We study forward and backward $\pi -\pi$ scattering within a QCD model based on the Dyson-Schwinger, Bethe-Salpeter equations truncated to the rainbow-ladder level. Our microscopic relativistic quark formulation preserves chiral symmetry and reproduces the observed scattering lengths for total isospin zero, one and two. At higher energies both scalar and vector meson resonances naturally occur in the scattering amplitudes. We also report a comparative study with phenomenological meson-exchange models and find such approaches are reasonable especially near $\pi -\pi$ resonances.

We study 4D QED in which one spatial dimension is dynamically generated from the 3D action, following the mechanism proposed by Arkani-Hamed, Cohen, and Georgi. In this model, the generated fourth dimension is discretized by an interval parameter a. We examine the phenomenological constraint on the parameter a coming from collider experiments on the QED process $e^{+}{e}^{-}\to \gamma \gamma .$ It is found that the CERN $e^{+}{e}^{-}$ collider LEP2 experiments give the constraint of $1/a\gtrsim 461\mathrm{GeV}.$ The expected bound on the same parameter a at a future $e^{+}{e}^{-}$ linear collider is briefly discussed.

We present a phenomenological study of $\tau$ sleptons ${\tilde{\tau }}_{1,2}$ and $\tau$ sneutrinos ${\tilde{\nu }}_{\tau }$ in the minimal supersymmetric standard model with complex parameters $A_{\tau },$ $\mu$ and $M_1.$ We analyze the production and decays of the ${\tilde{\tau }}_{1,2}$ and ${\tilde{\nu }}_{\tau }$ at a future $e^{+}{e}^{-}$ collider. We present numerical predictions for the important decay rates, paying particular attention to their dependence on the complex parameters. The branching ratios of the fermionic decays of ${\tilde{\tau }}_1$ and ${\tilde{\nu }}_{\tau }$ show a significant phase dependence for $\tan \beta \lesssim 10.$ For $\tan \beta \gtrsim 10$ the branching ratios for the ${\tilde{\tau }}_2$ decays into Higgs bosons depend very sensitively on the phases. We show how information on the phase ${\phi }_{A_{\tau }}$ and the other fundamental ${\tilde{\tau }}_i$ parameters can be obtained from measurements of the ${\tilde{\tau }}_i$ masses, polarized cross sections and bosonic and fermionic decay branching ratios, for small and large $\tan \beta$ values. We estimate the expected errors of these parameters. Given favorable conditions, the error of $A_{\tau }$ is about 10% to 20%, while the errors of the remaining stau parameters are in the range of approximately 1% to 3%. We also show that the induced electric dipole moment of the $\tau$ lepton is well below the current experimental limit.

We calculate the Yukawa corrections of order $\mathcal{O}\left({\alpha }_{\mathrm{ew}}{m}_{t\left(b\right)\mathrm{}}^2{/m}_W^2\right),$ $\mathcal{O}\left({\alpha }_{\mathrm{ew}}{m}_{t\left(b\right)\mathrm{}}^3{/m}_W^3\right),$ and $\mathcal{O}\left({\alpha }_{\mathrm{ew}}{m}_{t\left(b\right)\mathrm{}}^4{/m}_W^4\right)$ to the widths of the decays $t_2\to t_1{+(h}^0{,H}^0{,A}^0)$ in the minimal supersymmetric standard model, and perform a detailed numerical analysis. We also compare the results with the ones presented in earlier literature, where the $\mathcal{O}\left({\alpha }_s\right)$ supersymmetric (SUSY) QCD corrections to the same three decay processes have been calculated. Our numerical results show that, for the decays $t_2\to t_1{+h}^0,t_2\to t_1{+H}^0,$ the Yukawa corrections are significant in most of the parameter range, and can reach approximately 10%; for the decay $t_2\to t_1{+A}^0,$ the Yukawa corrections are smaller, only a few percent. The numerical calculations also show that using the running quark masses and the running trilinear coupling $A_t,$ including the QCD, SUSY QCD, and SUSY-electroweak effects, and resumming all high order $\left(\tan \beta \right)$-enhanced effects, can vastly improve the convergence of the perturbation expansion. We also discuss the effects of the running of the Higgsino mass parameter $\mu$ on the corrections, and find that they are significant, too, especially for large $\tan \beta .$

Theoretical predictions show that at low values of Bjorken x the spin structure function $g_1$ is influenced by large logarithmic corrections ${\ln }^2\mathrm{}(1/x),$ which may be predominant in this region. These corrections are also partially contained in the next leading order (NLO) part of the standard Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution. Here we calculate the nonsinglet component of the nucleon structure function, $g_1^{\mathrm{NS}}{=g}_1^p-g_1^n,$ and its first moment, using a unified evolution equation. This equation incorporates the terms describing the NLO DGLAP evolution and the terms contributing to the ${\ln }^2\mathrm{}(1/x)\mathrm{}$ resummation. In order to avoid double counting in the overlapping regions of the phase space, a unique way of including the NLO terms into the unified evolution equation is proposed. The scheme-independent results obtained from this unified evolution are compared to the NLO fit to experimental data, GRSV2000. An analysis of the first moments of $g_1^{\mathrm{NS}}$ shows that the unified evolution including the ${\ln }^2\mathrm{}(1/x)\mathrm{}$ resummation goes beyond the NLO DGLAP analysis. Corrections generated by double logarithms at low x influence the $Q^2$ dependence of the first moments strongly.

The infrared behavior of the medium modified gluon propagator in nonequilibrium situations is studied in the covariant gauge using the Schwinger-Keldysh closed-time path formalism. It is shown that the magnetic screening mass is nonzero at the one loop level whenever the initial gluon distribution function is nonisotropic with the assumption that the distribution function of the gluon is not divergent at zero transverse momentum. For isotropic gluon distribution functions, such as those describing local equilibrium, the magnetic mass at the one loop level is zero, which is consistent with finite temperature field theory results. Assuming that a reasonable initial gluon distribution function can be obtained from a perturbative QCD calculation of minijets, we determine these out of equilibrium values for the initial magnetic and Debye screening masses at energy densities appropriate to BNL RHIC and CERN LHC. We also compare the magnetic masses obtained here with those obtained using finite temperature lattice QCD methods at similar temperatures at RHIC and LHC.

A generalization of the pinch technique to all orders in perturbation theory is presented. The effective Green’s functions constructed with this procedure are singled out in a unique way through the full exploitation of the underlying Becchi-Rouet-Stora-Tyutin symmetry. A simple all-order correspondence between the pinch technique and the background field method in the Feynman gauge is established.

We propose an alternative perturbative expansion for QCD. All scheme and scale dependence is reduced to one free parameter. Fixing this parameter with a fastest apparent convergence criterion gives sensible results in the whole energy region. We apply the expansion to the calculation of the zero flavor triple gluon vertex, the quark gluon vertex, the gluon propagator, and the ghost propagator. A qualitative agreement with the corresponding lattice results is found.

We perform a careful analysis of constraints on the neutrino mass from current cosmological data. Combining data from the cosmic microwave background and the 2dF galaxy survey yields an upper limit on the sum of the three neutrino mass eigenstates of $\sum m_{\nu }<~3\mathrm{eV}$ (95% C.L.), without including additional priors. Including data from SNIa observations, big bang nucleosynthesis, and HST Hubble key project data on $H_0$ tightens the limit to $\sum m_{\nu }<~2.5\mathrm{eV}$ (95% C.L.). We also perform a Fisher matrix analysis which illustrates the cosmological parameter degeneracies affecting the determination of $\sum m_{\nu }.$

We study gravitational waves propagating through an anisotropic Bianchi type I dust-filled universe (containing the Einstein–de Sitter universe as a special case). The waves are modeled as small perturbations of this background cosmological model and we choose a family of null hypersurfaces in this space-time to act as the histories of the wave fronts of the radiation. We find that the perturbations we generate can describe pure gravitational radiation if and only if the null hypersurfaces are shear-free. We calculate the gauge-invariant small perturbations explicitly in this case. How these differ from the corresponding perturbations when the background space-time is isotropic is clearly exhibited.

We study the peculiar motion of nonrelativistic matter in a fully covariant way. The exact nonlinear equations are derived and then applied to the case of pressure-free matter, moving relatively to a quasi-Newtonian Eulerian frame. Our two-frame formalism facilitates the study of the nonlinear kinematics of the matter, as the latter decouples from the background expansion and starts to “turn around” and collapse. Applied to second perturbative order, our equations provide a fully covariant formulation of the Zeldovich approximation, which by construction addresses the mildly nonlinear regime of structure formation. Employing a dynamical system approach, we show that, just like in the Newtonian case, the relativistic treatment also predicts that pancakes are the natural end structures for any generic overdensity.

We study the problem of vortex solutions in the background of an electrically charged black string. We show numerically that the Abelian Higgs field equations in the background of a four-dimensional black string have vortex solutions. These solutions which have axial symmetry show that the black string can support the Abelian Higgs field as hair. This situation holds also in the case of the extremal black string. We also consider the self-gravity of the Abelian Higgs field and show that the effect of the vortex is to induce a deficit angle in the metric under consideration.

We find quasinormal modes of near extremal black branes by solving a singular boundary value problem for the Heun equation. The corresponding eigenvalues determine the dispersion law for the collective excitations in the dual strongly coupled $\mathcal{N}=4\mathrm{}$ supersymmetric Yang-Mills theory at finite temperature.

The flatness of an accelerating universe model (characterized by a dark energy scalar field $\chi )$ is mimicked from a curved model that is filled with, apart from the cold dark matter component, a quintessencelike scalar field Q. In this process, we characterize the original scalar potential $V\left(Q\right)\mathrm{}$ and the mimicked scalar potential $V\left(\chi \right)$ associated with the scalar fields Q and $\chi ,$ respectively. The parameters of the original model are fixed through the mimicked quantities that we relate to the present astronomical data, such as the equation of state parameter $w_{\chi }$ and the dark energy density parameter ${\Omega }_{\chi }.$

We investigate light-cone structure on the world volume of an unstable D-brane with a tachyon decaying inhomogeneously by using a field theoretical description. It is shown that (i) light cones governing open strings are narrower than those governing closed strings and will eventually collapse inward in all directions except at kinks, where the tachyon remains at the top of its potential, and that (ii) light cones governing open strings at a kink will be narrowed only in the direction perpendicular to the kink surface. It is also shown that (iii) future-directed light cones governing open strings near a kink are tilted towards the kink, compared with those governing closed strings. Result (i) implies that open strings except at kinks are redshifted, compared with closed strings, and will eventually cease to be dynamical. On the other hand, result (ii) shows that open strings on a kink surface can move freely along the kink surface and are dynamical but do not feel the existence of the spatial dimension perpendicular to the kink surface. Result (iii) indicates that open strings near a kink have a tendency to move towards the kink. Hence, the light-cone structure vividly illustrates how open strings behave during the dynamical formation of a kink. We also discuss about a possibility that the early universe has a network of various dimensional D-branes, black-branes, and tachyon matter. A problem associated with the network and a possible solution to the problem are discussed.

Using a specific model for the expansion rate of the Universe as a function of scale factor, it is demonstrated that the equation of state of the dark energy cannot be determined uniquely from observations at redshifts $z\lesssim \mathrm{a}\mathrm{}\mathrm{few}$ unless the fraction of the mass density of the Universe in nonrelativistic particles, ${\Omega }_M,$ somehow can be found independently. A phenomenological model is employed to discuss the utility of additional constraints from the formation of large scale structure and the positions of cosmic microwave background peaks in breaking the degeneracy among models for the dark energy.

We explore the constant intensity cut method that is widely used for the derivation of the cosmic ray energy spectrum, for comparisons of data obtained at different atmospheric depths, for measuring average shower profiles, and for estimates of the proton-air cross section from extensive air shower data. The constant intensity cut method is based on the selection of air showers by charged particle or muon size and therefore is subject to intrinsic shower fluctuations. We demonstrate that, depending on the selection method, shower fluctuations can strongly influence the characteristics of the selected showers. Furthermore, a mixture of different primaries in the cosmic ray flux complicates the interpretation of measurements based on the method of constant intensity cuts. As an example we consider data published by the Akeno Collaboration. The interpretation of the Akeno measurements suggests that more than $60-70\%$ of cosmic ray primaries in the energy range ${10}^{16}-{10}^{17}\mathrm{eV}$ are heavy nuclei. Our conclusions depend only weakly on the hadronic interaction model chosen to perform the simulations, namely SIBYLL and QGSJET.

Protons accelerated in the cores of active galactic nuclei can effectively produce neutrinos only if the soft radiation background in the core is sufficiently high. We find restrictions on the spectral properties and luminosity of blazars under which they can be strong neutrino sources. We analyze the possibility that the neutrino flux is highly beamed along the rotation axis of the central black hole. The enhancement of the neutrino flux compared to the GeV $\gamma$-ray flux from a given source makes the detection of neutrino point sources more probable. At the same time the smaller open angle reduces the number of possible neutrino-loud blazars compared to the number of $\gamma$-ray loud ones. We present a table of 15 blazars which are the most likely candidates for the detection by future neutrino telescopes.

In the quest to develop viable designs for third-generation optical interferometric gravitational-wave detectors (e.g., LIGO-III and EURO), one strategy is to monitor the relative momentum or speed of the test-mass mirrors, rather than monitoring their relative position. A previous paper analyzed a straightforward but impractical design for a speed-meter interferometer that accomplishes this. This paper describes some practical variants of speed-meter interferometers. Like the original interferometric speed meter, these designs in principle can beat the gravitational-wave standard quantum limit (SQL) by an arbitrarily large amount, over an arbitrarily wide range of frequencies. These variants essentially consist of a Michelson interferometer plus an extra “sloshing” cavity that sends the signal back into the interferometer with opposite phase shift, thereby cancelling the position information and leaving a net phase shift proportional to the relative velocity. In practice, the sensitivity of these variants will be limited by the maximum light power $W_{\mathrm{circ}}$ circulating in the arm cavities that the mirrors can support and by the leakage of vacuum into the optical train at dissipation points. In the absence of dissipation and with squeezed vacuum (power squeeze factor $e^{-2R}\simeq 0.1)$ inserted into the output port so as to keep the circulating power down, the SQL can be beat by ${h/h}_{\mathrm{SQL}}\sim \sqrt{W_{\mathrm{circ}}^{\mathrm{SQL}}{e}^{-2R}{/W}_{\mathrm{circ}}}$ at all frequencies below some chosen $f_{\mathrm{opt}}\simeq 100\mathrm{Hz}.$ Here $W_{\mathrm{circ}}^{\mathrm{SQL}}\simeq 800\mathrm{kW}{(f}_{\mathrm{opt}}/100\mathrm{}\mathrm{}\mathrm{Hz}{)}^3$ is the power required to reach the SQL in the absence of squeezing. (However, as the power increases in this expression, the speed meter becomes more narrow band; additional power and reoptimization of some parameters are required to maintain the wide band. See Sec. III B.) Estimates are given of the amount by which vacuum leakage at dissipation points will debilitate this sensitivity (see Fig. 12); these losses are 10% or less over most of the frequency range of interest $\left(f\gtrsim 10\mathrm{Hz}\right).\mathrm{}$ The sensitivity can be improved, particularly at high freqencies, by using frequency-dependent homodyne detection, which unfortunately requires two 4-km-long filter cavities (see Fig. 4).

A commonly accepted mechanism of generating baryon asymmetry in the minimal supersymmetric standard model (MSSM) depends on the CP violating relative phase between the gaugino mass and the Higgsino $\mu$ term. The direct constraint on this phase comes from the limit of electric dipole moments (EDM’s) of various light fermions. To avoid such a constraint, a scheme which assumes that the first two generation sfermions are very heavy is usually evoked to suppress the one-loop EDM contributions. We point out that under such a scheme the most severe constraint may come from a new contribution to the electric dipole moment of the electron, the neutron, or atoms via the chargino sector at the two-loop level. As a result, the allowed parameter space for baryogenesis in the MSSM is severely constrained, independent of the masses of the first two generation sfermions.