We present a completely numerical method of calculating one-loop amplitudes. Our approach is built upon two different existing methods: the contour deformation and the extrapolation methods. Taking the best features of each of them, we devise an intuitive, stable and robust procedure which circumvents the problem of large cancellations and related numerical instabilities by calculating the complete amplitude at once. As a proof of concept, we use our method to calculate the $2\gamma \to (N-2)\gamma$ benchmark process, as well as the Higgs decay amplitude $H\to \gamma \gamma$.

We study electron-positron pair production by spatially inhomogeneous electric fields. Depending on the localization of the field, a critical point (critical surface) exists in the space of field configurations where the pair production probability vanishes. Near criticality, pair production exhibits universal properties similar to those of continuous phase transitions. We extend results previously obtained in the semiclassical (weak-field) critical regime to the deeply critical regime for arbitrary peak field strength. In this regime, we find an enhanced universality, featuring a unique critical exponent $\beta =3$ for all sufficiently localized fields. For a large class of field profiles, we also compute the nonuniversal amplitudes.

Perturbative probability conservation provides a strong constraint on the presence of new interactions of the Higgs boson. In this work we consider $CP$-violating Higgs interactions in conjunction with unitarity constraints in the gauge-Higgs and fermion-Higgs sectors. Injecting signal strength measurements of the recently discovered Higgs boson allows us to make concrete and correlated predictions of how $CP$ violation in the Higgs sector can be directly constrained through collider searches for either characteristic new states or telltale enhancements in multi-Higgs processes.

We revisit the multilepton $(ml)+{\cancel{E}}_T+X$ signatures of the inert doublet model (IDM) of dark matter in future LHC experiments for $m=3$, 4 and simulate, for the first time, the $m=5$ case. Here $X$ stands for any number of jets. We illustrate these signals with benchmark points consistent with the usual constraints like unitarity, perturbativity, the precision electroweak data, the observed dark matter relic density of the Universe and, most importantly, the stringent LHC constraints from the post–Higgs ($h$) discovery era like the measured $M_h$ and the upper bound on the invisible width of $h$ decay, which were not included in earlier analyses of multilepton signatures. We find that if the IDM is embedded in a grand desert scenario so that the unitarity constraint holds up to a very high scale, the whole of the highly restricted parameter space allowed by the above constraints can be probed at the LHC via the $3l$ signal for an integrated luminosity $\sim 3000{\mathrm{fb}}^{-1}$. On the other hand, if any new physics shows up at a scale $\sim 10\mathrm{TeV}$, only a part of the enlarged allowed parameter space can be probed. The $4l$ and $5l$ signals can help to discriminate among different IDM scenarios as and when sufficient integrated luminosity accumulates.

We utilize the LHC run-1 and -2 Higgs data to constrain the $CP$-violating top-Higgs couplings. In order to satisfy the current full Higgs data sets at $2\sigma$ level, the $CP$-odd component $C_t^p$ and the $CP$-even component $C_t^s$ have to be within the ranges $|C_t^p|<0.37$ and $0.85<C_t^s<1.20$, respectively, which is stronger than the LHC run-1 bound $|C_t^p|<0.54$ and $0.68<C_t^s<1.20$. With the new bound, we explore the impact on the $CP$-violating top-Higgs couplings in the Higgs production processes $pp\to t\overline{t}h,thj,hh$ at 13 TeV LHC, and $e^{+}{e}^{-}\to hZ,h\gamma$ at future 240 GeV Higgs factories. We find that the cross sections of $pp\to t\overline{t}h$, $pp\to thj$, $pp\to hh$, $e^{+}{e}^{-}\to hZ$ and $e^{+}{e}^{-}\to h\gamma$ can be enhanced up to 1.41, 1.18, 2.20, 1.001 and 1.09 times as large as the SM predictions, respectively. The future precision measurement of the process $e^{+}{e}^{-}\to h\gamma$ with an accuracy of 5% will be able to constrain $|C_t^p|<0.19$ at most at a 240 GeV $e^{+}{e}^{-}$ Higgs factory.

The more carefully defined and more appropriate $2^{++}$ tensor glueball current is a $S{U}_c(3)$ gauge-invariant, symmetric, traceless, and conserved Lorentz-irreducible tensor. After Lorentz decomposition, the invariant amplitude of the correlation function is abstracted and calculated based on the semiclassical expansion for quantum chromodynamics (QCD) in the instanton liquid background. In addition to taking the perturbative contribution into account, we calculate the contribution arising from the interaction (or the interference) between instantons and the quantum gluon fields, which is infrared free. Instead of the usual zero-width approximation for the resonances, the Breit-Wigner form with a correct threshold behavior for the spectral function of the finite-width three resonances is adopted. The properties of the $2^{++}$ tensor glueball are investigated via a family of the QCD Laplacian sum rules for the invariant amplitude. The values of the mass, decay width, and coupling constants for the $2^{++}$ resonance in which the glueball fraction is dominant are obtained.

We investigate the decays of the charmed baryons aiming at the systematic understanding of hadron internal structures based on the quark model by paying attention to heavy quark symmetry. We evaluate the decay widths from the one-pion emission for the known excited states, ${\mathrm{\Lambda }}_c^{*}(2595)$, ${\mathrm{\Lambda }}_c^{*}(2625)$, ${\mathrm{\Lambda }}_c^{*}(2765)$, ${\mathrm{\Lambda }}_c^{*}(2880)$, and ${\mathrm{\Lambda }}_c^{*}(2940)$, as well as for the ground states ${\mathrm{\Sigma }}_c(2455)$ and ${\mathrm{\Sigma }}_c^{*}(2520)$. The decay properties of the lower excited charmed baryons are well explained, and several important predictions for higher excited baryons are given. We find that the axial-vector-type coupling of the pion to the light quarks is essential, which is expected from chiral symmetry, to reproduce the decay widths especially of the low-lying ${\mathrm{\Lambda }}_c^{*}$ baryons. We emphasize the importance of the branching ratios of $\mathrm{\Gamma }({\mathrm{\Sigma }}_c^{*}\pi )/\mathrm{\Gamma }({\mathrm{\Sigma }}_c\pi )$ for the study of the nature of higher excited ${\mathrm{\Lambda }}_c^{*}$ baryons.

Semileptonic $B$ meson decays into the four lightest excited charmed meson states ($D_0^{*}$, $D_1^{*}$, $D_1$, and $D_2^{*}$) and their counterparts with $s$ quarks are investigated, including the full lepton mass dependence. We derive the standard model predictions for the differential branching fractions, as well as predictions for the ratios of the semitauonic and light-lepton semileptonic branching fractions. These can be systematically improved using future measurements of the total or differential semileptonic rates to $e$ and $\mu$, as well as the two-body hadronic branching fractions with a pion, related by factorization to the semileptonic rate at maximal recoil. To illustrate the different sensitivities to new physics, we explore the dependence of the ratio of semitauonic and light-lepton branching fractions to possible four-fermion scalar interactions.

We propose a unified description for the constants of motion for superintegrable deformations of the oscillator and Coulomb systems on $N$-dimensional Euclidean space, sphere, and hyperboloid. We also consider the duality between these generalized systems and present some examples.

A recent study by Bojowald and Paily [M. Bojowald and G. M. Paily, Phys. Rev. D 87, 044044 (2013).] provided a path toward the identification of an effective quantum-spacetime picture of loop quantum gravity, applicable in the “Minkowski regime,” the regime where the large-scale (coarse-grained) spacetime metric is flat. A pivotal role in the analysis is played by loop-quantum-gravity-based modifications to the hypersurface deformation algebra, which leave a trace in the Minkowski regime. We here show that the symmetry-algebra results reported by Bojowald and Paily are consistent with a description of spacetime in the Minkowski regime given in terms of the $\kappa$-Minkowski noncommutative spacetime, whose relevance for the study of the quantum-gravity problem had already been proposed for independent reasons.

In this paper, we have constructed boson star (BS) solutions in four-dimensional scalar-Gauss-Bonnet (sGB) theory. In order to have a nontrivial effect from the Gauss-Bonnet term, we invoked nonminimal coupling between a complex scalar field and the Gauss-Bonnet term with a coupling parameter, $\alpha$. We show that the scalar field can no longer take arbitrary value at the center of the star. Furthermore, boson stars in our higher-derivative theory turn out to be slightly massive but much more compact than those in the usual Einstein’s gravity. Interestingly, we found that for $\alpha <-0.4$ and $\alpha >0.8$, binding energy for all possible boson stars is always negative. This implies that these stars are intrinsically stable against the decay by dispersion. However, for $-0.4<\alpha <0.8$, boson stars can have both positive and negative binding energy depending on scalar field value at the center of the star. We also present the mass-radius and mass-frequency curves for boson stars and compare them with other compact objects in gravity models derived from the Gauss-Bonnet term.

Binary black holes have been in the limelight of late due to the detection of gravitational waves from coalescing compact binaries in the events GW150914 and GW151226. In this paper we study gravitational lensing by the binary black holes modeled as an equal mass Majumdar-Papapetrou dihole metric and show that this system displays features that are quite unprecedented and absent in any other lensing configuration investigated so far in the literature. We restrict our attention to the light rays which move on the plane midway between the two identical black holes, which allows us to employ various techniques developed for the equatorial lensing in the spherically symmetric spacetimes. If distance between the two black holes is below a certain threshold value, then the system admits two photon spheres. As in the case of a single black hole, infinitely many relativistic images are formed due to the light rays which turn back from the region outside the outer (unstable) photon sphere, all of which lie beyond a critical angular radius with respect to the lens. However, in the presence of the inner (stable) photon sphere, the effective potential after admitting minimum turns upwards and blows up for the smaller values of radii and the light rays that enter the outer photon sphere can turn back, leading to the formation of a new set of infinitely many relativistic images, all of which lie below the critical radius from the lens mentioned above. As the distance between the two black holes is increased, two photon spheres approach one another, merge and eventually disappear. In the absence of the photon sphere, apart from the formation of a finite number of discrete relativistic images, the system remarkably admits a radial caustic, which has never been observed in the context of relativistic lensing before. Thus the system of the binary black hole admits novel features both in the presence and absence of photon spheres. We discuss possible observational signatures and implications of the binary black hole lensing.

Motivated by the projectable Horava–Lifshitz model/mimetic matter scenario, we consider a particular modification of standard gravity, which manifests as an imperfect low pressure fluid. While practically indistinguishable from a collection of nonrelativistic weakly interacting particles on cosmological scales, it leaves drastically different signatures in the Solar system. The main effect stems from gravitational focusing of the flow of imperfect dark matter passing near the Sun. This entails strong amplification of imperfect dark matter energy density compared to its average value in the surrounding halo. The enhancement is many orders of magnitude larger than in the case of cold dark matter, provoking deviations of the metric in the second order in the Newtonian potential. Effects of gravitational focusing are prominent enough to substantially affect the planetary dynamics. Using the existing bound on the post-Newtonian parameter ${\beta }_{\mathrm{PPN}}$, we deduce a stringent constraint on the unique constant of the model.

The purpose of this paper is to check the impact of observer and Palatini $f(R)$ terms in the formulations of inhomogeneity factors of spherical relativistic systems. We consider the Lemaître-Tolman-Bondi dynamical model as a compact object and studied its evolution with both tilted and nontilted observers. We performed our analysis for particular cases of fluid distribution in tilted frame and found some energy density irregularity variables. We found that these variables are drastically different from those observed by a nontilted observer. The conformal flat dust and perfect matter contents are homogeneous as long as they impregnate vacuum core. However, this restriction is relaxed, when the complexity in the fluid description is increased. The radial fluid velocity due to tilted congruences and Palatini $f(R)$ curvature terms tends to produce hindrances in the appearance of energy-density inhomogeneities in the initially regular spherical stellar populations.

We describe the dimensional reduction of massive and partially massless spin-2 fields on general Einstein direct product manifolds. As with massless fields, the higher-dimensional gauge symmetry of the partially massless field displays itself upon dimensional reduction as a tower of Stückelberg symmetries for the massive modes of the tower. Unlike the massless case, the zero mode of the gauge symmetry does not display itself as a lower-dimensional non-Stückelberg gauge symmetry enforcing partial masslessness on the zero mode. Partial masslessness is destroyed by the dimensional reduction and the zero-mode gauge symmetry instead serves to eliminate the radion. In addition, we study the fully nonlinear dimensional reduction of de Rham-Gabadadze-Tolley massive gravity on a circle, which results in a massive scalar-tensor-vector theory which we expect to be ghost free, and whose scalar-tensor sector is a special case of mass-varying massive gravity.

Glitches in the rotational frequency of a spinning neutron star could be promising sources of gravitational wave signals lasting between a few microseconds to a few weeks. The emitted signals and their properties depend upon the internal properties of the neutron star. In neutron stars, the most important physical properties of the fluid core are the viscosity of the fluid, the stratification of flow in the equilibrium state, and the adiabatic sound speed. Such models were previously studied [C. A. van Eysden and A. Melatos, Classical Quantum Gravity 25, 225020 (2008); M. F. Bennett, C. A. van Eysden, and A. Melatos, Mon. Not. R. Astron. Soc. 409, 1705 (2010)] following simple assumptions on all contributing factors, in which the post-glitch relaxation phase could be driven by the well-known process of Ekman pumping [G. Walin, J. Fluid Mech. 36, 289 (1969); M. Abney and R. I. Epstein, J. Fluid Mech. 312, 327 (1996)]. We explore the hydrodynamic properties of the flow of fluid during this phase following more relaxed assumptions on the stratification of flow and the pressure-density gradients within the neutron star than previously studied. We calculate the time scales of duration as well as the amplitudes of the resulting gravitational wave signals, and we detail their dependence on the physical properties of the fluid core. We find that it is possible for the neutron star to emit gravitational wave signals in a wide range of decay time scales and within the detection sensitivity of aLIGO for selected domains of physical parameters.

In the context of generalized Brans-Dicke cosmology we use the Killing tensors of the minisuperspace in order to determine the unspecified potential of a scalar-tensor gravity theory. Specifically, based on the existence of contact symmetries of the field equations, we find four types of potentials which provide exactly integrable dynamical systems. We investigate the dynamical properties of these potentials by using a critical point analysis and we find solutions which lead to cosmic acceleration and under specific conditions we can have de-Sitter points as stable late-time attractors.

We study both the cosmological self-tuning and the local predictions (inside the Solar System) of the most general shift-symmetric beyond Horndeski theory. We first show that the cosmological self-tuning is generic in this class of theories: By adjusting a mass parameter entering the action, a large bare cosmological constant can effectively be reduced to a small observed one. Requiring then that the metric should be close enough to the Schwarzschild solution in the Solar System, to pass the experimental tests of general relativity, and taking into account the renormalization of Newton’s constant, we select a subclass of models which presents all desired properties: It is able to screen a big vacuum energy density, while predicting an exact Schwarzschild–de Sitter solution around a static and spherically symmetric source. As a by-product of our study, we identify a general subclass of beyond Horndeski theory for which regular self-tuning black hole solutions exist, in the presence of a time-dependent scalar field. We discuss possible future development of the present work.

We use a spherical model and an extended excursion set formalism with drifting diffusive barriers to predict the abundance of cosmic voids in the context of general relativity as well as $f(R)$ and symmetron models of modified gravity. We detect spherical voids from a suite of N-body simulations of these gravity theories and compare the measured void abundance to theory predictions. We find that our model correctly describes the abundance of both dark matter and galaxy voids, providing a better fit than previous proposals in the literature based on static barriers. We use the simulation abundance results to fit for the abundance model free parameters as a function of modified gravity parameters, and show that counts of dark matter voids can provide interesting constraints on modified gravity. For galaxy voids, more closely related to optical observations, we find that constraining modified gravity from void abundance alone may be significantly more challenging. In the context of current and upcoming galaxy surveys, the combination of void and halo statistics including their abundances, profiles and correlations should be effective in distinguishing modified gravity models that display different screening mechanisms.

We conduct an analysis of the Planck 2015 data that is complete in reionization observables from the large angle polarization $E$-mode spectrum in the redshift range $6<z<30$. Based on 5 principal components, all of which are constrained by the data, this single analysis can be used to infer constraints on any model for reionization in the same range; we develop an effective likelihood approach for applying these constraints to models. By allowing for an arbitrary ionization history, this technique tests the robustness of inferences on the total optical depth from the usual steplike transition assumption, which is important for the interpretation of many other cosmological parameters such as the dark energy and neutrino mass. The Planck 2015 data not only allow a high redshift $z>15$ component to the optical depth but prefer it at the $2\sigma$ level. This preference is associated with excess power in the multipole range $10\lesssim \ell \lesssim 20$ and may indicate high redshift ionization sources or unaccounted for systematics and foregrounds in the 2015 data.