamical excitation of quasinormal modes (QNMs) through the plunge, merger and ringdown of an extreme-mass-ratio-inspiral into a Schwarzschild black hole, for generic orbital configurations. We work out the QNM causality condition, crucial to eliminate amplitude divergences and to incorporate horizon redshift effects. We then use it to derive a model of the time-dependent QNM excitation via a Green’s function approach, driven by the point-particle source on a given trajectory. Our model predicts that: (i) QNMs propagates along hyperboloidal slices in the minimal gauge; (ii) the signal is composed of an “activation” term, depending on the source past history, and a local “impulsive” term; (iii) amplitudes grow in time in an “activation function” fashion, and the waveform displays a stationary ringdown regime at times $\sim 10–20M$ after its peak; (iv) at these late times, an infinite tower of nonoscillatory, exponentially damped terms appear: the redshift terms. The model is in good agreement with numerical solutions, capturing the main waveform features after the peak. Additional components of the Green’s function are required to complement the QNM description and reproduce the plunge-merger waveform. We predict the late-time, stationary amplitude of the quadrupolar mode as a function of eccentricity, in agreement with accurate numerical solutions, marking the first time that QNM amplitudes are predicted for generic binary configurations. Our work provides a first solid step toward analytically modeling the inspiral’s imprint onto ringdown signals, generalizable to include higher orders in the mass ratio, black hole spin, nonvacuum configurations and corrections to the Einstein-Hilbert action.

The second data release (DR2) of the Dark Energy Spectroscopic Instrument (DESI), containing data from the first three years of observations, doubles the number of Lyman-$\alpha$ ($\mathrm{Ly}\alpha$) forest spectra in DR1 and it provides the largest dataset of its kind. To ensure a robust validation of the baryonic acoustic oscillation (BAO) analysis using $\mathrm{Ly}\alpha$ forests, we have made significant updates compared to DR1 to both the mocks and the analysis framework used in the validation. In particular, we present CoLoRe-QL, a new set of $\mathrm{Ly}\alpha$ mocks that use a quasilinear input power spectrum to incorporate the nonlinear broadening of the BAO peak. We have also increased the number of realizations used in the validation to 400, compared to the 150 realizations used in DR1. Finally, we present a detailed study of the impact of quasar redshift errors on the BAO measurement, and we compare different strategies to mask damped Lyman-$\alpha$ absorbers in our spectra. The BAO measurement from the $\mathrm{Ly}\alpha$ dataset of DESI DR2 is presented in a companion publication.

In this work, we explore the range of validity of the semiclassical approximation of a quantum master equation designed to describe the $c\overline{c}$ dynamics in a quark-gluon plasma at various temperatures, in the quantum Brownian regime. We perform a comparative study of various properties, e.g., the charmonia yield, of the Wigner density obtained both with the Lindblad equation and with the associated semiclassical Fokker-Planck equation. The semiclassical description is found to reproduce with a remarkable accuracy the results obtained through the full quantum description. We show that, to a large extent, this can be attributed to the nonunitary components of the dynamics that result from the contact of the $c\overline{c}$ subsystem with the thermal quark-gluon bath, leading to a rapid classicalization of the subsystem.

Gravitational waves propagating across gravitational potentials undergo lensing effects that, in the wave-optics regime, manifest as frequency-dependent amplitude and phase modulations. In this work, we revisit the diffraction integral formalism of gravitational lensing and demonstrate that it admits a natural and transparent interpretation within the framework of scattering theory. We establish a direct correspondence between the lensing amplification factor and the scattering amplitude of waves propagating in curved spacetime, clarifying how familiar lensing limits map onto distinct scattering regimes. In particular, we show that the diffraction integral matches exactly the eikonal limit of the scattering amplitude at lowest post-Minkowskian order, after a change in coordinates and the inclusion of finite-distance effects. We further extend the standard formalism by including subleading corrections to the post-Minkowskian and eikonal approximations. Our results provide a unified theoretical framework for the interpretation of lensed gravitational-wave signals and open the way to more accurate waveform modeling for future lensed observations.

Neutrinos are produced during stellar evolution by means of thermal and thermonuclear processes. We model the cumulative neutrino flux expected at Earth from all stars in the Milky Way: the Galactic stellar neutrino flux ($\mathrm{GS}\nu \mathrm{F}$). We account for the star formation history of our Galaxy and reconstruct the spatial distribution of Galactic stars by means of a random sampling procedure based on Gaia Data Release 2. We use the stellar evolution code mesa to compute the neutrino emission for a suite of stellar models with solar metallicity and zero-age-main-sequence mass between $0.08M_{\odot }$ and $100M_{\odot }$, from their premain sequence phase to their final fates. We then reconstruct the evolution of the neutrino spectral energy distribution for each stellar model in our suite. The $\mathrm{GS}\nu \mathrm{F}$ lies between $\mathcal{O}(1)\mathrm{keV}$ and $\mathcal{O}(10)\mathrm{MeV}$, with thermal (thermonuclear) processes responsible for shaping neutrino emission at energies smaller (larger) than 0.1 MeV. Stars with mass larger than $\mathcal{O}(1M_{\odot })$, located in the thin disk of the Galaxy, provide the largest contribution to the $\mathrm{GS}\nu \mathrm{F}$. Moreover, most of the $\mathrm{GS}\nu \mathrm{F}$ originates from stars distant from Earth about 5–10 kpc, implying that a large fraction of stellar neutrinos can reach us from the Galactic Center. Solar neutrinos and the diffuse supernova neutrino background have energies comparable to those of the $\mathrm{GS}\nu \mathrm{F}$, challenging the detection of the latter. However, directional information of solar neutrino and $\mathrm{GS}\nu \mathrm{F}$ events, together with the annual modulation of the solar neutrino flux, could facilitate the $\mathrm{GS}\nu \mathrm{F}$ detection; this will kick off a new era for low-energy neutrino astronomy, also providing a novel probe to discover new physics.

The LHAASO observatory has recently measured details of the cosmic-ray (CR) spectrum in the knee region (1–10 PeV) with unprecedented precision, including its average CR mass composition and the spectrum of the proton component. We use these precision measurements, combined with direct measurements of CRs by space-based detectors, to derive predictions for the spectrum of diffuse $\gamma$-ray and neutrino emission from the interstellar medium under the assumption that the CR spectrum is universal throughout the Milky Way. We compare these predictions with the Fermi-LAT and LHAASO measurements of the diffuse $\gamma$-ray flux from inner and outer Galactic plane regions and with estimates of the neutrino flux based on the IceCube data for the same Galactic plane regions. We notice that the model predictions exceed LHAASO $\gamma$-ray measurements at energies above 100 TeV. This excess can be interpreted within a CR knee model assuming a “local PeV CR bubble.” Within this model, we infer the extension of the local PeV CR bubble of $1.1\pm 0.2\mathrm{kpc}$ in the direction of the inner Galaxy and of $0.5\pm 0.3\mathrm{kpc}$ toward the outer Galaxy.

X-ray reflection spectroscopy has evolved as one of the leading methods to measure black hole spins. However, the question is whether its measurements are subjected to systematic biases, especially considering the possible discrepancy between the spin measurements inferred with this technique and those from gravitational wave observations. In this work, we use general relativistic magnetohydrodynamic (GRMHD) simulations of thin accretion disks around spinning black holes for modeling the accretion process, and then we simulate NuSTAR observations to test the capability of modern reflection models in recovering the input spins. For the first time, we model the electron density and ionization profiles from GRMHD-simulated disks. Our study reveals that current reflection models work well only for fast-rotating black holes. We model the corona as the base of the jet and we find that reflection models with lamppost emissivity profiles fail to recover the correct black hole spins. Reflection models with broken power-law emissivity profiles perform better. As we increase the complexity of the simulated models, it is more difficult to recover the correct input spins, pointing toward the need to update our current reflection models with more advanced accretion disks and coronal geometries.

We introduce a novel method to bootstrap crossing equations in conformal field theory (CFT) and apply it to finite temperature theories on $S^1\times {\mathbb{R}}^{d-1}$. The proposed approach does not rely on positivity constraints and does not employ uncontrolled truncation schemes. Instead, we capture the contribution of an infinite number of operators in conformal block expansions using suitable functions, which are bootstrapped (numerically) together with a finite number of exposed CFT data. Our approach at finite temperature employs three key ingredients: (1) the Kubo-Martin-Schwinger (KMS) condition, (2) thermal dispersion relations, and (3) neural networks that model spin-dependent tail functions within the conformal block expansions. We test the efficiency of the new method in the case of generalized free fields and use it to perform a preliminary bootstrap analysis of double-twist thermal data in holographic CFTs.

We investigate the asymmetric propagation of 100 TeV electrons (whose radiation mainly concentrates on 20–30 TeV) in turbulent magnetic fields around pulsars, using graphics processing unit-accelerated simulations to explore their trajectories and interactions within pulsar wind nebulae and the interstellar medium. Key results include the identification of “mirage” sources indicating significant offsets in high-energy emissions from their originating pulsars, challenging the results of traditional symmetric diffusion models. By varying parameters like source distance, magnetic field strength, and electron injection spectral index, the study delineates their effects on observable phenomena such as the identified number of sources, as well as the source separation. Our results offer insights into some puzzling sources observed recently by the Large High Altitude Air Shower Observatory and shed light on the cosmic-ray transport mechanism in the interstellar medium.

We present a cosmological analysis of the third-order aperture mass statistic using Dark Energy Survey Year 3 (DES Y3) data. We perform a complete tomographic measurement of the three-point correlation function of the Y3 weak lensing shape catalog with the four fiducial source redshift bins. Building upon our companion methodology paper, we apply a pipeline that combines the two-point function ${\xi }_{\pm }$ with the mass aperture skewness statistic $⟨{\mathcal{M}}_{\mathrm{ap}}^3⟩$, which is an efficient compression of the full shear three-point function. We use a suite of simulated shear maps to obtain a joint covariance matrix. By jointly analyzing ${\xi }_{\pm }$ and $⟨{\mathcal{M}}_{\mathrm{ap}}^3⟩$ measured from DES Y3 data with a $\mathrm{\Lambda }\mathrm{CDM}$ model, we find $S_8=0.780\pm 0.015$ and ${\mathrm{\Omega }}_{\mathrm{m}}=0.266_{-0.040}^{+0.039}$, yielding 111% of figure-of-merit improvement in the ${\mathrm{\Omega }}_m\text{−}{S}_8$ plane relative to ${\xi }_{\pm }$ alone, consistent with expectations from simulated likelihood analyses. With a $w\mathrm{CDM}$ model, we find $S_8=0.749_{-0.026}^{+0.027}$ and $w_0=-1.39\pm 0.31$, which gives an improvement of 22% on the joint $S_8\text{−}{w}_0$ constraint. Our results are consistent with $w_0=-1$. Our new constraints are compared to CMB data from the Planck satellite, and we find that with the inclusion of $⟨{\mathcal{M}}_{\mathrm{ap}}^3⟩$ the existing tension between the datasets is at the level of $2.3\sigma$. We show that the third-order statistic enables us to self-calibrate the mean photometric redshift uncertainty parameter of the highest redshift bin with little degradation in the figure of merit. Our results demonstrate the constraining power of higher-order lensing statistics and establish $⟨{\mathcal{M}}_{\mathrm{ap}}^3⟩$ as a practical observable for joint analyses in current and future surveys.

We present a “dictionary” to expedite the identification of potential deviations in gravitational waveforms from those predicted by general relativity (GR) during the inspiral phase of black hole binaries. Assuming deviations from GR can be described by a local effective field theory (EFT) formulated in terms of curvature operators (and possibly additional scalar fields), this dictionary characterizes how deviations scale with the masses of the binary components and identifies the leading order post-Newtonian corrections in generic theories constructed within the EFT framework. By establishing a direct connection between observations and candidate theories beyond GR, this dictionary also aids in distinguishing genuine physical effects from systematic errors. These results can be readily incorporated into essentially all existing tests for the inspiral regime and, in particular, facilitate a more efficient combination of data from multiple events.

We present a new set of numerical-relativity simulations of merging binary neutron stars, aiming to identify possible observable signatures of the slope of the symmetry energy $L_{\mathrm{sym}}$. To achieve this goal, we employ a set of equations of state based on a parametrization of the covariant density functional theory of nuclear matter that allows controlled variations of $L_{\mathrm{sym}}$ and the skewness $Q_{\mathrm{sat}}$, holding the latter fixed. For a set of our simulations, we identify a steep energy gradient in the equation of state at subsaturation densities, which acts as a source of heating with subsequent stiffening produced by thermal support. Accounting for related structural modifications in the tidal deformability reconciles our results with theoretical expectations. On the other hand, we show that gravitational waves are unlikely to distinguish the role of $L_{\mathrm{sym}}$. In contrast to this, we find that the ejecta composition is significantly altered in our simulations, which employ an M1 moment scheme, when $L_{\mathrm{sym}}$ is varied. Based on our extracted dynamical ejecta properties, we compute r-process yields and find that they are distinct for the different $L_{\mathrm{sym}}$, especially at lower mass numbers $A\lesssim 120$. This suggests that electromagnetic counterparts are more likely to exhibit signatures; however, a direct connection to $L_{\mathrm{sym}}$ remains a challenge, given the complex interplay between details of the ejecta properties and the kilonova signal.

Dynamical tides of neutron stars in the late stages of binary inspirals provide a viable probe into dense matter through gravitational waves and potentially trigger electromagnetic precursors. We model the tidal response as a set of driven harmonic oscillators, where the natural frequencies are given by the quasinormal modes of a nonrotating neutron star. These modes are calculated in general relativity by applying linear perturbation theory to stellar models that include a solid crust and compositional stratification. For the mode spectrum, we find that the canonical interface mode associated with crust-core boundary vanishes in stratified neutron stars and is replaced by compositional gravity modes with mixed gravity-interfacial character, driven primarily by strong buoyancy in the outer core. We also find that fluid modes such as the core gravity mode and the fundamental mode can penetrate the crust, and we establish a criterion for such penetration. Regarding the tidal interaction, we find that transfer of binding energy to oscillations is dominated by the fundamental mode despite its frequency being too high to resonate with the tidal forcing. In general, we find that lower-frequency modes induce gravitational-wave phase shifts smaller than $\sim {10}^{-3}\mathrm{rad}$ for the equation of state we consider. We discover that nonresonant fundamental and crustal shear modes can trigger crust breaking already near the first gravity-mode resonance, while gravity-mode resonance concentrates strain at the base of the crust and may marginally crack it. These results suggest that both resonant and nonresonant excitations can overstress the crust and may channel energy into the magnetosphere prior to merger, potentially powering electromagnetic precursors. Our work represents an important step toward realistic modeling of dynamical tides of neutron stars in multimessenger observations.