Using $pp$ collision data collected by LHCb at center-of-mass energies $\sqrt{s}=7\mathrm{TeV}$ and 8 TeV, corresponding to an integrated luminosity of $3{\mathrm{fb}}^{-1}$, the ratio of the branching fraction of the $B_c^{+}\to \psi (2S){\pi }^{+}$ decay relative to that of the $B_c^{+}\to J/\psi {\pi }^{+}$ decay is measured to be $0.268\pm 0.032(\mathrm{stat})\pm 0.007(\mathrm{syst})\pm 0.006(\mathrm{BF})$. The first uncertainty is statistical, the second is systematic, and the third is due to the uncertainties on the branching fractions of the $J/\psi \to {\mu }^{+}{\mu }^{-}$ and $\psi (2S)\to {\mu }^{+}{\mu }^{-}$ decays. This measurement is consistent with the previous LHCb result, and the statistical uncertainty is halved.

The grand partition function of a model of confined quarks is exactly calculated at arbitrary temperatures and quark chemical potentials. The model is inspired by a version of QCD with a soft breaking of the Becchi-Rouet-Stora-Tyutin symmetry and possesses a quark mass function compatible with nonperturbative analyses of lattice simulations and Dyson-Schwinger equations. Even though the model is defined at tree level, we show that it produces a nontrivial and stable thermodynamic behavior at any temperature or chemical potential. Results for the pressure, the entropy and the trace anomaly as a function of the temperature are qualitatively compatible with the effect of nonperturbative interactions as observed in lattice simulations. The finite density thermodynamics is also shown to contain nontrivial features, being far away from an ideal gas picture.

A recent suggestion that vector potentials in electrodynamics (ED) are nontensorial objects under four-dimensional (4D) frame rotations is found to be both unnecessary and confusing. As traditionally used in ED, a vector potential $A$ always transforms homogeneously under 4D rotations in spacetime, but if the gauge is changed by the rotation, one can restore the gauge back to the original gauge by adding an inhomogeneous term. It is then not a 4-vector, but two 4-vectors: one for rotation and one for translation. For such a gauge, it is much more important to preserve explicit homogeneous Lorentz covariance by simply skipping the troublesome gauge-restoration step. A gauge-independent separation of $A$ into a dynamical term and a nondynamical term in Abelian gauge theories is redefined more generally as the terms caused by the presence and absence, respectively, of the 4-current term in the inhomogeneous Maxwell equations for $A$. Such a separation cannot in general be extended to non-Abelian theories where $A$ satisfies nonlinear differential equations. However, in the linearized iterative solution that is perturbation theory, the usual Abelian quantizations in the usual gauges can be used. Some nonlinear complications are briefly reviewed.

We study the renormalization group flow of ${\mathbb{Z}}_2$-invariant supersymmetric and nonsupersymmetric scalar models in the local potential approximation using functional renormalization group methods. We focus our attention on the fixed points of the renormalization group flow of these models, which emerge as scaling solutions. In two dimensions these solutions are interpreted as the minimal (supersymmetric) models of conformal field theory, while in three dimensions they are manifestations of the Wilson-Fisher universality class and its supersymmetric counterpart. We also study the analytically continued flow in fractal dimensions between 2 and 4 and determine the critical dimensions for which irrelevant operators become relevant and change the universality class of the scaling solution. We include novel analytic and numerical investigations of the properties that determine the occurrence of the scaling solutions within the method. For each solution we offer new techniques to compute the spectrum of the deformations and obtain the corresponding critical exponents.

It is known that a near-extremal Kerr black hole can be spun up beyond its extremal limit by capturing a test particle. Here we show that overspinning is always averted once backreaction from the particle’s own gravity is properly taken into account. We focus on nonspinning, uncharged, massive particles thrown in along the equatorial plane and work in the first-order self-force approximation (i.e., we include all relevant corrections to the particle’s acceleration through linear order in the ratio, assumed small, between the particle’s energy and the black hole’s mass). Our calculation is a numerical implementation of a recent analysis by two of us [Phys. Rev. D 91, 104024 (2015)], in which a necessary and sufficient “censorship” condition was formulated for the capture scenario, involving certain self-force quantities calculated on the one-parameter family of unstable circular geodesics in the extremal limit. The self-force information accounts both for radiative losses and for the finite-mass correction to the critical value of the impact parameter. Here we obtain the required self-force data and present strong evidence to suggest that captured particles never drive the black hole beyond its extremal limit. We show, however, that, within our first-order self-force approximation, it is possible to reach the extremal limit with a suitable choice of initial orbital parameters. To rule out such a possibility would require (currently unavailable) information about higher-order self-force corrections.

We investigate the gravitational lensing scenario due to Schwarzschild-like black hole surrounded by quintessence (Kiselev black hole). We work for the special case of Kiselev black hole where we take the state parameter $w_q=-\frac{2}{3}$. For the detailed derivation and analysis of the bending angle involved in the deflection of light, we discuss three special cases of Kiselev black hole: nonextreme, extreme, and naked singularity. We also calculate the approximate bending angle and compare it with the exact bending angle. We found the relation of bending angles in the decreasing order as: naked singularity, extreme Kiselev black hole, nonextreme Kiselev black hole, and Schwarzschild black hole. In the weak field approximation, we compute the position and total magnification of relativistic images as well.

We present the gravitational waveforms computed in ab initio two-dimensional core collapse supernova models evolved with the chimera code for progenitor masses between 12 and $25{\mathrm{M}}_{\odot }$. All models employ multifrequency neutrino transport in the ray-by-ray approximation, state-of-the-art weak interaction physics, relativistic transport corrections such as the gravitational redshift of neutrinos, two-dimensional hydrodynamics with the commensurate relativistic corrections, Newtonian self-gravity with a general-relativistic monopole correction, and the Lattimer-Swesty equation of state with 220 MeV compressibility, and begin with the most recent Woosley-Heger nonrotating progenitors in this mass range. All of our models exhibit robust explosions. Therefore, our waveforms capture all stages of supernova development: 1) a relatively short and weak prompt signal, 2) a quiescent stage, 3) a strong signal due to convection and standing accretion shock instability activity, 4) termination of active accretion onto the proto-neutron star, and 5) a slowly increasing tail that reaches a saturation value. Fourier decomposition shows that the gravitational wave signals we predict should be observable by AdvLIGO for Galactic events across the range of progenitors considered here. The fundamental limitation of these models is in their imposition of axisymmetry. Further progress will require counterpart three-dimensional models, which are underway.

We compute the renormalized expectation value of the square of a massless, conformally coupled, quantum scalar field on the brane of a higher-dimensional black hole. Working in the AADD brane-world scenario, the extra dimensions are flat and we assume that the compactification radius is large compared with the size of the black hole. The four-dimensional on-brane metric corresponds to a slice through a higher-dimensional Schwarzschild-Tangherlini black hole geometry and depends on the number of bulk space-time dimensions. The quantum scalar field is in a thermal state at the Hawking temperature. An exact, closed-form expression is derived for the renormalized expectation value of the square of the quantum scalar field on the event horizon of the black hole. Outside the event horizon, this renormalized expectation value is computed numerically. The answer depends on the number of bulk space-time dimensions, with a magnitude which increases rapidly as the number of bulk space-time dimensions increases.

The bulk-to-boundary mapping for massive scalar fields is constructed, providing a de Sitter analog of the Lehmann-Symanzik-Zimmermann reduction formula. The set of boundary correlators thus obtained defines a potentially new class of conformal field theories based on principal series representations of the global conformal group. Conversely, we show that bulk field operators in de Sitter may be reconstructed from boundary operators. While consistent at the level of the free field theory, the boundary conformal field theory does not satisfy cluster decomposition. The resulting conformal field theory does not satisfy the basic axioms of Euclidean quantum field theory due to Osterwalder and Schrader, so it is likely not well defined once interactions are included.

We investigate the influence of a cosmological constant $\mathrm{\Lambda }$ on gravitational lensing effects. By the method of an elliptic integral, we give the solution to the null geodesic equation in Schwarzschild–de Sitter spacetime. The deflection angle of light is obtained by studying the intrinsic geometry of the spatial equatorial plane in Schwarzschild–de Sitter spacetime. By applying the expansion of elliptic integrals, we find the deflection angle in the weak field limit and in the strong field limit, respectively. We verify that the deflection angle, angular position, and magnification of images are all monotonically decreasing functions of $\mathrm{\Lambda }$.

We formulate a generic Newtonian-like analogous potential for static spherically symmetric general relativistic (GR) spacetime and subsequently derived proper Newtonian-like analogous potential corresponding to Janis-Newman-Winicour (JNW) and Reissner-Nordström (RN) spacetimes, both exhibiting naked singularities. The derived potentials were found to reproduce the entire GR features including the orbital dynamics of the test particle motion and the orbital trajectories, with precise accuracy. The nature of the particle orbital dynamics including their trajectory profiles in JNW and RN geometries show altogether different behaviors with distinctive traits as compared to the nature of particle dynamics in Schwarzschild geometry. Exploiting the Newtonian-like analogous potentials, we found that the radiative efficiency of a geometrically thin and optically thick Keplerian accretion disk around naked singularities corresponding to both JNW and RN geometries, in general, is always higher than that for Schwarzschild geometry. The derived potentials would thus be useful to study astrophysical processes, especially to investigate more complex accretion phenomena in active galactic nuclei (AGNs) or in x-ray binaries (XRBs) in the presence of naked singularities and thereby to explore any noticeable differences in their observational features from those in the presence of black holes (BHs) to ascertain outstanding debatable issues relating to gravity—whether the end state of gravitational collapse in our physical Universe renders BH or naked singularity.

The opportunity to study physics at supra-nuclear densities through x-ray observations of neutron stars has led to in-depth investigations of certain approximately universal relations that can remove degeneracies in pulse profile models. One such set of relations determines all of the multipole moments of a neutron star just from the first three (the mass monopole, the current dipole and the mass quadrupole moment) approximately independently of the equation of state. These three-hair relations were found to hold in neutron stars that rotate rigidly, as is the case in old pulsars, but neutron stars can also rotate differentially, as is the case for proto-neutron stars and hypermassive transient remnants of binary mergers. We here extend the three-hair relations to differentially rotating stars for the first time with a generic rotation law using two approximations: a weak-field scheme (an expansion in powers of the neutron star compactness) and a perturbative differential rotation scheme (an expansion about rigid rotation). These approximations allow us to analytically derive approximately universal relations that allow us to determine all of the multipole moments of a (perturbative) differentially rotating star in terms of only the first four moments. These new four-hair relations for differentially rotating neutron stars are found to be approximately independent of the equation of state to a higher degree than the three-hair relations for uniformly rotating stars. Our results can be instrumental in the development of four-hair relations for rapidly differentially rotating stars in full general relativity using numerical simulations.

Using an $SO(10)$-inspired form for the Dirac neutrino mass, we map the neutrino data to the right-handed neutrino Majorana mass matrix, $\mathcal{M}$, and investigate a special form with seesaw tribimaximal mixing; it predicts a normal hierarchy, and the values of the light neutrino masses. It may be generated by mapping he top quark hierarchy onto the vacuum values of familon fields transforming under the family group ${\mathcal{P}\mathcal{S}\mathcal{L}}_2(7)$. Next, we investigate the hypothesis that these familons play a dual role, generating a hierarchy in the supersymmetric $\mathit{\mu }$-mass matrix of Higgs bosons carrying family quantum numbers. A special ${\mathcal{P}\mathcal{S}\mathcal{L}}_2(7)$ invariant coupling produces a $\mu$ matrix with a hierarchy of thirteen orders of magnitude. Only one Higgs field (per hypercharge sector) is light enough (with a $\mu$ mass $\sim 10–100\mathrm{GeV}$) to be destabilized by supersymmetry soft breaking at the TeV scale, and upon spontaneous symmetry breaking, gives tree-level masses for the heaviest family.

In order to significantly reduce the fine-tuning associated with the electroweak symmetry breaking in the minimal supersymmetric standard model (MSSM), we consider not only the minimal gravity mediation effects but also the minimal gauge mediation ones for a common supersymmetry breaking source at a hidden sector. In this “minimal mixed mediation model,” the minimal forms for the Kähler potential and the gauge kinetic function are employed at tree level. The MSSM gaugino masses are radiatively generated through the gauge mediation. Since a “focus point” of the soft Higgs mass parameter, $m_{h_u}^2$ appears around 3–4 TeV energy scale in this case, $m_{h_u}^2$ is quite insensitive to top squark masses. Instead, the naturalness of the small $m_{h_u}^2$ is more closely associated with the gluino mass rather than the top squark mass, unlike the conventional scenario. As a result, even a 3–4 TeV top squark mass, which is known to explain the 125 GeV Higgs mass at three-loop level, can still be compatible with the naturalness of the electroweak scale. On the other hand, the requirements of various fine-tuning measures much smaller than 100 and $|\mu |<600\mathrm{GeV}$ constrain the gluino mass to be $1.6\mathrm{TeV}\lesssim m_{\tilde{g}}\lesssim 2.2\mathrm{TeV}$, which is well inside the discovery potential range of LHC Run II.

In two Higgs doublet models, there exists an interesting possibility, the hidden light Higgs scenario, that the discovered SM-like Higgs boson is the heavier $CP$-even Higgs boson $H^0$ and the lighter $CP$-even $h^0$ has not been observed yet in any experiment. We study the current status of this scenario in Types I, II, X, and Y, through the scans of the parameters with all relevant theoretical and experimental constraints. We employ not only the most up-to-date Higgs signal strength measurements with the feed-down effects, but also all the available LHC exclusion limits from heavy Higgs searches. Adjusting the heavier $H^0$ to the 125 GeV state while hiding the lighter $h^0$ from the LEP Higgs search prohibits the extreme decoupling limit: there exist upper bounds on the masses of the pseudoscalar $A^0$ and the charged Higgs $H^{\pm }$ below about 600 GeV. In addition, the $Z_2$ symmetry is shown to be a good approximate symmetry since the soft $Z_2$ symmetry breaking parameter $m_{12}^2$ should be less than about $(45\mathrm{GeV}{)}^2$. Most interestingly, a few parameters in the Higgs potential and the related Higgs triple and quartic couplings are shown to be meaningfully constrained by the current data. The double Higgs-strahlung process at an $e^{+}{e}^{-}$ collider is also studied.

Nonuniform background electromagnetic fields, once implemented in lattice quantum chromodynamics calculations of hadronic systems, provide a means to constrain a large class of electromagnetic properties of hadrons and nuclei, from their higher electromagnetic moments and charge radii to their electromagnetic form factors. We show how nonuniform fields can be constructed on a periodic hypercubic lattice under certain conditions and determine the precise form of the background $U(1)$ gauge links that must be imposed on the quantum chromodynamics gauge-field configurations to maintain periodicity. Once supplemented by a set of quantization conditions on the background-field parameters, this construction guarantees that no nonuniformity occurs in the hadronic correlation functions across the boundary of the lattice. The special cases of uniform electric and magnetic fields, a nonuniform electric field that varies linearly in one spatial coordinate (relevant to the determination of quadruple moment and charge radii), nonuniform electric and magnetic fields with given temporal and spatial dependences (relevant to the determination of nucleon spin polarizabilities) and plane-wave electromagnetic fields (relevant to the determination of electromagnetic form factors) are discussed explicitly.

There exist candidates for the negative-parity states ${\mathrm{\Lambda }}_{c,b}(1/2^{-},3/2^{-})$ consisting of an isospin-zero, spin-zero light diquark $[ud]$ with one unit of orbital angular momentum with respect to a $c,b$ quark. However, there exists only one candidate for the orbital excitations of the ${\mathrm{\Sigma }}_c(1/2^{+})$ and ${\mathrm{\Sigma }}_c^{*}(3/2^{+})$, and none for the orbital excitations of ${\mathrm{\Sigma }}_b(1/2^{+})$ or ${\mathrm{\Sigma }}_b^{*}(3/2^{+})$. We extend a previous discussion of odd-parity ${\mathrm{\Lambda }}_{c,b}$ states and explore some patterns of the odd-parity ${\mathrm{\Sigma }}_{c,b}$ baryons consisting of a light isospin-one nonstrange diquark $(uu,ud,dd)$ in a state of $L=1$ with respect to the spin-$1/2$ heavy quark $(c,b)$.

Brodsky, Llanes-Estrada, and Szczepaniak emphasized the importance of the $J=0$ fixed-pole manifestation in real and (deeply) virtual Compton scattering measurements and argued that the $J=0$ fixed pole is universal, i.e., independent on the photon virtualities [Phys. Rev. D 79, 033012 (2009)]. In this paper we review the $J=0$ fixed-pole issue in deeply virtual Compton scattering. We employ the dispersive approach to derive the sum rule that connects the $J=0$ fixed-pole contribution and the subtraction constant, called the $D$-term form factor for deeply virtual Compton scattering. We show that in the Bjorken limit the $J=0$ fixed-pole universality hypothesis is equivalent to the conjecture that the $D$-term form factor is given by the inverse moment sum rule for the Compton form factor. This implies that the $D$-term is an inherent part of the corresponding generalized parton distribution (GPD). Any supplementary $D$-term added to a GPD results in an additional $J=0$ fixed-pole contribution and implies the violation of the universality hypothesis. We argue that there exists no theoretical proof for the $J=0$ fixed-pole universality conjecture.

A dynamical coupled-channels (DCC) model for neutrino-nucleon reactions in the resonance region is developed. Starting from the DCC model that we have previously developed through an analysis of $\pi N,\gamma N\to \pi N,\eta N,K\mathrm{\Lambda },K\mathrm{\Sigma }$ reaction data for $W\le 2.1\mathrm{GeV}$, we extend the model of the vector current to $Q^2\le 3.0(\mathrm{GeV}/c{)}^2$ by analyzing electron-induced reaction data for both proton and neutron targets. We derive axial-current matrix elements that are related to the $\pi N$ interactions of the DCC model through the partially conserved axial current (PCAC) relation. Consequently, the interference pattern between resonant and nonresonant amplitudes is uniquely determined. We calculate cross sections for neutrino-induced meson productions, and compare them with available data. Our result for the single-pion production reasonably agrees with the data. We also make a comparison with the double-pion production data. Our model is the first DCC model that can give the double-pion production cross sections in the resonance region. We also make comparison of our result with other existing models to reveal an importance of testing the models in the light of PCAC and electron reaction data. The DCC model developed here will be a useful input for constructing a neutrino-nucleus reaction model and a neutrino event generator for analyses of neutrino experiments.