Papers

We compute the thermal photon production rate from a hot and dense quark-gluon plasma. While the mutual cancellation of the intermediate momentum cutoff $k_c$ between the hard and soft regimes in the presence of finite baryon density has been previously established only numerically, we demonstrate here, for the first time, that this cutoff independence can be shown analytically even in the presence of a nonzero quark chemical potential $\mu$. This resolves a long-standing issue addressed in Ref.[1]. The final expression for the photon rate can be treated as a generalization of the results obtained in Refs.[2,3] in the presence of $\mu$ and can be implemented directly in the space-time evolution of a hot and dense QGP medium using relativistic hydrodynamics.

Rogers and Mulders identified color entanglement as a mechanism that breaks transverse-momentum-dependent (TMD) factorization in nearly back-to-back dijet production. Using the double-Sivers asymmetry in their model, we quantify the contribution of color entanglement in the intermediate region $\Lambda_{\rm QCD}\ll q_T\ll P_T$, where $q_T$ is the transverse-momentum imbalance of the dijet and $P_T$ is the hard transverse momentum. We compare the collinear twist-three result with the TMD-factorization prediction, expressing both in terms of the Qiu–Sterman functions. In the absence of color entanglement, the factorized prediction would involve the Sivers functions of semi-inclusive deep-inelastic scattering (SIDIS). Diagrams without crossed attachments reproduce the hard coefficient obtained from the perturbative tails of these Sivers functions. Crossed diagrams, in which each coherent gluon attaches to the other hadron's quark line, contribute an extra term equal to $4/(N_c^2-1)$ times this coefficient.

We investigate the complementarity between collider searches and gravitational-wave (GW) observations in the classically scale-invariant general $U(1)_X$ extension of the Standard Model. The $U(1)_X$ scale is generated radiatively through the Coleman-Weinberg mechanism, while the electroweak scale is induced through the Higgs portal, without explicit mass terms in the scalar potential. Three right-handed neutrinos are introduced to ensure anomaly cancellation and acquire Majorana masses upon $U(1)_X$ symmetry breaking, which also generates the mass of the neutral gauge boson $Z'$. In the strongly supercooled regime, a tachyonic $U(1)_X$ phase transition can produce a stochastic GW background. Assuming three heavy Majorana neutrinos, we study their effects on the phase-transition dynamics and reheating, and estimate the resulting GW signals. We identify the regions of the $U(1)_X$ gauge coupling and $Z'$ mass accessible to future GW observatories, including LISA and DECIGO, and compare them with existing LEP and LHC constraints. We find that GWs from tachyonic phase transitions can probe regions with small gauge couplings and heavy $Z'$ bosons that are difficult to access through collider searches, demonstrating the complementarity of these probes.

Different stages of cosmic evolution impose different requirements on the dark matter annihilation cross section. Sommerfeld enhancement provides a possible way to accommodate them. However, in the point-like dark matter scenario, satisfying these requirements with either $s$-wave or $p$-wave Sommerfeld enhancement can strongly constrain the dark matter and mediator masses and their coupling. A finite dark matter size introduces an additional parameter and may relax these constraints. Motivated by this possibility, in this work we study the $p$-wave Sommerfeld resonances of finite-size dark matter (like proton or neutron) without specifying its internal structure. We find that the $p$-wave contribution can exceed the $s$-wave contribution. Nevertheless, the finite-size $p$-wave resonances are weaker than those in the point-like case. Despite this suppression, their velocity dependence remains similar to that of point-like dark matter. We then extend our analysis to nugget dark matter composed of a small number of constituents. In this case, the $p$-wave Sommerfeld enhancement exhibits behavior similar to that of point-like dark matter.

The three gauge couplings of the Standard Model (SM) can be parameterized as the fine structure constant $\alpha$, the weak mixing angle $\sin^2\theta_w$, and the strong coupling $\alpha_s$. They are fundamental constants whose values remain unexplained. Previously we showed that minimizing magic production in charged-lepton scattering reproduces $\sin^2\theta_w$ with great precision. Here we study magic production in the six flavor-diagonal color-singlet channels $q\bar q\to q\bar q$ at tree level, including photon, gluon, $W/Z$, and Higgs exchange. Varying only $\alpha_s$, with all other inputs fixed at each center-of-mass energy, we find that the finite-$\alpha_s$ magic minimum in the top channel reproduces the $\overline{\mathrm{MS}}$ value of $\alpha_s$ to within $5\%$ from $1~$TeV to $10^9~$GeV. Higgs exchange involving the large top Yukawa coupling is essential for this agreement. All six channels produce near-minimal magic at the SM couplings, and reducing $\alpha_s$ toward $\alpha$ increases their magic production, potentially explaining why the strong interaction is “strong.” To understand why minimizing magic reproduces both $\sin^2\theta_w$ and $\alpha_s$, we conjecture that the parameters of fundamental interactions among color singlets reflect a principle of quantum computational efficiency, with the physical universe emerging from a quantum simulation subject to constrained resources.

Ultralight bosons are well-motivated candidates for physics beyond the Standard Model and may constitute part or all of the dark matter. Black-hole superradiance provides a powerful means of probing these particles through their gravitational interaction with rotating black holes. This mechanism has motivated a growing body of constraints from electromagnetic measurements of black-hole spins and, more recently, gravitational-wave observations. Gravitational-wave probes draw on several distinct signatures: the spins of merging binary black holes, gravitational radiation emitted by boson clouds, and potential imprints of cloud-induced changes to binary dynamics. The interpretation of these probes depends on method-specific astrophysical and theoretical assumptions, including black hole formation, natal spin, age, accretion history, population priors, and boson self-interactions. In this paper, we review the principal electromagnetic and gravitational-wave constraints derived from black-hole superradiance, with particular emphasis on their underlying assumptions and systematic uncertainties. The distinct observational signatures and systematic uncertainties of these approaches offer complementary perspectives on the viability of ultralight-boson models. In particular, their overlapping coverage around boson masses of $10^{-13}$-$10^{-12}$ eV makes this region particularly informative for comparing constraints, with attention to the assumptions underlying each result.

We investigate CP violation in the decays of a GeV-scale dark scalar boson into mesons, muons and photons. Both scalar and pseudoscalar couplings to the SM fermions are considered to study how the CP structure of the dark scalar boson can be probed through its decays. The scalar and pseudoscalar interactions predominantly induce decays into two-meson and three-meson final states, respectively. We propose the simultaneous observation of these two classes of decay modes as a probe of CP violation in the dark scalar sector. The expected signal rates at the SHiP and FASER2 experiments are evaluated based on the dark scalar production from heavy-meson decays. We find that the ratio of three-meson to two-meson decay events at SHiP has the potential to probe a wide range of the CP-violating parameter space for dark scalar masses around the GeV scale. We also show that the two-muon and di-photon channels can provide complementary information for the CP violation search.

I propose a Hamiltonian framework for chiral gauge theories (CGT) based on a Euclidean formulation which uses 2n dimensional chiral fermions on the boundary of a 2n+1 dimensional disk. In the original Euclidean formulation, boundary gauge fields were extended into the bulk using $2n + 1$ dimensional gauge field equations of motion (EOM) which creates a bottleneck for constructing a Hamiltonian. I present an alternate proposal for extending the gauge fields into the bulk that is compatible with both a Hamiltonian framework and a Euclidean path integral. Applying this to Abelian gauge fields produces exact expressions of interior fields as a functional of the boundary fields, which can be directly used in a Hamiltonian formulation. Euclidean analysis of the new gauge field extension shows that it can preserve the non-perturbative content of the original construction, including the behavior of topological charge, associated chiral fermion zero modes and an absence of the strong CP problem when applied to the Standard Model. This construction opens up a route to a Hamiltonian treatment and future quantum simulation of CGTs on a disk boundary.

Using the Mellin-Barnes representation of de Sitter propagators, we reduce tree-level heavy-particle exchange to finite integrals that converge at physical kinematics on mass-independent contours, and one-loop diagrams to the same integrand times a flat-space momentum factor. We evaluate the triple-exchange bispectrum without analytic continuation and compute the complete one-loop triangle at general mass. These give cosmological collider predictions, the oscillatory signatures of heavy particles during inflation, for multiple exchanges and loops at arbitrary masses.

Femtoscopic correlations in proton-proton and heavy ion collisions are commonly calculated using emission sources from microscopic transport models, where emitted particles are represented by classical phase-space points with simultaneously specified positions and momenta. This point-emitter picture neglects the finite phase-space localization required by quantum mechanics, which can become relevant when the localization scale approaches the femtoscopic source size, particularly in small collision systems. We formulate a quantum treatment by replacing each transport phase-space point with a minimum-uncertainty Gaussian phase-space distribution. Finite localization then induces both spatial and momentum smearing; in the presence of coordinate-momentum correlations, the latter produces a nontrivial modification of the emission source. Using proton–proton collisions at $\sqrt{s}=7~\mathrm{TeV}$ simulated with the microscopic Parton–Hadron–String Dynamics transport approach, we show that this effect significantly modifies the proton-pair source and its momentum correlation. Our results expose a quantum localization effect overlooked in transport-based femtoscopy and establish the regime in which the classical point-emitter approximation is valid.

We study the observational features of thin-disk accretion and emission spectra for static, spherically symmetric dyonic black holes in non-linear electrodynamics (NLED). In contrast to classical Maxwell theory, where electromagnetic duality assumes equal charges, the coupling parameters in NLED introduce a new gravitational potential and modify the geometry in the strong-field regime. We also study the kinematic characteristics of particles on circular orbits, such as their angular velocity, specific energy, and specific angular momentum. It is found that modifications of NLED lead to a shrinkage of the ISCO radius, resulting in a shift of the radiation spectrum thermal maximum towards smaller radii and, consequently, an increase in the local effective temperature in comparison with the standard Schwarzschild and Reissner-Nordström solutions. Additionally, we compute null-geodesic orbits to determine the optical edge of both the photon sphere and the black hole shadow. In order to assess the observational validity of the aforementioned alternatives, we carry out a $\chi^2$ goodness-of-fit test through the angular diameter constraints at the horizon scale collected by the Event Horizon Telescope (EHT) concerning Sagittarius A* ($\text{Sgr A}^*$). We prove that both these dyonic NLED and purely magnetic models have good statistical agreement with experimental data.

We consider the SM extended by a 4th generation of vector-like leptons. This model generates strongly correlated contributions to the lepton masses, Higgs couplings and dipole moments. At leading order the Higgs coupling restricts the magnetic and electric dipole moments to an ellipse. Here we compute the one-loop corrections to the Higgs coupling and two-loop corrections to the dipole moments to obtain the correlation at next-to-leading order using the framework of SMEFT. In addition we resum the leading logarithmic corrections from SM couplings through the SMEFT renormalisation group equations. With these results we compute the RG improved correlation at NLO and discuss the implications for the muon, electron and tau correlations. Specifically, for the muon we find that the corrections contract the ellipse such that a larger part of parameter space becomes compatible with the updated SM value of the muon magnetic moment.

We determine the infrared-sensitive contribution to the pressure of hot and dense massless quantum electrodynamics (QED) at $O({e}^6)$ in the electric charge $e$, obtaining a representation valid across the crossover between the thermally dominated and degenerate regimes. This contribution arises from a hard-thermal-loop (HTL) resummed soft photon dressed by either the one-loop power correction or the two-loop next-to-leading-order photon self-energy. After separating the static and nonstatic sectors, we obtain the static contribution in closed form and perform the nonstatic Matsubara sum analytically in terms of the digamma function, reducing the remaining finite coefficient to a one-dimensional numerical integral. The finite-temperature HTL counterterm cancels the factorization divergence before expansion; at strictly zero temperature $T$, this divergence instead cancels against the hard four-loop contribution. At vanishing chemical potential, the static sector reproduces the complete known $O\left(e^5\right)$ pressure. Taking the cold limit of the dimensionally regulated, unsubtracted nonstatic contribution reproduces the correct cold mixed result. Crucially, at any fixed $T>0$, the nonstatic result remains analytic in $e^2$. The zero-temperature $O(e^6\ln e)$ term in QED arises only in the nonuniform limit ${T}/{m_{\rm{E}}}\to0$ where $m_{\rm{E}}$ is the electric screening mass, demonstrating that the weak-coupling and zero-temperature limits do not commute.

Primordial black holes, whose formation in the early Universe was first hypothesized by Ya.B.~Zel'dovich and I.D.~Novikov in 1966 (the text of this pioneering article is provided in Appendix II to this review), have attracted increasing attention in recent years. Modern astronomical data across the electromagnetic spectrum, together with observations of gravitational waves and cosmic neutrinos, have revealed a number of unique astrophysical phenomena that may be related to primordial black holes formed in the pre-stellar cosmological epoch. This review describes various models of primordial black hole formation, as well as methods for testing these models with astronomical and astrophysical observations. In particular, we discuss in detail the formation of primordial black holes and their clusters through the collapse of closed domain walls and through effects associated with extra spatial dimensions of the Universe.

The energy-energy correlator (EEC) is one of a handful of collider observables that can be computed analytically to high orders. As an energy-weighted cross-section, it exposes features of quantum field theory that scattering amplitudes do not, and it can be compared directly to data. As with scattering amplitudes, the analytic expressions require special functions beyond polylogarithms. In Henn et al., the EEC was computed to next-to-next-to-leading order (NNLO) for $\mathcal{N}=4$ super Yang-Mills (SYM) theory, and the result is expressed in terms of both harmonic polylogarithms (HPLs) and one two-fold integral, which contains elliptic curves. In this work, we report a complete result including the remaining elliptic sector, which is closely related to the sunrise Feynman integrals. We find the $j$-invariants of the EEC and the sunrise agree identically under a Möbius map, and thus the elliptic sector in the EEC lives on the $\Gamma_1(6)$ modular curve of the sunrise integral. We then express the answer in terms of iterated Eisenstein integrals, which can be evaluated to high precision quickly. The analytic form also allows a first study of the EEC Landau bootstrap, and the understanding of its function space in $\mathcal{N}=4$ SYM offers a concrete handle on the elliptic sector of the EEC in QCD. Many of the technical results in this paper were completed with AI under human supervision.

Tree-level matrix elements sit at the heart of collider event generation, but their cost rises rapidly just where additional resolved radiation becomes most important. We present pyAmpliCol, a public generator aimed at extending the practical reach of colour-resolved matrix elements to higher multiplicities. It builds on the colour-ordered, off-shell-current strategy of AmpliCol, providing fast access to individual leading-colour flows while retaining the option of next-to-leading or exact full colour. The latter introduces its own high-multiplicity bottleneck: the dense interference of factorially many colour orderings. pyAmpliCol addresses this contraction with a fast Fourier transform on the symmetric group, preserving the exact colour result while avoiding the direct pairwise sum. Representative full-colour benchmarks demonstrate substantial speedups over the reference calculations considered here. It supports Standard Model processes and a broad class of UFO models, selected or summed helicities, vectorised evaluation and controllable numerical precision. It further provides colour- and spin-correlated Born quantities and tree-level colour connections at arbitrary perturbative order, opening the same framework to local subtraction and other higher-order applications. Together, these capabilities connect high-multiplicity matrix elements to their use in event generation, merging, parton showers and precision calculations within a single generator.

Upcoming experiments are set to dramatically improve the search for charged lepton flavor violation, with the sensitivity to the rates of $\mu\to eee$ decay and $\mu N\to eN$ conversion expected to improve by four orders of magnitude in the near future. We study how these measurements reshape our understanding of fundamental interactions and their implications for the Higgs hierarchy problem. We consider the framework of Strongly Interacting Light Higgs with partial compositeness. In generic models of partial compositeness, the existing constraints from $\mu\to e\gamma$ and the electric dipole moment (EDM) of the electron require the scale of Higgs compositeness to be above $\sim\mathcal{O}(100)$ TeV. These mass scales lie beyond the direct reach of the LHC and envisioned future colliders and are comparable to, or higher than, those accessible to future $\mu\to3e$ and $\mu N\to eN$ searches. We show, however, that models where the strongly coupled sector has an accidental $U(3)\times\mathrm{CP}$ or $U(2)\times U(1) \times\mathrm{CP}$ symmetry, broken by the elementary–composite mixings, can substantially relax these constraints. In the $U(3)$ case, these symmetries (1) lead to an accidental alignment of the Yukawa and dipole couplings at leading order, suppressing $\mu\to e\gamma$ and the electron EDM, allowing the compositeness scale to lie in the few-TeV range; (2) are probed by the upcoming $\mu\to eee$ and $\mu N\to eN$ experiments; and (3) provide a direct target for current and future collider experiments. In the $U(2)\times U(1)$ case, $\mu\to e\gamma$ and the electron EDM remain important constraints, while upcoming searches for $\mu\to eee$, $\mu N\to eN$ and flavor-violating $\tau$ decays provide complementary probes. We discuss how these accidental symmetries can arise in the infrared compatibly with the dynamical generation of flavor hierarchies in the ultraviolet.

We construct the entanglement entropy of a general scattering process between one particle species (denoted as $A$) and the rest of the final state. Assuming a pure initial momentum eigenstate, we show that the reduced density matrix in particle $A$'s Fock space is block-diagonal in zero-, one- and multi-particle states, and is diagonal in the momentum basis for the one-particle state. As a result, we could write down the Von Neumann entropy of particle $A$, $S_A$, in terms of scattering probabilities and differential cross sections, assuming no more than one particle $A$ is produced in the final state. $S_A$ contains the information of both the total scattering probabilities (or cross sections) and the differential distributions — the latter depends on a phase-space resolution factor as a result of the infinite-dimensional momentum Hilbert space. Our result is general and model-independent since we consider the full final state from time evolution ($S|i\rangle$) rather than a specific outcome, and is applicable as long as the probability for producing multiple particle $A$ is subleading. We also obtain the $n\geq2$ Tsallis and Rényi entropies in our framework and find out that, at the leading order, they are proportional to the total scattering probability and carry no differential information.

Koide and Alikhanov proposed intriguing empirical relations among charged-lepton masses and neutrino mass splittings, respectively. We present mass-matrix textures that realise these relations and can jointly account for the observed lepton mixing angles, while yielding predictive correlations among them and the neutrino CP phases.

We study the gamma-ray sky at high latitudes for energies between 0.3 and 900 GeV. We search for a contribution in the high-latitude sky and in the region of the Galactic Stellar Halo that would be beyond known astrophysical emissions, i.e., the galactic diffuse emission, the isotropic mostly extragalactic gamma-ray background, the Fermi Bubbles, Loop I, the contribution from the Galactic Center Excess, and the known point and extended gamma-ray sources detected by the Fermi-LAT Collaboration. We perform a sequence of template fits to the Fermi gamma-ray data, testing different regions of interest of the galactic sky, utilizing a large set of alternative galactic diffuse emission models, and implementing alternative fitting schemes to assess the impact of increased modeling complexity of the gamma-ray sky. We find that the halo-like emission recently reported by Totani (2025) is real, but it is likely due to emission from the Fermi Bubbles rather than dark matter annihilation in the Galactic halo. We provide new templates for the Fermi Bubbles, including an updated model for the Flat Bubbles and a detailed model of their substructures, the Cocoons and the Inner Bubbles. In combination, these components account for the previously reported halo-like emission. We also estimate the associated fluxes and spectral properties of the Flat Bubbles, the Inner Bubbles, and the Cocoons. This updated model for the Fermi Bubbles provides new input toward understanding their origin.

We show how to construct perturbative effective field theories for strong phase transitions, where the standard tools of high-temperature dimensional reduction fail. By identifying the relevant power counting relations for the couplings, masses and background fields, we construct a controlled perturbative expansion adapted to this regime. We find that the order parameter field remains light at the transition, so that there is a controlled derivative expansion, even though large external fields need to be resummed. The resulting effective field theories for strong phase transitions live in three dimensions and have nonpolynomial field dependence. Applying our framework to a two-scalar model, we verify renormalisation scale cancellation through next-to-next-to-leading order and find decreasing corrections to the latent heat as the perturbative order is increased. Extending to include fermions and gauge fields, we identify a broad class of models in which strong-transition thermodynamics are systematically improvable.

The observed matter-antimatter asymmetry can be generated dynamically via leptogenesis, where a non-zero lepton asymmetry is generated first and then gets converted into baryon asymmetry via sphalerons. Creation of non-zero lepton asymmetry typically requires lepton number violation (LNV) which, within the seesaw framework, results in the Majorana nature of light neutrinos. With no signs of LNV at terrestrial experiments, we propose a novel leptogenesis scenario where LNV occurs at high temperatures while zero-temperature physics is consistent with the pure Dirac nature of neutrinos. In a concrete model of this "Dirac-Majorana flip-flop", the right chiral parts of Dirac neutrinos initially acquire a large Majorana mass in the early Universe when a singlet scalar field with two units of lepton number acquires a non-zero vacuum expectation value (VEV), thereby facilitating leptogenesis from out-of-equilibrium decay of heavy Majorana fermions. At lower temperatures, the VEV of the scalar singlet gets restored to zero to be consistent with lepton number conservation. A first-order VEV-restoring phase transition can lead to observable gravitational waves, while light Dirac neutrinos can generate detectable dark radiation at cosmic microwave background experiments.

We use the massive spinor-helicity formalism to describe a novel construction for massive spinors which allows one to connect the many choices of bases useful in the representation of amplitudes involving massive particles, and we use this to derive a new formulation for the general BCFW shift that is valid regardless whether or which of the particles involved are massive or massless. This formalism should help facilitate a more coherent implementation of on-shell recursion for computing amplitudes involving massive particles in four dimensions.

We solve the neutrino equations of motion in a half annulus, accounting for two spatial dimensions. At any location in the annulus, the neutrino momentum is characterized by a polar-angle distribution, two effective azimuthal angles, and an energy distribution. We explore how neutrinos change their flavor while decoupling from matter in the presence of the neutrino-driven hydrodynamical instability LESA (i.e., the Lepton-number Emission Self-sustained Asymmetry) during the stalled-shock phase of a core-collapse supernova. In our setup, LESA is responsible for an excess of $\nu_e$'s ($\bar\nu_e$'s) in the Northern (Southern) region of the annulus. Crossings in the $\nu_e$-$\bar\nu_e$ angular distributions appear in the ELN-depleted Southern region of the annulus, while crossings in the energy distributions of $\nu_e$-$\nu_x$ and $\bar\nu_e$-$\bar\nu_x$ are present throughout the annulus. We find that collisional instabilities drive flavor conversion just before neutrino decoupling, fast instabilities are prominent in the Southern region of the annulus, and slow instabilities dominate otherwise. Flavor conversion is most efficient in the Southern region and is responsible for a $5$-$10\%$ enhancement of the LESA dipole, independent of the neutrino-mass ordering. Our findings suggest that direction-dependent flavor conversion can have implications for the development of global neutrino asymmetries and hydrodynamical instabilities in core-collapse supernovae.

We show that a scale-invariant $U(1)$ gauge theory can naturally realize large curvature perturbations around the end of thermal inflation, seeding the formation of primordial black holes (PBHs). The allowed nonminimal gravitational interaction $\xi$ of the Higgs field induces a Hubble-scale negative mass-squared term for positive $\xi \sim \mathcal{O}(1)$, and triggers a second order phase transition that ends thermal inflation while keeping the extra $e$-folds small. This sharp contrast to the minimally coupled case allows the gauge coupling to be much smaller than unity. It turns out that field fluctuations are dominated by thermal fluctuations around the onset of the phase transition, and sufficiently amplified to produce an appreciable amount of PBHs with a wide range of possible masses. The associated scalar-induced gravitational waves (GWs) are accompanied by cosmic-string induced GWs coming from the breaking of the $U(1)$ symmetry. As a result, the generated PBH population can have a correlated GW signature relevant to pulsar timing arrays, space-based interferometers, or ground-based detectors.

Recent pulsar timing array (PTA) observations have reported evidence for a common low frequency signal consistent with a stochastic gravitational wave background. In this work, we investigate the cosmic string interpretation of this signal in a non-standard cosmological history between big bang nucleosynthesis and recombination, featuring an early matter-dominated era followed by a kination phase. Previous studies have shown that kination can significantly modify the cosmic-string-induced gravitational wave spectrum, generating characteristic features in the nanohertz range and producing a shape consistent with current PTA data. Building on this, we perform separate Bayesian analyses of the NANOGrav 15-year and EPTA DR2 New+ datasets to quantify the extent to which such a cosmological history is favored by the data. We find substantial evidence for a transient period of matter and kination domination over the standard cosmological history within a cosmic-string interpretation of the gravitational-wave signal, with a Bayes factor $3.63^{+0.22}_{-0.21}$ from the NANOGrav 15-year dataset, while leaving the inferred cosmic-string tension nearly unchanged. This cosmic-string-dominated scenario is particularly relevant if the contribution from supermassive black hole binaries (SMBHBs) is small, as hinted at by astrophysical population simulations. Compared with a scenario where gravitational waves are produced purely by SMBHBs, cosmic-string interpretations with and without an additional contribution from SMBHBs, across both expansion histories and datasets, reveal no significant preference.

We describe the construction of a spanning set of individually pure, planar master integrals involving massless particles in four dimensions which include all maximal-weight contributions at two loops. In this basis, every independent region associated with infrared divergence is individually matched by specific masters, with all other masters being manifestly finite in four dimensions.

In view of potential future improvements in the branching fractions of leptonic $\tau$ decays $\tau\to\ell\nu_\tau\bar\nu_\ell$, $\ell=e,\mu$, it is timely to derive the corresponding Standard-Model predictions beyond next-to-leading order. We provide such benchmark values for the fully inclusive decay widths, profiting from higher-order corrections that have been studied in the $\overline{\text{MS}}$ scheme up to three-loop order in the case of muon decay. To obtain complete next-to-next-to-leading-order results, we perform a numerical calculation of the two-loop coefficients in the on-shell scheme, including an evaluation of the hadronic effects, and compare the leptonic results to the known $\overline{\text{MS}}$ coefficients where available. Our final results are presented in the $\overline{\text{MS}}$ scheme, to be able to also include an estimate of the three-loop contribution. In addition, we comment on radiative and rare decays, whose consideration is critical for the conversion between $\overline{\text{MS}}$ and on-shell results.

It has been argued that in quantum gravity the Hilbert space associated with any closed universe is trivially one-dimensional. To reconcile this argument with the richness of our own universe, it was suggested that a nontrivial Hilbert space will emerge once an “observer" is included. Such an “observer" has been modeled in different ways. There are three concrete classes of models: $\textbf{1)}$ The “observer" is modeled by a term in the full Hamiltonian of the system which is linear in a phase space variable; $\textbf{2)}$ The “observer" is modeled in the quantum circuit model of holography as a subsystem in the closed universe which is entangled with an external non-gravitational system; $\textbf{3)}$ The “observer" is argued to be described by the emergent Goldstone bosons when the diffeomorphisms are spontaneously broken. In fact, the third class was discovered by an attempt to physically realize the first class. In this paper, we will show that the second class can also be unified into the third class. Our result indicates that the emergence of the “observer" is a manifestation of the $\textit{Massive Islands}$ paradigm. It demonstrates that the graviton mass is a feature of the quantum state. One should think of the islands as closed universes and the Goldstone boson associated with the graviton mass as the “observer", which is exactly the case at late-times for evaporating black holes. An implication of this work is that the “observer" can “observe" global symmetries in quantum gravity.

We present results from a detailed finite-size scaling analysis of the $3$-$d$, $Z(2)$ and $O(2)$ spin models in an external field $H$. Using high statistics Monte Carlo data, we obtain the leading finite-size scaling correction to the infinite volume scaling functions. We show that these corrections are proportional to $\widetilde{z}_L^2=1/(H L^{3/(1+1/\delta))})^{2}$. This provides the parametric form for finite-size corrections to bulk thermodynamic observables as well as the pseudo-critical temperatures determined at non-vanishing $H$. In particular, it allows to eliminate systematic errors in the analysis of the chiral phase transition temperature in (2+1)-flavor QCD, that arose from the previously not well-controlled ansatz for infinite volume extrapolations. We also establish the validity range of this leading order correction and point out that there are significant differences between the $3$-$d$, $O(2)$ and $Z(2)$ universality classes.