In order to find reliable and efficient numerical approximation schemes, we suggest to identify the functional renormalization group flow equations of one-particle irreducible two-point functions as Hamilton-Jacobi(-Bellman)-type partial differential equations. Based on this reformulation and reinterpretation we adopt a numerical scheme for the solution of field-dependent flow equations as nonlinear partial differential equations. We demonstrate this novel approach by first applying it to a simple fermion-boson system in zero spacetime dimensions—which itself presents as an interesting playground for method development. Afterwards, we show how the gained insights can be transferred to more interesting problems: one is the bosonic ${\mathbb{Z}}_2$-symmetric model in three Euclidean dimensions within a truncation that involves the field-dependent effective potential and field-dependent wave function renormalization. The other example is the ($1+1$)-dimensional Gross-Neveu model within a truncation that involves a field-dependent potential and a field-dependent fermion mass/Yukawa coupling at nonzero temperature, chemical potential, and finite fermion number.

This work sets out to compute the corrections to the Euler-Heisenberg effective action that arise from spacetime-dependent background anisotropies that violate Lorentz symmetry. To accomplish our task, we evaluate the functional determinant of the modified Dirac operator using the spectral regularization method. Within the framework of the Standard Model extension (SME), these Lorentz-violating parameters correspond to the coefficients $m_5(x)$, $a_{\mu }(x)$, and $b_{\mu }(x)$. The corrected effective action is attained up to the second-order in the background parameters. Our results indicate a violation of Furry’s theorem at second-order for specific C-odd combinations of these parameters, in agreement with previous analyses based on explicit Feynman diagram calculations in scenarios with Lorentz-symmetry violation. In the kinetic (bilinear) piece of the effective action, nondynamical axionlike terms emerge, resembling structures commonly encountered in condensed-matter systems, such as Weyl semimetals. We show how this procedure modifies the Maxwell equations, from which we present both the corresponding (non)conservation of the energy-momentum tensor and the wave equation. We also notice that the vacuum behaves as an inhomogeneous medium, and compute the local dispersion relation by working in the eikonal approximation. As a result of the spacetime-dependence of the background, there appear imaginary contributions in the dispersion relation and, consequently, the wave amplitudes may be amplified or attenuated, which expresses the energy-momentum exchange between the waves and the background.

The gauge principle is a cornerstone of particle-physics model building. Nevertheless, many constructions leave certain global $U(1)$ redundancies ungauged. In this work, we take the gauge principle to its logical extreme by promoting all $SU(N)$ symmetries to $U(N)$. We focus on a model based on local $U(3)\times U(2)$ invariance. This framework accounts for several otherwise ad hoc features of the Standard Model, including charge quantization and the observed hypercharge assignments, which emerge here as unique predictions. Furthermore, the internal consistency of the model requires the introduction of right-handed neutrinos and implies the presence of an additional $U(1)$ factor that can be identified with $B-L$, thereby naturally yielding nonzero neutrino masses. In light of these findings, we hypothesize that $U(3)\times U(2)$ constitutes the underlying symmetry of the strong and electroweak interactions. More importantly, our approach opens up novel avenues for model building, driven by this extended interpretation of the gauge principle.

Lepton-flavor-violating (LFV) interactions involving dark matter (DM) particles remain a largely unexplored area. In this study, we systematically investigate LFV DM interactions within the framework of effective field theories by analyzing astrophysical photons and positrons produced from DM annihilation. Employing the astrophysical photon and positron data collected by Fermi-LAT, INTEGRAL, XMM-Newton, and AMS-02, we place meaningful constraints on all leading-order effective operators involving a DM pair and a flavor-violating charged lepton pair. Our analysis covers the three well-known DM candidates: a scalar, a fermion, and a vector particle. For the photon flux, we consider contributions from final-state radiation, radiative decay, and inverse Compton scattering and examine their respective sensitivity regions across different DM masses and photon energies. We find that, for DM masses below $\mathcal{O}(20\mathrm{GeV})$, INTEGRAL provides the most stringent constraints on annihilation cross sections and effective operators in all three LFV channels, whereas AMS-02 offers the strongest constraints above $\mathcal{O}(20\mathrm{GeV})$.

We explore the electroweak supersymmetry (EWSUSY) scenario within the minimal supersymmetric Standard Model under the generalized minimal supergravity (GmSUGRA) framework, given that the anomalous magnetic moment of the muon may now be consistent with the Standard Model (SM) prediction, we consider both signs of the Higgsino mass parameter, $\mu <0$ and $\mu >0$. A comprehensive scan of the parameter space is performed, subject to the experimental constraints from the LHC SUSY searches, Planck 2018 relic density, and LUX-ZEPLIN (LZ) direct detection limits. We identify the viable regions featuring neutralino dark matter production via coannihilation with stau, chargino, stop, sbottom, and gluino, as well as through $A$-funnel, Higgs-resonance, and $Z$-resonance mechanisms. Notably, the $\mu <0$ scenario yields a broader allowed parameter space, including for the first time sbottom-neutralino coannihilation solutions in GmSUGRA, which are absent for $\mu >0$. While the Higgs-pole and $Z$-pole regions for $\mu >0$ are largely excluded by the current LZ bounds, substantial viable regions remain for $\mu <0$. Gluino coannihilation scenarios are strongly constrained by the current LHC data. The characteristic mass ranges of interest include sbottoms (0.7–1.3 TeV), stops (up to 1.0 TeV for $\mu >0$ and 1.3 TeV for $\mu <0$), staus and charginos (up to 1.5 TeV), and pseudoscalar Higgs bosons in the $A$ funnel (0.4–1.4 TeV). Moreover, the supersymmetric contributions to the muon anomalous magnetic moment remain within a $2\sigma$ deviation from the SM prediction. And our findings suggest that significant portions of the parameter space can be probed at the future LHC SUSY searches and upcoming dark matter direct detection experiments.

We argue that a detailed analysis of semileptonic decays can test the possibility of a massive neutrino. The key observable, related to the forward–backward asymmetry, is exactly zero for a massless neutrino but becomes nonzero if the neutral lepton is heavy and interacts with Standard Model fields via lefthanded operators. For righthanded interactions, this quantity differs significantly from zero even for a massless righthanded neutrino. We demonstrate this explicitly using the example of a pseudoscalar meson decaying into another pseudoscalar meson. A similar discussion applies to decays into a vector meson, with an additional subtlety addressed in this work.

The matrix element in the proton of the eikonal Odderon operator, with a helicity flip, has been shown to correspond to the dipole gluon Sivers function. We employ a three quark light-front model of the proton to determine the Sivers function at moderately small $x_0\sim 0.1$ and transverse momentum $k_{\perp }\lesssim 1\mathrm{GeV}$. The model light-cone (LC) wave function predicts the properties of $x{f}_{1T}^{\perp g}(x,k_{\perp })$ such as its overall magnitude, the position of its peak in $k_{\perp }$, and its behavior at small $k_{\perp }$. We then compute numerically the Balitsky-Fadin-Kuraev-Lipatov anomalous dimension characterizing the power-law tail at $k_{\perp }\gtrsim 1.5\mathrm{GeV}$ of the gluon Sivers function at small (but preasymptotic) LC momentum fractions $x\sim x_0{e}^{-1/{\alpha }_s}$: $x{f}_{1T}^{\perp g}(x,k_{\perp })\sim k_{\perp }^{-3.3}$.

We present the first complete QCD corrections to the inclusive decay width ${\mathrm{\Gamma }}_t$, the $W$-helicity fractions $f_{\mathrm{L},\mathrm{R},0}$ and semi-inclusive distributions for the top-quark decay process $t\to b+W^{+}+X_{\mathrm{QCD}}$ at next-to-next-to-next-to-leading order (NNNLO) in the strong coupling constant ${\alpha }_s$. In particular, the pure NNNLO QCD correction decreases ${\mathrm{\Gamma }}_t$ by about 0.8% relative to the previous next-to-next-to-leading order (NNLO) result at the scale of the top-quark pole mass, exceeding the uncertainty estimated by the conventional scale-variation prescription. After taking into account errors from various sources, we get ${\mathrm{\Gamma }}_t=1.3148_{-0.005}^{+0.003}\times |V_{tb}{|}^2+0.027(m_t-172.69)\mathrm{GeV}$, whose uncertainty meets the request of future colliders. On the other hand, the NNNLO QCD effects on $f_{\mathrm{L},\mathrm{R},0}$ are found to be much smaller, at the level of one one per mille for the dominant $f_0$, making them precision observables for the top-quark decay process.

Studying heavy-flavor jets in $pp$ collisions is important since it can test perturbative QCD calculations and be used as a reference for heavy-ion collisions. Jets in this analysis are reconstructed from charged particles using the anti-$k_{\mathrm{T}}$ algorithm with a resolution parameter $R=0.4$ at midrapidity $|\eta |<0.5$. Beauty jets are tagged using a machine learning model that uses a convolutional neural network trained on information extracted from the jet, tracks, and secondary vertices. Results show that this model is superior in b-jet-tagging compared to other traditional tagging methods.

We present a model calculation of the transverse-momentum-dependent distributions (TMDs) for gluons in a tensor-polarized deuteron. Our model is based on the assumption that an on-shell deuteron can emit a timelike off-shell gluon, while the remaining system is treated as a single on-shell spectator particle whose mass spans a continuous real-value distribution parametrized via a spectral function. For spin-1 hadrons, the polarization is characterized not only by a spin vector $S$ but also by a symmetric traceless spin tensor $T$. The deuteron-gluon-spectator coupling is described by an effective vertex containing three form factors. We obtain analytical expressions for thirteen T-even gluon TMDs. We also provide numerical results for the $x$-dependence and ${\mathit{k}}_{\mathrm{T}}$-dependence of these TMDs. Our analysis reveals non-negligible results of these gluon TMDs, especially for tensor-polarized hadrons, which could potentially be explored in future experimental measurements.

This paper presents a fully corrected measurement of the energy-energy correlator (EEC) within jets in pp collisions. The EEC traces the energy flow as a highly energetic parton undergoes a QCD shower followed by the confinement of partons into hadrons, probing the correlation function of the energy flow inside jets. The EEC observable is measured as a function of the charged particle pair angular distance, $R_{\mathrm{L}}$, for $20<p_{\mathrm{T}}^{\mathrm{ch}\mathrm{jet}}<80\mathrm{GeV}/c$. In the perturbative region (large $R_{\mathrm{L}}$), a good agreement between the data and a next-to-leading-log perturbative QCD calculation is observed. In the nonperturbative region (small $R_{\mathrm{L}}$), the data exhibit a linear $R_{\mathrm{L}}$ dependence. There is a transition region in between, characterized by a turnover in the EEC distribution, indicating where hadronization effects begin to dominate. The peak of this transition region is located at $2.43\pm 0.14\mathrm{GeV}/c/⟨p_{\mathrm{T}}^{\mathrm{ch}\mathrm{jet}}⟩$ for jets of various energies, indicating a common energy scale for the hadronization process. State-of-the-art Monte Carlo event generators are compared with the measurements, and can be used to constrain the parton shower and hadronization mechanisms.

Understanding the detailed structure of energy flow within jets, a field known as jet substructure, plays a central role in searches for new physics, and precision studies of QCD. Many applications of jet substructure require an understanding of jets initiated by heavy quarks, whose description has lagged behind remarkable recent progress for massless jets. In this Letter, we initiate a study of correlation functions of energy flow operators on beauty and charm jets to illuminate the effects of the intrinsic mass of the elementary particles of QCD. We present a factorization theorem incorporating the mass of heavy quarks, and show that the heavy quark jet functions for energy correlators have a simple structure in perturbation theory. Our results achieve the very first full next-to-leading-logarithmic calculation of the heavy quark jet substructure observable at the LHC. Using this framework, we study the behavior of the correlators, and show that they exhibit a clear transition from a massless scaling regime, at precisely the scale of the heavy quark mass. This manifests the long-sought-after dead-cone effect and illustrates fundamental effects from the intrinsic mass of beauty and charm quarks in a perturbative regime, before they are confined inside hadrons. Our theoretical framework for studying energy correlators using heavy jets has many exciting applications for improving the description of mass effects in next generation parton shower event generators, probing the QGP, and studying heavy flavor fragmentation functions.

The two-dimensional effective Polyakov action is often realized as the anomalous contributions of string theories and fermions coupled to gravity in two dimensions. However, as a result of the reparametrization invariance, one finds that the effective action produces vanishing Hamiltonians as constraints even in disparate gauges such as the dynamical light-cone and the Arnowitt-Deser-Misner (ADM) formalism of the metric. On the other hand, two-dimensional gravitational theories naturally arise as geometric actions on the coadjoint orbits of the Virasoro algebra. The Thomas-Whitehead gravity formalism extends the effective Polyakov action in such a way that the defining coadjoint element for the orbit becomes a dynamical field, viz. the diffeomorphism field. In this work, we examine the role the diffeomorphism field plays through the well-understood quantization of the two-dimensional anomalous contributions to gravity. This is first done in the dynamical light-cone and then with the ADM formalisms of the metric. To examine a dynamical diffeomorphism field, the constraint analysis is then repeated in a Minkowski background, where the dynamics of the diffeomorphism field arise from the Thomas-Whitehead action. Adding dynamics to the diffeomorphism field appears to remove the vanishing Hamiltonians; however, expressing the diffeomorphism in terms of the P-tensor recovers the Hamiltonian constraint. One can compare this investigation to that of a gauge Wess-Zumino-Witten action where the gauge field has become dynamical through the inclusion of a Yang-Mills term.

We analyze finite-temperature effects in the perturbative large volume scenario (LVS), examining the dynamics of thermalized Kähler moduli and the stability of thermally induced vacua. We determine the maximum decompactification temperature $T_{\max }$, showing its dependence on winding-loop corrections in the effective theory. Moduli stabilization arises from perturbative logarithmic loop corrections to the Kähler potential, with higher-derivative $F^4$ terms used to test vacuum robustness. We derive cosmological implications, including bounds on reheating, and show that the model favors high scale inflationary scenarios with the heavy modulus decaying before dominating the energy density of the universe. We also analyze thermal metastability, demonstrating that the recovery of the $T=0$ vacuum is sensitive to the postinflationary thermal history, potentially yielding either an Anti-de Sitter vacuum, a metastable phase, or a stable de-Sitter configuration. We conclude by briefly discussing the relevance of finite-temperature effects for entropy-assisted tunneling and the broader string landscape.

Celestial ${\mathrm{CFT}}_d$ with symmetry group $\mathrm{ISO}(d+1,1)$ is the putative dual of quantum gravity in asymptotically flat ($d+2$) dimensional space time. We argue that a class of $d$ dimensional field theories with symmetry group $\mathrm{ISO}(d+1,1)$, refereed to as Poincaré ${\mathrm{CFT}}_d$, can be engineered via ${\mathrm{AdS}}_{d+1}\text{−}{\mathrm{CFT}}_d$ correspondence. Celestial and Poincaré ${\mathrm{CFT}}_d$ may share common features determined by the kinematics because they have the same symmetry group. So understanding Poincaré CFTs may help us better understand some features of celestial CFTs. Our argument is based on the observation that if we zoom in near the boundary of (Euclidean) ${\mathrm{AdS}}_{d+1}$ then the conformal isometry group of ${\mathrm{EAdS}}_{d+1}$, which is $\mathrm{SO}(d+2,1)$, contracts to the Poincaré group $\mathrm{ISO}(d+1,1)$. This suggests that the near boundary scaling limit of a theory of conformal gravity on ${\mathrm{EAdS}}_{d+1}$ should be dual to a boundary ${\mathrm{CFT}}_d$ with $\mathrm{ISO}(d+1,1)$ symmetry. This dual ${\mathrm{CFT}}_d$ is an example of a Poincaré ${\mathrm{CFT}}_d$. Similarly, if we have a nonconformal theory of gravity on ${\mathrm{EAdS}}_{d+1}$ then the near boundary scaling limit of such a theory is dual to a Poincaré ${\mathrm{CFT}}_d$ with only [$\mathrm{SO}(d+1,1)$] Lorentz invariance. This class of less symmetric Poincaré ${\mathrm{CFT}}_d$ is analogous to celestial ${\mathrm{CFT}}_d$ which computes the leaf amplitudes. Now following this logic we discuss, among other things, the near boundary scaling limit of the bosonic string theory on Euclidean ${\mathrm{AdS}}_3$ in the presence of the NS-NS B field. The ${\mathrm{AdS}}_3$ part of the world sheet theory is free in this limit and has been studied in the literature in different contexts. This limit describes a “long string” which wraps the (Euclidean) ${\mathrm{AdS}}_3$ boundary and it has been argued that the space-time ${\mathrm{CFT}}_2$ which describes the radial fluctuations of a long string is a Liouville CFT. According to our proposal, the dual ${\mathrm{CFT}}_2$ which describes the long string sector is an example of a Poincaré ${\mathrm{CFT}}_2$ with only [SO(3,1)] Lorentz invariance. We do not get a full ISO(3,1) invariant Poincaré ${\mathrm{CFT}}_2$ in this way because the string theory does not have target space conformal invariance.

In this work, we show examples when a perturbatively irrelevant operator becomes relevant in the infrared because of the presence of an IR singularity (IR Landau pole). An example of this behavior is the four-fermion interaction that allows the formation of bound states. The reason for the appearance of the IR Landau pole is not the singular loop as in the purely perturbative case, but the infinite number of modes appearing in the renormalization group flow.

Motivated by the low-energy effective action of heterotic string theory, where the Kalb-Ramond (KR) two-form and nonlinear gauge corrections arise simultaneously, we investigate a static, spherically symmetric black hole in Einstein gravity coupled to a KR field and ModMax nonlinear electrodynamics. The solution depends, beyond mass and charge, on the Lorentz-symmetry-breaking parameter $\ell$, the ModMax deformation parameter $\gamma$, and a discrete branch selector $\zeta =\pm 1$. We show that the ordinary branch admits extremal and nonextremal configurations, while the phantom branch generically supports a single-horizon geometry. Black hole thermodynamics is analyzed within the Tsallis nonextensive framework, revealing branch-dependent stability and Joule-Thomson behavior. Weak gravitational lensing is computed via the Ono-Ishihara-Asada extension of the Gauss-Bonnet theorem, yielding a negative topological correction that reduces light bending relative to the Schwarzschild baseline—opposite in sign to Barriola-Vilenkin monopole backgrounds. Photon-sphere properties in plasma environments and tidal forces through geodesic deviation are also studied, revealing a universal tidal balance ratio $R_{\mathrm{rad}}/R_{\mathrm{ang}}=3/2$ in the ordinary branch. These multichannel signatures provide concrete observational handles for constraining the KR-ModMax framework through Event Horizon Telescope data and next-generation interferometric arrays.

In this work, we investigate the critical behavior of photon rings in the Kerr-Bertotti-Robinson spacetime, describing a rotating black hole immersed in a background magnetic field. We analyze the radial and angular motions of photons under the small magnetic field approximation. Focusing on unstable spherical orbits, we determine three key parameters, $\gamma$, $\delta$, and $\tau$, which characterize radial compression, azimuthal advancement, and time delay. We then examine how these parameters depend on the black hole spin, magnetic field strength, and observer inclination for both on-axis and off-axis observers, and we further analyze the properties of higher-order images through near-critical lens equations. The results show that the magnetic field modifies the geodesic structure and leads to observable changes in the fine structure of photon rings, providing a useful framework for probing magnetized black hole environments.

Gravitational waves from binary black hole mergers allow us to test general relativity in the strong-field, high-curvature regime. However, existing gravitational waves-based tests for this have so far assumed noneccentric signal sources, limiting their range of applicability. In this work, we present pTEOBResumS, a new parametrized inspiral-merger-ringdown model for null tests of general relativity that incorporates both orbital eccentricity and spin precession, building on the effective-one-body model TEOBResumS-Dalí. We introduce parametrized deviations from general relativity both in the inspiral and the merger-ringdown regimes. We validate the model through parameter estimation of synthetic signals generated with the model itself or from numerical simulations, including of systems featuring physics beyond general relativity. We thus establish the model’s consistency, demonstrate its capability to identify effects beyond general relativity, and gauge the impact of eccentricity on the recovery of deviation parameters. We then analyze a set of binary black hole events from the first three LIGO-Virgo-KAGRA observing runs, under either the eccentric, spin-aligned or precessing, quasicircular hypotheses, searching for deviations from general relativity in the remnant black hole’s fundamental quasinormal mode. We find no statistically significant evidence for such deviations in any of the events. We combine single event results either by multiplying likelihoods, or via a hierarchical procedure, assuming an underlying normal distribution for the deviations. Consistent with previous works, we infer a mild preference for longer remnant quasinormal mode damping times than expected, although the limited event sample and potential systematics reduce the significance of this finding. We find no support for orbital eccentricity among the analyzed events, except for GW200129. An eccentric description is strongly favored for this event, although as previous works have noted this result could be influenced by data quality issues.

Recent findings collectively suggest that pulsar timing arrays (PTAs) have detected the stochastic gravitational-wave background in the nanohertz frequency band, opening new avenues for testing theories of gravity and cosmology. PTAs serve as a unique tool for probing the nanohertz stochastic gravitational-wave background, enabling studies of supermassive black hole evolution and early-Universe physics. PTA data analysis fundamentally relies on cross-correlating timing residuals from pulsar pairs, for which the overlap reduction functions (ORFs) are critical in determining the sensitivity of such analyses. Conventional ORF calculations based on the “short-wavelength approximation” break down when handling the scalar longitudinal polarization mode and fail to accurately describe frequency-dependent effects and anisotropies. This work presents a significant advance by rigorously deriving the full response functions within an analytical cross-correlation framework. We systematically reveal, for the first time, the intrinsic symmetries and mathematical relationships among the anisotropic ORF integrals for different polarization modes. Through variable substitutions and coordinate rotations, we transform the complex integrals into analytically tractable forms, resolving the divergence difficulties encountered in the vector and scalar longitudinal modes. Building on these theoretical advances, we establish a universal framework capable of deriving fully analytical expressions for anisotropic ORFs to arbitrary order for all six polarization modes. As a direct application of this framework, we provide complete analytical expressions for anisotropic ORFs up to the order of $\ell \le 5$. This universal framework is free from approximations; its (0,0) component naturally corresponds to the isotropic case and recovers the well-known Hellings-Downs curve. Compared to numerical integration, our results offer broader applicability, significantly faster computation, and higher precision. They provide a valuable theoretical and computational foundation for conducting high-precision anisotropic sky mapping, polarization-mode separation, and searches for new physics using PTA data.