We derive model-independent, universal upper bounds on the operator product expansion coefficients in unitary 4-dimensional conformal field theories. The method uses the conformal block decomposition and the crossing symmetry constraint of the 4-point function. In particular, the operator product expansion coefficient of three identical dimension $d$ scalar primaries is found to be bounded by $\simeq 10(d-1)$ for $1<d<1.7$. This puts strong limits on unparticle self-interaction cross sections at the LHC.

Large $N$ matrices can describe covariant derivatives in curved space. Applying this interpretation to the Ishibashi, Kawai, Kitazawa, and Tsuchiya matrix model, the field equation of gravity is derived from the matrix equation of motion. We study classical solutions of this field equation with torsion degrees of freedom in empty spacetime. Time-dependent solutions with homogeneity and isotropy, and time-independent solutions with spherical symmetry are investigated under particular settings of torsions.

Results for the gravitational Wilson loop, in particular, the area law for large loops in the strong coupling region, and the argument for an effective positive cosmological constant, discussed in a previous paper, are extended to other proposed theories of discrete Euclidean quantum gravity in the strong coupling limit. We argue that the area law is a generic feature of almost all nonperturbative Euclidean lattice formulations, for sufficiently strong gravitational coupling. The effects on gravitational Wilson loops of the inclusion of various types of light matter coupled to lattice quantum gravity are discussed as well. One finds that significant modifications to the area law can only arise from extremely light matter particles. The paper ends with some general comments on possible, physically observable, consequences.

Consider a spherically symmetric spacetime generated by a self-gravitating massless scalar field $\varphi$ and let $\psi$ be a test (nonspherical) massless scalar field propagating on this dynamical background. Gundlach, Price, and Pullin [Phys. Rev. D 49, 890 (1994).] computed numerically the late-time tails for different multipoles of the field $\psi$ and suggested that solutions with compactly supported initial data decay in accord with Price’s law as $t^{-(2\ell +3)}$ at timelike infinity. We show that in the case of the time-dependent background dispersing to Minkowski spacetime Price’s law holds only for $\ell =0$ while for each $\ell \ge 1$ the tail decays as $t^{-(2\ell +2)}$.

We have developed a 532 nm iodine stabilized laser system that may be suitable for the LISA mission (Laser Interferometer Space Antenna) or other future spaceborne missions. This system is based on an externally frequency-doubled Nd:YAG laser source and uses the molecular transfer spectroscopy technique for the frequency stabilization. This technique has been optimized for LISA: compactness (less than $1.1\times 1.1{\mathrm{m}}^2$), vacuum compatibility, ease of use and initialization, minimization of the number of active components (acousto-optic modulators are both used for frequency shifting and phase modulating the pump beam). By locking on the $a_{10}$ hyperfine component of the R(56)32-0 transition, we find an Allan standard deviation ($\sigma$) of $3\times {10}^{-14}$ at 1 s and $\sigma <2\times {10}^{-14}$ for $20\mathrm{s}\le \tau \le {10}^3\mathrm{s}$. In terms of linear spectral density, this roughly corresponds to a stability better than $30\mathrm{Hz}/\sqrt{\mathrm{Hz}}$ between ${10}^{-2}$ and 1 Hz with a stability decrease close to $1/f$ below 10 mHz.

We reanalyze constraints on the mass spectrum of the chiral fourth generation fermions and the Higgs bosons for the standard model (SM4) and the two Higgs doublet model. We find that the Higgs mass in the SM4 should be larger than roughly the fourth generation up-type quark mass, while the light $CP$ even Higgs mass in the two Higgs doublet model can be smaller. Various mass spectra of the fourth generation fermions and the Higgs bosons are allowed. The phenomenology of the fourth generation models is still rich.

The $\mathcal{N}=1$ supersymmetric Born-Infeld action is known to describe the vector Goldstone multiplet for partially broken $\mathcal{N}=2$ rigid supersymmetry, and this model is believed to be unique. However, it can be deformed by adding the Fayet-Iliopoulos term without losing the second nonlinearly realized supersymmetry. Although the first supersymmetry then becomes spontaneously broken, the deformed action still describes partial $\mathcal{N}=2\to \mathcal{N}=1$ supersymmetry breaking. The unbroken supercharges in this theory correspond to a different choice of $\mathcal{N}=1$ subspace in the $\mathcal{N}=2$ superspace, as compared with the undeformed case. Implications of the Fayet-Iliopoulos term for general models for self-dual nonlinear supersymmetric electrodynamics are discussed. The known ubiquitous appearance of the Volkov-Akulov action in such models is explained. We also present a two-parameter duality-covariant deformation of the $\mathcal{N}=1$ supersymmetric Born-Infeld action as a model for partial breaking of $\mathcal{N}=2$ supersymmetry.

We systematically study spherically symmetric static spacetimes filled with a fluid in the Horava-Lifshitz theory of gravity with the projectability condition, but without the detailed balance. We establish that when the spacetime is spatially Ricci flat the unique vacuum solution is the de Sitter Schwarzshcild solution, while when the spacetime has a nonzero constant curvature, there exist two different vacuum solutions; one is an (Einstein) static universe, and the other is a new spacetime. This latter spacetime is maximally symmetric and not flat. We find all the perfect fluid solutions for such spacetimes, in addition to a class of anisotropic fluid solutions of the spatially Ricci flat spacetimes. To construct spacetimes that represent stars, we investigate junction conditions across the surfaces of stars and obtain the general matching conditions with or without the presence of infinitely thin shells. It is remarkable that, in contrast to general relativity, the radial pressure of a star does not necessarily vanish on its surface even without the presence of a thin shell, due to the presence of high order derivative terms. Applying the junction conditions to our explicit solutions, we show that it is possible to match smoothly these solutions (all with nonzero radial pressures) to vacuum spacetimes without the presence of thin matter shells on the surfaces of stars.

We derive the slow-roll conditions for a nonminimally coupled scalar field (extended quintessence) during the radiation/matter dominated era extending our previous results for thawing quintessence. We find that the ratio $\ddot{\varphi }/3H\dot{\varphi }$ becomes constant but negative, in sharp contrast to the ratio for the minimally coupled scalar field. We also find that the functional form of the equation of state of the scalar field asymptotically approaches that of the minimally coupled thawing quintessence.

A third quantization formalism is applied to a simplified multiverse scenario. A well-defined quantum state of the multiverse is obtained which agrees with standard boundary condition proposals. These states are found to be squeezed, and related to accelerating universes: they share similar properties to those obtained previously by Grishchuk and Siderov. We also comment on related works that have criticized the third quantization approach.

The rare top quark couplings $t{u}_i\gamma$ and $t{u}_i\gamma \gamma$ ($u_i=u$, $c$) induced at the one-loop level by a flavor violating $t{u}_{i}H$ vertex are studied within the context of an effective Yukawa sector that incorporates $S{U}_L(2)\times U_Y(1)$-invariant operators of up to dimension six. Data on the recently observed $D^0-{\overline{D}}^0$ mixing are employed to constrain the $t{u}_{i}H$ vertex, which is then used to predict the $t\to u_{i}H$, $t\to u_i\gamma$, and $t\to u_i\gamma \gamma$ decays, as well as the $\gamma \gamma \to \overline{t}{u}_i+t{\overline{u}}_i$ reaction in the context of the ILC. It is found that the $t\to cH$ and $t\to c\gamma \gamma$ decays can reach sizable branching ratios as high as $5\times {10}^{-3}$ and ${10}^{-4}$, respectively. As for the $t\to c\gamma$ decay, it can have a branching ratio of $5\times {10}^{-8}$ that is about 6 orders of magnitude larger than the standard model prediction, which, however, is still very small to be detected. As for $tc$ production, it is found that, due to the presence of a resonant effect in the convoluted cross section $\sigma (e^{+}{e}^{-}\to \gamma \gamma \to t\overline{c}+\overline{t}c)$, about $(0.5–2.7)\times {10}^3$ $tc$ events may be produced at the ILC for a value of the Higgs mass near to the top mass.

We discuss how a possible violation of the combined symmetry $CPT$ in the $B$ meson system can be investigated at the LHC. We show how a tagged and an untagged analysis of the decay modes of both $B_d$ and $B_s$ mesons can lead not only to a possible detection of a $CPT$-violating new physics but also to an understanding of its precise nature. The implication of $CPT$ violation to a large mixing phase in the $B_s$ system is also discussed.

We consider the Friedberg-Lee symmetry for the quark sector and show that the symmetry closely relates to both quark masses and mixing angles. We also extend our scheme to the fourth generation quark model and find the relation $|V_{t{b}^{\prime }}|\simeq |V_{t^{\prime }b}|\simeq m_b/m_{b^{\prime }}<{\lambda }^2$ with $\lambda \simeq 0.22$ for $m_b=4.2\mathrm{GeV}$ and $m_{b^{\prime }}>199\mathrm{GeV}$.

We study the production of a single resonance at the LHC and its decay into a pair of $Z$ bosons. We demonstrate how full reconstruction of the final states allows us to determine the spin and parity of the resonance and restricts its coupling to vector gauge bosons. Full angular analysis is illustrated with the simulation of the production and decay chain, including all spin correlations and the most general couplings of spin-zero, -one, and -two resonances to standard model matter and gauge fields. We note implications for analysis of a resonance decaying to other final states.

We explore the potential of the Large Hadron Collider to observe the $h_1\to a_1{a}_1\to 4\mu$ signal from the lightest scalar Higgs boson ($h_1$) decaying into the two lightest pseudoscalar Higgs bosons ($a_1$), followed by their decays into four muons in the next-to-minimal supersymmetric standard model (NMSSM). The signature under study applies to the region of the NMSSM parameter space in which $m_{a_1}<2m_{\tau }$, which has not been studied previously. In such a scenario, the suggested strategy of searching for a four-muon signal with the appropriate background suppression would provide a powerful method to discover the lightest $CP$-even and $CP$-odd NMSSM Higgs bosons $h_1$ and $a_1$.

Spontaneous $CP$ violation motivates the introduction of two Higgs doublets in the electroweak theory, such a simple extension of the standard model has five physical Higgs bosons and rich $CP$-violating sources. Exploration on more than one Higgs boson is a direct evidence for new physics beyond the standard model. The neutral Higgs production at LHC is investigated in such a general two-Higgs-doublet model with spontaneous $CP$ violation, it is shown that the production cross section and decays of the neutral Higgs boson can significantly be different from the predictions from the standard model.

The top quark has a large Yukawa coupling with the Higgs boson. In the usual extensions of the standard model the Higgs sector includes extra scalars, which also tend to couple strongly with the top quark. Unlike the Higgs, these fields have a natural mass above $2m_t$, so they could introduce anomalies in $t\overline{t}$ production at the LHC. We study their effect on the $t\overline{t}$ invariant mass distribution at $\sqrt{s}=7\mathrm{TeV}$. We focus on the bosons $(H,A)$ of the minimal supersymmetric model and on the scalar field ($r$) associated with the new scale $f$ in Little Higgs (LH) models. We show that in all cases the interference with the standard amplitude dominates over the narrow-width contribution. As a consequence, the mass difference between $H$ and $A$ or the contribution of an extra $T$-quark loop in LH models becomes an important effect in order to determine if these fields are observable there. We find that a $1{\mathrm{fb}}^{-1}$ luminosity could probe the region $\tan \beta \le 3$ of supersymmetry and $v/(\sqrt{2}f)\ge 0.3$ in LH models.

The ${\pi }^{+}{\Sigma }^{+}$, ${\pi }^{+}{\Xi }^0$, $K^{+}p$, $K^{+}n$, and ${\overline{K}}^0{\Xi }^0$ scattering lengths are calculated in mixed-action Lattice QCD with domain-wall valence quarks on the asqtad-improved coarse MILC configurations at four light-quark masses, and at two light-quark masses on the fine MILC configurations. Heavy-baryon chiral perturbation theory with two and three flavors of light quarks is used to perform the chiral extrapolations. To the order we work in the three-flavor chiral expansion, the kaon-baryon processes that we investigate show no signs of convergence. Using the two-flavor chiral expansion for extrapolation, the pion-hyperon scattering lengths are found to be $a_{{\pi }^{+}{\Sigma }^{+}}=-0.197\pm 0.017\mathrm{fm}$, and $a_{{\pi }^{+}{\Xi }^0}=-0.098\pm 0.017\mathrm{fm}$, where the comprehensive error includes statistical and systematic uncertainties.

In this paper, in the framework of nonrelativistic QCD we study the light hadron (LH) decays of the spin-triplet ($S=1$) $D$-wave heavy quarkonia. The short-distance coefficients of all Fock states in the ${}^{3}D_J$ ($J=1$, 2, 3) quarkonia including the $D$-wave color singlet, $P$-wave color octet, and $S$-wave color singlet and color octet are calculated perturbatively at ${\alpha }_s^3$ order. The operator evolution equations of the four-fermion operators are also derived and are used to estimate the numerical values of the long-distance matrix elements. We find that for the $c\overline{c}$ system, the LH decay widths of $\psi (1{}^{3}D_J)$ predicted by nonrelativistic QCD is about $2\sim 3$ times larger than the phenomenological potential model results, while for the $b\overline{b}$ system the two theoretical estimations of $\Gamma ({\rm Y}(1{}^{3}D_J)\to \mathrm{LH})$ are in coincidence with each other. Our predictions for $\psi (1{}^{3}D_J)$ LH decay widths are $\Gamma (\psi (1{}^{3}D_J)\to \mathrm{LH})=(435,50,172)\mathrm{keV}$ for $J=1$, 2, 3; and for ${\rm Y}(1{}^{3}D_J)$, $\Gamma ({\rm Y}(1{}^{3}D_J)\to \mathrm{LH})=(6.91,0.75,2.75)\mathrm{keV}$ for $J=1$, 2, 3.

We study the hadronic $D$ meson decays into a pseudoscalar meson $P$ and an even-parity meson $M$, where $M$ represents a scalar meson $S$, an axial-vector meson $A$, or a tensor meson $T$. These decays are first analyzed in the flavor-diagram approach. Fits to the $SP$ modes with $S$ being a nonstrange scalar meson show that neither the simple $q\overline{q}$ picture nor the $q^2{\overline{q}}^2$ scheme is favored by data. Current measurements on the $AP$ decays are insufficient for a meaningful analysis. Some $TP$ data are inconsistent with the others. In certain cases, the $W$-annihilation diagrams indicated by the data are unexpectedly large. As a comparison, we also compute their decay rates in the factorization approach using form factors extracted from the covariant light-front model. We find that factorization works well for Cabibbo-allowed $D^{+}\to SP$, $AP$ decays free of the weak annihilation contributions ($W$-exchange or $W$-annihilation). For the other $SP$ and $AP$ modes, it is necessary to include weak annihilation contributions to account for the data. However, factorization fails for $D\to TP$ decays for some unknown reason; the predicted rates are in general too small by at least 2 orders of magnitude compared to experiment. We also examine the finite-width effects of resonances. Some decay modes which are kinematically forbidden become physically allowed due to the finite width of the resonance. We show that the branching fraction of $D^{+}\to \sigma {\pi }^{+}$ extracted from three-body decays is enhanced by a factor of 2, whereas $\mathcal{B}(D^0\to f_2(1270){\overline{K}}^0)$ is reduced by a factor of 4 by finite-width effects.