We clarify the role of gauge invariance for the computation of quantum non-Gaussian correlators in inflation. A gauge invariant generating functional for $n$-point functions is given and the special status of the spatially flat gauge is pointed out. We also comment on the relation between gauge transformations, field redefinitions, the choice of $t=\mathrm{const}$ hypersurfaces and the use of boundary terms in computations of non-Gaussianity.

We study inclusive dipion decays using a sample of $108\times {10}^6{\rm Y}(3S)$ events recorded with the BABAR detector. We search for the decay mode ${\rm Y}(3S)\to {\pi }^{+}{\pi }^{-}{h}_b(1P)$ and find no evidence for the bottomonium spin-singlet state $h_b(1P)$ in the invariant mass distribution recoiling against the ${\pi }^{+}{\pi }^{-}$ system. Assuming the $h_b(1P)$ mass to be $9.900\mathrm{GeV}/c^2$, we measure the upper limit on the branching fraction $\mathcal{B}[{\rm Y}(3S)\to {\pi }^{+}{\pi }^{-}{h}_b(1P)]<1.2\times {10}^{-4}$, at 90% confidence level. We also investigate the ${\chi }_{bJ}(2P)\to {\pi }^{+}{\pi }^{-}{\chi }_{bJ}(1P)$, ${\rm Y}(3S)\to {\pi }^{+}{\pi }^{-}{\rm Y}(2S)$, and ${\rm Y}(2S)\to {\pi }^{+}{\pi }^{-}{\rm Y}(1S)$ dipion transitions and present an improved measurement of the branching fraction of the ${\rm Y}(3S)\to {\pi }^{+}{\pi }^{-}{\rm Y}(2S)$ decay and of the ${\rm Y}(3S)-{\rm Y}(2S)$ mass difference.

In the framework of the induced matter theory of gravity, we derive a five-dimensional solution of the field equations that can describe a four-dimensional cosmological scenario where the dark fluid (dark matter plus dark energy) equation of state has a geometrical origin. There is not a natural separation of the dark sector into different components, and so the model may provide a geometrical explanation for the existence of a dark degeneracy in cosmological scenarios.

We study tunneling between vacua in multidimensional field spaces in the thin wall approximation. The thin wall action generically gives rise to two types of saddle points. The first type corresponds to the well-known spherical instantons, but when the field space is multidimensional we find that it is necessary to include codimension two junctions to regulate and compute the fluctuation determinant and the tunneling rate. The second type of saddle point is novel and is present only when the field space is more than one dimensional. These saddle points have two or more negative modes, which confirms that in the presence of additional field directions spherical instantons continue to dominate vacuum decay. We identify regimes in parameter space in which additional field directions may quench certain channels of vacuum decay.

Motivated by recent works of Neyrinck et al. 2009 and Scherrer et al. 2010, we proposed a Gaussian transformation to Gaussianize the non-Gaussian lensing convergence field $\kappa$. It performs a local monotonic transformation $\kappa \to y$ pixel by pixel to make the fine-scale one-point probability distribution function of the new variable $y$ Gaussian. We tested whether the whole $y$ field is Gaussian through $N$-body simulations. (1) We found that the proposed Gaussianization suppresses the non-Gaussianity by orders of magnitude, in measures of the skewness, the kurtosis, the 5th- and 6th-order cumulants of the $y$ field smoothed over various angular scales, relative to that of the corresponding smoothed $\kappa$ field. The residual non-Gaussianities are often consistent with zero within the statistical errors. (2) The Gaussianization significantly suppresses the bispectrum. Furthermore, the residual scatters about zero, depending on the configuration in the Fourier space. (3) The Gaussianization works with even better performance for the 2D fields of the matter density projected over $\sim 300h^{-1}\mathrm{Mpc}$ distance interval centered at $z\in (0,2)$, which can be reconstructed from the weak lensing tomography. (4) We identified imperfectness and complexities of the proposed Gaussianization. We noticed weak residual non-Gaussianity in the $y$ field. We verified the widely used logarithmic transformation as a good approximation to the Gaussian transformation. However, we also found noticeable deviations.

We use cosmological constraints from current data sets and a figure of merit approach in order to probe any deviations from general relativity at cosmological scales. The figure of merit approach is used to study and compare the constraining power of various combinations of data sets on the modified gravity (MG) parameters. We use the recently refined HST-COSMOS weak-lensing tomography data, the ISW-galaxy cross correlations from 2MASS and SDSS luminous red galaxy surveys, the matter power spectrum from SDSS-DR7 (MPK), the WMAP7 temperature and polarization spectra, the baryon acoustic oscillations from Two-Degree Field and SDSS-DR7, and the Union2 compilation of type Ia supernovae, in addition to other bounds from Hubble parameter measurements and big bang nucleosynthesis. We use three parametrizations of MG parameters that enter the perturbed field equations. In order to allow for variations of the parameters with the redshift and scale, the first two parametrizations use recently suggested functional forms while the third is based on binning methods. Using the first parametrization, we find that the $\mathrm{CMB}+\mathrm{ISW}+\mathrm{WL}$ combination provides the strongest constraints on the MG parameters followed by $\mathrm{CMB}+\mathrm{WL}$ or $\mathrm{CMB}+\mathrm{MPK}+\mathrm{ISW}$. Using the second parametrization or the binning methods, we find that the combination $\mathrm{CMB}+\mathrm{MPK}+\mathrm{ISW}$ consistently provides some of the strongest constraints. This shows that the constraints are parametrization dependent. We find that adding up current data sets does not improve consistently the uncertainties on MG parameters due to tensions between the best-fit MG parameters preferred by different data sets. Furthermore, some functional forms imposed by the parametrizations can lead to an exacerbation of these tensions. Next, unlike some studies that used the CFHTLS lensing data, we do not find any deviation from general relativity using the refined HST-COSMOS data, confirming previous claims in those studies that their result may have been due to some systematic effect. Finally, for all the parametrizations and binning methods used, we find that the values corresponding to general relativity are within the 95% confidence level contours for all data set combinations.

The different ground-state energies of $N$-pion and $M$-kaon systems for $N+M\le 12$ are studied in lattice QCD. These energies are then used to extract the various two- and three-body interactions that occur in these systems. Particular attention is paid to additional thermal states present in the spectrum because of the finite temporal extent. These calculations are performed using one ensemble of $2+1$ flavor anisotropic lattices with a spatial lattice spacing $a_s\sim 0.125\mathrm{fm}$, an anisotropy factor $\xi =a_s/a_t=3.5$, and a spatial volume $L^3\sim (2.5\mathrm{fm}{)}^3$. The quark masses used correspond to pion and kaon masses of $m_{\pi }\sim 383\mathrm{MeV}$ and $m_K\sim 537\mathrm{MeV}$, respectively. The isospin and strangeness chemical potentials of these systems are found to be in the region where chiral perturbation theory and hadronic models predict a phase transition between a pion-condensed phase and a kaon-condensed phase.

The existing predictions for the like-sign dimuon charge asymmetry at the Tevatron are expressed in terms of parameters related to $B$ mesons’ mixing and inclusive production fractions. We show that in the realistic case when phase-space cuts are applied, the asymmetry depends also on the details of the production mechanism for the $B$ mesons. In particular, it is sensitive to the difference in the fragmentation functions of $B_d^0$ and $B_s^0$ mesons. We estimate these fragmentation effects and find that they shift the theory prediction for this observable by approximately 10%. We also point out the approximately 20% sensitivity of the asymmetry depending on which set of values for the $B$ meson production fractions is used: as measured at the $Z$ pole or at the Tevatron. The impact of these effects on the extraction of $A_{\mathrm{SL}}^s$ from the D0 measurement is presented.

We study the photon-triggered light and heavy meson production in both $\mathrm{p}+\mathrm{p}$ and $\mathrm{A}+\mathrm{A}$ collisions. We find that a parton energy loss approach that successfully describes inclusive hadron attenuation in nucleus-nucleus reactions at RHIC can simultaneously describe well the experimentally determined photon-triggered light hadron fragmentation functions. Using the same framework, we generalize our formalism to study photon-triggered heavy meson production. We find that the nuclear modification of photon-tagged heavy meson fragmentation functions in $\mathrm{A}+\mathrm{A}$ collision is very different from that of the photon-tagged light hadron case. While photon-triggered light hadron fragmentation functions in $\mathrm{A}+\mathrm{A}$ collisions are suppressed relative to $\mathrm{p}+\mathrm{p}$, photon-triggered heavy meson fragmentation functions can be either enhanced or suppressed, depending on the specific kinematic region. The anticipated smaller energy loss for $b$-quarks manifests itself as a flatter photon-triggered $B$-meson fragmentation function compared to that for the $D$-meson case. We make detailed predictions for both RHIC and LHC energies. We conclude that a comprehensive comparative study of both photon-tagged light and heavy meson production can provide new insights in the details of the jet quenching mechanism.

We report on the feasibility of the direct measurement of the top Yukawa coupling $g_t$ at the International Linear Collider during its first phase of operation with a center-of-mass energy of 500 GeV. The signal and background models incorporate the nonrelativistic QCD corrections which enhance the production cross section near the $t\overline{t}$ threshold. The $e^{+}{e}^{-}\to t\overline{t}H$ signal is reconstructed in the $6\mathrm{\text{−}}\mathrm{\text{jet}}+\mathrm{\text{lepton}}$ and the 8-jet modes. The results from the two channels are combined. The background processes considered are $e^{+}{e}^{-}\to t\overline{b}{W}^{-}/\overline{t}b{W}^{+}$ (which includes $e^{+}{e}^{-}\to t\overline{t}$), $e^{+}{e}^{-}\to t\overline{t}Z$, and $e^{+}{e}^{-}\to t\overline{t}{g}^{*}\to t\overline{t}b\overline{b}$. We use a realistic fast Monte Carlo detector simulation. Signal events are selected using event shape variables, through jet clustering, and by identifying heavy flavor jets. Assuming a Higgs mass of 120 GeV, polarized electron and positron beams with $(P_{e^{-}},P_{e^{+}})=(-0.8,+0.3)$, and an integrated luminosity of $1{\mathrm{ab}}^{-1}$, we estimate that the $e^{+}{e}^{-}\to t\overline{t}H$ events can be seen with a statistical significance of $5.2\sigma$, corresponding to the relative top Yukawa coupling measurement accuracy of $|\Delta g_t/g_t|=10\%$.

Current experimental data on the neutrino parameters are in good agreement with tribimaximal mixing and may indicate the presence of an underlying family symmetry. For 76 flavor groups, we perform a systematic scan for models: The particle content is that of the standard model plus up to three flavon fields, and the effective Lagrangian contains all terms of mass dimension $\le 6$. We find that 44 groups can accommodate models that are consistent with experiment at $3\sigma$, and 38 groups can have models that are tribimaximal. For $A_4\times {\mathbb{Z}}_3$, $T_7$, and $T_{13}$ we look at correlations between the mixing angles and make a prediction for ${\theta }_{13}$ that will be testable in the near future. We present the details of a model with ${\theta }_{12}=33.9°$, ${\theta }_{23}=40.9°$, ${\theta }_{13}=5.1°$ to show that the recent tentative hints of a nonzero ${\theta }_{13}$ can easily be accommodated. The smallest group for which we find tribimaximal mixing is $T_7$. We argue that $T_7$ and $T_{13}$ are as suited to produce tribimaximal mixing as $A_4$ and should therefore be considered on equal footing. In the appendixes, we present some new mathematical methods and results that may prove useful for future model building efforts.

We measure the mass dependence of the forward-backward charge asymmetry in 157 553 $p\overline{p}\to Z/{\gamma }^{*}\to e^{+}{e}^{-}$ interactions, corresponding to $5.0{\mathrm{fb}}^{-1}$ of integrated luminosity collected by the D0 experiment at the Fermilab Tevatron Collider at $\sqrt{s}=1.96$ TeV. The effective weak mixing angle (${\theta }_{\mathrm{eff}}^{\ell }$) from this process involving predominantly the first generation of quarks is extracted as ${sin}^2{\theta }_{\mathrm{eff}}^{\ell }=0.2309\pm 0.0008(\mathrm{stat}.)\pm 0.0006(\mathrm{syst}.)$. We also present the most precise direct measurement of the vector and axial-vector couplings of $u$ and $d$ quarks to the $Z$ boson.

In whatever Lorentz-invariant theory, the presence of extended $d$-dimensional objects inside a higher dimensional bulk space-time, like for instance $D$-branes in string theories, induces a spontaneous breakdown of the Poincaré invariance of the bulk; however, the effective action describing these extended objects should still respect this larger invariance through a nonlinear realization of the full symmetry. Here the specific form of such a realization in the presence of an electromagnetic field is uncovered. The Dirac-Born-Infeld type action for a $D$-brane turns out to be invariant under such transformations. Conversely, it is explicitly demonstrated in some simple cases that the most general invariant action, as long as derivatives of the field strength (and second derivatives of the scalars) can be neglected, is a linear combination of terms of the Dirac-Born-Infeld type with different scale parameters.

Using the AdS/CFT correspondence, we probe the scale dependence of thermalization in strongly coupled field theories following a sudden injection of energy via calculations of two-point functions, Wilson loops, and entanglement entropy in $d=2$, 3, 4. In the saddle-point approximation these probes are computed in AdS space in terms of invariant geometric objects—geodesics, minimal surfaces, and minimal volumes. Our calculations for two-dimensional field theories are analytical. In our strongly coupled setting, all probes in all dimensions share certain universal features in their thermalization: (1) a slight delay in the onset of thermalization, (2) an apparent nonanalyticity at the endpoint of thermalization, (3) top-down thermalization where the UV thermalizes first. For homogeneous initial conditions the entanglement entropy thermalizes slowest and sets a timescale for equilibration that saturates a causality bound over the range of scales studied. The growth rate of entanglement entropy density is nearly volume-independent for small volumes, but slows for larger volumes.

We investigate the two- and three-point correlation functions of the dyonic magnon and spike, which correspond to the solitonic string moving in the Poincaré AdS and three-dimensional sphere. We show that the coupling between two dyonic magnons or spikes, together with a marginal scalar operator in the string theory, is exactly the same as one obtained by the renormalization group analysis in the gauge theory.

The spherically symmetric static solutions are searched for in some $f(T)$ models of gravity theory with a Maxwell term. To do this, we demonstrate that reconstructing the Lagrangian of $f(T)$ theories is sensitive to the choice of frame, and then we introduce a particular frame based on the conformally Cartesian coordinates. In this particular frame, the existence conditions of various solutions are presented. Our results imply that only a limited class of $f(T)$ models can be solved in this frame. For more general models, the search for spherically symmetric static solutions is still an open and challenging problem, hopefully solvable in other frames.

In general neutron stars in binaries are spinning. Because of the existence of millisecond pulsars we know that these spins can be substantial. We argue that spins with periods on the order of a few dozen milliseconds could influence the late inspiral and merger dynamics. Thus numerical simulations of the last few orbits and the merger should start from initial conditions that allow for arbitrary spins. We discuss quasiequilibrium approximations one can make in the construction of binary neutron star initial data with spins. Using these approximations we are able to derive two new matter equations. As in the case of irrotational neutron star binaries, one of these equations is algebraic and the other elliptic. If these new matter equations are solved together with the equations for the metric variables following the Wilson-Mathews or conformal thin sandwich approach, one can construct neutron star initial data. The spin of each star is described by a rotational velocity that can be chosen freely so that one can create stars in arbitrary rotation states. Our new matter equations reduce to the well-known limits of both corotating and irrotational neutron star binaries.

The fitting formula for the location of the first acoustic peak in the matter power spectrum is revised. We discuss the physics that leads to baryon acoustic oscillations: the recombination history, the tight coupling approximation, and the velocity overshoot effect. A new fitting formula is proposed, which is in accordance within 5% with numerical results for a suitable range of cosmological parameters, whereas previous results yield deviations of up to (15–20)%. The crucial improvement turns out to be the accuracy of the recombination history.

Adopting the $q$-theory approach to the cosmological constant problem, a simple field-theoretic model is presented which generates an effective cosmological constant (remnant vacuum energy density) of the observed order of magnitude, ${\Lambda }_{\mathrm{eff}}\sim (\mathrm{meV}{)}^4$, if there exist new TeV-scale ultramassive particles with electroweak interactions. The model is simple, in the sense that it involves only a few types of fields and two energy scales, the gravitational energy scale $E_{\mathrm{Planck}}\sim {10}^{15}\mathrm{TeV}$ and the electroweak (new-physics) energy scale $E_{\mathrm{ew}}\sim 1–10\mathrm{TeV}$.

We consider a neutrino mass model where all leptonic mixing is induced by a heavy Majorana sector through the seesaw type I mechanism, while the Dirac mass matrices are diagonal. Such a pattern occurs naturally in grand unified theories. Constraints on the parameters of the models are considered and it is shown that a normal neutrino mass hierarchy is preferred. The lightest neutrino mass is typically small, leading to nonobservable rates for neutrinoless double beta decay in the normal hierarchy case.