Loop quantum cosmology (LQC) predicts a nonsingular evolution of the universe through a bounce in the high energy region. But LQC has an ambiguity about the quantization scheme. Recently, the authors in [Phys. Rev. D 77, 124008 (2008)] proposed a new quantization scheme. Similar to others, this new quantization scheme also replaces the big bang singularity with the quantum bounce. More interestingly, it introduces a quantum singularity, which is traversable. We investigate this novel dynamics quantitatively with a tachyon scalar field, which gives us a concrete example. Our result shows that our universe can evolve through the quantum singularity regularly, which is different from the classical big bang singularity. So this singularity is only a weak singularity.

It has recently been pointed out by Kowalski et. al. [Astrophys. J. 686, 749 (2008).] that there is “an unexpected brightness of the SnIa data at $z>1$.” We quantify this statement by constructing a new statistic which is applicable directly on the type Ia supernova (SnIa) distance moduli. This statistic is designed to pick up systematic brightness trends of SnIa data points with respect to a best fit cosmological model at high redshifts. It is based on binning the normalized differences between the SnIa distance moduli and the corresponding best fit values in the context of a specific cosmological model (e.g. $\Lambda \mathrm{CDM}$). These differences are normalized by the standard errors of the observed distance moduli. We then focus on the highest redshift bin and extend its size toward lower redshifts until the binned normalized difference (BND) changes sign (crosses 0) at a redshift $z_c$ (bin size $N_c$). The bin size $N_c$ of this crossing (the statistical variable) is then compared with the corresponding crossing bin size $N_{mc}$ for Monte Carlo data realizations based on the best fit model. We find that the crossing bin size $N_c$ obtained from the Union08 and Gold06 data with respect to the best fit $\Lambda \mathrm{CDM}$ model is anomalously large compared to $N_{mc}$ of the corresponding Monte Carlo data sets obtained from the best fit $\Lambda \mathrm{CDM}$ in each case. In particular, only 2.2% of the Monte Carlo $\Lambda \mathrm{CDM}$ data sets are consistent with the Gold06 value of $N_c$ while the corresponding probability for the Union08 value of $N_c$ is 5.3%. Thus, according to this statistic, the probability that the high redshift brightness bias of the Union08 and Gold06 data sets is realized in the context of a $(w_0,w_1)=(-1,0)$ model ($\Lambda \mathrm{CDM}$ cosmology) is less than 6%. The corresponding realization probability in the context of a $(w_0,w_1)=(-1.4,2)$ model is more than 30% for both the Union08 and the Gold06 data sets indicating a much better consistency for this model with respect to the BND statistic.

Many models of electroweak symmetry breaking have an additional light pseudoscalar. If the Higgs boson can decay to a new pseudoscalar, LEP searches for the Higgs can be significantly altered and the Higgs can be as light as 86 GeV. Discovering the Higgs boson in these models is challenging when the pseudoscalar is lighter than 10 GeV because it decays dominantly into tau leptons. In this paper, we discuss discovering the Higgs in a subdominant decay mode where one of the pseudoscalars decays to a pair of muons. This search allows for potential discovery of a cascade-decaying Higgs boson with the complete Tevatron data set or early data at the LHC.

Relativistic corrections to the color-singlet $J/\psi$ hadroproduction at the Tevatron and LHC are calculated up to $\mathcal{O}(v^2)$ in nonrelativistic QCD (NRQCD). The short-distance coefficients are obtained by matching full QCD with NRQCD results for the subprocess $g+g\to J/\psi +g$. The long-distance matrix elements are extracted from observed $J/\psi$ hadronic and leptonic decay widths up to $\mathcal{O}(v^2)$. Using the CTEQ6 parton distribution functions, we calculate the leading-order production cross sections and relativistic corrections for the process $p+\overline{p}(p)\to J/\psi +X$ at the Tevatron and LHC. We find that the enhancement of $\mathcal{O}(v^2)$ relativistic corrections to the cross sections over a wide range of large transverse momentum $p_t$ is negligible, only at a level of about 1%. This tiny effect is due to the smallness of the correction to short-distance coefficients and the suppression from long-distance matrix elements. These results indicate that relativistic corrections cannot help to resolve the large discrepancy between leading-order prediction and experimental data for $J/\psi$ production at the Tevatron.

We report a measurement of the ratio of branching fractions of the decays $B^{\pm }\to J/\psi {\pi }^{\pm }$ and $B^{\pm }\to J/\psi K^{\pm }$ using the CDF II detector at the Fermilab Tevatron Collider. The signal from the Cabbibo-suppressed $B^{\pm }\to J/\psi {\pi }^{\pm }$ decay is separated from $B^{\pm }\to J/\psi K^{\pm }$ using the $B^{\pm }\to J/\psi K^{\pm }$ invariant mass distribution and the kinematical differences of the hadron track in the two decay modes. From a sample of $220{\mathrm{pb}}^{-1}$ of $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$, we observe $91\pm 15$ $B^{\pm }\to J/\psi {\pi }^{\pm }$ events together with $1883\pm 34$ $B^{\pm }\to J/\psi K^{\pm }$ events. The ratio of branching fractions is found to be $\mathcal{B}(B^{\pm }\to J/\psi {\pi }^{\pm })/\mathcal{B}(B^{\pm }\to J/\psi K^{\pm })=(4.86\pm 0.82(\mathrm{stat})\pm 0.15(\mathrm{syst}))\%$.

We report on a study of the relative rates of $B$ meson decays into $\psi (2S)$ and $J/\psi$ mesons using $1.3{\mathrm{fb}}^{-1}$ of $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ recorded by the D0 detector operating at the Fermilab Tevatron Collider. We observe the channels $B_s^0\to \psi (2S)\varphi$, $B_s^0\to J/\psi \varphi$, $B^{\pm }\to \psi (2S)K^{\pm }$, and $B^{\pm }\to J/\psi K^{\pm }$ and we measure the relative branching fractions for these channels to be $\frac{\mathcal{B}(B_s^0\to \psi (2S)\varphi )}{\mathcal{B}(B_s^0\to J/\psi \varphi )}=0.53\pm 0.10(\mathrm{stat})\pm 0.07(\mathrm{syst})\pm 0.06(\mathcal{B}),\frac{\mathcal{B}(B^{\pm }\to \psi (2S)K^{\pm })}{\mathcal{B}(B^{\pm }\to J/\psi K^{\pm })}=0.63\pm 0.05(\mathrm{stat})\pm 0.03(\mathrm{syst})\pm 0.07(\mathcal{B}),$where the final error corresponds to the uncertainty in the $J/\psi$ and $\psi (2S)$ branching ratio into two muons.

A nonsupersymmetric grand unified theory can exhibit a “radiative fermion mass hierarchy”, in which the heavier quarks and leptons get mass at tree level and the lighter ones get mass from loop diagrams. Recently the first predictive model of this type was proposed. Here it is analyzed numerically and it is shown to give an excellent fit to the quark and lepton masses and mixings, including the $CP$ violating phase ${\delta }_{\mathrm{CKM}}$. A relation between the neutrino angle ${\theta }_{13}$ and the atmospheric neutrino angle is obtained.

The effects of the IR aspects of gravity on quantum mechanics is investigated. At large distances where, due to gravity, the space-time is curved, there appears nonzero minimal uncertainty $\Delta p_0$ in the momentum of a quantum mechanical particle. We apply the minimal uncertainty momentum to some quantum mechanical interferometry examples and show that the phase shift depends on the area surrounded by the path of the test particle. We also put some limits on the related parameters. This prediction may be tested through future experiments. The assumption of minimal uncertainty in momentum can also explain the anomalous excess of the mass of the Cooper pair in a thin, rotating, superconductor ring.

We solve two-dimensional large-$N$ QCD in the presence of a nonzero baryon number $B$, and for arbitrary quark mass $m$ and volume $L$. We fully treat the dynamics of the gluonic zero modes and check how this affects results from previous studies of the $B=0$ and $B=1$ systems. For a finite density of baryons, and for any $m>0$, we find that the ground state contains a baryon crystal with expectation values for $⟨\overline{\psi }{\gamma }_{\mu }\psi ⟩$ that have a helixlike spatial structure. We study how these evolve with $B$ and see that the volume integral of $⟨\overline{\psi }\psi ⟩$ strongly changes with the baryon density. We compare this emerging crystal structure with the sine-Gordon crystal, which is expected to be a good approximation for light quarks, and find that it is a very good approximation for surprisingly heavy quarks. We also calculate the way the ground state energy $E$ changes as a function of the baryon number $B$, and find that for sufficiently large densities the function $E(B)$ is well described by the equation of state for free massless quarks, thus suggesting a quark-Hadron continuity. From $\partial E(B)/\partial B$ we calculate the quark chemical potential $\mu$ as a function of $B$ and see that the baryons repel each other. The way $\mu$ depends on $B$ also allows us to translate our findings to the grand-canonical ensemble. The resulting phase structure along the $\mu$ axis contains a phase transition that occurs at a value of $\mu$ equal to the baryon mass divided in $N$, and that separates a $\mu$-independent phase with intact translation symmetry from a $\mu$-dependent phase with spontaneously broken translation symmetry. Finally, our calculations confirm the presence of a partial large-$N$ Eguchi-Kawai volume independence, as described in [Phys. Rev. D 79, 105021 (2009)], that arises only if one treats the gluonic zero modes correctly.

We compute the even part of the two-loop seven-point planar MHV amplitude in $\mathcal{N}=4$ supersymmetric Yang-Mills theory. We find that the even part is expressed in terms of conformal integrals with simple rational coefficients. We also compute the even part of two all-$n$ cuts. An important feature of the result is that no hexagon (or higher polygon) loops appear among the integrals detected by the cuts we computed. We also present a “leg addition rule,” which allows us to express some integral coefficients in the $n+1$-point MHV amplitude in terms of the integral coefficients of the $n$-point MHV amplitude.

We present a numerical work aiming at the computation of excised initial data for black hole spacetimes in full general relativity, using the Dirac gauge in the context of a constrained formalism for the Einstein equations. Introducing the isolated horizon formalism for black hole excision, we especially solve the conformal metric part of the equations, and assess the boundary condition problem for it. In the stationary single black hole case, we present and justify a no-boundary treatment on the black hole horizon. We compare the data obtained with the well-known analytic Kerr solution in Kerr-Schild coordinates, and assess the widely used conformally flat approximation for simulating axisymmetric black hole spacetimes. Our method shows good concordance on physical and geometrical issues, with the particular application of the isolated horizon multipolar analysis to confirm that the solution obtained is indeed the Kerr spacetime. Finally, we discuss a previous suggestion in the literature for the boundary conditions for the conformal geometry on the horizon.

Using matrix theory as a concrete example of a fundamental holographic theory, we show that the emergent macroscopic spacetime displays a new macroscopic quantum structure, holographic geometry, and a new observable phenomenon, holographic noise, with phenomenology similar to that previously derived on the basis of a quasimonochromatic wave theory. Traces of matrix operators on a light sheet with a compact dimension of size $R$ are interpreted as transverse position operators for macroscopic bodies. An effective quantum wave equation for spacetime is derived from the matrix Hamiltonian. Its solutions display eigenmodes that connect longitudinal separation and transverse position operators on macroscopic scales. Measurements of transverse relative positions of macroscopically separated bodies, such as signals in Michelson interferometers, are shown to display holographic nonlocality, indeterminacy, and noise, whose properties can be predicted with no parameters except $R$. Similar results are derived using a detailed scattering calculation of the matrix wave function. Current experimental technology will allow a definitive and precise test or validation of this interpretation of holographic fundamental theories. In the latter case, they will yield a direct measurement of $R$ independent of the gravitational definition of the Planck length, and a direct measurement of the total number of degrees of freedom.

We study the fluxes emitted by black holes when using dispersive field theories. We work with stationary one-dimensional backgrounds which are asymptotically flat on both sides of the horizon. The asymptotic fluxes are governed by a $3\times 3$ Bogoliubov transformation. The fluxes emitted by the corresponding white holes are regular and governed by the inverse transformation. We numerically compute the spectral properties of these fluxes for both sub- and superluminal quartic dispersion. The leading deviations with respect to the dispersionless flux are computed and shown to be governed by a critical frequency above which there is no radiation. Unlike the UV scale governing dispersion, its value critically depends on the asymptotic properties of the background. We also study the flux outside the robust regime. In particular we show that its low-frequency part remains almost thermal but with a temperature which significantly differs from the standard one. Applications to four-dimensional black holes and Bose-Einstein condensates are in preparation.

The future finite-time singularities emerging in alternative gravity dark energy models are classified and studied in Jordan and Einstein frames. It is shown that such singularity may occur even in flat spacetime for the specific choice of the effective potential. The conditions for the avoidance of finite-time singularities are presented and discussed. The problem is reduced to the study of a scalar field evolving on an effective potential by using the conformal transformations. Some viable modified gravity models are analyzed in detail and the way to cure singularity is considered by introducing the higher order curvature corrections. These results may be relevant for the resolution of the conjectured problem in the relativistic star formation in such modified gravity where finite-time singularity is also manifested.

We consider a left-right symmetric $SU(4{)}_c\times SU(2{)}_L\times SU(2{)}_R$ (4-2-2) model with gravity mediated supersymmetry breaking. We find that with 4-2-2 compatible nonuniversal gaugino masses, $t-b-\tau$ Yukawa coupling unification is consistent with neutralino dark matter abundance and with constraints from collider experiments (except $(g-2{)}_{\mu }$). The gluino mass lies close to that of the lightest neutralino, so that the gluino coannihilation channel plays an important role in determining the neutralino relic abundance. By relaxing the Yukawa unification constraint we find stau and stop masses as low as 200–220 GeV. We highlight some benchmark points for these cases with $40\le \tan \beta \le 58$.

The electromagnetic form factors of nucleons are calculated using an anti–de Sitter (AdS)/QCD model by considering a Dirac field coupled to a vector field in the five-dimensional AdS space. We also calculate a gravitational or energy-momentum form factor by perturbing the metric from the static AdS solution. We consider both the hard-wall model where the AdS geometry is cut off at $z_0$ and the soft-wall model where the geometry is smoothly cut off by a background dilaton field.

We study semileptonic and radiative $B$ decays involving the strange tensor meson $K_2^{*}(1430)$ in the final state. Using the large energy effective theory (LEET) techniques, we formulate the $B\to K_2^{*}$ transition form factors in large recoil region. All the form factors can be parametrized in terms of two independent LEET functions ${\zeta }_{\perp }$ and ${\zeta }_{\parallel }$. The magnitude of ${\zeta }_{\perp }$ is estimated from the data for $\mathcal{B}(B\to K_2^{*}(1430)\gamma )$. Assuming a dipole $q^2$ dependence for the LEET functions and ${\zeta }_{\parallel }/{\zeta }_{\perp }=1.0\pm 0.2$, for which the former consists with the QCD counting rules, and the latter is favored by the $B\to \varphi K_2^{*}$ data, we investigate the decays $B\to K_2^{*}{\ell }^{+}{\ell }^{-}$ and $B\to K_2^{*}\nu \overline{\nu }$, where the contributions due to ${\zeta }_{\parallel }$ are suppressed by $m_{K_2^{*}}/m_B$. For the $B\to K_2^{*}{\ell }^{+}{\ell }^{-}$ decay, in the large recoil region where the hadronic uncertainties are considerably reduced, the longitudinal distribution $d{F}_L/ds$ is reduced by 20–30% due to the flipped sign of $c_7^{\mathrm{eff}}$ compared with the standard model result. Moreover, the forward-backward asymmetry zero is about $3.4{\mathrm{GeV}}^2$ in the standard model, but changing the sign of $c_7^{\mathrm{eff}}$ yields a positive asymmetry for all values of the invariant mass of the lepton pair. We calculate the branching fraction for $B\to K_2^{*}\nu \overline{\nu }$ in the standard model. Our result exhibits the impressed resemblance between $B\to K_2^{*}(1430){\ell }^{+}{\ell }^{-}$, $\nu \overline{\nu }$, and $B\to K^{*}(892){\ell }^{+}{\ell }^{-}$, $\nu \overline{\nu }$.

Van Holten’s covariant Hamiltonian framework is used to find conserved quantities for an isospin-carrying particle in a non-Abelian monopolelike field. For a Wu-Yang monopole we find the most general scalar potential such that the combined system admits a conserved Runge-Lenz vector. In the effective non-Abelian field for nuclear motion in a diatomic molecule due to Moody, Shapere, and Wilczek, a conserved angular momentum is constructed, despite the nonconservation of the electric charge. No Runge-Lenz vector has been found.

We express the Noether charge entropy density of a black brane in anti–de Sitter space in terms of local operators in the anti–de Sitter space bulk. We find that Wald’s expression for the Noether charge entropy needs to be modified away from the horizon by an additional term that vanishes on the horizon. We then determine the field theory dual of the Noether charge entropy for theories that asymptote to Einstein theory. We do so by calculating the value of the entropy density at the anti–de Sitter space boundary and applying the standard rules of the AdS/CFT correspondence. We interpret the variation of the entropy density operator from the horizon to the boundary as due to the renormalization of the effective gravitational couplings as they flow from the ultraviolet to the infrared. We discuss the cases of Einstein-Hilbert theory and $f(R)$ theories in detail and make general comments about more complicated cases.

A formula for the two-loop infrared singularities of dimensionally regularized QCD scattering amplitudes with an arbitrary number of massive and massless legs is derived. The singularities are obtained from the solution of a renormalization-group equation, and factorization constraints on the relevant anomalous-dimension matrix are analyzed. The simplicity of the structure of the matrix relevant for massless partons does not carry over to the case with massive legs, where starting at two-loop order new color and momentum structures arise, which are not of the color-dipole form. The resulting two-loop three-parton correlations can be expressed in terms of two functions, for which some general properties are derived. This explains observations recently made by Mitov et al. in terms of symmetry arguments.