Various theories that aim at unifying gravity with quantum mechanics suggest modifications of the Heisenberg algebra for position and momentum. From the perspective of quantum mechanics, such modifications lead to new uncertainty relations that are thought (but not proven) to imply the existence of a minimal observable length. Here we prove this statement in a framework of sufficient physical and structural assumptions. Moreover, we present a general method that allows us to formulate optimal and state-independent variance-based uncertainty relations. In addition, instead of variances, we make use of entropies as a measure of uncertainty and provide uncertainty relations in terms of min and Shannon entropies. We compute the corresponding entropic minimal lengths and find that the minimal length in terms of min entropy is exactly 1 bit.

It has been shown that a self-gravitating system of massive keV fermions in thermodynamic equilibrium correctly describes the dark matter (DM) distribution in galactic halos (from dwarf to spiral and elliptical galaxies) and that, at the same time, it predicts a denser quantum core towards the center of the configuration. Such a quantum core, for a fermion mass in the range of $50\mathrm{keV}\lesssim m{c}^2\lesssim 345\mathrm{keV}$, can be an alternative interpretation of the central compact object in Sgr A*, traditionally assumed to be a black hole (BH). We present in this work the gravitational lensing properties of this novel DM configuration in nearby Milky-Way-like spiral galaxies. We describe the lensing effects of the pure DM component both on halo scales, where we compare them to the effects of the Navarro-Frenk-White and the nonsingular isothermal sphere DM models, and near the galaxy center, where we compare them with the effects of a Schwarzschild BH. For the particle mass leading to the most compact DM core, $m{c}^2\approx 10^2\mathrm{keV}$, we draw the following conclusions. At distances $r\gtrsim 20\mathrm{pc}$ from the center of the lens the effect of the central object on the lensing properties is negligible. However, we show that measurements of the deflection angle produced by the DM distribution in the outer region at a few kpc, together with rotation curve data, could help to discriminate between different DM models. In the inner regions $10^{-6}\lesssim r\lesssim 20\mathrm{pc}$, the lensing effects of a DM quantum core alternative to the BH scenario becomes a theme of an analysis of unprecedented precision which is challenging for current technological developments. We show that at distances $\sim 10^{-4}\mathrm{pc}$ strong lensing effects, such as multiple images and Einstein rings, may occur. Large differences in the deflection angle produced by a DM central core and a central BH appear at distances $r\lesssim 10^{-6}\mathrm{pc}$; in this regime the weak-field formalism is no longer applicable and the exact general-relativistic formula has to be used for the deflection angle which may become bigger than $2\pi$. An important difference in comparison to BHs is in the fact that quantum DM cores do not show a photon sphere; this implies that they do not cast a shadow (if they are transparent). Similar conclusions apply to the other DM distributions for other fermion masses in the above-specified range and for other galaxy types.

One of the primary gravitational wave (GW) sources for pulsar timing arrays (PTAs) is the stochastic background formed by supermassive black holes binaries (SMBHBs). In this paper, we investigate how the environments of SMBHBs effect the sensitivity of PTAs by deriving scaling laws for the signal-to-noise ratio (SNR) of the optimal cross-correlation statistic. The presence of gas and stars around SMBHBs accelerates the merger at large distances, depleting the GW stochastic background at low frequencies. We show that environmental interactions may delay detection by a few years or more, depending on the PTA configuration and the frequency at which the dynamical evolution transitions from being dominated by environmental effects to GW dominated.

We study the influence of external parallel electric and magnetic fields and a chiral chemical potential ${\mu }_5$ on the chiral phase transition of quantum chromodynamics. Our theoretical framework is a Nambu–Jona-Lasinio model with a contact interaction. Within this model we compute the critical temperature of chiral symmetry restoration $T_c$ as a function of the chiral chemical potential and field strengths. We find that the fields inhibit and ${\mu }_5$ enhances chiral symmetry breaking, in agreement with previous studies.

The Adler-Weisberger sum rule for the nucleon axial-vector charge, $g_A$, offers a unique signature of chiral symmetry and its breaking in QCD. Its derivation relies on both algebraic aspects of chiral symmetry, which guarantee the convergence of the sum rule, and dynamical aspects of chiral symmetry breaking—as exploited using chiral perturbation theory—which allow the rigorous inclusion of explicit chiral symmetry breaking effects due to light-quark masses. The original derivations obtained the sum rule in the chiral limit and, without the benefit of chiral perturbation theory, made various attempts at extrapolating to nonvanishing pion masses. In this paper, the leading, universal, chiral corrections to the chiral-limit sum rule are obtained. Using PDG data, a recent parametrization of the pion-nucleon total cross sections in the resonance region given by the SAID group, as well as recent Roy-Steiner equation determinations of subthreshold amplitudes, threshold parameters, and correlated low-energy constants, the Adler-Weisberger sum rule is confronted with experimental data. With uncertainty estimates associated with the cross-section parametrization, the Goldberger-Treimann discrepancy, and the truncation of the sum rule at $\mathcal{O}(M_{\pi }^4)$ in the chiral expansion, this work finds $g_A=1.248\pm 0.010\pm 0.007\pm 0.013$.

We study the interplay between the Kondo effect and (color) superconductivity in doped Dirac metals with magnetic impurities and in quark matter with colorful impurities. We first point out that the overscreened Kondo effect arises in the normal state of these systems. Next the (color) superconducting gap is incorporated as a mean field and the phase diagram for a varying gap and temperature is constructed nonperturbatively. A rich phase structure emerges from a competition of effects unique to a multichannel system. The Kondo-screened phase is shown to disappear for a sufficiently large gap. Peculiarity of quark matter due to the confining property of non-Abelian gauge fields is noted. We also investigate the spectrum of sub-gap excited states, called Shiba states. Based on a model calculation and physical reasoning we predict that, as the coupling of the impurity to the bulk is increased, there will be more than one quantum phase transition due to level crossing among overscreened states.

This paper presents a full simulation study of the measurement of the production cross section (${\sigma }_{ZH}$) of the Higgsstrahlung process $e^{+}{e}^{-}\to ZH$ and the Higgs boson mass ($M_{\mathrm{H}}$) at the International Linear Collider (ILC), using events in which a Higgs boson recoils against a $Z$ boson decaying into a pair of muons or electrons. The analysis is carried out for three center-of-mass energies $\sqrt{s}=250$, 350, and 500 GeV, and two beam polarizations $e_{\mathrm{L}}^{-}{e}_{\mathrm{R}}^{+}$ and $e_{\mathrm{R}}^{-}{e}_{\mathrm{L}}^{+}$, for which the polarizations of $e^{-}$ and $e^{+}$ are $(P{e}^{-},P{e}^{+})=(-80\%,+30\%)$ and ($+80\%$, $-30\%$), respectively. Assuming an integrated luminosity of $250{\mathrm{fb}}^{-1}$ for each beam polarization at $\sqrt{s}=250\mathrm{GeV}$, where the best lepton momentum resolution is obtainable, ${\sigma }_{ZH}$ and $M_{\mathrm{H}}$ can be determined with a precision of 2.5% and 37 MeV for $e_{\mathrm{L}}^{-}{e}_{\mathrm{R}}^{+}$ and 2.9% and 41 MeV for $e_{\mathrm{R}}^{-}{e}_{\mathrm{L}}^{+}$, respectively. Regarding a 20 year ILC physics program, the expected precisions for the HZZ coupling and $M_{\mathrm{H}}$ are estimated to be 0.4% and 14 MeV, respectively. The event selection is designed to optimize the precisions of ${\sigma }_{ZH}$ and $M_{\mathrm{H}}$ while minimizing the bias on the measured ${\sigma }_{ZH}$ due to discrepancy in signal efficiencies among Higgs decay modes. For the first time, model independence has been demonstrated to a sub-percent level for the ${\sigma }_{ZH}$ measurement at each of the three center-of-mass energies. The results presented show the impact of center-of-mass energy and beam polarization on the evaluated precisions and serve as a benchmark for the planning of the ILC run scenario.

The Schwinger pairs production rate is calculated numerically in the soft-wall model with the help of a simpler method in determining the soft-wall’s position beyond which probe strings connecting the Schwinger pairs do not fall into. The critical behavior of the production rate and linear part in the middle region are both studied carefully. The latter manifests interesting new features. The results are compared with those in previous hard-wall models.

We consider an asymptotically free vectorial gauge theory, with gauge group $G$ and $N_f$ fermions in a representation $R$ of $G$, having an infrared (IR) zero in the beta function at ${\alpha }_{\mathrm{IR}}$. We present general formulas for scheme-independent series expansions of quantities, evaluated at ${\alpha }_{\mathrm{IR}}$, as powers of an $N_f$-dependent expansion parameter, ${\mathrm{\Delta }}_f$. First, we apply these to calculate the derivative $d\beta /d\alpha$ evaluated at ${\alpha }_{\mathrm{IR}}$, denoted ${\beta }_{\mathrm{IR}}^{\prime }$, which is equivalent to the anomalous dimension of the $\mathrm{Tr}(F_{\mu \nu }{F}^{\mu \nu })$ operator, to order ${\mathrm{\Delta }}_f^4$ for general $G$ and $R$, and to order ${\mathrm{\Delta }}_f^5$ for $G=\mathrm{SU}(3)$ and fermions in the fundamental representation. Second, we calculate the scheme-independent expansions of the anomalous dimension of the flavor-nonsinglet and flavor-singlet bilinear fermion antisymmetric Dirac tensor operators up to order ${\mathrm{\Delta }}_f^3$. The results are compared with rigorous upper bounds on anomalous dimensions of operators in conformally invariant theories. Our other results include an analysis of the limit $N_c\to \infty$, $N_f\to \infty$ with $N_f/N_c$ fixed, calculation and analysis of Padé approximants, and comparison with conventional higher-loop calculations of ${\beta }_{\mathrm{IR}}^{\prime }$ and anomalous dimensions as power series in $\alpha$.

We obtain a family of regular static, spherically symmetric solutions in Einstein-Cartan theory with an electromagnetic field and a nonminimally coupled scalar field with the correct sign of kinetic energy density. At different values of its parameters, the solution, being asymptotically flat at large values of the radial coordinate, describes (i) twice asymptotically flat symmetric wormholes, (ii) asymmetric wormholes with an AdS asymptotic at the “far end,” (iii) regular black holes with an extremal horizon or two simple horizons, and (iv) black universes with a de Sitter asymptotic at the far end. As in other black universe models, it is a black hole as seen by a distant observer, but beyond its horizon there is a nonsingular expanding universe. In all these cases, both the metric and the torsion are regular in the whole space.

We investigate how baryogenesis can occur by the presence of an $f(T)$-related gravitational term. We study various cases of $f(T)$ gravity, and we discuss in detail the effect of the novel terms on the baryon-to-entropy ratio. Additionally, we study the constraints imposed by the observational values of the baryon-to-entropy ratio, and we discuss how more generalized cosmologies can contribute successfully, in a viable and consistent way, in the gravitational baryogenesis mechanism.

We investigate the growth factor for subhorizon modes during late times in $f(T,\mathcal{T})$ gravity, where $T$ is the torsion scalar and $\mathcal{T}$ is the trace of the stress-energy tensor. This is achieved by obtaining the modified Mészáros equation, which describes the evolution of the perturbations of the matter energy density, and obtaining numerical results. Such results are obtained by solving the modified continuity equation and analyzing the behavior of the solutions of the latter using various constraints on the integration constants. Furthermore, the role of the anisotropic term ${\pi }^S$ is investigated.

The precession of a test gyroscope along unbound equatorial plane geodesic orbits around a Kerr black hole is analyzed with respect to a static reference frame whose axes point towards the “fixed stars.” The accumulated precession angle after a complete scattering process is evaluated and compared with the corresponding change in the orbital angle. Limiting results for the nonrotating Schwarzschild black hole case are also discussed.

We present the results of the search for decaying dark matter with particle mass in the 6–40 keV range with NuSTAR deep observations of COSMOS and ECDFS empty sky fields. We show that the main contribution to the decaying dark matter signal from the Milky Way galaxy comes through the aperture of the NuSTAR detector, rather than through the focusing optics. The high sensitivity of the NuSTAR detector, combined with the large aperture and large exposure times of the two observation fields, allows us to improve previously existing constraints on the dark matter decay time by up to an order of magnitude in the mass range 10–30 keV. In the particular case of the $\nu \mathrm{MSM}$ sterile neutrino dark matter, our constraints impose an upper bound $m<20\mathrm{keV}$ on the dark matter particle mass. We report detection of four unidentified spectral lines (including the line at 3.51 keV) in our data set. These line detections are either due to the systematic effects (uncertainties of calibrations of the NuSTAR detectors) or have an astrophysical origin. We discuss different possibilities for testing the nature of the detected lines.

We investigate the interplay between moduli dynamics and inflation, focusing on the Kachru-Kallosh-Linde-Trivedi scenario and cosmological $\alpha$-attractors. General couplings between these sectors can induce a significant backreaction and potentially destroy the inflationary regime; however, we demonstrate that this generically does not happen for $\alpha$-attractors. Depending on the details of the superpotential, the volume modulus can either be stable during the entire inflationary trajectory or become tachyonic at some point and act as a waterfall field, resulting in a sudden end of inflation. In the latter case there is a universal supersymmetric minimum where the scalars end up, preventing the decompactification scenario. The gravitino mass is independent from the inflationary scale with no fine-tuning of the parameters. The observational predictions conform to the universal value of attractors, fully compatible with the Planck data, with possibly a capped number of $e$-folds due to the interplay with moduli.

N-body simulations predict that galaxies at the Milky Way scale host a large number of dark matter (DM) subhalos. Some of these subhalos, if they are massive enough or close enough to the Earth, might be detectable in $\gamma$ rays due to the DM annihilation. 3FGL $\mathrm{J}2212.5+0703$, an unidentified gamma-ray source, has been suggested to be the counterpart candidate of a DM subhalo by Bertoni et al. In this work we analyze the Fermi-LAT Pass 8 data of 3FGL $\mathrm{J}2212.5+0703$ to independently test the DM subhalo hypothesis of this source. In order to suppress the possible contamination from two nearby very bright blazars, we just take into account the front-converting gamma rays which have better angular resolutions than that of the back-converting photons. In addition to the spatial distribution analysis, we have extended the spectrum analysis down to the energies of $\sim 100\mathrm{MeV}$, and thoroughly examined the variability of the emission during the past 8 years. We confirm that 3FGL $\mathrm{J}2212.5+0703$ is a steady and spatially extended gamma-ray emitter at a high confidence level. The spectrum is well consistent with that expected from DM annihilation into $b\overline{b}$. The introduction of a phenomenological LogParabola spectrum just improves the fit slightly. All these results suggest that 3FGL $\mathrm{J}2212.5+0703$ could be indicative of a DM subhalo.

We of $Q$-balls in Dirac-Born-Infeld type $k$ field theory, whose action includes a nonlinear kinetic term, $\sqrt{1-b{g}^{\mu \nu }{\partial }_{\mu }{\varphi }^a{\partial }_{\nu }{\varphi }^a}/b$. Specifically, for two potentials, $V_3=m^2{\varphi }^2/2-\mu {\varphi }^3+\lambda {\varphi }^4$ and $V_4=m^2{\varphi }^2/2-\lambda {\varphi }^4+{\varphi }^6/M^2$, we survey equilibrium solutions for the whole parameter space and analyze their stability through the use of catastrophe theory. Our analysis shows that $V_3$ and $V_4$ models fall into fold catastrophe and cusp catastrophe types, respectively, just as for canonical $Q$-balls. We also find that, as long as the absolute minimum of $V(\varphi )$ is located at $\varphi =0$, equilibrium solutions exist without any additional constraint on charge $Q$ no matter how large $b$ (nonlinearity) is.

We present a parity-doublet theorem for the representation of the intrinsic parity of Majorana fermions, which is expected to be useful also in condensed matter physics, and it is illustrated to provide a criterion of neutron-antineutron oscillation in a Bardeen–Cooper–Schrieffer type of effective theory with $\mathrm{\Delta }B=2$ baryon number-violating terms. The $CP$ violation in the present effective theory causes no direct $CP$-violating effects in the oscillation itself, which is demonstrated by the exact solution, although it influences the neutron electric dipole moment in the leading order of small $\mathrm{\Delta }B=2$ parameters. An analog of Bogoliubov transformation, which preserves $P$ and $CP$, is crucial in the analysis.

We study constraints on one-loop neutral naturalness at the LHC by considering gluon partners which are required to ameliorate the tuning in the Higgs mass-squared arising at two loops. This is done with a simple orbifold model of folded supersymmetry which not only contains color-neutral stops but also bifundamental gluinos that are charged under the Standard Model color group $SU(3{)}_C$ and a separate $SU(3{)}_C^{\prime }$ group. The bifundamental gluinos reduce the Higgs mass tuning at two loops and maintain naturalness provided the gluinos are lighter than approximately 1.9 TeV for a 5 TeV cutoff scale. Limits from the LHC already forbid bifundamental gluinos below 1.4 TeV, and other noncolored states such as electroweakinos, $Z^{\prime }$ bosons and dark sector bound states may be probed at future colliders. The search for bifundamental gluinos therefore provides a direct probe of one-loop neutral naturalness that can be fully explored at the LHC.

We derive corrections to atomic energy levels from disformal couplings in Galileon theories. Through Bayesian inference, we constrain the cutoff radii and Galileon scale via these corrections. To connect different atomic systems, we assume the various cutoff radii related by a one-parameter family of solutions. This introduces a new parameter $\alpha$ which is also constrained. In this model, we predict shifts to muonic helium of $\delta E_{{\mathrm{He}}^3}=1.97_{-1.87}^{+9.28}\mathrm{meV}$ and $\delta E_{{\mathrm{He}}^4}=1.69_{-1.61}^{+9.25}\mathrm{meV}$ as well as for true muonium, $\delta E_{\mathrm{TM}}=0.06_{-0.05}^{+0.46}\mathrm{meV}$.