Radiative corrections to the decay rate of charged fermions caused by the presence of a thermal bath of photons are calculated in the limit when temperatures are below the masses of all charged particles involved. The cancellation of finite-temperature infrared divergences in the decay rate is described in detail. Temperature-dependent radiative corrections to a two-body decay of a hypothetical charged fermion and to electroweak decays of a muon $\mu \to e{\nu }_{\mu }{\overline{\nu }}_e$ are given. We touch upon possible implications of these results for charged particles in the early Universe.

There are several instances where quantum anomalies of continuous and discrete classical symmetries play an important role in fundamental physics. Examples come from chiral anomalies in the Standard Model of fundamental interactions and gravitational anomalies in string theories. Their generic origin is the fact that classical symmetries may not preserve the domains of quantum operators like the Hamiltonian. In this work, we show by simple examples that anomalous symmetries can often be implemented at the expense of working with mixed states having nonzero entropies. In particular there is the result on color breaking by non-abelian magnetic monopoles. This anomaly can be rectified by using impure states. We also argue that non-abelian groups of twisted bundles are always anomalous for pure states sharpening an earlier argument of Sorkin and Balachandran [A. P. Balachandran, G. Marmo, B. S. Skagerstam, and A. Stern, Classical Topology and Quantum States (World Scientific, Singapore, 1991).]. This is the case of mapping class groups of geons [A. P. Balachandran, G. Marmo, B. S. Skagerstam, and A. Stern, Classical Topology and Quantum States (World Scientific, Singapore, 1991).] indicating that large diffeos are anomalous for pure states in the presence of geons. Nevertheless diffeo invariance may be restored by using impure states. This work concludes with examples of these ideas drawn from molecular physics. The above approach using impure states is entirely equivalent to restricting all states to the algebra of observables invariant under the anomalous symmetries. For anomalous gauge groups such as color, this would mean that we work with observables singlet under global gauge transformations. For color, this will mean that we work with color singlets, a reasonable constraint.

We give a systematic treatment of a spin $1/2$ particle in a combined electromagnetic field and a weak gravitational field that is produced by a slowly moving matter source. This paper continues previous work on a spin zero particle, but it is largely self-contained and may serve as an introduction to spinors in a Riemann space. The analysis is based on the Dirac equation expressed in generally covariant form and coupled minimally to the electromagnetic field. The restriction to a slowly moving matter source, such as the earth, allows us to describe the gravitational field by a gravitoelectric (Newtonian) potential and a gravitomagnetic (frame-dragging) vector potential, the existence of which has recently been experimentally verified. Our main interest is the coupling of the orbital and spin angular momenta of the particle to the gravitomagnetic field. Specifically, we calculate the gravitational g-factor to be ${\mathrm{g}}_{\mathrm{g}}=1$; this is to be compared with the electromagnetic g-factor of ${\mathrm{g}}_e=2$ for a Dirac electron. Lastly, we discuss a number of possible experimental approaches to observing gravitomagnetic effects in atomic and macroscopic systems.

Interacting massive fields with $m>\frac{dH}{2}$ in $d+1$ dimensional de Sitter space are fundamentally unstable. Scalar fields in this mass range can decay to themselves. This process (which is kinematically forbidden in Minkowski space) can lead to an important change to the propagator and the physics of these fields. We compute this decay rate by doing a 1-loop computation for a massive scalar field with a cubic interaction. We resum the 1-loop result by consistently solving the Schwinger-Dyson equations. We also perform an explicit resummation of all chain graphs in the case of the retarded propagator. The decay rate is exponentially suppressed for large $m/H$ and the flat-space answer (vanishing decay rate) is reproduced in that limit.

Using the effective-one-body (EOB) formalism and a time-domain Teukolsky code, we generate inspiral, merger, and ringdown waveforms in the small-mass-ratio limit. We use EOB inspiral and plunge trajectories to build the Teukolsky-equation source term, and compute full coalescence waveforms for a range of black-hole spins. By comparing EOB waveforms that were recently developed for comparable-mass binary black holes to these Teukolsky waveforms, we improve the EOB model for the (2, 2), (2, 1), (3, 3), and (4, 4) modes. Our results can be used to quickly and accurately extract useful information about merger waves for binaries with spin and should be useful for improving analytic models of such binaries.

We analyze the physical properties of boson stars, which possess counterparts in flat space-time, Q-balls. Applying a stability analysis via catastrophe theory, we show that the families of rotating and nonrotating boson stars exhibit two stable regions, separated by an unstable region. Analogous to the case of white dwarfs and neutron stars, these two regions correspond to compact stars of lower and higher densities. Moreover, the high density phase ends when the black hole limit is approached. Here another unstable phase is encountered, exhibiting the typical spiralling phenomenon close to the black hole limit. When the interaction terms in the scalar field potential become negligible, the properties of mini-boson stars are recovered, which possess only a single stable phase.

Recently, a class of theories of massive gravity has been shown to be ghost-free. We study the spherically symmetric solutions in the bigravity formulation of such theories. In general, the solutions admit both a Lorentz-invariant and a Lorentz-breaking asymptotically flat behavior and also fall into two branches. In the first branch, all solutions can be found analytically and are Schwarzschild-like, with no modification as is found for other classes of theories. In the second branch, exact solutions are hard to find, and relying on perturbation theory, Yukawa-like modifications of the static potential are found. The general structure of the solutions suggests that the bigravity formulation of massive gravity is crucial and more than a tool.

We provide analytic solutions for the power spectrum and bispectrum of curvature fluctuations produced by a step feature in the inflaton potential, valid in the limit that the step is short and sharp. In this limit, the bispectrum is strongly scale dependent and its effective nonlinearity attains a large oscillatory amplitude. The perturbations to the curvature power spectrum, on the other hand, remain a small component on top of the usual spectrum of fluctuations generated by slow roll. We utilize our analytic solutions to assess the observability of the predicted non-Gaussian signatures and show that, if present, only very sharp steps on scales larger than $\sim 2\mathrm{Gpc}$ are likely to be able to be detected by Planck. Such features are not only consistent with WMAP7 data, but can also improve its likelihood by $2\Delta \ln L\approx 12$ for two extra parameters, the step location and height. If this improvement were due to a slow roll violating step as considered here, a bispectrum or corresponding polarization power spectrum detection would provide definitive checks as to its primordial origin.

Generic Kerr orbits exhibit intricate three-dimensional motion. We offer a classification scheme for these intricate orbits in terms of periodic orbits. The crucial insight is that for a given effective angular momentum $L$ and angle of inclination $\iota$, there exists a discrete set of orbits that are geometrically $n$-leaf clovers in a precessing orbital plane. When viewed in the full three dimensions, these orbits are periodic in $r-\theta$. Each $n$-leaf clover is associated with a rational number, $1+q_{r\theta }={\omega }_{\theta }/{\omega }_r$, that measures the degree of perihelion precession in the precessing orbital plane. The rational number $q_{r\theta }$ varies monotonically with the orbital energy and with the orbital eccentricity. Since any bound orbit can be approximated as near one of these periodic $n$-leaf clovers, this special set offers a skeleton that illuminates the structure of all bound Kerr orbits, in or out of the equatorial plane.

The formalism to compute the geometrical and topological one-point statistics of mildly non-Gaussian two-dimensional and three-dimensional (3D) cosmological fields is developed. Leveraging the isotropy of the target statistics, the Gram-Charlier expansion is reformulated with rotation-invariant variables. This formulation allows us to track the geometrical statistics of the cosmic field to all orders. It then allows us to connect the one-point statistics of the critical sets to the growth factor through perturbation theory, which predicts the redshift evolution of higher-order cumulants. In particular, the cosmic nonlinear evolution of the skeleton’s length, together with the statistics of extrema and Euler characteristic are investigated in turn. In two dimensions, the corresponding differential densities are analytic as a function of the excursion set threshold and the shape parameter. In 3D, the Euler characteristics and the field isosurface area are also analytic to all orders in the expansion. Numerical integrations are performed and simple fits are provided whenever closed form expressions are not available. These statistics are compared to estimates from N-body simulations and are shown to match well the cosmic evolution up to root mean square of the density field of $\sim 0.2$. In 3D, gravitational perturbation theory is implemented to predict the cosmic evolution of all the relevant Gram-Charlier coefficients for universes with scale-invariant matter distribution. The one-point statistics of critical sets could be used to constrain primordial non-Gaussianities and the dark energy equation of state on upcoming cosmic surveys; this is illustrated on idealized experiments.

A class of calculable global models for neutrino oscillations based on Lorentz and $CPT$ violation is presented. One simple example matches established neutrino data from accelerator, atmospheric, reactor, and solar experiments, using only 2 degrees of freedom instead of the usual five. A third degree of freedom appears in the model, and it naturally generates the MiniBooNE low-energy anomalies. More involved models in this class can also accommodate the LSND anomaly and neutrino-antineutrino differences of the MINOS type. The models predict some striking signals in various ongoing and future experiments.

The dilaton, a pseudo-Nambu-Goldstone boson appearing in spontaneous scale symmetry breaking at a TeV scale $f$, may be found in Higgs boson searches. The dilaton couples to standard model fermions and weak bosons with the same structure as the Higgs boson except for the overall strength. Additionally, the dilaton couples to a Higgs boson pair. The couplings of the dilaton to a gluon pair and a photon pair, appearing at loop level, are largely enhanced compared to the corresponding Higgs couplings. We present regions of the mass and vacuum expectation value (VEV) of the dilaton allowed by $WW$, $ZZ$, and $\gamma \gamma$ limits from the LHC at 7 TeV with $1.0–2.3{\mathrm{fb}}^{-1}$ integrated luminosity. A scale of $f$ less than 1 TeV is nearly excluded. We discuss how the dilaton $\chi$ can be distinguished from the Higgs boson $h^0$ by observation of the decays $\chi \to \gamma \gamma$ and $\chi \to h^0{h}^0\to (WW)(WW)$.

We study the Drell-Yan process mediated by a new bosonic resonance at the LHC. The bosons of spin-0, 1, and 2 with the most general leading-order couplings to standard model fermions and gluons are considered, which provides a model-independent formulation for future exploration of the resonance properties, such as its spin, mass and couplings. In the case of neutral resonances, we demonstrate how the shapes of the kinematical distributions change as one varies the chiral couplings of the quarks and leptons, and show how to analyze the couplings by making use of the forward-backward asymmetry. In the case of charged resonances, we propose a novel technique to effectively reconstruct the angular distribution in the center-of-mass frame, to a large extent avoiding the two-fold ambiguity due to the missing neutrino. Similar to the case of a neutral resonance, the spin information of the resonance can be extracted unambiguously, and chiral couplings and the asymmetries can be explored in a statistical manner. With the current LHC data, we present bounds on the mass and cross section times branching fraction of the new resonance and estimate the future reach.

We present a calculation of the branching ratio of orthopositronium decay into an invisible mode, which is done in the context of mirror world models, where ordinary positronium can disappear from our world due to oscillation into its mirror twin. In this revision we clarify some formulas and approximations used previously, correct them at some places, add new effects relevant for a feasible experiment, and finally perform a combined analysis. We include into consideration various effects due to external magnetic and electric fields, collisions with cavity walls, and scattering off gas atoms in the cavity. Oscillations of the Rydberg positroniums are also considered. To perform a numerical estimate in a realistic case we wrote computer code, which can be adopted in any experimental setup. Its work is illustrated with an example of a planned positronium experiment within the AEgIS project.

By using lattice QCD computations we determine the sigma terms and strangeness content of all octet baryons by means of an application of the Hellmann-Feynman theorem. In addition to polynomial and rational expressions for the quark-mass dependence of octet members, we use $SU(3)$ covariant baryon chiral perturbation theory to perform the extrapolation to the physical up and down quark masses. Our $N_f=2+1$ lattice ensembles include pion masses down to about 190 MeV in large volumes ($M_{\pi }L\gtrsim 4$), and three values of the lattice spacing. Our main results are the nucleon sigma term ${\sigma }_{\pi N}=39(4){(}_{-7}^{+18})$ and the strangeness content $y_N=0.20(7){(}_{-17}^{+13})$. Under the assumption of validity of covariant baryon $\chi \mathrm{PT}$ in our range of masses one finds $y_N=0.276(77){(}_{-62}^{+90})$.

The pseudoscalar and vector heavy-meson masses are calculated in the $ϵ$-regime of Heavy Meson Chiral Perturbation Theory to order ${ϵ}^4$. The results presented will allow the determination of low-energy coefficients (LECs) directly from Lattice QCD calculations of the heavy-mesons masses for lattices that satisfy the $ϵ$-regime criteria. In particular, the LECs that parametrize the next-to-leading order volume dependence of the heavy-meson masses are necessary for evaluating the light-pseudoscalar meson $(\pi ,K,\eta )$ and heavy meson ($\{D^0,D^{+},D_s^{+}\}$, $\{B^{-},{\overline{B}}^0,{\overline{B}}_s^0\}$) scattering phase shifts.

The production of the heavy $(c\overline{c})$-quarkonium, $(c\overline{b})$-quarkonium, and $(b\overline{b})$-quarkonium states [$(Q{\overline{Q}}^{\prime })$ quarkonium for short], via the $W^{+}$ semi-inclusive decays, has been systematically studied within the framework of the nonrelativistic QCD. In addition to the two color-singlet $S$-wave states, we also discuss the production of the four color-singlet $P$-wave states $|(Q{\overline{Q}}^{\prime })({}^{1}P_1{)}_{\mathbf{1}}⟩$ and $|(Q{\overline{Q}}^{\prime })({}^{3}P_J{)}_{\mathbf{1}}⟩$ [with $J=(0,1,2)$] together with the two color-octet components $|(Q{\overline{Q}}^{\prime })({}^{1}S_0{)}_{\mathbf{8}}⟩$ and $|(Q{\overline{Q}}^{\prime })({}^{3}S_1{)}_{\mathbf{8}}⟩$. Improved trace technology is adopted to derive the simplified analytic expressions at the amplitude level, which shall be useful for dealing with the following cascade decay channels. At the LHC with the luminosity $\mathcal{L}\propto {10}^{34}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$ and the center-of-mass energy $\sqrt{S}=14\mathrm{TeV}$, sizable heavy-quarkonium events can be produced through the $W^{+}$ boson decays; i.e., $2.57\times {10}^6$ ${\eta }_c$, $2.65\times {10}^{6}J/\Psi$, and $2.40\times {10}^6$ $P$-wave charmonium events per year can be obtained, and $1.01\times {10}^5$ $B_c$, $9.11\times {10}^4$ $B_c^{*}$, and $3.16\times {10}^4$ $P$-wave $(c\overline{b})$-quarkonium events per year can be obtained. Main theoretical uncertainties have also been discussed. By adding the uncertainties caused by the quark masses in quadrature, we obtain ${\Gamma }_{W^{+}\to (c\overline{c})+c\overline{s}}={524.8}_{-258.4}^{+396.3}\mathrm{KeV}$, ${\Gamma }_{W^{+}\to (c\overline{b})+b\overline{s}}={13.5}_{-3.29}^{+4.73}\mathrm{KeV}$, ${\Gamma }_{W^{+}\to (c\overline{b})+c\overline{c}}={1.74}_{-0.73}^{+1.98}\mathrm{KeV}$, and ${\Gamma }_{W^{+}\to (b\overline{b})+c\overline{b}}={38.6}_{-9.69}^{+13.4}\mathrm{eV}$.

The main Higgs production channel at hadron colliders is gluon fusion via heavy-quark loops. We present the results of a fully exclusive simulation of gluon fusion Higgs production based on the matrix elements for $h+0$, 1, 2 partons including full heavy-quark loop dependence, matched to a parton shower. We consider a Higgs with standard model couplings as well as models where the Higgs has enhanced couplings to bottom quarks ($b$-philic). We study the most relevant kinematic distributions, such as jet and Higgs $p_T$ spectra and find that matched samples provide an accurate description of the final state. For the SM Higgs, we confirm the excellent accuracy of the large heavy-quark-mass approximation also in differential distributions over all phase space, with significant effects arising only at large $p_T$. For a $b$-philic Higgs however, the loops have a dramatic impact on the kinematics of the Higgs as well as of the jets and need to be accounted for exactly to achieve reliable event simulations.

We show that very light (50–90 GeV) axigluons with flavor-universal couplings of order $g_s/3$ may explain the anomalous top forward-backward asymmetry reported by both CDF and D0 collaborations. The model is naturally consistent with the observed $t\overline{t}$ invariant mass distribution and evades bounds from light Higgs searches, LEP event shapes, and hadronic observables at the $Z$ pole. Very light axigluons can appear as resonances in multijet events, but searches require sensitivity to masses below current limits.

We present a search for new phenomena in events with two reconstructed $Z$ bosons and large missing transverse momentum, sensitive to processes $p\overline{p}\to X_2{X}_2\to ZZ{X}_1{X}_1$, where $X_2$ is an unstable particle decaying as $X_2\to Z{X}_1$ and $X_1$ is undetected. The particles $X_1$ and $X_2$ may be, among other possibilities, fourth-generation neutrinos or supersymmetric particles. We study the final state in which one $Z$ boson decays to two charged leptons and the second decays hadronically. In data corresponding to an integrated luminosity of $4.2{\mathrm{fb}}^{-1}$ from proton-antiproton collisions recorded by the CDF II detector at the Tevatron, with center-of-mass energy of 1.96 TeV, we find agreement between data and standard-model backgrounds. We calculate 95% confidence level upper limits on the cross section of the process $p\overline{p}\to X_2{X}_2\to ZZ{X}_1{X}_1$ ranging from 50 fb to 1 pb, depending on the masses of $X_1$ and $X_2$.