The usual fluid equations describing the large-scale evolution of mass density in the universe can be written as local in the density, velocity divergence, and velocity potential fields. As a result, the perturbative expansion in small density fluctuations, usually written in terms of convolutions in Fourier space, can be written as a series of products of these fields evaluated at the same location in configuration space. Based on this, we establish a new method to numerically evaluate the 1-loop power spectrum (i.e., Fourier transform of the 2-point correlation function) with one-dimensional fast Fourier transforms. This is exact and a few orders of magnitude faster than previously used numerical approaches. Numerical results of the new method are in excellent agreement with the standard quadrature integration method. This fast model evaluation can in principle be extended to higher loop order where existing codes become painfully slow. Our approach follows by writing higher order corrections to the 2-point correlation function as, e.g., the correlation between two second-order fields or the correlation between a linear and a third-order field. These are then decomposed into products of correlations of linear fields and derivatives of linear fields. The method can also be viewed as evaluating three-dimensional Fourier space convolutions using products in configuration space, which may also be useful in other contexts where similar integrals appear.

The relaxion scenario presents an intriguing extension of the standard model in which the particle introduced to solve to the strong $CP$ problem, the axion, also achieves the dynamical relaxation of the Higgs boson mass term. In this work we complete this framework by proposing a scenario of inflationary cosmology that is consistent with all the observational constraints: the relaxion hybrid inflation with an asymmetric waterfall. In our scheme, the vacuum energy of the inflaton drives inflation in a natural way while the relaxion slow rolls. The constraints on the present inflationary observables are then matched through a subsequent inflationary epoch driven by the inflaton. We quantify the amount of fine-tuning of the proposed inflation scenario, concluding that the inflaton sector severely decreases the naturalness of the theory.

Measuring the absolute scale of the neutrino masses is one of the most exciting opportunities available with near-term cosmological data sets. Two quantities that are sensitive to neutrino mass, scale-dependent halo bias $b(k)$ and the linear growth parameter $f(k)$ inferred from redshift-space distortions, can be measured without cosmic variance. Unlike the amplitude of the matter power spectrum, which always has a finite error, the error on $b(k)$ and $f(k)$ continues to decrease as the number density of tracers increases. This paper presents forecasts for statistics of galaxy and lensing fields that are sensitive to neutrino mass via $b(k)$ and $f(k)$. The constraints on neutrino mass from the auto- and cross-power spectra of spectroscopic and photometric galaxy samples are weakened by scale-dependent bias unless a very high density of tracers is available. In the high-density limit, using multiple tracers allows cosmic variance to be beaten, and the forecasted errors on neutrino mass shrink dramatically. In practice, beating the cosmic-variance errors on neutrino mass with $b(k)$ will be a challenge, but this signal is nevertheless a new probe of neutrino effects on structure formation that is interesting in its own right.

In the present-day cosmic ray data, the strongest indication of anisotropy of the ultrahigh energy cosmic rays is the 20-degree hotspot observed by the Telescope Array with the statistical significance of $3.4\sigma$. In this work, we study the possibility of detecting such a spot by space-based all-sky observatories. We show that if the detected luminosity of the hotspot is attributed to a physical effect and not a statistical fluctuation, the KLYPVE and JEM-EUSO experiments would need to collect $\sim 300$ events with $E>57\mathrm{EeV}$ in order to detect the hotspot at the $5\sigma$ confidence level with the 68% probability. We also study the dependence of the detection prospects on the hotspot luminosity.

Future space-borne gravitational wave detectors will require a precise definition of calibration signals to ensure the achievement of their design sensitivity. The careful design of the test signals plays a key role in the correct understanding and characterization of these instruments. In that sense, methods achieving optimal experiment designs must be considered as complementary to the parameter estimation methods being used to determine the parameters describing the system. The relevance of experiment design is particularly significant for the LISA Pathfinder mission, which will spend most of its operation time performing experiments to characterize key technologies for future space-borne gravitational wave observatories. Here we propose a framework to derive the optimal signals—in terms of minimum parameter uncertainty—to be injected into these instruments during the calibration phase. We compare our results with an alternative numerical algorithm which achieves an optimal input signal by iteratively improving an initial guess. We show agreement of both approaches when applied to the LISA Pathfinder case.

We study the equilibration of a class of far-from-equilibrium strongly interacting systems using gauge-gravity duality. The systems we analyze are $2+1$ dimensional and have a four-dimensional gravitational dual. A prototype example of a system we analyze is the equilibration of a two-dimensional fluid which is translational invariant in one direction and is attached to two different heat baths with different temperatures at infinity in the other direction. We realize such setup in gauge-gravity duality by joining two semi-infinite asymptotically anti-de Sitter (AdS) black branes of different temperatures, which subsequently evolve towards equilibrium by emitting gravitational radiation towards the boundary of AdS. At sufficiently late times the solution converges to a similarity solution, which is only sensitive to the left and right equilibrium states and not to the details of the initial conditions. This attractor solution not only incorporates the growing region of equilibrated plasma but also the outwardly propagating transition regions, and can be constructed by solving a single ordinary differential equation.

We consider the propagation of a chiral spin-$3/2$ particle in a background medium using the thermal field theory (TFT) method, in analogy to the cases of a spin-$1/2$ fermion (e.g., a neutrino) and the photon. We present a systematic decomposition of the thermal self-energy, from which the dispersion relation of the modes that propagate in the medium are obtained. We find that there are several modes and in each case we obtain the equation for the dispersion relation as well as the corresponding spin-$3/2$ spinor. As an example of the general procedure and results, we consider a model in which the chiral spin-$3/2$ particle couples to a spin-$1/2$ fermion and a scalar particle, and propagates in a thermal background composed of such particles. The dispersion relations and corresponding spinors are detemined explicitly in this case from the 1-loop TFT expression for the self-energy. The results in this case share some resemblance and analogies with the photon and the chiral fermion cases but, as already noted, there are also differences. The present work provides the groundwork for considering problems related to the properties of chiral spin-$3/2$ particles in a medium, in analogy to the case of neutrinos for example, which can be relevant in physical contexts of current interest.

We scrutinize the evidences recently reported by the ATLAS and CMS collaborations for compatible 750 GeV resonances which appear in the diphoton channels of the two experiments in both the 8 and 13 TeV data sets. Similar resonances in diboson, dilepton, dijet, and $t\overline{t}$ final states are instead not detected. After discussing the properties and the compatibility of the reported signals, we study the implications on the physics beyond the Standard Model with particular emphasis on possible scalar extensions of the theory such as singlet extensions and the two Higgs doublet models. We also analyze the significance of the new experimental indications within the frameworks of the minimal supersymmetric standard model and of technicolor models. Our results show that a simple effective singlet extension of the SM achieves phenomenological viability with a minimal number of free parameters. The minimal supersymmetric model and the two Higgs doublet model, on the other hand, cannot explain the 750 GeV diphoton excess. Compatibility with the observed signal requires the extension of the particle content of these models, for instance by heavy vector quarks in the case of the two Higgs doublet model.

In the supersymmetric standard model which is not minimal, the Higgs potential does not conserve $CP$ symmetry generally. Assuming that there exists an SU(2)-triplet Higgs field, we discuss resultant $CP$-violating effects on the Higgs bosons. The experimentally observed Higgs boson, which should be $CP$ even in the standard model, could decay into two photons of $CP$-odd polarization state non-negligibly. For the second lightest Higgs boson, in a sizable region of parameter space, the dominant decay modes are different from those expected by the standard model. The two-photon decay could yield both even and odd $CP$ final states at a ratio of the order of unity.

In this paper, we revisit a visible heavy QCD axion model in light of the recent reports on the 750 GeV diphoton resonance by the ATLAS and CMS experiments. In this model, the axion is made heavy with the help of the mirror copied sector of the Standard Model, while the successful Peccei-Quinn mechanism is kept intact. We identify the 750 GeV resonance as the scalar boson associated with spontaneous breaking of the Peccei-Quinn symmetry, which mainly decays into a pair of axions. We find that the mixing between the axion and $\eta$ and ${\eta }^{\prime }$ plays important roles in its decays and the resultant branching ratio into two photons. The axion decay length can be suitable for explaining the diphoton excess by the di-axion production when its decay constant $f_a\simeq 1\mathrm{TeV}$. We also find that our model allows multiple sets of the extra fermions without causing the domain wall problem, which is advantageous to explain the diphoton signal.

We explore several perturbative scenarios in which the diphoton excess at 750 GeV can potentially be explained: a scalar singlet, a two Higgs doublet model (2HDM), a 2HDM with an extra singlet, and the decays of heavier resonances, both vector and scalar. We draw the following conclusions: (i) due to gauge invariance a 750 GeV scalar singlet can accommodate the observed excess more readily than a scalar $SU(2{)}_L$ doublet; (ii) scalar singlet production via gluon fusion is one option, however, vector boson fusion can also provide a large enough rate, (iii) 2HDMs with an extra singlet and no extra fermions can only give a signal in a severely tuned region of the parameter space; (iv) decays of heavier resonances can give a large enough diphoton signal at 750 GeV, while simultaneously explaining the absence of a signal at 8 TeV.

For the flavor-singlet heavy-quark system of charmonia in the pseudoscalar [${\eta }_c(1S)$] channel, we calculate the elastic (EFF) and transition form factors (TFFs) [${\eta }_c(1S)\to \gamma {\gamma }^{*}$] for a wide range of photon momentum transfer squared ($Q^2$). The framework for this analysis is provided by a symmetry-preserving Schwinger-Dyson equation and Bethe-Salpeter equation treatment of a $\text{vector}\times \text{vector}$ contact interaction. We also employ an algebraic model, developed earlier to describe the light-quark systems. It correctly correlates infrared and ultraviolet dynamics of quantum chromodynamics (QCD). The contact interaction results agree with the lattice data for low $Q^2$. For $Q^2\ge Q_0^2$, the results start deviating from the lattice results by more than 20%. $Q_0^2\approx 2.5{\mathrm{GeV}}^2$ for the EFF, and $\approx 25{\mathrm{GeV}}^2$ for the TFF. We also present the results for the EFF, TFF, and ${\eta }_c(1S)$ parton distribution amplitude for the algebraic model. Wherever the comparison is possible, these results are in excellent agreement with the lattice, perturbative QCD, results obtained through a Schwinger-Dyson equation–Bethe-Salpeter equation study, employing refined truncations, and the experimental findings of the BABAR experiment.

The state ${\chi }_{c0}(3915)$ has recently been demoted by the Particle Data Group from its previous status as the conventional $c\overline{c}$ $2^3{P}_0$ state, largely due to the absence of expected $D\overline{D}$ decays. We propose that ${\chi }_{c0}(3915)$ is actually the lightest $c\overline{c}s\overline{s}$ state, and calculate the spectrum of such states using the diquark model, identifying many of the observed charmoniumlike states that lack open-charm decay modes as $c\overline{c}s\overline{s}$. Among other results, we argue that $Y(4140)$ is a $J^{PC}=1^{++}$ $c\overline{c}s\overline{s}$ state that has been not been seen in two-photon fusion largely as a consequence of the Landau-Yang theorem.

Motivated by recent results from the LHCb, BABAR, and Belle Collaborations on $B\to D^{(*)}{\ell }^{-}{\overline{\nu }}_{\ell }$ decays, which significantly deviate from the Standard Model and hint at the possible new physics beyond the Standard Model, we probe the $R$-parity violating supersymmetric effects in $B_c^{-}\to {\ell }^{-}{\overline{\nu }}_{\ell }$ and $B\to D^{(*)}{\ell }^{-}{\overline{\nu }}_{\ell }$ decays. We find the following: (i) $\mathcal{B}(B_c^{-}\to e^{-}{\overline{\nu }}_e)$ and $\mathcal{B}(B_c^{-}\to {\mu }^{-}{\overline{\nu }}_{\mu })$ are sensitive to the constrained slepton exchange couplings. (ii) The normalized forward-backward asymmetries of $B\to D{e}^{-}{\overline{\nu }}_e$ decays have been greatly affected by the constrained slepton exchange couplings, and their signs could be changed. (iii) All relevant observables in the exclusive $b\to c{\tau }^{-}{\overline{\nu }}_{\tau }$ decays and ratios $\mathcal{R}(D^{(*)})$ are sensitive to the slepton exchange coupling, and $\mathcal{R}(D^{*})$ could be enhanced by the constrained slepton exchange coupling to reach each 95% confidence level experimental ranges from BABAR, Belle, and LHCb but not the lower limit of the 95% confidence level experimental average. Our results in this work could be used to probe $R$-parity violating effects and will correlate with searches for direct supersymmetric signals at the running LHCb and the forthcoming Belle-II.

Our article is devoted to the study of the rare $B_s\to \varphi {\ell }^{+}{\ell }^{-}$ decay where $\ell =\mu$, $\tau$. We compute the relevant form factors in the framework of the covariant quark model with infrared confinement in the full kinematical momentum transfer region. The calculated form factors are used to evaluate branching fractions and polarization observables in the cascade decay $B\to \varphi (\to K^{+}{K}^{-}){\ell }^{+}{\ell }^{-}$. We compare the obtained results with available experimental data and the results from other theoretical approaches.

We investigate oscillating solutions of the equation of motion for the Higgs potential. The solutions are described by Jacobian elliptic functions. Classifying the classical solutions, we evaluate a possible parameter space for the initial conditions. To construct the field theory around the oscillating solutions, quantum fluctuations are introduced. This alternative perturbation method is useful to describe the nontrivial quantum theory around the oscillating state. This perturbation theory reduces to the standard one if we take the solution at the vacuum expectation value. It is shown that the transition probability between the vacuum and multiquanta states is finite as long as the initial field configuration does not start from the true vacuum.

The larger center-of-mass energy of the Large Hadron Collider Run 2 opens up the possibility of a more detailed study of the quartic vertices of the electroweak gauge bosons. Our goal in this work is to classify all operators possessing quartic interactions among the electroweak gauge bosons that do not exhibit triple gauge-boson vertices associated to them. We obtain all relevant operators in the nonlinear and linear realizations of the $SU(2{)}_L\otimes U(1{)}_Y$ gauge symmetry.

The skewness and the kurtosis of the baryon number distributions are computed within QCD-improved low energy effective models including quantum thermal and density fluctuations. The results are compared with the Beam Energy Scan experiment at RHIC. The theoretical results agree with the experimental measurements up to errors, for the collision energy $\sqrt{s}\ge 19.6\mathrm{GeV}$. For smaller collision energies a discrepancy between theoretical and experimental results develops. This discrepancy partially relates to the lack of precision of the current setup for small collision energies. It is outlined how this deficiency can be overcome.

String bit models provide a possible method to formulate a string as a discrete chain of pointlike string bits. When the bit number $M$ is large, a chain behaves as a continuous string. We study the simplest case that has only one bosonic bit and one fermionic bit. The creation and annihilation operators are adjoint representations of the $U(N)$ color group. We show that the supersymmetry reduces the parameter number of a Hamiltonian from 7 to 3 and, at $N=\infty$, ensures a continuous energy spectrum, which implies the emergence of one spatial dimension. The Hamiltonian $H_0$ is constructed so that in the large $N$ limit it produces a world sheet spectrum with one Grassmann world sheet field. We concentrate on the numerical study of the model in finite $N$. For the Hamiltonian $H_0$, we find that the would-be ground energy states disappear at $N=(M-1)/2$ for odd $M\le 11$. Such a simple pattern is spoiled if $H$ has an additional term $\xi \mathrm{\Delta }H$ which does not affect the result of $N=\infty$. The disappearance point moves to higher (lower) $N$ when $\xi$ increases (decreases). Particularly, the $\pm (H_0-\mathrm{\Delta }H)$ cases suggest a possibility that the ground state could survive at large $M$ and $M\gg N$. Our study reveals that the model has stringy behavior: when $N$ is fixed and large enough, the ground energy decreases linearly with respect to $M$, and the excitation energy is roughly of order $M^{-1}$. We also verify that a stable system of Hamiltonian $\pm H_0+\xi \mathrm{\Delta }H$ requires $\xi \ge \mp 1$.

We show how to consistently renormalize $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetric Yang-Mills theories in flat space with a local (i.e. spacetime-dependent) renormalization scale in a holomorphic scheme. The action gets enhanced by a term proportional to derivatives of the holomorphic coupling. In the $\mathcal{N}=2$ case, this new action is exact at all orders in perturbation theory.