Correlation functions of matrix-valued fields are not generally known for massive renormalized field theories. We find the large-$N$ limit of form factors of the ($1+1$)-dimensional sigma model with $\mathrm{SU}(N)\times \mathrm{SU}(N)$ symmetry. These form factors give a correction to the free-field approximation for the $N=\infty$ Wightman function. The method is a combination of the $1/N$ expansion of the $S$ matrix and Smirnov’s form-factor axioms. We expand the renormalized field in terms of a free massive bosonic field as $N\to \infty$.

Instantons are tunneling solutions that connect two vacua, and under a small change in the potential, instantons sometimes disappear. We classify these disappearances as smooth (decay rate $\to 0$ at disappearance) or abrupt (decay rate $\ne 0$ at disappearance). Abrupt disappearances mean that a small change in the parameters can produce a drastic change in the physics, as some states become suddenly unreachable. The simplest abrupt disappearances are associated with annihilation by another Euclidean solution with higher action and one more negative mode; higher-order catastrophes can occur in cases of enhanced symmetry. We study a few simple examples, including the six-dimensional Einstein-Maxwell theory, and give a unified account of instanton disappearances.

The famous equivalence theorem is reexamined in order to make it applicable to the case of effective theories. We slightly modify the formulation of this theorem and prove it based on the notion of the generating functional for Green functions. This allows one to trace (directly in terms of graphs) the mutual cancellation of different groups of contributions.

In this paper we study the relation between $F(R)$ and scalar-tensor Hořava-Lifshitz gravity. We find that due to the broken diffeomorphism invariance which is a characteristic property of Hořava-Lifshitz gravities corresponding scalar-tensor theory that is related to $F(R)$ Hořava-Lifshitz gravity by specific Weyl transformation has a more complicated form than in the case of the full diffeomorphism invariant $F(R)$ theory of gravity and its scalar-tensor formulation. We also show that in the low energy limit this theory reduces to the relativistic scalar-tensor theory of gravity.

In this work, we obtain isotropic extensions of the usual spherically symmetric vacuum geometries in general relativity. Exact and perturbative solutions are derived. The classes of geometries obtained include black holes in compact and noncompact universes, wormholes in the interior region of cosmological horizons, and anti-de Sitter geometries with excess/deficit solid angle. The tools developed here are applicable in more general contexts.

The dynamics of extended spinning bodies in the Kerr spacetime is investigated in the pole-dipole particle approximation and under the assumption that the spin-curvature force only slightly deviates the particle from a geodesic path. The spin parameter is thus assumed to be very small and the back reaction on the spacetime geometry neglected. This approach naturally leads to solve the Mathisson-Papapetrou-Dixon equations linearized in the spin variables as well as in the deviation vector, with the same initial conditions as for geodesic motion. General deviations from generic geodesic motion are studied, generalizing previous results limited to the very special case of an equatorial circular geodesic as the reference path.

Dark energy of phantom or quintessence nature with an equation of state parameter $w$ almost equal to $-1$ often leads the universe evolution to a finite-time future singularity. An elegant solution to this problem has been recently proposed [P. H. Frampton, K. J. Ludwick, and R. J. Scherrer, Phys. Rev. D 84, 063003 (2011).] under the form of the so-called little rip cosmology, which appears to be a realistic alternative to the $\Lambda \mathrm{CDM}$ model. A viscous little rip cosmology is here proposed. Whereas generically bulk viscosity tends to promote the big rip, we find that there are a number of situations where this is not the case and where the formalism nicely adjusts itself to the little rip scenario. We prove, in particular, that a viscous fluid (or, equivalently, one with an inhomogeneous [imperfect] equation of state) is perfectly able to produce a little rip cosmology as a purely viscosity effect. The possibility of its induction as a combined result of viscosity and a general (powerlike) equation of state is also investigated in detail. To finish, a physical, inertial force interpretation of the dissolution of bound structures in the little rip cosmology is presented.

In classical gravity, deviations from the predictions of the Einstein theory are often discussed within the framework of the conformal Newtonian gauge, where scalar perturbations are described by two potentials $\varphi$ and $\psi$. In this paper we use the above gauge to explore possible cosmological consequences of a running Newton’s constant $G(\square )$, as suggested by the nontrivial ultraviolet fixed point scenario arising from the quantum field-theoretic treatment of Einstein gravity with a cosmological constant term. Here we focus on the effects of a scale-dependent coupling on the so-called gravitational slip functions $\eta =\psi /\varphi -1$, whose classical general relativity value is zero. Starting from a set of manifestly covariant but nonlocal effective field equations derived earlier, we compute the leading corrections in the potentials $\varphi$ and $\psi$ for a nonrelativistic, pressureless fluid. After providing an estimate for the quantity $\eta$, we then focus on a comparison with results obtained in a previous paper on matter density perturbations in the synchronous gauge, which gave an estimate for the growth index parameter $\gamma$, also in the presence of a running $G$. Our results indicate that, in the present framework and for a given $G(\square )$, the corrections tend to be significantly larger in magnitude for the perturbation growth exponents than for the conformal Newtonian gauge slip function.

Obscuration due to Galactic emission complicates the extraction of information from cosmological surveys, and requires some combination of the (typically imperfect) modeling and subtraction of foregrounds, or the removal of part of the sky. This particularly affects the extraction of information from the largest observable scales. Maximum-likelihood estimators for reconstructing the full-sky spherical harmonic coefficients from partial-sky maps have recently been shown to be susceptible to contamination from within the sky cut, arising due to the necessity to band-limit the data by smoothing prior to reconstruction. Using the WMAP 7-year data, we investigate modified implementations of such estimators which are robust to the leakage of contaminants from within masked regions. We provide a measure, based on the expected amplitude of residual foregrounds, for selecting the most appropriate estimator for the task at hand. We explain why the related quadratic maximum-likelihood estimator of the angular power spectrum does not suffer from smoothing-induced bias.

We study forecasts for the accuracy of the determination of cosmological parameters from future large-scale photometric surveys obtained using the full shape of the 2-point galaxy angular correlation function. The effects of linear redshift-space distortion, photometric redshift Gaussian errors, galaxy bias and nonlinearities in the power spectrum are included on our analysis. The Fisher information matrix is constructed with the full covariance matrix, including the correlation between nearby redshift shells arising from the photometric redshift error. We show that under some reasonable assumptions, a survey such as the imminent Dark Energy Survey should be able to constrain the dark energy equation of state parameter $w$ and the cold dark matter density ${\Omega }_{\mathrm{cdm}}$ with a precision of the order of 20% and 13%, respectively, from the full shape of the angular correlation function alone. When combined with priors from other observations the precision in the determination of these parameters improve to 8% and 4%, respectively.

Higher order Laguerre-Gauss (LG) beams have been proposed for use in future gravitational wave detectors, such as upgrades to the Advanced LIGO detectors and the Einstein Telescope, for their potential to reduce the effects of the thermal noise of the test masses. This paper details the theoretical analysis and simulation work carried out to investigate the behavior of LG beams in realistic optical setups, in particular, the coupling between different LG modes in a linear cavity. We present a new analytical approximation to compute the coupling between modes, using Zernike polynomials to describe mirror surface distortions. We apply this method in a study of the behavior of the ${\mathrm{LG}}_{33}$ mode within realistic arm cavities, using measured mirror surface maps from the Advanced LIGO project. We show mode distortions that can be expected to arise due to the degeneracy of higher order spatial modes within such cavities and relate this to the theoretical analysis. Finally, we identify the mirror distortions which cause significant coupling from the ${\mathrm{LG}}_{33}$ mode into other order 9 modes and derive requirements for the mirror surfaces.

We study the bounds that space-based gravitational-wave detectors could realistically place on the graviton Compton wavelength ${\lambda }_g=h/(m_{g}c)$ by observing multiple inspiralling black hole binaries. Observations of individual inspirals will yield mean bounds ${\lambda }_g\sim 3\times {10}^{15}$ km, but the combined bound from observing $\sim 50$ events in a two-year mission is about ten times better: ${\lambda }_g\simeq 3\times {10}^{16}$ km ($m_g\simeq 4\times {10}^{-26}$ eV). The bound improves faster than the square root of the number of observed events, because typically a few sources provide constraints as much as three times better than the mean. This result is only mildly dependent on details of black hole formation and detector characteristics. The bound achievable in practice should be an order of magnitude better than this figure, because our calculations ignore the merger/ringdown portion of the waveform.

We construct $\pi \pi$ amplitudes that fulfill exact elastic unitarity, account for one-loop chiral perturbation theory contributions and include all $1/N_C$ leading terms, with the only limitation of considering just the lowest-lying nonet of exchanged resonances. Within such a scheme, the $N_C$ dependence of $\sigma$ and $\rho$ masses and widths is discussed. Robust conclusions are drawn in the case of the $\rho$ resonance, confirming that it is a stable meson in the limit of a large number of QCD colors, $N_C$. Less definitive conclusions are reached in the scalar-isoscalar sector. With the present quality of data, we cannot firmly conclude whether or not the $N_C=3$ $f_0(600)$ resonance completely disappears at large $N_C$ or if it has a subdominant component in its structure, which would become dominant for a number of quark colors sufficiently large.

We investigate the method for constructing the invariant mass using the $M_{T2}$-assisted on-shell (MAOS) approximation to the invisible particle momenta in the cascade decays of a new particle resonance produced at hadron colliders. We note that the MAOS reconstruction can be defined in several different ways, while keeping the efficiency of approximation at a similar level, and one of them provides a unique solution for each event. It is shown that the invariant mass distribution constructed with the MAOS momenta exhibits a peak at the heavy resonance mass, regardless of the chosen MAOS scheme and the detailed mass spectrum of the particles in the cascade. We stress that the MAOS invariant mass can be used as a clean signal of new particle resonance produced at the Large Hadron Collider, as well as a model-independent method to measure the masses of new particles involved in the event.

The search for the Higgs boson is entering a decisive phase. The Large Hadron Collider experiments have collected more than $1{\mathrm{fb}}^{-1}$ of data and are now capable of efficiently probing the high Higgs mass region, $m_H>140\mathrm{GeV}$. The low mass region is more challenging at the LHC, but if the Higgs has standard model-like properties, the LHC should find evidence for it by the end of next year. In low energy supersymmetric extensions of the standard model, the situation is similar for large values of the $CP$-odd Higgs mass $m_A$, but more interesting for lower values of $m_A$. The ($\sqrt{s}=7\mathrm{TeV}$) LHC searches for a low mass standard model Higgs boson predominantly in the $h\to \gamma \gamma$, $WW$ decay modes, which may be suppressed by an increase in the $h\to b\overline{b}$, ${\tau }^{+}{\tau }^{-}$ partial widths (and thus the total $h$ width) for $m_A\lesssim 500\mathrm{GeV}$. Although $h\to b\overline{b}$, ${\tau }^{+}{\tau }^{-}$ are sought at the LHC, these channels are not powerful enough to fully counter this suppression in the first year of running. We consider two alternative possibilities for probing the low $m_A$ region: nonstandard Higgs boson searches at the LHC, and a statistical combination with the Tevatron, where $Vh\to b\overline{b}$ is the primary search channel for light $h$. We also study a minimal supersymmetric standard model scenario in which the $h\to \gamma \gamma$ rate is enhanced at low $m_A$ to the point where discovery is possible in the near future.

It is possible that at low temperatures and large density there exists a confining matter with restored chiral symmetry, just after the dense nuclear matter with broken chiral symmetry. Such a phase has, so far, been studied within a confining and chirally symmetric model, assuming a rigid quark Fermi surface. In the confining quarkyonic matter, however, near the Fermi surface, quarks group into color-singlet baryons. Interaction between quarks leads to a diffusion of the quark Fermi surface. Here, we study effects of such diffusion and verify that it does not destroy a possible existence of a confining but chirally symmetric matter at low temperatures.

It was recently shown that light LSP neutralinos could be found in the framework of the Next-to-Minimal Supersymmetric Standard Model (NMSSM). These candidates would escape known particle physics constraints even though they are relatively light. We now investigate the astrophysical limits which can be set on these particles. We show, in particular, that the Fermi observation of dwarf spheroidal galaxies enable to constrain the parameter space associated with these candidates. Combined with the XENON100 experimental limits, our results illustrate the complementarity between direct and indirect searches for dark matter. Yet, our findings also suggest that probing light neutralinos in the Next-to-Minimal Supersymmetric Standard Model (NMSSM) scenario will be very difficult because the sensitivity of both dark matter direct and indirect detection experiments would have to be improved by at least six orders of magnitude compared to present values in order to explore the entire parameter space. Finally, we show that the parameter space compatible with the CoGeNT signal (albeit disfavored by the XENON100 limit) is not excluded by gamma nor radio observations.

We discuss the possibility of new sources of flavor violation in the squark sector of supersymmetric models in the context of the dark matter relic density. We show that the corresponding nonminimal flavor violation terms in the squark mass matrices can have an important impact on the thermally averaged (co)annihilation cross section of the neutralino, and in consequence can modify its predicted relic density. We discuss in detail the relevant effects and present a numerical study of neutralino annihilation and coannihilation in this context. We also comment on the LHC phenomenology of the corresponding scenarios.

The $b\tau j\mathrm{E̸}T$ signal at the ongoing LHC experiments is simulated with Pythia in the minimal supergravity (mSUGRA) and other models of supersymmetry (SUSY) breaking. Special attention is given to the compatibility of this signature with the low mass neutralino dark matter (LMNDM) scenario consistent with the Wilkinson Microwave Anisotropy Probe data. In the mSUGRA model the above signal as well as the LMNDM scenario are strongly disfavored due to the constraints from the ongoing SUSY searches at the LHC. This tension, however, originates from the model dependent correlations among the parameters in the strong and electroweak sectors of mSUGRA. That there is no serious conflict between the LMNDM scenario and the LHC data is demonstrated by constructing generic phenomenological models such that the strong sector is unconstrained or mildly constrained by the existing LHC data and parameters in the electroweak sector, unrelated to the strong sector, yield dark matter relic density consistent with the Wilkinson Microwave Anisotropy Probe data. The proposed models, fairly insensitive to the conventional SUSY searches in the $\mathrm{\text{jets}}+{\mathrm{E̸}}_T$ and other channels, yield observable signal in the suggested channel for $\mathcal{L}\gtrsim 1{\mathrm{fb}}^{-1}$ of data. They are also consistent with the LMNDM scenario and can be tested by the direct dark matter search experiments in the near future. Some of these models can be realized by nonuniversal scalar and gaugino masses at the grand unified theory scale.

We investigate the gluon distribution functions and their contributions to the Higgs boson production in $pp$ collisions in the transverse momentum-dependent factorization formalism. In addition to the usual azimuthal symmetric transverse momentum-dependent gluon distribution, we find that the azimuthal correlated gluon distribution also contributes to the Higgs boson production. This explains recent findings on the additional contribution in the transverse momentum resummation for the Higgs boson production as compared to that for electroweak boson production processes. We further examine the small-x naive $k_t$-factorization in the dilute region and find that the azimuthal correlated gluon distribution contribution is consistently taken into account. The result agrees with the transverse momentum-dependent factorization formalism. We comment on the possible breakdown of the naive $k_t$-factorization in the dense medium region, due to the unique behaviors for the gluon distributions.