Bottomonium $S$-wave states were studied using lattice NRQCD. Masses of ground and excited states were calculated using multiexponential fitting to a set of correlation functions constructed using both local and wavefunction-smeared operators. Three-point functions for M1 transitions between vector and pseudoscalar states were computed. Robust signals for transitions involving the first two excited states were obtained. The qualitative features of the transition matrix elements are in agreement with expectations. The calculated values of matrix elements for ${\rm Y}(2S)$ and ${\rm Y}(3S)$ decay are considerably larger than values inferred from measured decay widths.

We address the question of to what extent JIMWLK evolution is capable of taking into account angular correlations in a high energy hadronic wave function. Our conclusion is that angular (and indeed other) correlations in the wave function cannot be reliably calculated without taking into account Pomeron loops in the evolution. As an example we study numerically the energy evolution of angular correlations between dipole scattering amplitudes in the framework of the large $N_c$ approximation to JIMWLK evolution (the “projectile dipole model”). Target correlations are introduced via averaging over an (isotropic) ensemble of anisotropic initial conditions. We find that correlations disappear very quickly with rapidity even inside the saturation radius. This is in accordance with our physical picture of JIMWLK evolution. The actual correlations inside the saturation radius in the target QCD wave function, on the other hand, should remain sizable at any rapidity.

We recently derived explicit solutions of the leading-order Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equations for the $Q^2$ evolution of the singlet structure function $F_s(x,Q^2)$ and the gluon distribution $G(x,Q^2)$ using very efficient Laplace transform techniques. We apply our results here to a study of the HERA data on deep inelastic $ep$ scattering as recently combined by the H1 and ZEUS groups. We use initial distributions $F_2^{\gamma p}(x,Q_0^2)$ and $G(x,Q_0^2)$ determined for $x<0.1$ by a global fit to the HERA data, and extended to $x=1$ using the shapes of those distributions determined in the CTEQ6L and MSTW2008LO analyses from fits to other data. Our final results are insensitive at small $x$ to the details of the extension. We obtain the singlet quark distribution $F_s(x,Q_0^2)$ from $F_2^{\gamma p}(x,Q_0^2)$ using small nonsinglet quark distributions taken from either the CTEQ6L or the MSTW2008LO analyses, evolve $F_s$ and $G$ to arbitrary $Q^2$, and then convert the results to individual quark distributions. Finally, we show directly from a study of systematic trends in a comparison of the evolved $F_2^{\gamma p}(x,Q^2)$ with the HERA data that the assumption of leading-order DGLAP evolution is inconsistent with those data.

We discuss expectations for the total and inelastic cross sections at LHC CM energies $\sqrt{s}=7\mathrm{TeV}$ and 14 TeV obtained in an eikonal minijet model augmented by soft gluon $k_t$-resummation, which we describe in some detail. We present a band of predictions which encompass recent LHC data and suggest that the inelastic cross section described by two-channel eikonal models include only uncorrelated processes. We show that this interpretation of the model is supported by the LHC data.

We study the LHC potential for discovering TeV-scale $SU(2{)}_L$ 5-plet fermions introduced recently to explain small neutrino masses. We show that the Drell-Yan production and the decays of new exotic $\Sigma$ leptons are testable at the LHC. Their production is abundant due to nontrivial electroweak gauge charges. For $1{\mathrm{fb}}^{-1}$ of integrated luminosity at the present LHC $\sqrt{s}=7\mathrm{TeV}$, there can be 270 $\Sigma -\overline{\Sigma }$ pairs produced for $M_{\Sigma }=400\mathrm{GeV}$. Besides producing same-sign dilepton events, they could lead, due to a chosen small mixing between heavy and light leptons, to $\sim 10$ golden decays ${\Sigma }^{+++}(\overline{{\Sigma }^{+++}})\to W^{\pm }{W}^{\pm }{l}^{\pm }$ with a specific decay signature.

We propose a generalized Einstein-Planck relation for photons which is invariant under the change $\lambda /a{l}_P$ to $a{l}_P/\lambda$, $\lambda$ being the photon wavelength, $l_P$ Planck’s length, and $a$ a numerical constant. This yields a wavelength-dependent speed of light $v(\lambda )=c/(1+a^2(l_P/\lambda {)}^2)$, with $c$ the usual speed of light in vacuo, indicating that the speed of light should decrease for sufficiently short wavelengths. We discuss the conceptual differences with the previous proposals related to a possible decrease of the speed of light for very short wavelengths based on quantum fluctuations of the space-time, as well as its consequences on Heisenberg’s uncertainty principle up to second order in $l_P$.

The classical Green-Schwarz superstring action, with $\mathcal{N}=1$ or $\mathcal{N}=2$ spacetime supersymmetry, exists for spacetime dimensions $D=3$, 4, 6, 10, but quantization in the light-cone gauge breaks Lorentz invariance unless either $D=10$, which leads to critical superstring theory, or $D=3$. We give details of results presented previously for the bosonic and $\mathcal{N}=1$ closed 3D (super)strings and extend them to the $\mathcal{N}=2$ 3D superstring. In all cases, the spectrum is parity-invariant and contains anyons of irrational spin.

The problem of the vacuum energy decay is studied for both signs of the cosmological constant, through the analysis of the vacuum survival amplitude, defined in terms of the conformal time, $z$, by $\mathcal{A}(z,z^{\prime })\equiv ⟨\mathrm{vac}z|\mathrm{vac}{z}^{\prime }⟩$. Transition amplitudes are computed for finite time span, $Z\equiv z^{\prime }-z$, and their late time behavior (directly related to the putative decay width of the state), and the transients are discussed up to first order in the coupling constant, $\lambda$.

We analyze the physical implications of adding a topological density term $\theta \mathrm{Tr}(F\wedge F)$ to a gauge theory in a bounded region. In particular, we calculate the Casimir effect on a spherical region and we show that the result is not periodic in $\theta$, contrary to what would be expected for a true topological density. The topological nature of the $\theta$-term can be restored if an additional boundary term required by the Atiyah-Patodi-Singer theorem is included. Then, the periodicity is trivially restored because the resulting Casimir energy is independent of $\theta$. The results of the present work suggest that the observable effects of the $\theta$ term could be very small even without assuming $\theta$ itself to be small.

We consider scalar field perturbations of the asymptotically Gödel 5-dimensional charged rotating black holes with two equal angular momenta. It is shown that the spectrum of proper oscillations of the perturbation includes superradiant unstable modes. The reason for the instability is the confining Dirichlet boundary condition at the asymptotically far region of the Gödel Universe. The confining box makes superradiant modes extract rotational energy from the black hole and, after repeated reflections from the black hole, grow unboundedly. A similar instability takes place for rotating black holes in the asymptotically anti-de Sitter (AdS) space-time.

Motivated by the recent attempts to violate the weak cosmic censorship conjecture for near-extreme black holes, we consider the possibility of overcharging a near-extreme Reissner-Nordström black hole by the quantum tunneling of charged particles. We consider the scattering of spin-0 and spin-$\frac{1}{2}$ particles by the black hole in a unified framework and obtain analytically, for the first time, the pertinent reflection and transmission coefficients without any small charge approximation. Based on these results, we propose some gedanken experiments that could lead to the violation of the weak cosmic censorship conjecture due to the (classically forbidden) absorption of small energy charged particles by the black hole. As for the case of scattering in Kerr spacetimes, our results demonstrate explicitly that scalar fields are subject to (electrical) superradiance phenomenon, while spin-$\frac{1}{2}$ fields are not. Superradiance impose some limitations on the gedanken experiments involving spin-0 fields, favoring, in this way, the mechanisms for creation of a naked singularity by the quantum tunneling of spin-$\frac{1}{2}$ charged fermions. We also discuss the implications that vacuum polarization effects and quantum statistics might have on these gedanken experiments. In particular, we show that they are not enough to prevent the absorption of incident small energy particles and, consequently, the formation of a naked singularity.

This paper describes the most accurate analytical frequentist assessment to date of the uncertainties in the estimation of physical parameters from gravitational waves generated by nonspinning binary systems and Earth-based networks of laser interferometers. The paper quantifies how the accuracy in estimating the intrinsic parameters mostly depends on the network signal to noise ratio (SNR), but the resolution in the direction of arrival also strongly depends on the network geometry. We compare results for six different existing and possible global networks and two different choices of the parameter space. We show how the fraction of the sky where the one sigma angular resolution is below 2 square degrees increases about 3 times when transitioning from the Hanford (USA), Livingston (USA) and Cascina (Italy) network to a network made of five interferometers (while keeping the network SNR fixed). The technique adopted here is an asymptotic expansion of the uncertainties in inverse powers of the SNR where the first order is the inverse Fisher information matrix. We show that the commonly employed approach of using a simplified parameter spaces and only the Fisher information matrix can largely underestimate the uncertainties (the combined effect would lead to a factor 7 for the one sigma sky uncertainty in square degrees at a network SNR of 15).

The Hamiltonian formulation of Hořava gravity is derived. In a closed universe the Hamiltonian is a sum of generators of gauge symmetries, the foliation-preserving diffeomorphisms, and vanishes on shell. The scalar constraint is second class, except for a global, first-class part that generates time reparametrizations. A reduced phase space formulation is given in which the local part of the scalar constraint is solved formally for the lapse as a function of the 3 metric and its conjugate momentum. In the infrared limit the scalar constraint is linear in the square root of the lapse. For asymptotically flat boundary conditions the Hamiltonian is a sum of bulk constraints plus a boundary term that gives the total energy. This energy expression is identical to the one for Einstein-aether theory which, for static spherically symmetric solutions, is the usual Arnowitt-Deser-Misner energy of general relativity with a rescaled Newton constant.

The so-called spectral dimension is a scale-dependent number associated with both geometries and field theories that has recently attracted much attention, driven largely, though not exclusively, by investigations of causal dynamical triangulations and Hořava gravity as possible candidates for quantum gravity. We advocate the use of the spectral dimension as a probe for the kinematics of these (and other) systems in the region where spacetime curvature is small, and the manifold is flat to a good approximation. In particular, we show how to assign a spectral dimension (as a function of so-called diffusion time) to any arbitrarily specified dispersion relation. We also analyze the fundamental properties of spectral dimension using extensions of the usual Seeley–DeWitt and Feynman expansions and by using saddle point techniques. The spectral dimension turns out to be a useful, robust, and powerful probe, not only of geometry, but also of kinematics.

We propose a scenario for realizing inflation in the framework of supersymmetric $B-L$ extension of the standard model. We find that one of the associated right-handed sneutrinos (the superpartner of the standard model singlet fermion) can provide a new nontrivial inflationary trajectory at tree level (therefore breaking $B-L$ during inflation). As soon as the inflation ends, the right-handed sneutrino falls into the supersymmetric vacuum, with a vanishing vacuum expectation value, so that $B-L$ symmetry is restored. In this class of models, the $B-L$ gauge symmetry will be radiatively broken at a TeV scale and light neutrino masses are generated through the inverse seesaw mechanism.

Very old isolated neutron stars and white dwarfs have been suggested to be probes of dark matter. To play such a role, two requests should be fulfilled, i.e., the annihilation luminosity of the captured dark matter particles is above the thermal emission of the cooling compact objects (request-I) and also dominate over the energy output due to the accretion of normal matter onto the compact objects (request-II). Request-I calls for very dense dark matter medium and the critical density sensitively depends on the residual surface temperature of the very old compact objects. The accretion of interstellar/intracluster medium onto the compact objects is governed by the physical properties of the medium and by the magnetization and rotation of the stars and may outshine the signal of dark matter annihilation. Only in a few specific scenarios both requests are satisfied and the compact objects are dark matter burners. The observational challenges are discussed and a possible way to identify the dark matter burners is outlined.

In this paper, we show that the spin-0 gravitons appearing in Horava-Lifshitz gravity without the projectability condition can be eliminated by extending the gauge symmetries of the foliation-preserving diffeomorphisms to include a local U(1) symmetry. As a result, the problems of stability, ghosts, strong coupling, and different speeds in the gravitational sector are automatically resolved. In addition, with the detailed balance condition softly breaking, the number of independent coupling constants can be significantly reduced (from more than 70 down to 15), while the theory is still UV complete and possesses a healthy IR limit, whereby the prediction powers of the theory are considerably improved. The strong coupling problem in the matter sector can be cured by introducing an energy scale $M_{*}$, so that $M_{*}<{\Lambda }_{\omega }$, where $M_{*}$ denotes the suppression energy of high-order derivative terms, and ${\Lambda }_{\omega }$ the would-be strong coupling energy scale.

We consider the effect of the coupled variations of fundamental constants on the nucleon magnetic moment. The nucleon $g$-factor enters into the interpretation of the measurements of variations in the fine-structure constant, $\alpha$, in both the laboratory (through atomic clock measurements) and in astrophysical systems (e.g. through measurements of the 21 cm transitions). A null result can be translated into a limit on the variation of a set of fundamental constants, that is usually reduced to $\alpha$. However, in specific models, particularly unification models, changes in $\alpha$ are always accompanied by corresponding changes in other fundamental quantities such as the QCD scale, ${\Lambda }_{\mathrm{QCD}}$. This work tracks the changes in the nucleon $g$-factors induced from changes in ${\Lambda }_{\mathrm{QCD}}$ and the light quark masses. In principle, these coupled variations can improve the bounds on the variation of $\alpha$ by an order of magnitude from existing atomic clock and astrophysical measurements. Unfortunately, the calculation of the dependence of $g$-factors on fundamental parameters is notoriously model-dependent.

We present the solution of the Poincaré-covariant Faddeev equation for the $\Delta (1232)$ and $\Omega (1672)$ baryons. The covariant structure of the corresponding baryon amplitudes and their decomposition in terms of internal spin and orbital angular momentum is explicitly derived. The interaction kernel is truncated to a rainbow-ladder dressed-gluon exchange such that chiral symmetry and its dynamical breaking are correctly implemented. The resulting physical masses agree reasonably with experiment and their evolution with the pion mass compares favorably with lattice calculations. Evidence for the nonsphericity of the $\Delta$ resonance is discussed as well.