The properties of the $\sigma$ meson are studied using the QCD sum rules for tetraquark operators. In the SU(3) chiral limit, we separately investigate SU(3) singlet and octet tetraquark states as constituents of the $\sigma$ meson and discuss their roles for the classification of the light scalar nonets $\sigma$, $f_0$, $a_0$, and $\kappa$ as candidates of tetraquark states. All of our analyses are performed in the suitable Borel window which is indispensable to avoid the pseudopeak artifacts outside of the Borel window. We can set up acceptably wide Borel windows after preparing favorable linear combinations of operators and including the dimension 12 terms in the operator-product expansion. Taking into account the possible large widths, we evaluate masses for singlet and octet states as 700–850 and 600–750 MeV, respectively, although the octet operators have a smaller overlap with the tetraquark states than the singlet case, which requires careful interpretations. The splitting of the singlet and octet states emerges from the number of the $\overline{q}q$ annihilation diagrams, which include the color singlet annihilation processes $qq\overline{q}\overline{q}\to (q\overline{q}{)}_1$ and the color octet annihilation processes $qq\overline{q}\overline{q}\to G(q\overline{q}{)}_8$. The mass of the $\sigma$ meson is evaluated as 600–800 MeV, which is much closer to the experimental value $\sim 500\mathrm{MeV}$ than the mass evaluated by 2-quark correlator analyses, $\sim 1.0\mathrm{GeV}$. This indicates that the tetraquark state shares a larger fraction in the $\sigma$ meson than ordinary two quark meson states.

In this paper, we study the quantum statistical entropy in a 5D Ricci-flat black string solution, which contains a 4D Schwarzschild-de Sitter black hole on the brane, by using the improved thin-layer method with the generalized uncertainty principle. The entropy is the linear sum of the areas of the event horizon and the cosmological horizon without any cutoff and any constraint on the bulk’s configuration rather than the usual uncertainty principle. The system’s density of state and free energy are convergent in the neighborhood of horizon. The small-mass approximation is determined by the asymptotic behavior of metric function near horizons. Meanwhile, we obtain the minimal length of the position $\Delta x$, which is restrained by the surface gravities and the thickness of layer near horizons.

Several anomalies appear to be present in the large-angle cosmic microwave background (CMB) anisotropy maps of the Wilkinson Microwave Anisotropy Probe. One of these is a lack of large-scale power. Because the data otherwise match standard models extremely well, it is natural to consider perturbations of the standard model as possible explanations. We show that, as long as the source of the perturbation is statistically independent of the source of the primary CMB anisotropy, no such model can explain this large-scale power deficit. On the contrary, any such perturbation always reduces the probability of obtaining any given low value of large-scale power. We rigorously prove this result when the lack of large-scale power is quantified with a quadratic statistic, such as the quadrupole moment. When a statistic based on the integrated square of the correlation function is used instead, we present strong numerical evidence in support of the result. The result applies to models in which the geometry of spacetime is perturbed (e.g., an ellipsoidal universe) as well as explanations involving local contaminants, undiagnosed foregrounds, or systematic errors. Because the large-scale power deficit is arguably the most significant of the observed anomalies, explanations that worsen this discrepancy should be regarded with great skepticism, even if they help in explaining other anomalies such as multipole alignments.

We investigate the effects of quantum particle production on a classical sudden singularity occurring at finite time in a Friedmann universe. We use an exact solution to describe an initially radiation-dominated universe that evolves into a sudden singularity at finite time. We calculate the density of created particles exactly and find that it is generally much smaller than the classical background density and pressure which produce the sudden singularity. We conclude that, in the example studied, the quantum particle production does not lead to the avoidance or modification to the sudden future singularity. We argue that the effects of small residual anisotropies in the expansion will not change these results and show how they can be related to studies of classical particle production using a bulk viscosity. We conclude that we do not expect to see significant observable effects from local sudden singularities on our past light cone.

Any hint of non-Gaussianity in the cosmological initial conditions will provide us with a unique window into the physics of the early Universe. We show that the impact of a small local primordial non-Gaussianity (generated on superhorizon scales) on the statistics of collapsed objects (such as galaxies or clusters) can be approximated by using slightly modified, but Gaussian, initial conditions, which we describe through simple analytic expressions. Given that numerical simulations with Gaussian initial conditions are relatively well studied, this equivalence provides us with a simple tool to predict signatures of primordial non-Gaussianity in the statistics of collapsed objects. In particular, we describe the predictions for non-Gaussian mass function, and also confirm the recent discovery of a nonlocal bias on large scales [N. Dalal, O. Dore, D. Huterer, and A. Shirokov, Phys. Rev. D 77, 123514 (2008).][S. Matarrese and L. Verde, Astrophys. J. 677, L77 (2008).], as a signature of primordial non-Gaussianity. We then study the potential of galaxy surveys to constrain non-Gaussianity using their autocorrelation and cross correlation with the cosmic microwave background (CMB) (due to the integrated Sachs-Wolfe effect), as a function of survey characteristics, and predict that they will eventually yield an accuracy of $\Delta f_{NL}\sim 0.1$ and 3, respectively, which will be better than or competitive with (but independent of) the best predicted constraints from the CMB. Interestingly, the cross correlation of the CMB and the NRAO VLA Sky Survey galaxy survey already shows a hint of a large local primordial non-Gaussianity: $f_{NL}=236\pm 127$.

We develop a systematic derivation for the Limber approximation to the angular cross-power spectrum of two random fields, as a series expansion in $(\ell +1/2{)}^{-1}$. This extended Limber approximation can be used to test the accuracy of the Limber approximation and to improve the rate of convergence at large $\ell$’s. We show that the error in ordinary Limber approximation is $\mathcal{O}({\ell }^{-2})$. We also provide a simple expression for the 2nd order correction to the Limber formula, which improves the accuracy to $\mathcal{O}({\ell }^{-4})$. This correction can be especially useful for narrow redshift bins, or samples with small redshift overlap, for which the 0th order Limber formula has a large error. We also point out that using $\ell$ instead of $\ell +1/2$, as is often done in the literature, spoils the accuracy of the approximation to $\mathcal{O}({\ell }^{-1})$.

We study the consequences of the $f(R/\square )$ gravity models for the Solar System and the large-scale structure of the Universe. The spherically symmetric solutions can be used to obtain bounds on the constant and the linear parts of the correction terms. The evolution of cosmological matter structures is shown to be governed by an effectively time-dependent Newton’s constant. We also analyze the propagation of the perturbation modes. Tensor and vector modes are only slightly modified, but two new scalar degrees of freedom are present. Their causality and stability is demonstrated, and their formal ghost conditions are related to a singularity of the cosmological background. In general, the Newtonian limit of these models has no apparent conflicts with observations but can provide useful constraints.

We estimate the amplitude of perturbation in dark energy at different length scales for a quintessence model with an exponential potential. It is shown that on length scales much smaller than Hubble radius, perturbation in dark energy is negligible in comparison to that in dark matter. However, on scales comparable to the Hubble radius (${\lambda }_p>1000\mathrm{Mpc}$) the perturbation in dark energy in general cannot be neglected. As compared to the $\Lambda \mathrm{CDM}$ model, the large-scale matter power spectrum is suppressed in a generic quintessence dark energy model. We show that on scales ${\lambda }_p<1000\mathrm{Mpc}$, this suppression is primarily due to different background evolution compared to the $\Lambda \mathrm{CDM}$ model. However, on much larger scales perturbation in dark energy can affect the matter power spectrum significantly. Hence this analysis can act as a discriminator between the $\Lambda \mathrm{CDM}$ model and other generic dark energy models with $w_{\mathrm{de}}\ne -1$.

We examine the possibility of the ground observation of the GeV counterparts of two gamma ray bursts, the Swift GRB-080723 ($\mathrm{\text{Trigger}}=317662$) and the Fermi GRB081017474 ($\mathrm{\text{trigger}}=\mathrm{bn}081017474$). The data come from two small directional muon telescopes at sea level inside the South Atlantic Anomaly region. This characteristic offers the muon telescopes a low rigidity of response to primary and secondary charged particles ($\ge 0.4\mathrm{GV}$). In both cases, the GRB trigger coordinates are within the effective field of view of the vertical Tupi muon telescopes. There is a ground level enhancement (GLE) on the muon counting rate background, with a statistical significance above $4\sigma$, 38.22 minutes after the Swift trigger occurrence, and there are at least two GLEs, with a significance above $4\sigma$, at 7.2 minutes and 19.2 minutes after the Fermi trigger, respectively. We argue that the GeV counterpart of a keV GRB could be similar to the highest GRBs, observed by EGRET within BATSE’s field of view, where the high-energy emission arrives at the detector in fragments, and they are delayed and/or anticipated with respect to the keV-MeV burst. This behavior is observed in both cases. In short, the analysis suggests that they may be physically associated. Details and some implications of this possible association are reported in this work.

The recent observation of the mass difference in the $B_s$ system seems to be not in complete agreement with the corresponding standard model value. We consider the model with an extra vectorlike down quark to explain this discrepancy and obtain the constraints on the new physics parameters. Thereafter, we show that with these new constraints this model can successfully explain other observed deviations associated with $b\to s$ transitions, namely, $B_s\to \psi \varphi$, $B\to K\pi$, and $B\to \varphi K_s$.

Brane world oscillations manifest themselves as massive vector gauge fields. Their coupling to the standard model is deduced using the method of nonlinear realizations of the spontaneously broken higher dimensional space-time symmetries. Brane vectors are stable and weakly interacting and therefore escape particle detectors unnoticed. LEP and Tevatron data on the production of a single photon in conjunction with missing energy are used to delineate experimentally excluded regions of brane vector parameter space. The additional region of parameter space accessible to the LHC as well as a future lepton linear collider is also determined by means of this process.

We give an extensive description of the renormalization of the Higgs sector of the minimal supersymmetric model in sloops. sloops is an automatized code for the computation of one-loop processes in the MSSM. In this paper, the first in a series, we study in detail the nongauge invariance of some definitions of $\tan \beta$. We rely on a general nonlinear gauge-fixing constraint to make the gauge parameter dependence of different schemes for $\tan \beta$ explicit at one loop. In so doing, we update, within these general gauges, an important Ward-Slavnov-Taylor identity on the mixing between the pseudoscalar Higgs, $A^0$, and $Z^0$. We then compare the $\tan \beta$ scheme dependence of a few observables. We find that the best $\tan \beta$ scheme is the one based on the decay $A^0\to {\tau }^{+}{\tau }^{-}$ because of its gauge invariance, because it is unambiguously defined from a physical observable, and because it is numerically stable. The oft used $\overline{\mathrm{DR}}$ scheme performs almost as well on the last count, but is usually defined from nongauge-invariant quantities in the Higgs sector. The use of the heavier scalar Higgs mass in lieu of $\tan \beta$, though related to a physical parameter, induces radiative corrections that are too large in many instances, and is therefore not recommended.

We compute the scattering amplitude for pion scattering in Wilson chiral perturbation theory for two degenerate quark flavors. We consider two different regimes where the quark mass $m$ is of order (i) $a{\Lambda }_{\mathrm{QCD}}^2$ and (ii) $a^2{\Lambda }_{\mathrm{QCD}}^3$. Analytic expressions for the scattering lengths in all three isospin channels are given. As a result of the $O(a^2)$ terms the $I=0$ and $I=2$ scattering lengths do not vanish in the chiral limit. Moreover, additional chiral logarithms proportional to $a^2\ln M_{\pi }^2$ are present in the one-loop results for regime (ii). These contributions significantly modify the familiar results from continuum chiral perturbation theory.

We analyze the electromagnetic and strong decay properties of the light scalars $a_0(980)$ and $f_0(980)$ within a hadronic molecule interpretation. Both scalars are discussed within a covariant and gauge invariant model which also allows for finite size effects due to their spatially extended structure in the $K\overline{K}$-bound state picture. Allowing for $f_0\mathrm{\text{−}}{a}_0$ mixing we also study its influence on the radiative decays $f_0/a_0\to \gamma \gamma$, $f_0/a_0\to \gamma \omega$, and $f_0/a_0\to \gamma \rho$ as well as the $\varphi$ production of the $f_0$ and $a_0$. Furthermore, we apply our formalism to describe the strong $f_0\to \pi \pi$ and $a_0\to \pi \eta$ decay properties.

We study the vector–axial-vector mixing in a hot medium and its evolution toward the chiral phase transition using different symmetry restoration scenarios based on the generalized hidden local symmetry framework. We show that the presence of the $a_1$ meson reduces the vector spectral function around the $\rho$ meson mass and enhances it around the $a_1$ meson mass. The coupling strength of $a_1$ to $\rho$ and $\pi$ vanishes at the critical temperature due to the degenerate $\rho$-$a_1$ masses. This feature holds rigorously in the chiral limit and still stays intact to good approximation for the physical pion mass.

We report on a search for the decay $B^0\to {\rho }^0{\rho }^0$ and other charmless modes with a ${\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ final state, including $B^0\to {\rho }^0{\pi }^{+}{\pi }^{-}$, nonresonant $B^0\to 4{\pi }^{\pm }$, $B^0\to {\rho }^0{f}_0(980)$, $B^0\to f_0(980)f_0(980)$ and $B^0\to f_0(980){\pi }^{+}{\pi }^{-}$. These results are obtained from a data sample containing $657\times {10}^6$ $B\overline{B}$ pairs collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We set an upper limit on $\mathcal{B}(B^0\to {\rho }^0{\rho }^0)$ of $1.0\times {10}^{-6}$ at the 90% confidence level (C.L.). From our $B^0\to {\rho }^0{\rho }^0$ measurement and an isospin analysis, we determine the Cabibbo-Kobayashi-Maskawa phase ${\varphi }_2$ to be $91.7\pm 14.9$ degrees. We find excesses in $B^0\to {\rho }^0{\pi }^{+}{\pi }^{-}$ and nonresonant $B^0\to 4{\pi }^{\pm }$ with $1.3\sigma$ and $2.5\sigma$ significance, respectively. The corresponding branching fractions are less than $12.0\times {10}^{-6}$ and $19.3\times {10}^{-6}$ at the 90% C.L. In addition, we set 90% C.L. upper limits as follows: $\mathcal{B}(B^0\to {\rho }^0{f}_0(980))<0.3\times {10}^{-6}$, $\mathcal{B}(B^0\to f_0(980)f_0(980))<0.1\times {10}^{-6}$, and $\mathcal{B}(B^0\to f_0(980){\pi }^{+}{\pi }^{-})<3.8\times {10}^{-6}$.

The motion of a particle near the Reissner-Nordström black hole horizon is described by conformal mechanics. In this paper we present an extended one-dimensional analysis of the $N=4$ superconformal mechanics coupled to $n$ copies of $N=8$, $d=1$ vector supermultiplets. The scalar manifold of the vector multiplet sector of the constructed system possesses $N=8$, $d=1$ supersymmetry and, therefore, is of special Kähler type. Coupling the vector multiplets to a dilaton superfield makes the theory invariant under $N=4$ superconformal symmetry, thus reducing the number of supersymmetries under which the system is invariant to $N=4$. The superconformal symmetry completely fixes the resulting action. We show that the theory has exactly the same field content as that of $N=2$ $D=4$ Einstein action coupled to Maxwell fields and, moreover, with the same expression for the effective black hole potential. We explicitly demonstrate that the electric and magnetic charges, present in the effective black hole action, appear as a result of resolving constraints on the auxiliary components of the vector supermultiplets. We present the component action, supercharges, and Hamiltonian with all fermionic terms included. One of the possible ways to generalize the black hole potential is to consider a modified version of the $N=4$ superconformal multiplet where its auxiliary components acquire nonzero constant values. For this case we write down explicitly the corresponding modified black hole potential.

We explore cosmology of intersecting brane worlds with induced gravity on the branes. We find the cosmological equations that control the evolution of a moving codimension-one brane and a codimension-two brane that sits at the intersection. We study the Friedmann equation at the intersection, finding new contributions from the six-dimensional bulk. These higher dimensional contributions allow us to find new examples of self-accelerating configurations for the codimension-two brane at the intersection and we discuss their features.

Nonlinear growth of the bar-mode deformation is studied for a differentially rotating star with supercritical rotational energy. In particular, the growth mechanism of some azimuthal modes with odd wave numbers is examined by comparing a simplified mathematical model with a realistic simulation. Mode coupling to even modes, i.e., the bar mode and higher harmonics, significantly enhances the amplitudes of odd modes, unless they are exactly zero initially. Therefore, other modes which are not axially symmetric cannot be neglected at late times in the growth of the unstable bar mode even when starting from an almost axially symmetric state.

We investigate the background dynamics when dark energy is coupled to dark matter in the Universe described by Einstein cosmology and loop quantum cosmology. We introduce a new general form of dark sector coupling, which presents a more complicated dynamical phase space. Differences in the phase space in obtaining the accelerated scaling attractor in Einstein cosmology and loop quantum cosmology are disclosed.