Observation of neutron gravitational quantum states $E_n=mg{z}_n$ in the peV energy range ($z_1$ is about $10\mu \mathrm{m}$ in the vertical direction) in the experiment conducted at Laue-Langevin Institute, Grenoble, with ultracold neutrons was recently reported in a series of publications. The purpose of the present work is to analyze the experiment. The experimental apparatus is designed to measure a transmission function $T(z_a)$, namely, a horizontal flux of relatively fast neutrons ($k\gg k_z$ in wavelength terms) passing through a slit of variable height $z_a$ of upper absorbing wall. The quantum states in question are defined by the so-called Airy functions, which are solutions to the stationary 1D equation for a neutron “bouncing” above the perfect mirror in a linear potential field. The Airy functions describe the quantum bouncer (QB), the concept of which is subject to theoretical study of toy 1D models of gravitationally bound particles in nonrelativistic quantum mechanics (QM). This is essentially different from the 3D nonstationary QM object, “the running QB,” investigated in the experiment. The authors assume that there is a connection between $T(z_a)$ and the probability density distribution $P(z,z_a)$ for QB states. They devised the “phenomenological model,” in which the quantum pattern should be visible in the transmission curve. We argue, however, that the measured curve $T(z_a)$ is not sensitive to QB states. Instead, it is sensitive to dynamics of neutron horizontal transport inside the absorbing slit for neutrons of energy values about ${10}^5$ times greater than eigenvalues $E_n$. The latter are related to the neutron transverse mode $k_z$ and cannot be termed “energies of neutron gravitational quantum states.” We conclude that the experiment setup and real conditions are not adequate to the claimed objective, and the methodology of measured data treatment is flawed. The authors’ claim that “neutron gravitational quantum states are observed” is neither theoretically nor experimentally substantiated. Final, statistically significant results of the experiment are consistent with our physical reasoning that the experiment is not sensitive to “neutron gravitational quantum states” (in terms of Airy mode) and does not prove even their existence in rigorous quantum-mechanical terms.

Spherically symmetric oscillatons (also referred to as oscillating soliton stars) i.e. gravitationally bound oscillating scalar lumps are considered in theories containing a massive self-interacting real scalar field coupled to Einstein’s gravity in $1+D$ dimensional spacetimes. Oscillations are known to decay by emitting scalar radiation with a characteristic time scale which is, however, extremely long, it can be comparable even to the lifetime of our universe. In the limit when the central density (or amplitude) of the oscillaton tends to zero (small-amplitude limit) a method is introduced to compute the transcendentally small amplitude of the outgoing waves. The results are illustrated in detail on the simplest case, a single massive free scalar field coupled to gravity.

We introduce new models of $f(R)$ theories of gravity that are a generalization of Hořava-Lifshitz gravity.

Recently, traversable wormhole geometries were constructed in the context of $f(R)$ gravity. The latter is equivalent to a Brans-Dicke theory with a coupling parameter $\omega =0$, which is apparently excluded from the narrow interval, $-3/2<\omega <-4/3$, extensively considered in the literature of static wormhole solutions in vacuum Brans-Dicke theory. However, this latter interval is only valid for a specific choice of an integration constant of the field equations derived on the basis of a post-Newtonian weak field approximation, and there is no reason for it to hold in the presence of compact objects with strong gravitational fields. In this context, we construct a general class of vacuum Brans-Dicke wormholes that include the value of $\omega =0$.

We present a two-dimensional heterotic $\mathcal{N}=(0,2)$ $CP(N-1)$ model with twisted masses. It is supposed to describe internal dynamics of non-Abelian strings in massive $\mathcal{N}=2$ SQCD with $\mathcal{N}=1$-preserving deformations. We present gauge and geometric formulations of the world-sheet theory and check its $\mathcal{N}=(0,2)$ supersymmetry. It turns out that the set of twisted masses in the heterotic model has $N$ complex mass parameters, rather than $N-1$. In the general case, when all mass parameters are nonvanishing, $\mathcal{N}=(0,2)$ supersymmetry is spontaneously broken already at the classical level. If at least one of the above mass parameters vanishes, then $\mathcal{N}=(0,2)$ is unbroken at the classical level. The spontaneous breaking of supersymmetry in this case occurs through nonperturbative effects.

We investigate the finite-temperature spectral functions of heavy quarkonia by using the soft-wall anti-de Sitter/QCD model. We discuss the scalar, the pseudoscalar, the vector, and the axial-vector mesons and compare their qualitative features of the melting temperature and growing width. We find that the axial-vector meson melts earlier than the vector meson, while there appears only a slight difference between the scalar and pseudoscalar mesons, which also melt earlier than the vector meson.

Motivated by recent discussions, we revisit the issue of whether globally supersymmetric theories with nonzero Fayet-Iliopoulos terms may be consistently coupled to supergravity. In particular, we examine claims that a fundamental inconsistency arises due to the conflicting requirements which are imposed on the $R$-symmetry properties of the theory by the supergravity framework. We also prove that certain kinds of Fayet-Iliopoulos contributions to the supercurrent supermultiplets of theories with nonzero Fayet-Iliopoulos terms fail to exist. A key feature of our discussion is an explicit comparison between results from the chiral (or “old minimal”) and linear (or “new minimal”) formulations of supergravity, and the effects within each of these formalisms that are induced by the presence of nonzero Fayet-Iliopoulos terms.

We investigate the production and possible detection of gravitational waves stemming from the electroweak phase transition in the early universe in models of minimal walking technicolor. In particular we discuss the two possible scenarios in which one has only one electroweak phase transition and the case in which the technicolor dynamics allows for multiple phase transitions.

We study the tidal disruption of neutron stars in black hole-neutron star coalescing binaries. We calculate the critical orbital separation at which the star is disrupted by the black hole tidal field for several equations of state describing the matter inside the neutron star, and for a large set of the binary parameters. When the disruption occurs before the star reaches the innermost stable circular orbit, the gravitational wave (GW) signal emitted by the system is expected to exhibit a cutoff frequency ${\nu }_{\mathrm{GW}\mathrm{tide}}$, which is a distinctive feature of the waveform. We evaluate ${\nu }_{\mathrm{GW}\mathrm{tide}}$ and show that, if this frequency will be found in a detected gravitational wave, it will allow one to determine the neutron star radius with an error of a few percent, providing valuable information on the behavior of matter in the stellar core.

We compute the phenomenological signatures of a model [Watanabe et al. Phys. Rev. Lett. 102, 191302 (2009)] of anisotropic inflation driven by a scalar and a vector field. The action for the vector is U(1) invariant, and the model is free of ghost instabilities. A suitable coupling of the scalar to the kinetic term of the vector allows for a slow roll evolution of the vector vacuum expectation value, and hence for a prolonged anisotropic expansion; this provides a counter example to the cosmic no hair conjecture. We compute the nonvanishing two point correlation functions between physical modes of the system, and express them in terms of power spectra with angular dependence. The anisotropy parameter $g_{*}$ for the scalar-scalar spectrum (defined as in the Ackerman et al. [Phys. Rev. D 75, 0835002 (2007)] parametrization) turns out to be negative in the simplest realization of the model, which, therefore, cannot account for the angular dependence emerged in some analyses of the Wilkinson Microwave Anisotropy Probe data. A $g_{*}$ of order $-0.1$ is achieved when the energy of the vector is about 6–7 orders of magnitude smaller than that of the scalar during inflation. For such values of the parameters, the scalar-tensor correlation (which is in principle a distinctive signature of anisotropic spaces) is smaller than the tensor-tensor correlation.

Given a class of dark energy models, constraints from one set of cosmic acceleration observables make predictions for other observables. Here we present the allowed ranges for the expansion rate $H(z)$, distances $D(z)$, and the linear growth function $G(z)$ (as well as other, derived growth observables) from the current combination of cosmological measurements of supernovae, the cosmic microwave background, baryon acoustic oscillations, and the Hubble constant. With a cosmological constant as the dark energy and assuming near-minimal neutrino masses, the growth function is already predicted to better than 2% precision at any redshift, with or without spatial curvature. Direct measurements of growth that match this precision offer the opportunity to stringently test and potentially rule out a cosmological constant. While predictions in the broader class of quintessence models are weaker, it is remarkable that they are typically only a factor of 2–3 less precise than forecasted predictions for future space-based supernovae and Planck CMB measurements. In particular, measurements of growth at any redshift, or the Hubble constant $H_0$, that exceed $\Lambda \mathrm{CDM}$ predictions by substantially more than 2% would rule out not only a cosmological constant but also the whole quintessence class, with or without curvature and early dark energy. Barring additional systematic errors hiding in the data, such a discovery would require more exotic explanations of cosmic acceleration such as phantom dark energy, dark energy clustering, or modifications of gravity.

Direct detection experiments have reached the sensitivity to detect dark matter weakly interacting massive particles (WIMPs). Demonstrating that a putative signal is due to WIMPs, and not backgrounds, is a major challenge, however. The direction dependence of the WIMP scattering rate provides a potential WIMP “smoking gun.” If the WIMP distribution is predominantly smooth, the Galactic recoil distribution is peaked in the direction opposite to the direction of Solar motion. Previous studies have found that, for an ideal detector, of order 10 WIMP events would be sufficient to reject isotropy, and rule out an isotropic background. We examine how the median recoil direction could be used to confirm the WIMP origin of an anisotropic recoil signal. Specifically, we determine the number of events required to confirm the direction of solar motion as the median inverse recoil direction at 95% confidence. We find that for zero background 31 events are required, a factor of $\sim 2$ more than are required to simply reject isotropy. We also investigate the effect of a nonzero isotropic background. As the background rate is increased the number of events required increases, initially fairly gradually and then more rapidly, once the signal becomes subdominant. We also discuss the effect of features in the speed distribution at large speeds, as found in recent high resolution simulations, on the median recoil direction.

We analyze to what extent the complex Langevin method, which is in principle capable of solving the so-called sign problems, can be considered as reliable. We give a formal derivation of the correctness and then point out various mathematical loopholes. The detailed study of some simple examples leads to practical suggestions about the application of the method.

We determine the ratio $F_K/F_{\pi }$ in QCD with $N_f=2+1$ flavors of sea quarks, based on a series of lattice calculations with three different lattice spacings, large volumes, and a simulated pion mass reaching down to about 190 MeV. We obtain $F_K/F_{\pi }=1.192(7{)}_{\mathrm{stat}}(6{)}_{\mathrm{syst}}$. This result is then used to give an updated value of the Cabibbo-Kobayashi-Maskawa) matrix element $|V_{us}|$. The unitarity relation for the first row of this matrix is found to be well observed.

We have performed a coupled channel calculation of the $1^{++}$ $c\overline{c}$ sector including $q\overline{q}$ and $D{D}^{*}$ molecular configurations. The calculation was done within a constituent quark model which successfully describes the meson spectrum, in particular, the $c\overline{c}$ $1^{--}$ sector. Two and four-quark configurations are coupled using the ${}^{3}P_0$ model. The elusive $X(3872)$ meson appears as a new state with a high probability for the $D{D}^{*}$ molecular component. When the mass difference between neutral and charged states is included, a large $D^0{D}^{*0}$ component is found which dominates for large distances and breaks isospin symmetry in the physical state. The original $c\overline{c}(2{}^{3}P_1)$ state acquires a sizable $D{D}^{*}$ component and can be identified with the $X(3940)$. We study the $B\to K{\pi }^{+}{\pi }^{-}J/\psi$ and $B\to K{D}^0{D}^{*0}$ decays, finding a good agreement with Belle and BABAR experimental data.

We construct an effective action for QCD by expanding the quark determinant in powers of the chemical potential at finite temperature in the case of massless quarks. To cut the infinite series, we adopt the Weinberg power counting criteria. We compute the minimal effective action ($\sim p^4$), expanding in the external momentum, which implies the use of the hard thermal loop approximation. Our main result is a gauge invariant expression for the phase $\theta$ of the functional determinant in QCD and recovers dimensional reduction in the high-temperature limit. We compute, analytically, $⟨{\theta }^2⟩$ in the range of $p\ll 2\pi T$, including perturbative and nonperturbative contributions, the latter treated within the mean field approximation. Implications for lattice simulations are briefly discussed.

We describe the linear cosmological perturbations of a perfect fluid at the level of an action, providing thus an alternative to the standard approach based only on the equations of motion. This action is suited not only to perfect fluids with a barotropic equation of state, but also to those for which the pressure depends on two thermodynamical variables. By quantizing the system we find that (1) some perturbation fields exhibit a noncommutativity quite analogous to the one observed for a charged particle moving in a strong magnetic field, (2) local curvature and pressure perturbations cannot be measured simultaneously, (3) ghosts appear if the null energy condition is violated.

In this paper, the decay constants and mean square radii of pseudoscalar heavy mesons are studied in the $SU(3)$ symmetry breaking. Within the light-front framework, the ratios $f_{D_s}/f_D$ and $f_{B_s}/f_B$ are individually estimated using the hyperfine splittings in the $D_{(s)}^{*}-D_{(s)}$ and $B_{(s)}^{*}-B_{(s)}$ states and the light quark masses, $m_{s,q}$ ($q=u$, $d$), to extract the wave function parameter $\beta$. The values $f_{D_s}/f_D=1.29\pm 0.07$ and $f_{B_s}/f_B=1.32\pm 0.08$ are obtained, which are not only chiefly determined by the ratio of light quark masses $m_s/m_q$, but also insensitive to the heavy quark masses $m_{c,b}$ and the decay constants $f_{D,B}$. The dependence of $f_{B_c}/f_B$ on $\Delta M_{B_c{B}_c^{*}}$ with the varied charm quark masses is also shown. In addition, the mean square radii are estimated as well. The values $\sqrt{⟨r_{D_s^{+}}^2⟩/⟨r_{D^{+}}^2⟩}={0.740}_{+0.050}^{-0.041}$ and $\sqrt{⟨r_{B_s^0}^2⟩/⟨r_{B^0}^2⟩}={0.711}_{+0.058}^{-0.049}$ are obtained, and the sensitivities of $⟨r_P^2⟩$ on the heavy and light quark masses are similar to those of the decay constants.

Motivated by the similar mass splitting in light-light and heavy-light $J^P=0^{-}$ and $J^P=0^{+}$ mesons, the SU(3)-symmetry breaking effects splitting the masses in the $0^{-}$ and $0^{+}$ channels of the $D$ meson are analyzed in the framework of QCD sum rules with an underlying $c\overline{q}$ structure. We take into account operator mixing to obtain an infrared stable operator-product expansion method including complete nonperturbative and perturbative $\mathcal{O}(m_q)$ corrections to the correlation function. With the same threshold for both channels, the mass splitting arising from the sum rules has the same behavior as the observed spectrum. In particular, we obtain $m_{D_s}-m_{D_d}\sim 35\mathrm{MeV}$ in the $0^{-}$ channel and $m_{D_d}-m_{D_s}\sim 12\mathrm{MeV}$ in the $0^{+}$ channel at a renormalization scale $\mu =1\mathrm{GeV}$. The splitting can be attributed to the different roles of mass effects and the parity-dependent “force” induced from nonperturbative QCD vacuum. Further analysis shows that due to this parity-dependent force it is natural that the mass gap of the two states in the $0^{-}$ channel is larger than the $0^{+}$ channel. When we increase the renormalization scale to $\mu =1.3\mathrm{GeV}$ the splitting remains unchanged which demonstrates a correct scale invariance. Combined with heavy quark effective theory, generalizations to other channels of charmed mesons and $b$-systems are briefly discussed.

It is shown that type I seesaw models based on the standard model Lagrangian extended with three heavy Majorana right-handed fields do not have leptogenesis in leading order, if the symmetries of mass matrices are also the residual symmetry of the Lagrangian. In particular, flavor models that lead to a mass-independent leptonic mixing have a vanishing leptogenesis $CP$ asymmetry. Based on symmetry arguments, we prove that in these models the Dirac-neutrino Yukawa coupling combinations relevant for leptogenesis are diagonal in the physical basis where the charged leptons and heavy Majorana neutrinos are diagonal.