We study the prospects for testing classes of atmospheric mixing sum rules at precision neutrino facilities. Such sum rules, which correlate the atmospheric mixing angle ${\theta }_{23}$ with the recently measured reactor angle ${\theta }_{13}$ and the cosine of the oscillation phase $\delta$, are predicted by a variety of semidirect models based on discrete family symmetry classified in terms of finite von Dyck groups. We perform a detailed simulation of the performance of the next generation of oscillation experiments, including the wideband superbeam and low-energy neutrino factory proposals, and compare their discriminating power for testing atmospheric mixing sum rules.

Higgs cubic coupling plays a crucial role in probing an origin of electroweak symmetry breaking. It is expected that the cubic coupling is measured by Higgs pair production at the LHC and ILC, and the deviations from the standard model can be extracted from the Higgs pair production process, and those can give us a hint of new physics beyond the standard model. We consider a general potential that achieves the suitable electroweak symmetry breaking. As one of the interesting models, we suggest a nonperturbative Higgs model in which a runaway type of potential is used. In the model, the cross sections of pair production at the LHC are enlarged compared to the standard model. We also study the Higgs pair production induced by a noncanonical kinetic term of Higgs fields which will be important for searching the pair production at the ILC.

We study the standard model (SM) in its full perturbative validity range between ${\mathrm{\Lambda }}_{\mathrm{QCD}}$ and the $U{(1)}_Y$ Landau pole, assuming that a yet unknown gravitational theory in the UV does not introduce additional particle thresholds, as suggested by the tiny cosmological constant and the absence of new stabilizing physics at the electroweak scale. We find that, due to dimensional transmutation, the SM Higgs potential has a global minimum at ${10}^{26}\mathrm{GeV}$, invalidating the SM as a phenomenologically acceptable model in this energy range. We show that extending the classically scale invariant SM with one complex singlet scalar $S$ allows us to (i) stabilize the SM Higgs potential, (ii) induce a scale in the singlet sector via dimensional transmutation that generates the negative SM Higgs mass term via the Higgs portal, (iii) provide a stable $CP$-odd singlet as the thermal relic dark matter due to $CP$-conservation of the scalar potential, and (iv) provide a degree of freedom that can act as an inflaton in the form of the $CP$-even singlet. The logarithmic behavior of dimensional transmutation allows one to accommodate the large hierarchy between the electroweak scale and the Landau pole, while understanding the latter requires a new nonperturbative view on the SM.

The natural supersymmetry (SUSY) requires that the stop, sbottom, and gluino are around 1 TeV or lighter. By using the direct SUSY search bounds from both the ATLAS and CMS collaborations, we examine the constraints on the natural SUSY in the next to minimal supersymmetric Standard Model. We consider two cases of interpretations for the Higgs boson data: (1) the Standard Model (SM)-like Higgs boson is the lightest $CP$-even Higgs boson; (2) the SM-like Higgs boson is the second lightest $CP$-even Higgs boson. We choose 2400 points or so to perform a detailed Monte Carlo simulation analysis, and we observe that the direct SUSY searches at the LHC impose a strong constraint on these light gluino scenarios.

Applying the domain model to the G(2) gauge group and the thick center vortex model to the SU(2) and SU(3) subgroups of G(2), we calculate the potentials between static sources, as well as some parameters of the vortex profile. Comparing the results obtained from G(2) and its subgroups, we argue that SU(2) and SU(3) gauge groups have important roles in observing confinement in the G(2) gauge group.

We study possibilities to define a static quark-antiquark pair in a color-adjoint orientation based on Wilson loops with generator insertions, using both lattice QCD and leading-order perturbation theory in various gauges. Nonperturbatively, the only way to obtain nonzero results while maintaining positivity of the Hamiltonian is by using either temporal gauge or Coulomb gauge with some additional constraint on the temporal links removing the residual gauge symmetry. In this case the correlator is equivalent to a gauge invariant correlation function of a static quark-antiquark pair and a static adjoint quark; the resulting three-point potential is attractive. Saturating open color indices with color magnetic fields instead also leads to a gauge invariant correlator. However, this object is found to couple to the singlet sector only and results in a hybrid potential. None of the considered lattice observables reproduces the repulsive adjoint potential predicted by perturbation theory in Lorenz or Coulomb gauges.

We study the effect of scalar leptoquarks on some rare decays of $B_s$ mesons involving the quark level transition $b\to s$ $l^{+}{l}^{-}$. In particular we consider the decays $B_s\to {\mu }^{+}{\mu }^{-}$, ${\overline{B}}_d^0\to X_s{\mu }^{+}{\mu }^{-}$ and $B_s\to \varphi$ ${\mu }^{+}{\mu }^{-}$. The leptoquark parameter space is constrained using the recently measured branching ratio of the $B_s\to {\mu }^{+}{\mu }^{-}$ process at LHCb and CMS experiments. Using such parameters we obtain the branching ratio, forward-backward asymmetry and the $CP$ asymmetry parameters in the angular distribution of $B_s\to \varphi$ ${\mu }^{+}{\mu }^{-}$ process.

We consider a $U{(1)}^{\prime }$ gauge symmetry acting on three generations of right-handed neutrinos. The $U{(1)}^{\prime }$ symmetry is broken at the TeV scale, and its remnant discrete symmetry makes one of the right-handed neutrinos stable. As a natural consequence of the anomaly cancellation, the neutrino mass matrix consists of a combination of type I (TeV scale) seesaw and radiative corrections. The stable right-handed neutrino communicates with the Standard Model via $s$-channel exchange of the Higgs field and the $U{(1)}^{\prime }$ gauge boson, so that the observed relic density for dark matter is obtained in a wide range of the parameter space. The experimental signatures in collider and other experiments are briefly discussed.

We investigate the decay $B^{+}\to J/\psi \varphi K^{+}$ in a search for the $X(4140)$ state, a narrow threshold resonance in the $J/\psi \varphi$ system. The data sample corresponds to an integrated luminosity of $10.4{\mathrm{fb}}^{-1}$ of $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ collected by the D0 experiment at the Fermilab Tevatron collider. We observe a mass peak with a statistical significance of 3.1 standard deviations and measure its invariant mass to be $M=4159.0\pm 4.3(\text{stat})\pm 6.6(\text{syst})\mathrm{MeV}$ and its width to be $\mathrm{\Gamma }=19.9\pm 12.6{(\text{stat})}_{-8.0}^{+3.0}(\text{syst})\mathrm{MeV}$.

We study ($2+1$)-dimensional conformal field theories (CFTs) with a globally conserved U(1) charge, placed in a chemical potential which is periodically modulated along the spatial direction $x$ with zero average: $\mu (x)=V\cos (kx)$. The dynamics of such theories depends only on the dimensionless ratio $V/k$, and we expect that they flow in the infrared to new CFTs whose universality class changes as a function of $V/k$. We compute the frequency-dependent conductivity of strongly coupled CFTs using holography of the Einstein-Maxwell theory in four-dimensional anti–de Sitter space. We compare the results with the corresponding computation of weakly coupled CFTs, perturbed away from the CFT of free, massless Dirac fermions (which describes graphene at low energies). We find that the results of the two computations have significant qualitative similarities. However, differences do appear in the vicinities of an infinite discrete set of values of $V/k$: the universality class of the infrared CFT changes at these values in the weakly coupled theory, by the emergence of new zero modes of Dirac fermions which are remnants of local Fermi surfaces. The infrared theory changes continuously in holography, and the classical gravitational theory does not capture the physics of the discrete transition points between the infrared CFTs. We briefly note implications for a nonzero average chemical potential.

We consider a symmetric scalar theory with quartic coupling in two and three dimensions and compare the self-consistent four-point vertex obtained from the four-particle-irreducible effective action with the Bethe–Salpeter 4-vertex from the two-particle-irreducible effective action. At zero external momenta the two vertices agree well with each other when the coupling strength is small, but differences between them become more and more pronounced as the coupling strength is increased. We also study the momentum dependence of the two vertices and show that for certain momentum configurations they are almost identical but differ for general momentum arguments.

The growth rate of the large-scale structure of the Universe has been advocated as the observable par excellence for testing gravity on cosmological scales. By considering linear-order deviations from general relativity, we show that corrections to the growth rate, $f$, can be expressed as an integral over a “source” term, weighted by a theory-independent “response kernel.” This leads to an efficient and accurate “plug-and-play” expression for generating growth rates in alternative gravity theories, bypassing lengthy theory-specific computations. We use this approach to explicitly show that $f$ is sensitive to a degenerate combination of modified expansion and modified clustering effects. Hence the growth rate, when used in isolation, is not a straightforward diagnostic of modified gravity.

We investigate the variation of the fine-structure constant, $\alpha$, in symmetron models using N-body simulations in which the full spatial distribution of $\alpha$ at different redshifts has been calculated. In particular, we obtain simulated sky maps for this variation, and determine its power spectrum. We find that in high-density regions of space (such as deep inside dark matter halos) the value of $\alpha$ approaches the value measured on Earth. In the low-density outskirts of halos the scalar field value can approach the symmetry breaking value and leads to significantly different values of $\alpha$. If the scalar-photon coupling strength ${\beta }_{\gamma }$ is of order unity we find that the variation of $\alpha$ inside dark matter halos can be of the same magnitude as the recent claims by Webb et al. of a dipole variation. Importantly, our results also show that with low-redshift symmetry breaking these models exhibit some dependence of $\alpha$ on lookback time (as opposed to a pure spatial dipole) which could in principle be detected by sufficiently accurate spectroscopic measurements, such as those of ALMA and the ELT-HIRES.

The puncture method specifies black hole data on a hypersurface with the aid of a conformal rescaling of the metric that exhibits a coordinate singularity at the puncture point. When constructing puncture initial data by solving the Hamiltonian constraint for the conformal factor, the coordinate singularity requires special attention. The standard way to treat the pole singularity occurring in wormhole puncture data is not generally applicable to trumpet puncture data. We investigate a new approach based on inverse powers of the conformal factor and present numerical examples for single punctures of the wormhole and $1+\log$-trumpet type. Additionally, we describe a method to solve the Hamiltonian constraint for two $1+\log$ trumpets for a given extrinsic curvature with a nonvanishing trace. We investigate properties of this constructed initial data during binary black hole evolutions and find that the initial gauge dynamics is reduced.

We study inflation induced by (power-low) scalar curvature corrections to General Relativity. The class of inflationary scalar potentials $V(\sigma )\sim \text{exp}[n\sigma ]$, $n$ general parameter, is investigated in the Einstein frame, and the corresponding actions in the Jordan frame are derived. We found the conditions for which these potentials are able to reproduce viable inflation according to the last cosmological data and lead to large scalar curvature corrections that emerge only at a mass scale larger than the Planck mass. The cosmological constant may appear or be set equal to zero in the Jordan frame action without changing the behavior of the model during inflation. Moreover, polynomial corrections to General Relativity are analyzed in detail. When de Sitter space-time emerges as an exact solution of the models, it is necessary to use perturbative equations in the Jordan framework to study their dynamics during the inflation. In this case, we demonstrate that the Ricci scalar decreases after a correct amount of inflation, making the models consistent with the observable evolution of the Universe.

We investigate how higher-order nonlinear parameters affect lower-order ones through loop effects. We calculate the loop corrections up to two loops and explicitly show that the tree contribution is stable against loop terms in most cases. We argue that, nevertheless, observational constraints on nonlinear parameters such as $f_{\mathrm{NL}}$ and ${\tau }_{\mathrm{NL}}$ can also give a limit even for higher-order ones due to the loop contribution. We discuss these issues for both single-source and multisource cases.

The weak lensing power spectrum is a powerful tool to probe cosmological parameters. Additionally, lensing peak counts contain cosmological information beyond the power spectrum. Both of these statistics can be affected by the preferential selection of source galaxies in patches of the sky with high magnification, as well as by the dilution in the source galaxy surface density in such regions. If not accounted for, these biases introduce systematic errors for cosmological measurements. Here we quantify these systematic errors, using convergence maps from a suite of ray-tracing N-body simulations. At the cutoff magnitude $m$ of ongoing and planned major weak lensing surveys, the logarithmic slope of the cumulative number counts $s\equiv d\log n(>m)/d\log m$ is in the range $0.1\lesssim s\lesssim 0.5$. At $s\approx 0.2$, expected in the $I$ band for Large Synoptic Survey Telescope, the inferred values of ${\mathrm{\Omega }}_m$, $w$, and ${\sigma }_8$ are biased by many $\sigma$ (where $\sigma$ denotes the marginalized error), and therefore the biases will need to be carefully modeled. We also find that the parameters are biased differently in the $({\mathrm{\Omega }}_m,w,{\sigma }_8)$ parameter space when the power spectrum and the peak counts are used. In particular, $w$ derived from the power spectrum is less affected than $w$ derived from peak counts, while the opposite is true for the best-constrained combination of ${\sigma }_8{\mathrm{\Omega }}_m^{\gamma }$ (with $\gamma =0.62$ from the power spectrum and $\gamma =0.48$ from peak counts). This suggests that the combination of the power spectrum and peak counts can help mitigate the impact of magnification and size biases.

Recently it has been claimed that the Wheeler–DeWitt quantization of gravity is unable to avoid cosmological singularities. However, in order to make this assertion, one must specify the underlying interpretation of quantum mechanics which has been adopted. For instance, several nonsingular models were obtained in Wheeler–DeWitt quantum cosmology in the framework of the de Broglie–Bohm quantum theory. Conversely, there are specific situations where the singularity cannot be avoided in the framework of the consistent histories approach to quantum mechanics. In these specific situations, the matter content is described by a scalar field, and the Wheeler–DeWitt equation looks like a Klein–Gordon equation. The aim of this work is to study a possible singular behavior of quantum cosmological models in which the matter content is described by a hydrodynamical perfect fluid, where the resulting wave equation is a genuine Schrödinger equation. In this case, it is shown that the conclusions of the consistent histories and the de Broglie–Bohm approaches coincide in the quantum cosmological models where the curvature of the spatial sections is not positive definite, namely, that the cosmological singularities are eliminated. In the case of positive spatial curvature, the family of histories is no longer consistent, and no conclusion can be given in this framework.

The LHCb Collaboration has systematically measured the rates of $B_c\to J/\psi K$, $B_c\to J/\psi D_s$, $B_c\to J/\psi D_s^{*}$, and $B_c\to \psi (2S)\pi$. The new data enable us to study relevant theoretical models and further determine the model parameters. In this work, we calculate the form factors for the transitions $B_c\to J/\psi$ and $B_c\to \psi (2S)$ numerically and then determine the partial widths of the semileptonic and nonleptonic decays. The theoretical predictions on the ratios of $\mathrm{\Gamma }(B_c\to J/\psi K)/\mathrm{\Gamma }(B_c\to J/\psi \pi )$, $\mathrm{\Gamma }(B_c\to J/\psi D_s)/\mathrm{\Gamma }(B_c\to J/\psi \pi )$, and $\mathrm{\Gamma }(B_c\to J/\psi D_s^{*})/\mathrm{\Gamma }(B_c\to J/\psi \pi )$ are consistent with data within only $1\sigma$. Especially, for calculating $\mathrm{\Gamma }(B_c\to \psi (2S)X)$ the modified harmonic oscillator wave function which we developed in early works is employed, and the results indicate that the modified harmonic oscillator wave function works well.

The Bethe-Salpeter equation for a bound system, composed by two massive scalars exchanging a massive scalar, is quantitatively investigated in ladder approximation, within the Nakanishi integral representation approach. For the S-wave case, numerical solutions with a form inspired by the Nakanishi integral representation are calculated. The needed Nakanishi weight functions are evaluated by solving two different eigenequations, obtained directly from the Bethe-Salpeter equation applying the light-front projection technique. A remarkable agreement, in particular, for the eigenvalues, is achieved, numerically confirming that the Nakanishi uniqueness theorem for the weight functions demonstrated in the context of the perturbative analysis of the multileg transition amplitudes and playing a basic role in suggesting one of the two adopted eigenequations can be extended to a nonperturbative realm. The detailed, quantitative studies are completed by presenting both probabilities and light-front momentum distributions for the valence component of the bound state.