I present results for the two-loop soft anomalous dimensions for associated production of a single top quark with a $W$ boson or a charged Higgs boson. The calculation uses expressions for the massive cusp anomalous dimension, which are presented in different forms, and it allows soft-gluon resummation at next-to-next-to-leading-logarithm (NNLL) accuracy. From the NNLL resummed cross section I derive approximate NNLO cross sections for $bg\to t{W}^{-}$ and $bg\to t{H}^{-}$ at LHC energies of 7, 10, and 14 TeV.

We estimate the splitting between the spatial correlation lengths in the scalar and pseudoscalar channels in QCD at high temperature. The splitting is due to the contribution of the instanton/anti-instanton chains in the thermal ensemble, even though instanton contributions to thermodynamic quantities are suppressed. The splitting vanishes at asymptotically high temperatures as $\Delta M/M\propto ({\Lambda }_{\mathrm{QCD}}/T{)}^b$, where $b$ is the beta function coefficient.

A general analytic procedure is developed for the post-Newtonian limit of $f(R)$ gravity with the metric approach in the Jordan frame by using the harmonic gauge condition. In a pure perturbative framework and by using the Green function method, a general scheme of solutions up to $(v/c{)}^4$ order is shown. Considering the Taylor expansion of a generic function $f$, it is possible to parametrize the solutions by derivatives of $f$. At Newtonian order, $(v/c{)}^2$, the most important topics about the Gauss and Birkhoff theorems are discussed. The corrections to the “standard” gravitational potential ($tt$ component of the metric tensor) generated by an extended uniform mass ball-like source are calculated up to $(v/c{)}^4$ order. The corrections, Yukawa and oscillating-like, are found inside and outside the mass distribution. At last, when the limit $f\to R$ is considered, the $f(R)$ gravity converges in general relativity at the level of the Lagrangian, field equations, and their solutions.

We compute the growth of the mean square of quantum fluctuations of test fields with small effective mass during a slowly changing, nearly de Sitter stage which takes place in different inflationary models. We consider a minimally coupled scalar with a small mass, a modulus with an effective mass $\propto H^2$ (with $H$ the Hubble parameter), and a massless nonminimally coupled scalar in the test field approximation and compare the growth of their relative mean square with the one of gauge-invariant inflaton fluctuations. We find that in most of the single field inflationary models the mean square gauge-invariant inflaton fluctuation grows faster than any test field with a non-negative effective mass. Hybrid inflationary models can be an exception: the mean square of a test field can dominate over the gauge-invariant inflaton fluctuation one on suitably chosen parameters. We also compute the stochastic growth of quantum fluctuations of a second field, relaxing the assumption of its zero homogeneous value, in a generic inflationary model; as a main result, we obtain that the equation of motion of a gauge-invariant variable associated, order by order, with a generic quantum scalar fluctuation during inflation can be obtained only if we use the number of e-folds as the time variable in the corresponding Langevin and Fokker-Planck equations for the stochastic approach. We employ this approach to derive some bounds for the case of a model with two massive fields.

We investigate the thermodynamics of Lovelock-Lifshitz black branes. We begin by introducing the finite action of third order Lovelock gravity in the presence of a massive vector field for a flat boundary, and use it to compute the energy density of these black branes. Using the field equations, we find a conserved quantity along the $r$ coordinate that relates the metric parameters at the horizon and at infinity. Remarkably, though the subleading large-$r$ behavior of Lovelock-Lifshitz black branes differs substantively from their Einsteinian Lifshitz counterparts, we find that the relationship between the energy density, temperature, and entropy density is unchanged from Einsteinian gravity. Using the first law of thermodynamics to obtain the relationship between entropy and temperature, we find that it too is the same as the Einsteinian case, apart from a constant of integration that depends on the Lovelock coefficients.

Motivated by phenomenological questions in quantum gravity, we consider the propagation of a scalar field on a random lattice. We describe a procedure to calculate the dispersion relation for the field by taking a limit of a periodic lattice. We use this to calculate the lowest order coefficients of the dispersion relation for a specific one-dimensional model.

Light quark masses can be determined through lattice simulations in regularization invariant momentum-subtraction (RI/MOM) schemes. Subsequently, matching factors, computed in continuum perturbation theory, are used in order to convert these quark masses from a RI/MOM scheme to the $\overline{\mathrm{MS}}$ scheme. We calculate the two-loop corrections in QCD to these matching factors as well as the three-loop mass anomalous dimensions for the RI/SMOM and $\mathrm{RI}/{\mathrm{SMOM}}_{{\gamma }_{\mu }}$ schemes. These two schemes are characterized by a symmetric subtraction point. Providing the conversion factors in the two different schemes allows for a better understanding of the systematic uncertainties. The two-loop expansion coefficients of the matching factors for both schemes turn out to be small compared to the traditional RI/MOM schemes. For $n_f=3$ quark flavors they are about 0.6%–0.7% and 2%, respectively, of the leading order result at scales of about 2 GeV. Therefore, they will allow for a significant reduction of the systematic uncertainty of light quark mass determinations obtained through this approach. The determination of these matching factors requires the computation of amputated Green’s functions with the insertions of quark bilinear operators. As a by-product of our calculation we also provide the corresponding results for the tensor operator.

The minimal SU(5) theory augmented by the fermionic adjoint representation restores the coupling constant unification and gives realistic neutrino masses and mixing through the hybrid Type I and Type III seesaw. The crucial prediction of the theory is an SU(2) lepton triplet with the mass below TeV. We study the signature of these heavy leptons at the hadron and lepton colliders. The smoking gun evidence of the theory, as in general seesaw mechanisms, is $\Delta L=2$ lepton-number violation through events of a pair of like-sign leptons plus four jets without significant missing energy at hadron colliders. We find that via this unique channel the heavy lepton can be searched for up to a mass of 200 GeV at the Tevatron with $8{\mathrm{fb}}^{-1}$, and up to 450 (700) GeV at the LHC of 14 TeV C.M. energy with $10(100){\mathrm{fb}}^{-1}$. The 7 TeV LHC run of $1{\mathrm{fb}}^{-1}$ is expected to probe a mass window of 110–200 GeV. We also comment on how to distinguish this theory from other models with similar heavy leptons. Finally, we compare the production rates and angular distributions of heavy leptons in $e^{+}{e}^{-}$ collisions for various models.

We construct vertex operators for massless higher spin fields in Ramond-Neveu-Schwarz superstring theory and compute some of their three-point correlators, describing gauge-invariant cubic interactions of the massless higher spins. The Fierz-Pauli on-shell conditions for the higher spins (including tracelessness and vanishing divergence) follow from the Becchi-Rouet-Stora-Tyutin–invariance conditions for the vertex operators constructed in this paper. The gauge symmetries of the massless higher spins emerge as a result of the Becchi-Rouet-Stora-Tyutin–nontriviality conditions for these operators, being equivalent to transformations with the traceless gauge parameter in the Fronsdal’s approach. The gauge invariance of the interaction terms of the higher spins is therefore ensured automatically by that of the vertex operators in string theory. We develop a general algorithm to compute the cubic interactions of the massless higher spins and use it to explicitly describe the gauge-invariant interaction of two $s=3$ and one $s=4$ massless particles.

Gravitational parity violation is a possibility motivated by particle physics, string theory, and loop quantum gravity. One effect of it is amplitude birefringence of gravitational waves, whereby left and right circularly polarized waves propagate at the same speed but with different amplitude evolution. Here we propose a test of this effect through coincident observations of gravitational waves and short gamma-ray bursts from binary mergers involving neutron stars. Such gravitational waves are highly left or right circularly polarized due to the geometry of the merger. Using localization information from the gamma-ray burst, ground-based gravitational wave detectors can measure the distance to the source with reasonable accuracy. An electromagnetic determination of the redshift from an afterglow or host galaxy yields an independent measure of this distance. Gravitational parity violation would manifest itself as a discrepancy between these two distance measurements. We exemplify such a test by considering one specific effective theory that leads to such gravitational parity violation, Chern-Simons gravity. We show that the advanced LIGO-Virgo network and all-sky gamma-ray telescopes can be sensitive to the propagating sector of Chern-Simons gravitational parity violation to a level roughly 2 orders of magnitude better than current stationary constraints from the LAGEOS satellites.

To make predictions for an eternally inflating “multiverse,” one must adopt a procedure for regulating its divergent spacetime volume. Recently, a new test of such spacetime measures has emerged: normal observers—who evolve in pocket universes cooling from hot big bang conditions—must not be vastly outnumbered by “Boltzmann brains”—freak observers that pop in and out of existence as a result of rare quantum fluctuations. If the Boltzmann brains prevail, then a randomly chosen observer would be overwhelmingly likely to be surrounded by an empty world, where all but vacuum energy has redshifted away, rather than the rich structure that we observe. Using the scale-factor cutoff measure, we calculate the ratio of Boltzmann brains to normal observers. We find the ratio to be finite, and give an expression for it in terms of Boltzmann brain nucleation rates and vacuum decay rates. We discuss the conditions that these rates must obey for the ratio to be acceptable, and we discuss estimates of the rates under a variety of assumptions.

We consider the dilaton in the strong string-coupling limit and elaborate on the original idea of Damour and Polyakov whereby the dilaton coupling to matter is minimized and vanishes at a finite value of the dilaton field. Combining this type of coupling with an exponential potential, the effective potential of the dilaton becomes matter density dependent. We study the background cosmology, showing that the dilaton can play the role of dark energy. We also analyze the constraints imposed by the absence of violation of the equivalence principle. Imposing these constraints and assuming that the dilaton plays the role of dark energy, we consider the consequences of the dilaton on large scale structures and, in particular, the behavior of the slip functions and the growth index at low redshift.

We present a new analytical method to calculate the small angle cosmic microwave background (CMB) temperature angular power spectrum due to cosmic (super-)string segments. In particular, using our method, we clarify the dependence on the intercommuting probability $P$. We find that the power spectrum is dominated by Poisson-distributed string segments. The power spectrum for a general value of $P$ has a plateau on large angular scales and shows a power-law decrease on small angular scales. The resulting spectrum in the case of conventional cosmic strings is in very good agreement with the numerical result obtained by Fraisse et al.. Then we estimate the upper bound on the dimensionless tension of the string for various values of $P$ by assuming that the fraction of the CMB power spectrum due to cosmic (super-)strings is less than ten percent at various angular scales up to $\ell =2000$. We find that the amplitude of the spectrum increases as the intercommuting probability. As a consequence, strings with smaller intercommuting probabilities are found to be more tightly constrained.

We consider the presence of oscillations in the primordial bispectrum, inspired by three different cosmological models; features in the primordial potential, resonant type non-Gaussianities, and deviation from the standard Bunch-Davies vacuum. In order to put constraints on their bispectra, a logical first step is to put these into a factorized form which can be achieved via the recently proposed method of polynomial basis expansion on the tetrahedral domain. We investigate the viability of such an expansion for the oscillatory bispectra and find that one needs an increasing number of orthonormal mode functions to achieve a significant correlation between the expansion and the original spectrum as a function of their frequency. To reduce the number of modes required, we propose a basis consisting of Fourier functions orthonormalized on the tetrahedral domain. We show that the use of Fourier mode functions instead of polynomial mode functions can lead to the necessary factorizability with the use of only $1/5$ of the total number of modes required to reconstruct the bispectra with polynomial mode functions. Moreover, from an observational perspective, the expansion has unique signatures depending on the orientation of the oscillation due to a resonance effect between the mode functions and the original spectrum. This effect opens the possibility to extract information about both the frequency of the bispectrum as well as its shape while considering only a limited number of modes. The resonance effect is independent of the phase of the reconstructed bispectrum suggesting Fourier mode extraction could be an efficient way to detect oscillatory bispectra in the data.

We compare current and forecasted constraints on dynamical dark energy models from Type Ia supernovae and the cosmic microwave background using figures of merit based on the volume of the allowed dark energy parameter space. For a two-parameter dark energy equation of state that varies linearly with the scale factor, and assuming a flat universe, the area of the error ellipse can be reduced by a factor of $\sim 10$ relative to current constraints by future space-based supernova data and CMB measurements from the Planck satellite. If the dark energy equation of state is described by a more general basis of principal components, the expected improvement in volume-based figures of merit is much greater. While the forecasted precision for any single parameter is only a factor of 2–5 smaller than current uncertainties, the constraints on dark energy models bounded by $-1\le w\le 1$ improve for approximately 6 independent dark energy parameters resulting in a reduction of the total allowed volume of principal component parameter space by a factor of $\sim 100$. Typical quintessence models can be adequately described by just 2–3 of these parameters even given the precision of future data, leading to a more modest but still significant improvement. In addition to advances in supernova and CMB data, percent-level measurement of absolute distance and/or the expansion rate is required to ensure that dark energy constraints remain robust to variations in spatial curvature.

In this short reappraisal of spontaneous lepton number violation in a supersymmetric scenario implemented through singlet sneutrino vacuum expectation value (VEV), we contribute two new things in the context where the lepton number symmetry is global: (i) provide explicit expressions of $R$-parity violating couplings in terms of the neutrino Yukawa couplings and the singlet sneutrino VEV, and (ii) estimate the limit on this VEV using the current knowledge of the light neutrino mass and the astrophysical constraint on the Majoron-electron coupling. Besides, we put updated constraints on the VEV and Yukawa coupling of the singlet superfield when the lepton number is gauged.

We construct and analyze an ultraviolet extension of a model in which electroweak symmetry breaking is due to both technifermion and top-quark condensates. The model includes dynamical mechanisms for all of the various gauge symmetry breakings. We discuss certain aspects in which it requires additional ingredients to be more realistic.

Spectral weight functions are easily obtained from two-point correlation functions, and they might be used to distinguish single-particle from multiparticle states in a finite-volume lattice calculation, a problem crucial for many lattice QCD simulations. In previous studies, it has been shown that the spectral weight function for a broad resonance shares the typical volume dependence of a two-particle scattering state, i.e. proportional to $1/L^3$ in a large cubic box of size $L$, while the narrow resonance case requires further investigation. In this paper, a generalized formula is found for the spectral weight function which incorporates both the narrow and broad resonance cases. Within Lüscher’s formalism, it is shown that the volume dependence of the spectral weight function exhibits a single-particle behavior for an extremely narrow resonance and a two-particle behavior for a broad resonance. The corresponding formulas for both $A_1^{+}$ and $T_1^{-}$ channels are derived. The potential application of these formulas in the extraction of resonance parameters are also discussed.

We present the one-loop corrections originating from QCD and electroweak interactions of supersymmetric origin within the minimal supersymmetric standard model to the single-top processes $bq\to t{q}^{\prime }$ and $q{\overline{q}}^{\prime }\to t\overline{b}$. We illustrate their impact on top quark observables accessible at the LHC in the “$t+$jet” final state, such as total cross section, several differential distributions, and left-right plus forward-backward asymmetries. We find that in many instances these effects can be observable for planned LHC energies and luminosities, quite large as well as rather sensitive to several minimal supersymmetric standard model parameters.

We discuss the impact of anomalous $WW\gamma$ and $WWZ$ couplings on $WZ+\mathrm{\text{jet}}$ production at next-to-leading order QCD, including full leptonic decays of the electroweak gauge bosons. While the inclusive hadronic cross sections do not exhibit any particular sensitivity to anomalous couplings once the residual QCD scale uncertainties are taken into account, the transverse momentum distributions show substantial deviations from the standard model, provided that the anomalous vertices are probed at large enough momentum transfers.