We perform a QCD sum rule analysis for the $f_0$ light tetraquark taking into account the contribution arising from the two pion intermediate state. With the interpolating currents of the different chiral combinations of scalar and pseudoscalar diquarks, it is demonstrated that the interpolating current with maximum chirality has a large coupling to the two pion state, but the current with zero chirality interacts only weekly with this state. Taking into account the form factor in the $f_0$-two pion vertex, it is shown that the $f_0$ coupling to the two pion state leads to an increase of the lightest tetraquark mass by a value of about 100 MeV. The analysis of the resulting sum rule shows that the $\sigma (f_0(600))$-meson state might be treated as the four-quark bound state in the instanton field which has a rather strong coupling to the two pion state.

We present the results of our QCD analysis for nonsinglet unpolarized quark distributions and structure function $F_2(x,Q^2)$. New parameterizations are derived for the nonsinglet quark distributions for the kinematic wide range of $x$ and $Q^2$. The analysis is based on the Jacobi polynomials expansion of the structure function. The higher twist contributions of proton and deuteron structure function are obtained in the large $x$ region. Our calculations for nonsinglet unpolarized quark distribution functions based on the Jacobi polynomials method are in good agreement with the other theoretical models. The values of ${\Lambda }_{\mathrm{QCD}}$ and ${\alpha }_s(M_z^2)$ are determined.

We calculate the next-to-leading order fully unintegrated hard scattering coefficient for unpolarized gluon-induced deep inelastic scattering using the logical framework of parton correlation functions developed in previous work. In our approach, exact four-momentum conservation is maintained throughout the calculation. Hence, all nonperturbative functions, like parton distribution functions, depend on all components of parton four-momentum. In contrast to the usual collinear factorization approach where the hard scattering coefficient involves generalized functions (such as Dirac $\delta$ functions), the fully unintegrated hard scattering coefficient is an ordinary function. Gluon-induced deep inelastic scattering provides a simple illustration of the application of the fully unintegrated factorization formalism with a nontrivial hard scattering coefficient, applied to a phenomenologically interesting case. Furthermore, the gluon-induced process allows for a parametrization of the fully unintegrated gluon distribution function.

A sensitive way to test the anomalous $HVV$ ($V=W^{\pm },Z^0$) couplings via $pp\to W^{+}{W}^{+}jj\to {\ell }^{+}\nu {\ell }^{+}\nu jj$ at LHC was proposed by Zhang, Kuang, He, and Yuan [Phys. Rev. D 67, 114024 (2003)]. We studied the sensitivity to measure the anomalous gauge couplings of Higgs boson with optimized cuts. In this way, the sensitivity can be enhanced. Based on the optimized cuts and distribution of $\Delta Pt(\ell \ell )$, the measurement of the couplings can be further improved with a binned maximum likelihood fit. It shows that, with an integrated luminosity of $300{\mathrm{fb}}^{-1}$, the anomalous $HWW$ and $HZZ$ couplings can be measured at the level of 0.007–0.032 and $0.007–0.013{\mathrm{TeV}}^{-1}$, respectively, for the linearly realized effective Lagrangian.

We report the first observation of $e^{+}{e}^{-}\to {\rho }^{+}{\rho }^{-}$, in a data sample of $379{\mathrm{fb}}^{-1}$ collected with the BABAR detector at the PEP-II $e^{+}{e}^{-}$ storage ring at center-of-mass energies near $\sqrt{s}=10.58\mathrm{GeV}$. We measure a cross section of $\sigma (e^{+}{e}^{-}\to {\rho }^{+}{\rho }^{-})=8.3\pm 0.7(\mathrm{stat})\pm 0.8(\mathrm{syst})\mathrm{fb}$ within the range of $|\cos {\theta }^{*}|<0.8$ and $|\cos {\theta }_{\pm }|<0.85$, where ${\theta }^{*}$ is the center-of-mass polar angle of the ${\rho }^{\pm }$ meson and ${\theta }_{\pm }$ are the angles in the ${\rho }^{\pm }$ rest frame between the direction of the boost from the laboratory frame and the direction of the ${\pi }^{\pm }$. Assuming production through single-photon annihilation, there are three independent helicity amplitudes. We measure the ratios of their squared moduli to be $|F_{00}{|}^2:|F_{10}{|}^2:|F_{11}{|}^2=0.51\pm 0.14(\mathrm{stat})\pm 0.07(\mathrm{syst}):0.10\pm 0.04(\mathrm{stat})\pm 0.01(\mathrm{syst}):0.04\pm 0.03(\mathrm{stat})\pm 0.01(\mathrm{syst})$. The $|F_{00}{|}^2$ result is inconsistent with the prediction of 1.0 made by QCD models with a significance of 3.1 standard deviations including systematic uncertainties.

We study the renormalization of the O(N) model using the auxiliary field formalism (Hubbard-Stratonovich transformation) in the $1/N$ expansion at finite temperature. We provide the general strategy of renormalization for arbitrary order and make a calculation up to next-to-leading order. We show that renormalization is possible for any values of the condensates, prove the temperature independence of the counterterms, and determine the cutoff dependence of the first nontrivial counterterm parts.

For neutrinos streaming from a supernova core, dense matter suppresses self-induced flavor transformations if the electron density $n_e$ significantly exceeds the neutrino density $n_{\nu }$ in the conversion region. If $n_e$ is comparable to $n_{\nu }$, one finds multiangle decoherence, whereas the standard self-induced transformation behavior requires that in the transformation region $n_{\nu }$ is safely above $n_e$. This condition need not be satisfied in the early phase after the supernova core bounce. Our new multiangle effect is a subtle consequence of neutrinos traveling on different trajectories when streaming from a source that is not pointlike.

We present an identity satisfied by the kinematic factors of diagrams describing the tree amplitudes of massless gauge theories. This identity is a kinematic analog of the Jacobi identity for color factors. Using this we find new relations between color-ordered partial amplitudes. We discuss applications to multiloop calculations via the unitarity method. In particular, we illustrate the relations between different contributions to a two-loop four-point QCD amplitude. We also use this identity to reorganize gravity tree amplitudes diagram by diagram, offering new insight into the structure of the Kawai-Lewellen-Tye (KLT) relations between gauge and gravity tree amplitudes. This insight leads to similar but novel relations. We expect this to be helpful in higher-loop studies of the ultraviolet properties of gravity theories.

We study the effective actions in massive rank 2 and rank 3 antisymmetric tensor field models in curved space-time. These models are classically equivalent to massive vector field and massive scalar field with minimal coupling to gravity, respectively. We prove that the effective action for massive rank 2 antisymmetric tensor field is exactly equal to that for massive vector field and the effective action for massive rank 3 antisymmetric tensor field is exactly equal to that for massive scalar field. The proof is based on an identity for mass-dependent zeta functions associated with Laplacians acting on $p$ forms.

We study the dynamics of domain walls in the Einstein-Born–Infeld-dilaton theory. A dilaton is nontrivially coupled with the Born-Infeld electromagnetic field. We find three different types of solutions consistent with the dynamic domain walls. For every case, the solutions have singularity. Furthermore, in these backgrounds, we study the dynamics of domain walls. We qualitatively plot various forms of the bulk metrics and the potential encountered by the domain walls. In many cases, depending upon the value of the parameters, the domain walls show a bouncing universe and also undergo an inflationary phase followed by a standard decelerated expansion.

We derive the linearly perturbed matching conditions between a Schwarzschild spacetime region with stationary and axially symmetric perturbations and a Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime with arbitrary perturbations. The matching hypersurface is also perturbed arbitrarily and, in all cases, the perturbations are decomposed into scalars using the Hodge operator on the sphere. This allows us to write down the matching conditions in a compact way. In particular, we find that the existence of a perturbed (rotating, stationary, and vacuum) Schwarzschild cavity in a perturbed FLRW universe forces the cosmological perturbations to satisfy constraints that link rotational and gravitational wave perturbations. We also prove that if the perturbation on the FLRW side vanishes identically, then the vacuole must be perturbatively static and hence Schwarzschild. By the dual nature of the problem, the first result translates into links between rotational and gravitational wave perturbations on a perturbed Oppenheimer-Snyder model, where the perturbed FLRW dust collapses in a perturbed Schwarzschild environment which rotates in equilibrium. The second result implies, in particular, that no region described by FLRW can be a source of the Kerr metric.

The mode-sum method provides a practical means for calculating the self-force acting on a small particle orbiting a larger black hole. In this method, one first computes the spherical-harmonic $l$-mode contributions $F_l^{\mu }$ of the “full-force” field $F^{\mu }$, evaluated at the particle’s location, and then sums over $l$ subject to a certain regularization scheme. In the frequency-domain variant of this procedure the quantities $F_l^{\mu }$ are obtained by fully decomposing the particle’s self-field into Fourier-harmonic modes $lm\omega$, calculating the contribution of each such mode to $F_l^{\mu }$, and then summing over $\omega$ and $m$ for given $l$. This procedure has the advantage that one only encounters ordinary differential equations. However, for eccentric orbits, the sum over $\omega$ is found to converge badly at the particle’s location. This problem (reminiscent of the familiar Gibbs phenomenon of Fourier analysis) results from the discontinuity of the time-domain $F_l^{\mu }$ field at the particle’s worldline. Here we propose a simple and practical method to resolve this problem. The method utilizes the homogeneous modes $lm\omega$ of the self-field to construct $F_l^{\mu }$ (rather than the inhomogeneous modes, as in the standard method), which guarantees an exponentially fast convergence to the correct value of $F_l^{\mu }$, even at the particle’s location. We illustrate the application of the method with the example of the monopole scalar-field perturbation from a scalar charge in an eccentric orbit around a Schwarzschild black hole. Our method, however, should be applicable to a wider range of problems, including the calculation of the gravitational self-force using either Teukolsky’s formalism, or a direct integration of the metric perturbation equations.

We discuss how much we can probe the effective number of neutrino species $N_{\nu }$ with the cosmic microwave background alone. Using the data of the WMAP, ACBAR, CBI, and BOOMERANG experiments, we obtain a constraint on the effective number of neutrino species as $0.96<N_{\nu }<7.94$ at 95% C.L. for a power-law $\Lambda \mathrm{CDM}$ flat universe model. The limit is improved to be $1.39<N_{\nu }<6.38$ at 95% C.L. if we assume that the baryon density, $N_{\nu }$, and the helium abundance are related by the big bang nucleosynthesis theory. We also provide a forecast for the Planck experiment using a Markov chain Monte Carlo approach. In addition to constraining $N_{\nu }$, we investigate how the big bang nucleosynthesis relation affects the estimation for these parameters and other cosmological parameters.

Inflation predicts a stochastic background of gravitational waves over a broad range of frequencies, from those accessible with cosmic microwave background (CMB) measurements, to those accessible directly with gravitational-wave detectors, like NASA’s Big-Bang Observer (BBO), currently under study. In a previous paper [Phys. Rev. D 73, 023504 (2006)] we connected CMB constraints to the amplitude and tensor spectral tilt of the inflationary gravitational-wave background (IGWB) at BBO frequencies for four classes of models of inflation by directly solving the inflationary equations of motion. Here we extend that analysis by including results obtained in the Wilkinson Microwave Anisotropy Probe third-year data release as well as by considering two additional classes of inflationary models. As often noted in the literature, the recent indication that the primordial density power spectrum has a red spectral index implies (with some caveats) that the amplitude of the IGWB may be large enough to be observable in the CMB polarization. Here we also explore the implications for the direct detection of the IGWB.

In this paper, we combine the latest observational data, including the WMAP five-year data (WMAP5), BOOMERanG, CBI, VSA, ACBAR, as well as the baryon acoustic oscillations (BAO) and type Ia supernovae (SN) “union” compilation (307 sample), and use the Markov Chain Monte Carlo method to determine the cosmological parameters, such as the equation of state (EoS) of dark energy, the curvature of the universe, the total neutrino mass, and the parameters associated with the power spectrum of primordial fluctuations. In a flat universe, we obtain the tight limit on the constant EoS of dark energy as $w=-0.977\pm 0.056(\mathrm{stat})\pm 0.057(\mathrm{sys})$. For the dynamical dark energy models with the time evolving EoS parametrized as $w_{\mathrm{de}}(a)=w_0+w_1(1-a)$, we find that the best-fit values are $w_0=-1.08$ and $w_1=0.368$, while the $\Lambda \mathrm{CDM}$ model remains a good fit to the current data. For the curvature of the universe ${\Omega }_k$, our results give $-0.012<{\Omega }_k<0.009$ (95% C.L.) when fixing $w_{\mathrm{de}}=-1$. When considering the dynamics of dark energy, the flat universe is still a good fit to the current data, $-0.015<{\Omega }_k<0.018$ (95% C.L.). Regarding the neutrino mass limit, we obtain the upper limits, $\sum _{}^{}{m}_{\nu }<0.533\mathrm{eV}$ (95% C.L.) within the framework of the flat $\Lambda \mathrm{CDM}$ model. When adding the Sloan Digital Sky Survey Lyman-$\alpha$ forest power spectrum data, the constraint on $\sum _{}^{}{m}_{\nu }$ can be significantly improved, $\sum _{}^{}{m}_{\nu }<0.161\mathrm{eV}$ (95% C.L.). However, these limits can be weakened by a factor of 2 in the framework of dynamical dark energy models, due to the obvious degeneracy between neutrino mass and the EoS of the dark energy model. Assuming that the primordial fluctuations are adiabatic with a power law spectrum within the $\Lambda \mathrm{CDM}$ model, we find that the upper limit on the ratio of the tensor to scalar is $r<0.200$ (95% C.L.) and the inflationary models with the slope $n_s\ge 1$ are excluded at more than $2\sigma$ confidence level. However, in the framework of dynamical dark energy models, the allowed region in the parameter space of $(n_s,r)$ is enlarged significantly. Finally, we find no strong evidence for the large running of the spectral index.

We explore $CP$ violation effects on the neutrino propagation in dense environments, such as in core-collapse supernovae, where the neutrino self-interaction induces nonlinear evolution equations. We demonstrate that the electron (anti)neutrino fluxes are not sensitive to the $CP$ violating phase if the muon and tau neutrinos interact similarly with matter. On the other hand, we numerically show that new features arise, because of the nonlinearity and the flux dependence of the evolution equations, when the muon and tau neutrinos have different fluxes at the neutrinosphere (due to loop corrections or physics beyond the standard model). In particular, the electron (anti)neutrino probabilities and fluxes depend upon the $CP$ violating phase. We also discuss the $CP$ effects induced by radiative corrections to the neutrino refractive index.

We have studied the possible signals of unparticle in atomic parity violation (APV) along an isotope chain and in the NuTeV experiment. The effects of unparticle physics could be observed in APV, if the uncertainty in relative neutron/proton radius shift $\delta (\Delta \frac{R_N}{R_P})$ is less than a few times ${10}^{-4}$ by measuring the parity violating electron scattering. The constraints imposed by the NuTeV experiment on unparticle physics are discussed in detail. If the NuTeV results are confirmed by future experiments, we suggest that unparticle could account for a part of the NuTeV anomaly. There exist certain regions for the unparticle parameters (${\Lambda }_{\mathcal{U}}$, $d_{\mathcal{U}}$, $c_{V\mathcal{U}}$, and $c_{A\mathcal{U}}$), where the NuTeV discrepancy could be completely explained by unparticle effects and the strange quark asymmetry, even with or without the contributions from the isoscalarity violation, etc. It is remarkable that these parameter regions are consistent with the constraints from $b\to s\gamma$.

In supersymmetric generalizations of the standard model, all stable $Q$-balls are associated with some flat directions. We show that, if the flat direction has both the baryon number and the lepton number, the scalar field inside the $Q$-ball can deviate slightly from the flat direction in the ground state. We identify the true ground states of such nontopological solitons, including the electrically neutral and electrically charged $Q$-balls.

Recent analyses have shown that a sequential fourth generation can be consistent with precision electroweak data. We consider the possibility that the new generation could be a mirror generation with $V+A$ rather than $V-A$ interactions. Specifically we consider an extension of the minimal supersymmetric standard model with a light mirror generation. Implications of this extension are explored. One consequence is an enhancement of the $\tau$ neutrino magnetic moment by several orders of magnitude consistent with the current limits on the magnetic moment of the $\tau$. The masses of the mirror generation arise due to electroweak symmetry breaking, and if a mirror generation exists its mass spectrum must lie below a TeV, and thus should be discovered at the LHC. Mirror particles and mirror sparticles produce many characteristic signatures which should be detectable at the LHC. Heavy Higgs boson decays into mirror particles and an analysis of the forward-backward asymmetries can distinguish a mirror generation from a sequential fourth generation. The validity of the model can thus be tested at the LHC. A model of the type discussed here could arise from a more unified structure such as grand unification or strings where a mirror generation escapes the survival hypothesis, i.e., a generation and a mirror generation do not tie up to acquire a mass of size $M_{\mathrm{GUT}}$ or $M_{\mathrm{string}}$ due to a symmetry, and thus remain massless down to the electroweak scale.

Various processes have been proposed previously to study $a_0^0(980)\mathrm{\text{−}}{f}_0(980)$ mixing through the $f_0(980)\to a_0^0(980)$ transition. Here we investigate in detail the difference between $a_0^0(980)\to f_0(980)$ and $f_0(980)\to a_0^0(980)$ transitions. It is found that the $a_0^0(980)\to f_0(980)$ transition can provide additional constraints to the parameters of $a_0^0(980)$ and $f_0(980)$ mesons. A proposal is made to study $a_0^0(980)\mathrm{\text{−}}{f}_0(980)$ mixing from the ${\chi }_{c1}\to {\pi }^0{a}_0^0(980)\to {\pi }^0{f}_0(980)$ reaction at the upgraded Beijing electron positron collider with the BESIII detector.