Using staggered fermions and partially twisted boundary conditions, we calculate the $K$ meson semileptonic decay vector form factor at zero momentum transfer. The highly improved staggered quark formulation is used for the valence quarks, while the sea quarks are simulated with the asqtad action (MILC Collaboration $N_f=2+1$ configurations). For the chiral and continuum extrapolation, we use two-loop continuum $\chi \mathrm{PT}$, supplemented by partially quenched staggered $\chi \mathrm{PT}$ at one loop. Our result is $f_{+}^{K\pi }(0)=0.9667\pm 0.0023\pm 0.0033$, where the first error is statistical and the second is the sum in quadrature of the systematic uncertainties. This result is the first $N_f=2+1$ calculation with two lattice spacings and a controlled continuum extrapolation. It is also the most precise result to date for the vector form factor, and, although the central value is larger than previous unquenched lattice calculations, it is compatible with them within errors. Combining our value for $f_{+}^{K\pi }(0)$ with the latest experimental measurements of $K$ semileptonic decays, we obtain $|V_{us}|=0.2238\pm 0.0009\pm 0.0005$, where the first error is from $f_{+}^{K\pi }(0)$ and the second one is experimental. As a byproduct of our calculation, we obtain the combination of low-energy constants $(C_{12}^r+C_{34}^r-(L_5^r{)}^2)(M_{\rho })=(3.62\pm 1.00)\times {10}^{-6}$.

We study the implications of the existence of two equalities between the elements or cofactors of the neutrino mass matrix. There are 65 structures of this type for each case. Phenomenological implications for unknown parameters like the effective Majorana mass of the electron neutrino and $CP$-violating phases are examined for the viable cases. To illustrate how such forms of the neutrino mass matrices may be realized, we also present a simple $A_4$ model for one of the classes in each case.

Motivated by recent measurements which strongly support a nonzero reactor mixing angle ${\theta }_{13}$, we study a deviation from $S_3$ neutrino discrete symmetry by explicitly breaking the neutrino mass matrix with a general retrocirculant matrix. We show that nonzero ${\theta }_{13}$ and nonzero $CP$ violation parameter $J_{CP}$ arise due to the difference between $y_2$ and $y_3$. We demonstrate that it is possible to obtain the experimentally favored results for neutrino masses and mixing angles from this mass matrix. Furthermore, we estimate the effective masses $m_{\beta }$ and $m_{\beta \beta }$ and total neutrino mass $\sum _{}^{}|m_i|$ predicted by this mass matrix.

We mimic the Wolfenstein scheme of quark flavor mixing to describe neutrino oscillations in the standard model. We identify the parameter $\lambda$ with the experimentally measured value of the mixing element responsible for atmospheric neutrino oscillations. The matrix elements responsible for solar neutrino oscillations and the Chooz angle are taken to be proportional to ${\lambda }^2$ and ${\lambda }^3$, respectively. Using present world average data on neutrinos, we derive bounds on the other parameters, $A$, $\rho$, and $\eta$ of the new scheme.

Reactor antineutrinos are used to study neutrino oscillation, search for signatures of nonstandard neutrino interactions, and monitor reactor operation for safeguard applications. The flux and energy spectrum of reactor antineutrinos can be predicted from the decays of the nuclear fission products. A comparison of recent reactor calculations with past measurements at baselines of 10–100 m suggests a 7.2% deficit. Precision measurements of reactor antineutrinos at very short baselines $\mathcal{O}(1–10\mathrm{m})$ can be used to probe this anomaly and search for possible oscillations into sterile neutrino species. This paper studies the experimental requirements for a new reactor antineutrino measurement at very short baselines and calculates the sensitivity of various scenarios. We conclude that, given proper site optimization, detector design, and background reduction, an experiment at a typical research reactor can provide $5\sigma$ discovery potential for the favored oscillation parameter space with 3 years of detector live time.

A search for the decay $B_s^0\to D^{*\mp }{\pi }^{\pm }$ is presented using a data sample corresponding to an integrated luminosity of $1.0{\mathrm{fb}}^{-1}$ of $pp$ collisions collected by LHCb. This decay is expected to be mediated by a $W$-exchange diagram, with little contribution from rescattering processes, and therefore a measurement of the branching fraction will help us to understand the mechanism behind related decays such as $B_s^0\to {\pi }^{+}{\pi }^{-}$ and $B_s^0\to D\overline{D}$. Systematic uncertainties are minimized by using $B^0\to D^{*\mp }{\pi }^{\pm }$ as a normalization channel. We find no evidence for a signal, and set an upper limit on the branching fraction of $\mathcal{B}(B_s^0\to D^{*\mp }{\pi }^{\pm })<6.1(7.8)\times {10}^{-6}$ at 90% (95%) confidence level.

We set up the general formalism to model polytropic Newtonian stars with anisotropic pressure. We obtain the corresponding Lane-Emden equation. A heuristic model based on an ansatz to obtain anisotropic matter solutions from known solutions for isotropic matter is adopted to illustrate the effects of the pressure anisotropy on the structure of the star. In particular, we calculate the Chandrasekhar mass for a white dwarf. It is clearly displayed how the Chandrasekhar mass limit changes depending on the anisotropy. Prospective astrophysical applications of the proposed approach are discussed.

We study the consequences of cancellation of cubic Abelian anomalies in F-theory grand unified theory (GUT) models that use hypercharge flux in the presence of additional U(1) symmetries. We show that a mixed anomaly between the hypercharge and two U(1) gauge fields is not automatically canceled in local models based on the spectral cover and, therefore, imposes additional constraints on local models in F-theory that have not been accounted for so far. The constraints imply that, unless the local U(1)s are globally geometrically massive, there are only two possible classes of models in F-theory GUTs, which have fields on matter curves in noncomplete GUT representations that are not vectorlike under all U(1)s: the ones based on a $3+2$ and $2+2+1$ split. We comment on some phenomenological implications of these results for realizing models from F-theory GUTs like the next to minimal supersymmetric Standard Model.

The electromagnetic vacuum energy is considered in the presence of a perfectly conducting plane and a ball with dielectric permittivity $\epsilon$ and magnetic permeability $\mu$, $\mu \ne 1$. The attention is focused on the Casimir repulsion in this system caused by the magnetic permeability of the sphere. In the case of a perfectly permeable sphere, $\mu =\infty$, the vacuum energy is estimated numerically. The short- and long-distance asymptotes corresponding to the repulsive force and respective low-temperature corrections and high-temperature limits are found for a wide range of $\mu$. The constraints on the Casimir repulsion in this system are discussed.

The search for continuous gravitational waves from unknown isolated sources is computationally limited due to the enormous parameter space that needs to be covered and the weakness of the expected signals. Therefore, semicoherent search strategies have been developed and applied in distributed computing environments such as Einstein@Home, in order to narrow down the parameter space and identify interesting candidates. However, in order to optimally confirm or dismiss a candidate as a possible gravitational wave signal, a fully coherent follow-up using all the available data is required. We present a general method and implementation of a direct (two-stage) transition to a fully coherent follow-up on semicoherent candidates. This method is based on a gridless Mesh Adaptive Direct Search algorithm using the $\mathcal{F}$-statistic. We demonstrate the detection power and computing cost of this follow-up procedure using extensive Monte Carlo simulations on (simulated) semicoherent candidates from a directed, as well as from an all-sky search setup.

A projection method is proposed to treat the one-dimensional Schrödinger equation for a single particle when the generalized uncertainty principle (GUP) generates an ultraviolet (UV) wave-vector cutoff. The existence of a unique coordinate representation called the naive one is derived from the one-parameter family of discrete coordinate representations. In this bandlimited quantum mechanics a continuous potential is reconstructed from discrete sampled values observed by means of a particle in maximally localized states. It is shown that bandlimitation modifies the speed of the center and the spreading time of a Gaussian wave packet moving in free space. Indication is found that GUP accompanied by bandlimitation may cause departures of the low-lying energy levels of a particle in a box from those in ordinary quantum mechanics to be much less suppressed than commonly thought when GUP without bandlimitation is at work.

Understanding thermodynamics and statistical mechanics in the fully general relativistic context is an open problem. I give tentative definitions of equilibrium state, mean values, mean geometry, entropy and temperature, which reduce to the conventional ones in the nonrelativistic limit but remain valid for a general covariant theory. The formalism extends to quantum theory. The construction builds on the idea of thermal time, on a notion of locality for this time, and on the distinction between global and local temperature. The last is the temperature measured by a local thermometer and is given by $kT=\hslash d\tau /ds$, with $k$ the Boltzmann constant, $\hslash$ the Planck constant, $ds$ proper time and $d\tau$ the equilibrium thermal time.

We introduce a new framework for loop quantum gravity: mimicking the spin foam quantization procedure we propose to study the symmetric sectors of the theory imposing the reduction weakly on the full kinematical Hilbert space of the canonical theory. As a first application of quantum-reduced loop gravity we study the inhomogeneous extension of the Bianchi I model. The emerging quantum cosmological model represents a simplified arena on which the complete canonical quantization program can be tested. The achievements of this analysis could elucidate the relationship between loop quantum cosmology and the full theory.

We study an inflationary scenario with a two-form field to which an inflaton couples nontrivially. First, we show that anisotropic inflation can be realized as an attractor solution and that the two-form hair remains during inflation. A statistical anisotropy can be developed because of a cumulative anisotropic interaction induced by the background two-form field. The power spectrum of curvature perturbations has a prolate-type anisotropy, in contrast to the vector models having an oblate-type anisotropy. We also evaluate the bispectrum and trispectrum of curvature perturbations by employing the in-in formalism based on the interacting Hamiltonians. We find that the nonlinear estimators $f_{\mathrm{NL}}$ and ${\tau }_{\mathrm{NL}}$ are correlated with the amplitude $g_{*}$ of the statistical anisotropy in the power spectrum. Unlike the vector models, both $f_{\mathrm{NL}}$ and ${\tau }_{\mathrm{NL}}$ vanish in the squeezed limit. However, the estimator $f_{\mathrm{NL}}$ can reach the order of 10 in the equilateral and enfolded limits. These results are consistent with the latest bounds on $f_{\mathrm{NL}}$ constrained by Planck.

The ultracompact minihalos could be formed during the earlier epoch of the Universe. The dark matter annihilation within them is very strong due to the steep density profile, $\rho \sim r^{-2.25}$. The high-energy electrons and positrons from the dark matter annihilation can inverse Compton scatter with the background photons, such as cosmic microwave background photons, to acquire higher energy. On the other hand, the synchrotron radiation can also be produced when they meet the magnetic field. In this paper, we study the signals from the ultracompact minihalos (UCMHs) due to the dark matter annihilation for the radio, x-ray and $\gamma$-ray band. We found that for the radio emission, the UCMHs can provide one kind of source for the radio excess observed by ARCADE 2. But the x-ray signals due to the inverse Compton scatter effect or the $\gamma$-ray signals mainly due to the prompt emission from dark matter would exceed the present observations, such as Fermi, COMPTEL, and CHANDRA. We found that the strongest limits on the fraction of UCMHs come from the x-ray observations, and the constraints from the radio data are the weakest.

We determine both real and virtual next-to-leading order corrections to the gluon-induced forward jet vertex from the high energy effective action proposed by Lipatov. For these calculations we employ the same regularization and subtraction formalism developed in our previous work on the quark-initiated vertex. We find agreement with previous results in the literature.

We present a study of baryon ground states and low lying excitations of nonstrange and strange baryons. The results are based on seven gauge field ensembles with two dynamical light chirally improved quarks corresponding to pion masses between 255 and 596 MeV and a strange valence quark with mass fixed by the $\Omega$ baryon. The lattice spacing varies between 0.1324 and 0.1398 fm. Given in lattice units, the bulk of our results are for size ${16}^3\times 32$; for two ensembles with light pion masses (255 and 330 MeV) we also use ${24}^3\times 48$ lattices and perform an infinite volume extrapolation. We derive energy levels for the spin $1/2$ and $3/2$ channels for both parities. In general, our results in the infinite volume limit compare well with experiment. We analyze the flavor symmetry content by identifying the singlet/octet/decuplet contributions of the resulting eigenstates. The ground states’ compositions agree with quark model expectations. In some cases the excited states, however, disagree and we discuss possible reasons.

We compute the magnetic dipole transitions between low-lying heavy quarkonium states in a model-independent way. We use the weak-coupling version of the effective field theory named potential nonrelativistic QCD, with the static potential exactly incorporated in the leading order Hamiltonian. The precision we reach is $k_{\gamma }^3/m^2\times \mathcal{O}({\alpha }_{\mathrm{s}}^2,v^2)$ and $k_{\gamma }^3/m^2\times \mathcal{O}(v^4)$ for the allowed and forbidden transitions, respectively, where $k_{\gamma }$ is the photon energy. We also resum the large logarithms associated with the heavy quark mass scale. The specific transitions considered in this paper are the following: ${\rm Y}(1S)\to {\eta }_b(1S)\gamma$, $J/\psi (1S)\to {\eta }_c(1S)\gamma$, $h_b(1P)\to {\chi }_{b0,1}(1P)\gamma$, ${\chi }_{b2}(1P)\to h_b(1P)\gamma$, ${\rm Y}(2S)\to {\eta }_b(2S)\gamma$, ${\rm Y}(2S)\to {\eta }_b(1S)\gamma$ and ${\eta }_b(2S)\to {\rm Y}(1S)\gamma$. The effect of the new power counting is found to be large, and the exact treatment of the soft logarithms of the static potential makes the factorization scale dependence much smaller. The convergence for the $b\overline{b}$ ground state is quite good, and also quite reasonable for the $c\overline{c}$ ground state and the $b\overline{b}$ $1P$ state. For all of them we give solid predictions. For the $2S$ decays the situation is less conclusive, yet our results are perfectly consistent with existing data, as the previous disagreement with experiment for the ${\rm Y}(2S)\to {\eta }_b(1S)\gamma$ decay fades away. We also compute some expectation values like the electromagnetic radius, $⟨r^2⟩$, or $⟨p^2⟩$. We find $⟨r^2⟩$ to be nicely convergent in all cases, whereas the convergence of $⟨p^2⟩$ is typically worse.

We report on a search for heavy neutrinos in $B$-meson decays. The results are obtained using a data sample that contains $772\times {10}^{6}B\overline{B}$ pairs collected at the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. No signal is observed and upper limits are set on mixing of heavy neutrinos with left-handed neutrinos of the Standard Model in the mass range $0.5–5.0\mathrm{GeV}/c^2$.

We suggest a new scenario of gravitation in which gravity at the fundamental level is described by a Riemannian (i.e., locally Euclidean) theory without the notion of time. The Lorentzian metric structure and the notion of time emerge as effective properties at long distances. On the other hand, at short distances, higher derivative terms compatible with the Riemannian diffeomorphism become important and the system is described by a power-counting renormalizable Riemannian theory.