In the family grand unification theory (GUT) models, we propose that gauge U(1)’s beyond the minimal GUT gauge group are family gauge symmetries. For the symmetry $L_{\mu }-L_{\tau }$, i.e., $Q_2-Q_3$ in our case, to be useful for the LHC anomaly, we discuss an SU(9) family GUT and also present an example in Georgi’s SU(11) family GUT.

A new method for the model-independent determination of the light-cone distribution amplitude of the $B$-meson in heavy quark effective theory (HQET) is proposed by combining the large momentum effective theory and the numerical simulation technique on the Euclidean lattice. We demonstrate the autonomous scale dependence of the nonlocal quasi-HQET operator with the aid of the auxiliary field approach, and further determine the perturbative matching coefficient entering the hard-collinear factorization formula for the $B$-meson quasidistribution amplitude at the one-loop accuracy. These results will be crucial to explore the partonic structure of heavy-quark hadrons in the static limit and to improve the theory description of exclusive $B$-meson decay amplitudes based upon perturbative QCD factorization theorems.

We report the masses of the lightest spin-0 and spin-2 glueballs obtained in an extensive lattice study of the continuum and infinite volume limits of $Sp(N_c)$ gauge theories for $N_c=2$, 4, 6, 8. We also extrapolate the combined results toward the large-$N_c$ limit. We compute the ratio of scalar and tensor masses, and observe evidence that this ratio is independent of $N_c$. Other lattice studies of Yang-Mills theories at the same space-time dimension provide a compatible ratio. We further compare these results to various analytical ones and discuss them in view of symmetry-based arguments related to the breaking of scale invariance in the underlying dynamics, showing that a constant ratio might emerge in a scenario in which the $0^{++}$ glueball is interpreted as a dilaton state.

The dynamical instability of relativistic polytropic spheres, embedded in a spacetime with a repulsive cosmological constant, is studied in the framework of general relativity. We apply the methods used in our preceding paper to study the trapping polytropic spheres with $\mathrm{\Lambda }=0$, namely, the critical point method and the infinitesimal and adiabatic radial perturbations method developed by Chandrasekhar. We compute numerically the critical adiabatic index, as a function of the parameter $\sigma =p_{\mathrm{c}}/({\rho }_{\mathrm{c}}{c}^2)$, for several values of the cosmological parameter $\lambda$ giving the ratio of the vacuum energy density to the central energy density of the polytrope. We also determine the critical values for the parameter ${\sigma }_{\mathrm{cr}}$, for the onset of instability, by using both approaches. We found that for large values of the parameter $\lambda$, the differences between the values of ${\sigma }_{\mathrm{cr}}$ calculated by the critical point method differ from those obtained via the radial perturbations method. Our results, given by both applied methods, indicate that large values of the cosmological parameter $\lambda$ have relevant effects on the dynamical stability of the polytropic configurations.

Binary-black-hole orbits precess when the black-hole spins are misaligned with the binary’s orbital angular momentum. The apparently complicated dynamics can in most cases be described as simple precession of the orbital angular momentum about an approximately fixed total angular momentum. However, the imprint of the precession on the observed gravitational-wave signal is yet more complicated, with a nontrivial time-varying dependence on the black-hole dynamics, the binary’s orientation and the detector polarization. As a result, it is difficult to predict under which conditions precession effects are measurable in gravitational-wave observations, and their impact on both signal detection and source characterization. We show that the observed waveform can be simplified by decomposing it as a power series in a new precession parameter $b=\tan (\beta /2)$, where $\beta$ is the opening angle between the orbital and total angular momenta. The power series is made up of five harmonics, with frequencies that differ by the binary’s precession frequency, and individually do not exhibit amplitude and phase modulations. In many cases, the waveform can be well approximated by the two leading harmonics. In this approximation we are able to obtain a simple picture of precession as caused by the beating of two waveforms of similar frequency. This enables us to identify regions of the parameter space where precession is likely to have an observable effect on the waveform, and to propose a new approach to searching for signals from precessing binaries, based upon the two-harmonic approximation.

We calculate six invariant terms of a gravitational field theory that nonlinearly realizes the conformal/Poincaré quotient and reduce to the known conformal Galileons in the limit when only the conformal mode is kept. Five of the six terms are regular coset terms, while the sixth is a Wess-Zumino (WZ) term that gives the well-known gravitational action for the trace anomaly. The obtained terms can be embedded in a quantum effective field theory (EFT) without spoiling their key features, although at a cost of certain fine-tunings. The additional massive modes that appear in the EFT would have been troublesome, however, for sub-Planckian curvatures their masses are (super)-Planckian, and therefore the respective states are outside of the EFT regime. We discuss certain novel cosmological solution of this theory and their validity within the EFT. Furthermore, we show that the obtained 4D terms, except the WZ term, can also be derived from higher dimensional Lovelock terms by reducing the latter to the genuinely four-dimensional terms according to a well-defined algorithm.

The present paper derives the post-Newtonian Lagrangian of translational motion of $N$ arbitrarily structured bodies with all mass and spin multipoles in a scalar-tensor theory of gravity. The multipoles depend on time and evolve in accordance with their own dynamic equations of motion. The Lagrangian is retrieved from the post-Newtonian equations of motion by solving the inverse problem of the Lagrangian mechanics and generalizes a well-known Lagrangian of pole-dipole-quadrupole massive particles to the particles of higher multipolarity. Analytic treatment of the higher-order multipole contributions is important for more rigorous computation of gravitational waveform of inspiralling compact binaries at the latest stage of their orbital evolution before merger when tidal and rotational deformations of stars are no longer small and rapidly change in time. The Lagrangian of an $N$-body system with arbitrary mass and spin multipoles is instrumental for formulation of the post-Newtonian conservation laws of energy, momenta and the integrals of the center of mass.

The galaxy bispectrum contains a wealth of information about the early universe, gravity, as well as astrophysics such as galaxy bias. Here, we study the parity-odd imaginary part of the galaxy bispectrum which is hitherto largely unexplored. In the standard cosmological model, the odd-parity bispectrum is generated by galaxy velocities through redshift-space distortions, yielding a guaranteed signal which provides a useful consistency test of measurements of galaxy clustering. While small in the case of general relativity coupled with smooth dark energy, the signal could be larger in modified gravity scenarios. Thus, the odd bispectrum offers a clean way for searching for new physics.

We provide further evidence that a massless cosmological scalar field with a nonminimal coupling to the Ricci curvature of the type $M_{\mathrm{pl}}^2(1+\xi {\sigma }^n/M_{\mathrm{pl}}^n)$ alleviates the existing tension between local measurements of the Hubble constant and its inference from cosmic microwave background anisotropies and baryonic acoustic oscillations data in the presence of a cosmological constant. In these models, the expansion history is modified compared to $\mathrm{\Lambda }\mathrm{CDM}$ at early time, mimicking a change in the effective number of relativistic species, and gravity weakens after matter-radiation equality. Compared to $\mathrm{\Lambda }\mathrm{CDM}$, a quadratic ($n=2$) coupling increases the Hubble constant when Planck 2018 (alone or in combination with BAO and SH0ES) measurements data are used in the analysis. Negative values of the coupling, for which the scalar field decreases, seem favored and consistency with the Solar System can be naturally achieved for a large portion of the parameter space without the need of any screening mechanism. We show that our results are robust to the choice of $n$, also presenting the analysis for $n=4$.

Our Moon is a natural giant direct-detection target for constraining dark matter. By considering the dark matter capture rate of the Moon, we obtain some constraints of the spin-independent elastic scattering cross section of dark matter particles on nucleons ${\sigma }_p^{\mathrm{SI}}$ using the background neutrino data. The upper limits of ${\sigma }_p^{\mathrm{SI}}$ can be constrained to $\sim {10}^{-38}–{10}^{-36}{\mathrm{cm}}^2$ for certain “resonance dark matter mass” ranges. These stringent astrophysical constraints are complementary to the constraints obtained by the direct-detection experiments.

We show that the nonlocal two-flavor Nambu–Jona-Lasinio model predicts the enhancement of both chiral and axial symmetry breaking as the chiral imbalance of hot QCD matter, regulated by a chiral chemical potential ${\mu }_5$, increases. The two crossovers are reasonably close to each other in the range of ${\mu }_5$ examined here, and the pseudocritical temperatures rise with ${\mu }_5$. The curvatures of the chiral and axial crossovers for the chiral quark chemical potential approximately coincide and give ${\kappa }_5\simeq -0.011$. We point out that the presence of ${\mu }_5$ in thermodynamic equilibrium is inconsistent with the fact that the chiral charge is not a Noether-conserved quantity for massive fermions. The chiral chemical potential should not, therefore, be considered as a true chemical potential that sets a thermodynamically stable environment in the massive theory, but rather as a new coupling that may require a renormalization in the ultraviolet domain. The divergence of an unrenormalized chiral density, coming from zero-point fermionic fluctuations, is a consequence of this property. We propose a solution to this problem via a renormalization procedure.

We discuss the thermoelectric effect of hot and dense hadron gas within the framework of the hadron resonance gas model. Using the relativistic Boltzmann equation within the relaxation time approximation we estimate the Seebeck coefficient of the hot and dense hadronic medium with a gradient in temperature and baryon chemical potential. The hadronic medium in this calculation is modeled by the hadron resonance gas (HRG) model with hadrons and their resonances up to a mass cutoff $\mathrm{\Lambda }\sim 2.6\mathrm{GeV}$. We also extend the formalism of the thermoelectric effect for a nonvanishing magnetic field. The presence of magnetic field also leads to a Hall type thermoelectric coefficient (Nernst coefficient) for the hot and dense hadronic matter apart from a magneto-Seebeck coefficient. We find that generically in the presence of a magnetic field the Seebeck coefficient decreases while the Nernst coefficient increases with the magnetic field. At higher temperature and/or baryon chemical potential these coefficients approach to their values at vanishing magnetic field.

We present our studies of four-jet double parton scattering production in proton-nucleus collisions within the framework of the pythia8 event generator. We demonstrate that double absorptive processes in $\mathrm{p}A$ generated by the Angantyr model in pythia8 give an enhancement of the total double parton scattering cross section similar to the predictions by Strikman and Treleani in 2001. Additionally, we discuss how the growth of activity in the direction of a nucleus affects an $A$ scaling of a total double parton scattering cross section in proton-nucleus collisions.

We investigate open charm meson production in fixed-target LHCb experiment at $\sqrt{s}=86.6\mathrm{GeV}$ in $p+{}^4\mathrm{He}$ collisions. Theoretical calculations of charm cross section are done in the framework of the $k_T$-factorization approach. Its application in the kinematical range never examined before is carefully discussed. We consider different schemes for the calculations relevant for different unintegrated (transverse momentum dependent) parton densities in a proton. We include in the analysis both Catani-Ciafaloni-Fiorani-Marchesini (CCFM)—and Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP)-based models of unintegrated parton distributions appropriate for the considered kinematics. Integrated as well as differential cross sections as a function of $D^0$ meson rapidity and transverse momentum are shown and compared with the experimental data. As a reference point, predictions of next-to-leading order collinear approach are also presented and discussed. A very good agreement between the experimental data and the $k_T$-factorization predictions was obtained. Both the CCFM and the DGLAP-based frameworks for parton distributions in a proton are successfully used to explain the LHCb fixed-target open charm cross section.

We argue that the Landau-Hall states provide a suitable framework for formulating the Berezin-Toeplitz quantization of classical functions on a Kähler phase space. We derive the star-products for such functions in this framework and generalize the Berezin-Toeplitz quantization to matrix-valued classical functions. We also comment on how this is related to different calculations of the effective action for Hall systems.

We revisit supersymmetric nonlinear sigma models on the target manifold $C{P}^{N-1}$ and $SO(N)/SO(N-2)\times U(1)$ in four dimensions. These models are formulated as gauged linear models, but it is indicated that the Wess-Zumino term should be added to the linear model since the hidden local symmetry is anomalous. Applying a procedure used for the quantization of anomalous gauge theories to the nonlinear models, we determine the form of the Wess-Zumino term, by which a global symmetry in the linear model becomes smaller in the action than the conventional one. Moreover, we analyze the resulting linear model in the $1/N$ leading order. Consequently, we find that the model has a critical coupling constant similar to bosonic models. In the weak coupling regime, the $U(1)$ local symmetry is broken but supersymmetry is never broken. In contrast to the bosonic case, it is impossible to find stable vacua in the strong coupling regime as far as in the $1/N$ leading order. These results are straightforwardly generalized to the case of the Hermitian symmetric space.

We study the gauge covariance of the massless fermion propagator in three-dimensional quenched quantum electrodynamics in the framework of dimensional regularization in $d=3-2ϵ$. Assuming the finiteness of the quenched perturbative expansion, that is the existence of the limit $ϵ\to 0$, we state that, exactly in $d=3$, all odd perturbative coefficients, starting with the third order one, should be zero in any gauge.

In this new era of gravitational wave astrophysics, observations indicate the likely existence of black holes with significant spin. In order to better understand the potential imprint orbital dynamics have on the multimessenger data, we include rotation of the primary mass to leading order in the analysis of the stability boundary pertaining to the triangular equilibrium points, $L_4$ and $L_5$, in the relativistic, restricted, circular, three-body problem. For Lagrange point stability, these rotation effects are of the same order as the leading order relativistic corrections ignoring rotation, and they make both $L_4$ and $L_5$ more stable for retrograde orbital motion.

Detection of primordial gravitational-wave backgrounds generated during the early Universe phase transitions is a key science goal for future ground-based detectors. The rate of compact binary mergers is so large that their cosmological population produces a confusion background that could masquerade the detection of potential primordial stochastic backgrounds. In this paper, we study the ability of current and future detectors to resolve the confusion background to reveal interesting primordial backgrounds. The current detector network of LIGO and Virgo and the upcoming KAGRA and LIGO-India will not be able to resolve the cosmological compact binary source population, and its sensitivity to stochastic background will be limited by the confusion background of these sources. We find that a network of three (and five) third generation (3G) detectors of Cosmic Explorer and Einstein Telescope will resolve the confusion background produced by binary black holes leaving only about 1.3% (respectively, 0.075%) unresolved; in contrast, as many as 25% (respectively, 7.7%) of binary neutron star sources remain unresolved. Consequently, the binary black hole population will likely not limit observation of primordial backgrounds, but the binary neutron star population will limit the sensitivity of 3G detectors to ${\mathrm{\Omega }}_{\mathrm{GW}}\sim {10}^{-11}$ at 10 Hz (respectively, ${\mathrm{\Omega }}_{\mathrm{GW}}\sim 3\times {10}^{-12}$).

In gravity theories that exhibit spontaneous scalarization, astrophysical objects are identical to their general relativistic counterpart until they reach a certain threshold in compactness or curvature. Beyond this threshold, they acquire a nontrivial scalar configuration, which also affects their structure. The onset of scalarization is controlled only by terms that contribute to linear perturbation around solutions of general relativity. The complete set of these terms has been identified for generalized scalar-tensor theories. Stepping on this result, we study the onset on scalarization in generalized scalar-tensor theories and determine the relevant thresholds in terms of the contributing coupling constants and the properties of the compact object.