We evaluate the quartic ghost and quark Green’s functions as well as the gluon-ghost, gluon-quark and ghost-quark four-point functions of quantum chromodynamics at one loop at the fully symmetric point in a linear covariant gauge. Similar expressions for the analogous Green’s functions in quantum electrodynamics are also provided.

Critical overdensity ${\delta }_c$ is a key concept in estimating the number count of halos for different redshift and halo-mass bins, and therefore, it is a powerful tool to compare cosmological models to observations. There are currently two different prescriptions in the literature for its calculation, namely, the differential-radius and the constant-infinity methods. In this work we show that the latter yields precise results only if we are careful in the definition of the so-called numerical infinities. Although the subtleties we point out are crucial ingredients for an accurate determination of ${\delta }_c$ both in general relativity and in any other gravity theory, we focus on $f(R)$-modified gravity models in the metric approach; in particular, we use the so-called large ($F=1/3$) and small-field ($F=0$) limits. For both of them, we calculate the relative errors (between our method and the others) in the critical density ${\delta }_c$, in the comoving number density of halos per logarithmic mass interval $n_{\ln M}$, and in the number of clusters at a given redshift in a given mass bin $N_{\mathrm{bin}}$, as functions of the redshift. We have also derived an analytical expression for the density contrast in the linear regime as a function of the collapse redshift $z_c$ and ${\mathrm{\Omega }}_{m0}$ for any $F$.

One of the most intriguing hints of a departure from the standard cosmological model is a large-scale dipolar power asymmetry in the cosmic microwave background (CMB). If not a statistical fluke, its origins must lie in the modulation of the position-space fluctuations via a physical mechanism, which requires the observation of new modes to confirm or refute. We introduce an approach to describe such a modulation in $k$ space and calculate its effects on the CMB temperature and lensing. We fit the $k$-space modulation parameters to Planck 2015 temperature data and show that CMB lensing will not provide us with enough independent information to confirm or refute such a mechanism. However, our approach elucidates some poorly understood aspects of the asymmetry, in particular that it is weakly constrained. Also, it will be particularly useful in predicting the effectiveness of polarization in testing a physical modulation.

The long-standing anomaly in the anomalous magnetic moment of the muon indicates the presence of chirality violating new physics contributions. A possible solution involves scalar leptoquarks with left- and right-handed couplings to the top quark. Two such representations of scalar leptoquarks exist for which the contribution to $(g-2{)}_{\mu }$ can possess an $m_t/m_{\mu }$ enhancement compared to the Standard Model. The leptoquarks also induce loop corrections to $Z$ couplings to muons which probe as well new physics contributions which possess sources of $SU(2)$ symmetry breaking and we find that this effect should be observable at future experiments as GigaZ or TLEP. Furthermore, once interactions of the leptoquark with tau leptons and electrons are present, additional correlated effects in anomalous magnetic moments, $Z\to \ell {\ell }^{\prime }$ and $\ell \to {\ell }^{\prime }\gamma$, arise, which can be used to test the model and to determine the flavor structure of the couplings. We find that the two representations of leptoquarks can be distinguished also from low-energy experiments: one representation predicts constructive interference with the Standard Model in $Z$ couplings to leptons and effects in $B\to K^{(\star )}\nu \overline{\nu }$, while the other representation interferes destructively with the Standard Model in $Z$ couplings to leptons and gives a $C_9=C_{10}$-like contribution to $b\to s{\ell }^{+}{\ell }^{-}$ processes.

We show how successful supersymmetric hybrid inflation is realized in realistic models where the resolution of the minimal supersymmetric standard model $\mu$ problem is intimately linked with axion physics. The scalar fields that accompany the axion, such as the saxion, are closely monitored during and after inflation to ensure that the axion isocurvature perturbations lie below the observational limits. The scalar spectral index $n_{\mathrm{s}}\simeq 0.96–0.97$, while the tensor-to-scalar ratio $r$, a canonical measure of gravity waves, lies well below the observable range in our example. The axion domain walls are inflated away, and depending on the axion decay constant $f_{\mathrm{a}}$ and the magnitude of the $\mu$ parameter, the axions and/or the lightest supersymmetric particle compose the dark matter in the Universe. Nonthermal leptogenesis is naturally implemented in this class of models.

Observation of ${\tau }^{-}\to {\eta }^{(\prime )}{\pi }^{-}{\nu }_{\tau }$ decays at Belle-II would indicate either a manifestation of isospin symmetry breaking or genuine second class current (SCC) effects. The corresponding radiative ${\tau }^{-}\to {\eta }^{(\prime )}{\pi }^{-}{\nu }_{\tau }\gamma$ decay channels are not suppressed by $G$-parity considerations and may represent a serious background in searches of SCCs in the former. We compute the observables associated to these radiative decays using resonance chiral Lagrangians and conclude that vetoing photons with $E_{\gamma }>100\mathrm{MeV}$ should get rid of this background in the Belle-II environment while searching for the ${\tau }^{-}\to \eta {\pi }^{-}{\nu }_{\tau }$ channel. Similar considerations hold inconclusive for decays involving the ${\eta }^{\prime }$, given the theory’s uncertainties in the prediction of the ${\tau }^{-}\to {\eta }^{\prime }{\pi }^{-}{\nu }_{\tau }$ branching ratio. Still, additional kinematics-based cuts should be able to suppress this background in the ${\eta }^{\prime }$ case to a negligible level.

Single top quark production is a powerful process to search for new physics signs. In this work we propose and investigate a search for top quark flavor-changing neutral currents (FCNCs) via a photon using direct single top quark production events in proton-proton collisions at the LHC at CERN. We show that the direct single top quark final state can provide constraints on the strengths of top-quark-$\gamma$ and top-quark-gluon FCNC couplings simultaneously. Results of a search for direct single top quark production at the LHC at a center-of-mass energy of 8 TeV performed by the ATLAS Collaboration are used to set first experimental limits on the anomalous FCNC top decay branching fractions $\mathcal{B}(\mathrm{t}\to \mathrm{u}\gamma )<0.05\%$ and $\mathcal{B}(\mathrm{t}\to \mathrm{c}\gamma )<0.14\%$ via direct single top quark production. Finally, the sensitivity of the proposed channel for probing the top-quark-$\gamma$ couplings at 13 TeV is presented.

We perform three-dimensional numerical relativity simulations of homogeneous and inhomogeneous expanding spacetimes, with a view toward quantifying nonlinear effects from cosmological inhomogeneities. We demonstrate fourth-order convergence with errors less than one part in $10^6$ in evolving a flat, dust Friedmann-Lemaître-Roberston-Walker spacetime using the Einstein Toolkit within the Cactus framework. We also demonstrate agreement to within one part in $10^3$ between the numerical relativity solution and the linear solution for density, velocity and metric perturbations in the Hubble flow over a factor of $\sim 350$ change in scale factor (redshift). We simulate the growth of linear perturbations into the nonlinear regime, where effects such as gravitational slip and tensor perturbations appear. We therefore show that numerical relativity is a viable tool for investigating nonlinear effects in cosmology.

It has been shown that the product of the entropies of the inner Cauchy and outer event horizon of the charged axisymmetric and stationary black holes is a universal formula, which is independent of the black hole’s mass. In this paper, we investigate this universality for the two kinds of rotating black holes in the three-dimensional gravity models. In fact, we study the spacelike warped anti–de Sitter black hole in the new massive gravity and the Bañados, Teitelboim, and Zanelli black hole in the minimal massive gravity. We show that this rule is held in the first theory. By contrast, in the latter case which includes a holographic gravitational anomalous term, we obtain that the universality does not work and the product depends on the mass. As a complement to the above verification, we also study the thermodynamic properties of these black holes.

We examine the hypothesis that inflation is primarily driven by vacuum energy at a scale indicated by gauge coupling unification. Concretely, we consider a class of hybrid inflation models wherein the vacuum energy associated with a grand unified theory condensate provides the dominant energy during inflation, while a second “inflaton” scalar slow rolls. We show that it is possible to obtain significant tensor-to-scalar ratios while fitting the observed spectral index.

We present the generalization to nonpositive definite spectral functions of a recently proposed Bayesian deconvolution approach (BR method). The novel prior used here retains many of the beneficial analytic properties of the original method; in particular, it allows us to integrate out the hyperparameter $\alpha$ directly. To preserve the underlying axiom of scale invariance, we introduce a second default-model related function, whose role is discussed. Our reconstruction prescription is contrasted with existing direct methods, as well as with an approach where shift functions are introduced to compensate for negative spectral features. A mock spectrum analysis inspired by the study of gluon spectral functions in QCD illustrates the capabilities of this new approach.

We explore the influence of finite-volume effects on cumulants of baryon/quark number fluctuations in a nonperturbative chiral model. In order to account for soft modes, we use the functional renormalization group in a finite volume, using a smooth regulator function in momentum space. We compare the results for a smooth regulator with those for a sharp (or Litim) regulator, and show that in a finite volume, the latter produces spurious artifacts. In a finite volume there are only apparent critical points, about which we compute the ratio of the fourth- to the second-order cumulant of quark number fluctuations. When the volume is sufficiently small the system has two apparent critical points; as the system size decreases, the location of the apparent critical point can move to higher temperature and lower chemical potential.

Violation of $CP$ invariance is a quite relevant phenomenon that is found in the Standard Model, though in small amounts. This has been an incentive to look for high-energy descriptions in which $CP$ violation is increased, thus enhancing effects that are suppressed in the Standard Model, such as the electric dipole moments of elementary particles. In the present investigation, we point out that charged currents in which axial couplings are different from vector couplings are able to produce one-loop contributions to electric dipole moments of charged leptons if neutrinos are massive and if these currents violate $CP$. We develop our discussion around charged currents involving heavy neutrinos and a $W^{\prime }$ gauge boson coupling to Standard Model charged leptons. Using the most stringent bound on the electron electric dipole moment, provided by the ACME Collaboration, we determine that the upper bound on the difference between axial and vector currents lies within $\sim {10}^{-10}$ and $\sim {10}^{-7}$ for heavy-neutrino masses between 0.5 TeV and 6 TeV and if the $W^{\prime }$ mass is within 0.45 TeV–7 TeV. This possibility is analyzed altogether with the anomalous magnetic moments of charged leptons, among which we estimate, for the $\tau$ lepton, an anomalous magnetic moment contribution between $\sim {10}^{-8}$ and $\sim {10}^{-10}$ for neutrino masses ranging from 0.5 TeV to 6 TeV and a $W^{\prime }$ mass between 0.45 TeV and 7 TeV. The general charged currents are also used to calculate the branching ratio for $\mu \to e\gamma$, which gets suppressed if the set of masses of heavy neutrinos is quasidegenerate. In a scenario of nondegenerate neutrino masses, we find that regions of neutrino and $W^{\prime }$ masses in which the contributions to this flavor-changing branching ratio are lower than the current upper bound exist. We show that such regions can be widened if the $W^{\prime }$ gauge boson mass is larger.

In scenarios where dark matter interacts differently with protons and neutrons (isospin-violating dark matter), the interpretation of the experimental limits on the dark matter spin-independent cross section may be significantly modified. On the one hand, the direct detection constraints are shifted depending on the target nucleus, possibly changing the hierarchy among different experiments. On the other hand, the relative strength between the bounds from neutrino detectors and those from direct detection experiments is altered, allowing the former to be more competitive. In this paper, the status of isospin-violating dark matter is assessed in the light of recent data, and the prospects for its detection in the near future are analyzed. We find, for example, that there are regions in the parameter space where IceCube currently provides the most stringent limits on the spin-independent cross section, or others where the expected sensitivity of DEAP-3600 is well above the LUX exclusion limit. Our results highlight the complementarity among different targets in direct detection experiments, and between direct detection and neutrino searches in the quest for a dark matter signal.

The Abelian Higgs model is studied on the lattice with charge conjugate boundary conditions. A locally gauge invariant operator for the charged scalar field is constructed, and the charged scalar particle mass is calculated in the Coulomb phase of the lattice model. Agreement is found with the mass calculated in Coulomb gauge. The gauge invariant scalar field operator is used to calculate the Higgs boson mass in the Higgs region and to show that the charged particle disappears from the spectrum in the confined regime.

The phase diagram of strong interaction matter is analyzed utilizing the Nambu–Jona-Lasinio model. Special emphasis is placed on its dependence on an external magnetic field and isospin chemical potential. Using flavor mixing induced by instanton effects the influence of isospin breaking due to the magnetic field and the isospin chemical potential is compared. It is found that at low temperatures and large quark chemical potential the magnetic field, depending on its strength, induces a new critical endpoint or a triple point.

We compute the two-loop QCD corrections to $qg\to Hq$ and $q\overline{q}\to Hg$ amplitudes mediated by loops of nearly massless quarks. These amplitudes provide the last missing ingredient required to compute the next-to-leading-order QCD corrections to the top-bottom interference contribution to the Higgs boson transverse momentum distribution at hadron colliders.

We study the Casimir friction phenomenon in a system consisting of two flat, infinite, and parallel graphene sheets, which are coupled to the vacuum electromagnetic (EM) field. Those couplings are implemented, in the description we use, by means of specific terms in the effective action for the EM field. They incorporate the distinctive properties of graphene, as well as the relative sliding motion of the sheets. Based on this description, we evaluate two observables due to the same physical effect: the probability of vacuum decay and the frictional force. The system exhibits a threshold for frictional effects; namely, they only exist if the speed of the sliding motion is larger than the Fermi velocity of the charge carriers in graphene.