The distribution of effective spin ${\chi }_{\mathrm{eff}}$, a parameter that encodes the degree of spin-orbit alignment in a binary system, has been widely regarded as a robust discriminator between the isolated and dynamical formation pathways for merging binary black holes. Until the recent release of the GWTC-2 catalog, such tests have yielded inconclusive results due to the small number of events with measurable nonzero spins. In this work, we study the ${\chi }_{\mathrm{eff}}$ distribution of the binary black holes detected in the LIGO-Virgo O1–O3a observing runs. Our focus is on the degree to which the ${\chi }_{\mathrm{eff}}$ distribution is symmetric about ${\chi }_{\mathrm{eff}}=0$ and whether the data provide support for a population of negative-${\chi }_{\mathrm{eff}}$ systems. We find that the ${\chi }_{\mathrm{eff}}$ distribution is asymmetric at 95% credibility, with an excess of aligned-spin binary systems (${\chi }_{\mathrm{eff}}>0$) over antialigned ones. Moreover, we find that there is no evidence for negative-${\chi }_{\mathrm{eff}}$ systems in the current population of binary black holes. Thus, based solely on the ${\chi }_{\mathrm{eff}}$ distribution, dynamical formation is disfavored as being responsible for the entirety of the observed merging binary black holes, while isolated formation remains viable. We also study the mass distribution of the current binary black hole population, confirming that a single truncated power-law distribution in the primary source-frame mass, $m_{1\mathrm{s}}$, fails to describe the observations. Instead, we find that the preferred models have a steep feature at $m_{1\mathrm{s}}\sim 40{\mathrm{M}}_{\odot }$ consistent with a step and an extended, shallow tail to high masses.

Galactic charged cosmic rays (notably electrons, positrons, antiprotons, and light antinuclei) are powerful probes of dark matter annihilation or decay, in particular, for candidates heavier than a few MeV or tiny evaporating primordial black holes. Recent measurements by PAMELA, AMS-02, or Voyager on positrons and antiprotons already translate into constraints on several models over a large mass range. However, these constraints depend on Galactic transport models, in particular, the diffusive halo size, subject to theoretical and statistical uncertainties. We update the so-called MIN-MED-MAX benchmark transport parameters that yield generic minimal, median, and maximal dark-matter-induced fluxes; this reduces the uncertainties on fluxes by a factor of about 2 for positrons and 6 for antiprotons, with respect to their former version. We also provide handy fitting formulas for the associated predicted secondary antiproton and positron background fluxes. Finally, for more refined analyses, we provide the full details of the model parameters and covariance matrices of uncertainties.

By probing the population of binary black hole (BBH) mergers detected by LIGO-Virgo, we can infer properties about the underlying black hole formation channels. A mechanism known as pair-instability (PI) supernova is expected to prevent the formation of black holes from stellar collapse with mass greater than $\sim 40–65M_{\odot }$ and less than $\sim 120M_{\odot }$. Any BBH merger detected by LIGO-Virgo with a component black hole in this so-called PI mass gap likely originated from an alternative formation channel. Here, we firmly establish GW190521 as an outlier to the stellar-mass BBH population if the PI mass gap begins at or below $65M_{\odot }$. In addition, for a PI lower boundary of $40–50M_{\odot }$, we find it unlikely that the remaining distribution of detected BBH events, excluding GW190521, is consistent with the stellar-mass BBH population.

The method of using Hopf algebras for calculating Feynman integrals developed by Abreu et al. is applied to the two-loop nonplanar on-shell diagram with massless propagators and three external mass scales. We show that the existence of the method of cut Feynman diagrams comprising of the coproduct, the first entry condition and integrability condition that was found to be true for the planar case also holds for the nonplanar case; furthermore, the nonplanar symbol alphabet is the same as for the planar case. This is one of the main results of this work which have been obtained by a systematic analysis of the relevant cuts, using the symbolic manipulation codes hypexp and polylogtools. The obtained result for the symbol is cross-checked by an analysis of the known two-loop original Feynman integral result. In addition, we also reconstruct the full result from the symbol. This is the second main result of this paper.

We have performed a systematical analysis of lepton and quark mass models based on ${\mathrm{\Gamma }}_4\cong S_4$ modular symmetry with generalized $CP$ symmetry. We considered both cases; neutrinos are Majorana particles and Dirac particles. All possible nontrivial representation assignments of matter fields are considered, and the most general form of fermion mass matrices are given. The phenomenologically viable models with the lowest number of free parameters together with the results of fit are presented. We find out nine lepton models with seven real free parameters (including the real and imaginary parts of modulus for Majorana neutrinos) which can accommodate the lepton masses and neutrino oscillation data. The prediction for leptogenesis is studied in an example lepton model. The observed baryon asymmetry as well as lepton masses and mixing angles can be explained. For Dirac neutrinos, four lepton models with five real free couplings are compatible with the experimental data. Ten quark models containing seven couplings are found to be able to accommodate the hierarchical quark masses and mixing angles and the $CP$ violation phase. Furthermore, the $S_4$ modular symmetry can provide a unified description of lepton and quark flavor structure, and a benchmark model is presented.

In this paper, we show an explicit way to realize a TeV-scale vector leptoquark from the Pati-Salam unification with extra vectorlike families. The leptoquark mass is constrained to be heavier than PeV scale by the measurement of a flavor violating kaon decay, $K_L\to \mu e$, in conventional models. This strong constraint can be avoided by introducing vectorlike families consistently with the quark and lepton masses and Cabbibo-Kobayashi-Maskawa and Pontecorvo-Maki-Nakagawa-Sakata matrices. In this model, the vector leptoquark can be sufficiently light to explain the recent $b\to s\mu \mu$ anomaly, while the $b\to c\tau \nu$ anomaly is difficult to be explained due to the strong constraints from the $Z^{\prime }$ boson and vectorlike quark searches at the LHC. When the $b\to s\mu \mu$ anomaly is explained, we show that $\mathcal{O}(0.2)\%$ tuning is required in the fermion matrix, the future experiments in $\mu \to e\gamma$ and $\mu \text{−}e$ conversions will cover most available parameter space, and sizable neutral meson mixings, induced by the extra Higgs doublets, are unavoidable.

Motivated by the growing evidence for the possible lepton flavor universality violation after the first results from Fermilab’s muon $g-2$ measurement, we revisit one of the most widely studied anomaly free extensions of the standard model namely, gauged $L_{\mu }-L_{\tau }$ model, to find a common explanation for muon $g-2$ as well as baryon asymmetry of the universe via leptogenesis. The minimal setup allows TeV scale resonant leptogenesis satisfying light neutrino data while the existence of light $L_{\mu }-L_{\tau }$ gauge boson affects the scale of leptogenesis as the right handed neutrinos are charged under it. For $L_{\mu }-L_{\tau }$ gauge boson mass at GeV scale or above, the muon $g-2$ favored parameter space is already ruled out by other experimental data while bringing down its mass to sub-GeV regime leads to vanishing lepton asymmetry due to highly restrictive structures of lepton mass matrices at the scale of leptogenesis. Extending the minimal model with two additional Higgs doublets can lead to a scenario consistent with successful resonant leptogenesis and muon $g-2$ while satisfying all relevant experimental data.

We point out that light gauge boson mediators could induce new interference effects in neutrino-electron scattering that can be used to enhance the sensitivity of neutrino-flavor-selective high-intensity neutrino experiments, such as Deep Underground Neutrino Experiment (DUNE). We particularly emphasize a destructive interference effect, leading to a deficit between the Standard Model expectation and the experimental measurement of the differential cross sections, which is prominent only in either the neutrino or the antineutrino mode, depending on the mediator couplings. Therefore, the individual neutrino (or antineutrino) mode could allow for sensitivity reaches superior to the combined analysis and, moreover, could distinguish between different types of gauge boson mediators.

We analyze the lattice spacing dependence for the pion unpolarized matrix element of a quark bilinear operator with a Wilson link (parton quasidistribution functions operator, quasi-PDFs) in the rest frame, using 13 lattice spacings ranging from 0.032 to 0.121 fm. We compare results for three different fermion actions with or without good chiral symmetry on dynamical gauge ensembles from three collaborations. This investigation is motivated by the fact that the gauge link generates a $1/a$ divergence, the cancellation of which in many ratios can be numerically tricky. Indeed, our results show that this cancellation deteriorates with decreasing lattice spacing, and that the RI/MOM method leaves a linearly divergent residue for quasi-PDFs. We also show that in the Landau gauge the interaction between the Wilson link and the external state results in a linear divergence which depends on the discretized fermion action.

We calculate the gluon self-energy using quark energy projectors in a general quark-gluon plasma. By separating the quark field into positive- and a negative-energy modes, the quark loop constructed with the same mode is always convergent, and the divergence appears only in the mixed loop with different modes and is medium independent. After removing the divergence in vacuum, we obtain the one-loop gluon self-energy at finite temperature, chemical potential, and quark mass without approximation. With the method of quark-loop resummation, we calculate nonperturbatively the gluon Debye mass and thermodynamic potential. In the limit of small gluon momentum in comparison with temperature, chemical potential, and quark mass, our calculation comes back to the known HTL/HDL results in literature.

Krylov complexity, or K-complexity for short, has recently emerged as a new probe of chaos in quantum systems. It is a measure of operator growth in Krylov space, which conjecturally bounds the operator growth measured by the out of time ordered correlator (OTOC). We study Krylov complexity in conformal field theories by considering arbitrary 2d CFTs, free field, and holographic models. We find that the bound on OTOC provided by Krylov complexity reduces to bound on chaos of Maldacena, Shenker, and Stanford. In all considered examples including free and rational CFTs Krylov complexity grows exponentially, in stark violation of the expectation that exponential growth signifies chaos.

We construct three-dimensional, $\mathcal{N}=1$ off-shell supersymmetric massive Yang-Mills (YM) theory whose YM equation is “third-way” consistent. This means that the field equations of this model do not come from variation of a local action without additional fields, yet the gauge-covariant divergence of the YM equation still vanishes on shell. To achieve this, we modify the massive Majorana spinor equation so that its supersymmetry variation gives a modified YM equation whose bosonic part coincides with the third-way consistent pure massive YM model.

We derive a covariant expression for the renormalized holographic entanglement entropy for conformal field theories (CFTs) dual to quadratic curvature gravity in arbitrary dimensions. This expression is written as the sum of the bare entanglement entropy functional obtained using standard conical defect techniques, and a counterterm defined at the boundary of the extremal surface of the functional. The latter corresponds to the cod-2 self-replicating part of the extrinsic counterterms when evaluated on the replica orbifold. This renormalization method isolates the universal terms of the holographic entanglement entropy functional. We use it to compute the standard $C$-function candidate for CFTs of arbitrary dimension, and the type-B anomaly coefficient $c$ for four-dimensional CFTs.

We compute Schwinger-Keldysh effective action for a relativistic heavy quark (with constant background velocity) in strongly coupled $\mathcal{N}=4$ supersymmetric Yang-Mills plasma. The holographic dual description involves a noisy trailing string moving in Schwarzschild-${\mathrm{AdS}}_5$ black brane. The noise is caused by Hawking radiation emitted from string world sheet horizon. Besides quadratic terms, the effective action contains cubic interactions, which are entirely induced by the constant background velocity. The nonlinear fluctuation-dissipation relations for three-point functions are discussed based on holographic results.

We study covariant equations in quantum cosmology of an extended minisuperspace obtained by the Eisenhart–Duval lift. We find that a Dirac-type equation is naturally introduced in the extended minisuperspace. Explicit forms of the fundamental solutions are yielded for specific models. The possible further development in this direction is also discussed.

We provide evidence for the existence of a new strongly-coupled four dimensional $\mathcal{N}=2$ superconformal field theory arising as a nontrivial IR fixed point on the Coulomb branch of the mass-deformed superconformal Lagrangian theory with gauge group $G_2$ and four fundamental hypermultiplets. Notably, our analysis proceeds by using various geometric constraints to bootstrap the data of the theory, and makes no explicit reference to the Seiberg-Witten curve. We conjecture a corresponding vertex operator algebra and check that the vacuum character satisfies a linear modular differential equation of fourth order. We also propose an identification with existing class $\mathcal{S}$ constructions.

Covariant quantization of the electromagnetic field imposes the so-called gauge-fixing modification on the Lagrangian density. As a result of that, the total angular momentum operator receives at least one gauge-fixing-originated contribution, whose presence causes some confusion in the literature. The goal of this work is to discuss in detail why such a contribution, having no classical interpretation, is actually indispensable. For this purpose, we divide canonical and Belinfante-Rosenfeld total angular momentum operators into different components and study their commutation relations, their role in the generation of rotations of quantum fields, and their action on states from the physical sector of the theory. Then, we examine physical matrix elements of operators having gauge-fixing-related contributions, illustrating problems that one may encounter due to careless employment of the resolution of identity during their evaluation. The resolution of identity, in the indefinite-metric space of the covariantly quantized electromagnetic field, is extensively discussed because it takes a not-so-intuitive form if one insists on explicit projection onto states from the physical sector of the theory. Our studies are carried out in the framework of the Gupta-Bleuler theory of the free electromagnetic field. Relevant remarks about interacting systems, described by covariantly quantized electrodynamics, are given.

We extend the Lifshitz theory of the Casimir force to the case of two parallel magnetic metal plates possessing a spatially nonlocal dielectric response. By solving Maxwell equations in the configuration of an electromagnetic wave incident on the boundary plane of a magnetic metal semispace, the exact surface impedances are expressed in terms of its magnetic permeability and longitudinal and transverse dielectric functions. This allows application of the Lifshitz theory with reflection coefficients written via the surface impedances for calculation of the Casimir pressure between magnetic metal (Ni) plates whose dielectric responses are described by the alternative nonlocal response functions introduced for the case of nonmagnetic media. It is shown that at separations from 100 to 800 nm the Casimir pressures computed using the alternative nonlocal and local plasma response functions differ by less than 1%. At separations of a few micrometers, the predictions of these two approaches differ between themselves and between that one obtained using the Drude function by several tens of percent. We also compute the gradient of the Casimir force between Ni-coated surfaces of a sphere and a plate using the alternative nonlocal response functions and find a very good agreement with the measurement data. Implications of the obtained results determined by the off-shell quantum fluctuations to a resolution of longstanding problems in the Casimir physics are discussed.

We have explored the effect of both uniform and nonuniform distributed plasma medium on gravitational lensing around static black hole in the presence of perfect fluid dark matter (PFDM). We have shown that the PFDM and plasma parameters has opposite effect on the change of the value of the deflection angle of the light rays. It has been also shown that PFDM decreases the total magnification of image sources while the plasma causes opposite effect. Finally, we have analyzed the shadow cast by the black hole surrounded by PFDM and plasma. The increase of the PFDM parameter causes the decrease the size of the shadow of black hole.