We develop the formalism necessary to study four-point functions of the cosmic microwave background (CMB) temperature and polarization fields. We determine the general form of CMB trispectra, with the constraints imposed by the assumption of statistical isotropy of the CMB fields, and derive expressions for their estimators, as well as their Gaussian noise properties. We apply these techniques to initial non-Gaussianity of a form motivated by inflationary models. Because of the large number of four-point configurations, the sensitivity of the trispectra to initial non-Gaussianity approaches that of the temperature bispectrum at high multipole moment. These trispectra techniques will also be useful in the study of secondary anisotropies induced, for example, by the gravitational lensing of the CMB by the large scale structure of the universe.

We compute the gravitational self-force (or “radiation reaction” force) acting on a particle falling radially into a Schwarzschild black hole. Our calculation is based on the “mode-sum” method, in which one first calculates the individual l-multipole contributions to the self-force (by numerically integrating the decoupled perturbation equations) and then regularizes the sum over modes by applying a certain analytic procedure. We demonstrate the equivalence of this method with the $\zeta$-function scheme. The convergence rate of the mode-sum series is considerably improved here (thus reducing computational requirements) by employing an analytic approximation at large l.

We investigate what could be learned about the absolute scale of neutrino masses from comparisons among the patterns within quark and lepton mass hierarchies. First, we observe that the existing information on neutrino masses fits quite well the unexplained, but apparently present regularities in the quark and charged lepton sectors. Second, we discuss several possible mass patterns, pointing out that this is consistent with hierarchical neutrino mass patterns especially disfavoring the vacuum solution.

A nonperturbative approach to two-dimensional covariant gauge QCD is presented in the context of the Schwinger-Dyson equations and the corresponding Slavnov-Taylor identities. The distribution theory, complemented by the dimensional regularization method, is used in order to treat correctly the infrared singularities which inevitably appear in the theory. By working out the multiplicative renormalization program, we remove them from the theory on general grounds and in a self-consistent way, proving thus the infrared multiplicative renormalizability of two-dimensional QCD within our approach. This makes it possible to sum up the infinite series of the corresponding planar skeleton diagrams in order to derive a closed set of equations for the infrared renormalized quark propagator. We have shown that complications due to ghost degrees of freedom can be considerable within our approach. It is shown exactly that 2D covariant gauge QCD implies quark confinement (the quark propagator has no poles, indeed) as well as the dynamical breakdown of chiral symmetry (a chiral symmetry preserving solution is forbidden). We also show explicitly how to formulate the bound-state problem and the Schwinger-Dyson equations for the gluon propagator and the triple gauge field proper vertex, all free from the severe infrared singularities.

Nonperturbative and perturbative interaction mechanisms of Wilson loops are studied within the background field formalism. The first one operates when the distance between the minimal surfaces of the loops is small and may be important for sea quark effects and strong decay processes. The second mechanism—the perturbative interaction in a nonperturbative confining background—is found to be physically dominant for all loop configurations characteristic of scattering processes. It reduces to perturbative gluon exchanges at small distances, while at larger distances it corresponds to the t-channel exchange of glueball states. A comparison to other approaches is made and the possible physical applications are discussed.

Inspired by the recent Heidelberg-Moscow double beta decay experiment, we discuss the neutrinoless double beta decay in the supersymmetric seesaw model. Our numerical analysis indicates that we can naturally explain the data of the observed neutrinoless double beta decay, as well as that of the solar and atmospheric neutrino experiments with at least one Majorana-like sneutrino of middle energy scale in the model.

We consider a 5D SUSY ${\mathrm{SU}\left(3\right)\mathrm{}}_c\times {\mathrm{SU}\left(2\right)\mathrm{}}_L\times {U\left(1\right)\mathrm{}}_Y\times \mathcal{U}\mathrm{}\left(1\right)\mathrm{}$ model compactified on an $S^{\mathrm{}\left(1\right)\mathrm{}}{/Z}_2$ orbifold. To cancel anomalies arising from the presence of $\mathcal{U}\mathrm{}\left(1\right),$ we employ a Chern-Simons term and also chiral fields which could reside on the brane or in the bulk depending on the model. The presence of $\mathcal{U}\mathrm{}\left(1\right)\mathrm{}$ symmetry leads to baryon number conservation, gives rise to matter parity, and permits satisfactory neutrino masses and mixings even for a low fundamental scale. The brane Fayet-Iliopoulos D terms naturally break $\mathcal{U}\mathrm{}\left(1\right),$ leaving $N=1\mathrm{}$ SUSY unbroken in 4 dimensions.

We analyze theories in which a supersymmetric sector is coupled to a supersymmetry-breaking sector described by a nonlinear realization. We show how to consistently couple $\mathcal{N}=1\mathrm{}$ supersymmetric matter to nonsupersymmetric matter in such a way that all interactions are invariant under nonlinear supersymmetry transformations. We extend this formalism to couple $\mathcal{N}=2\mathrm{}$ supersymmetric matter to $\mathcal{N}=1\mathrm{}$ superfields that lack $\mathcal{N}=2\mathrm{}$ partners but transform in a nonlinear representation of the $\mathcal{N}=2\mathrm{}$ algebra. In particular, we show how to couple an $\mathcal{N}=2\mathrm{}$ vector to $\mathcal{N}=1\mathrm{}$ chiral fields in a consistent way. This has important applications to effective field theories describing the interactions of D-brane world-volume fields with bulk fields. We apply our method to study systems where different sectors break different halves of supersymmetry, which appear naturally in models of intersecting branes.

We reexamine the mass mixing and $\mathrm{CP}$ violation in the $B\overline{B}$ system in general ${\mathrm{SU}\left(2\right)\mathrm{}}_L\times {\mathrm{SU}\left(2\right)\mathrm{}}_R\times U\left(1\right)\mathrm{}$ models related to recent measurements without imposing manifest or pseudomanifest left-right symmetry. For certain parameter sets, the right-handed contributions can be sizable in $B\overline{B}$ mixing and $\mathrm{CP}$ asymmetry in B decays for a heavy $W^{\prime }$ even with a mass about 3 TeV. On the other hand the lower bound on the mass of $W^{\prime }$ can be taken down to approximately 300 GeV.

We present a new formalism describing neutralino physics in the context of the minimal supersymmetric standard model (MSSM), where $\mathrm{CP}$ violation induced by complex $M_1$ and $\mu$ parameters is allowed. The formalism is based on the construction of neutralino projectors, and can be directly generalized to nonminimal supersymmetric (SUSY) models involving any number of neutralinos. It extends a previous work applied to the real SUSY parameter case. In the MSSM, the method allows us to describe all physical observables related to a specific neutralino in terms of its $\mathrm{CP}$ eigenphase and three complex numbers called its “reduced projector elements.” As an example, $\sigma {(e}^{-}{e}^{+}\to {\tilde{\chi }}_i^0{\tilde{\chi }}_j^0)$ is presented in this language. As the experimental knowledge on the neutralino-chargino sectors is accumulated, the problem of extracting the various SUSY parameters will arise. Motivated by this, we consider various scenarios concerning the quantities that could be measured first. Analytical disentangled expressions determining the related SUSY parameters from them are then derived, which emphasize the efficiency of the formalism.

We explore the possible enhancement of the direct $\mathrm{CP}$-violating parameter ${\epsilon }^{\prime }/\epsilon$ in the general left-right model based on the $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\times \mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_R\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ gauge group. The mixing matrix of right-handed quarks, $V_{\mathrm{CKM}}^R,$ is observable in the left-right model, and provides a new source of the $\mathrm{CP}$-violating phase. We calculate the parameter ${\epsilon }^{\prime }/\epsilon$ in the left-right model and show that the new phases from $V_{\mathrm{CKM}}^R$ can yield a sizable contribution to the direct $\mathrm{CP}$ violation, enough to satisfy the recent measurements of $\mathrm{Re}({\epsilon }^{\prime }/\epsilon )$ from Fermilab KTeV and CERN NA48 experiments.

We present a new next-to-leading order calculation for fully differential single-top-quark final states. The calculation is performed using phase space slicing and dipole subtraction methods. The results of the methods are found to be in agreement. The dipole subtraction method calculation retains the full spin dependence of the final state particles. We show a few numerical results to illustrate the utility and consistency of the resulting computer implementations.

We present a complete set of one-loop matrix elements relevant for the hadroproduction of heavy quarks in next-to-leading order employing dimensional regularization to isolate ultraviolet and soft divergences. All results of the perturbative calculation are given in detail. These one-loop matrix elements can also be used as input in the determination of the corresponding next-to-leading-order cross sections for heavy flavor photoproduction and in photon-photon reactions, as well as for any of the relevant crossed processes. Our results are tested against the results of other related studies in which unpolarized and longitudinally polarized processes were considered.

In the framework of potential nonrelativistic QCD, we obtain the next-to-leading-log renormalization-group running of the matching coefficients for the heavy-quarkonium production currents near threshold. This allows us to obtain S-wave heavy-quarkonium production or annihilation observables with next-to-leading-log accuracy within perturbative QCD. In particular, we give expressions for the decays of heavy quarkonium to $e^{+}{e}^{-}$ and to two photons. We also compute the $O\left(m{\alpha }^8{\ln }^3\alpha \right)$ corrections to the hydrogen spectrum.

We put constraints on several products of R-parity violating $\lambda {\lambda }^{\prime }$ and ${\lambda }^{\prime }{\lambda }^{\prime }$ type couplings from leptonic and semileptonic $\tau ,$ $B_d,$ and $B_s$ decays. Most of them are one to two orders of magnitude better than the existing bounds, and almost free from theoretical uncertainties. A significant improvement of these bounds can be made in high luminosity tau charm or B factories.

From $J/\overrightarrow{\psi }p\overline{p},$ $\Lambda \overline{\Lambda },$ ${\Sigma }^0{\overline{\Sigma }}^0,$ and ${\Xi }^{+}{\Xi }^{-}$ decays we study the structure of baryons including nucleons, $\Lambda ,$ $\Sigma ,$ and $\Xi$ in the naive quark model. Considering the lowest-order quark diagrams for baryon-antibaryon pair production from $J/\psi$ decays we calculate the baryon-antibaryon angular distributions. Using the experimental data for the angular distribution for the process $J/\overrightarrow{\psi }p\overline{p}$ produced in $e^{+}{-e}^{-}$ collisions, we determine the range of parameters for the quark mass $m_q$ and the harmonic-oscillator parameter $\beta$ in the quark model. With these parameters, we calculate the branching fractions and angular distributions for the above $J/\psi$ decay processes and find that the calculated values are comparable with the measured ones.

In a two-flavor color superconductor, the ${\mathrm{SU}\left(3\right)\mathrm{}}_c$ gauge symmetry is spontaneously broken by diquark condensation. The Nambu-Goldstone excitations of the diquark condensate mix with the gluons associated with the broken generators of the original gauge group. It is shown how one can decouple these modes with a particular choice of ’t Hooft gauge. We then explicitly compute the spectral density for transverse and longitudinal gluons of adjoint color 8. The Nambu-Goldstone excitations give rise to a singularity in the real part of the longitudinal gluon self-energy. This leads to a vanishing gluon spectral density for energies and momenta located on the dispersion branch of the Nambu-Goldstone excitations.

The polarization measurement in inclusive B decay provides us with a simple test of how much the long-distance final-state interaction takes place as the energy of the observed meson varies in the final state. We give the expectation of perturbative QCD for the energy dependence of the helicity fractions in a semiquantitative form. Experiment will tell us for which decay processes the perturbative QCD calculation should be applicable.

Calculations of observables in quantum chromodynamics can be performed using a method in which all of the integrations, including integrations over virtual loop momenta, are performed numerically. We use the flexibility inherent in this method in order to perform next-to-leading order calculations for event shape variables in electron-positron annihilation in the Coulomb gauge. The use of the Coulomb gauge provides the potential to go beyond a purely order ${\alpha }_s^2$ calculation by including, for instance, renormalon or parton showering effects. We expect that the approximations needed to include such effects at all orders in ${\alpha }_s$ will be simplest in a gauge in which unphysically polarized gluons do not propagate over long distances.

We calculate the QCD corrections to the cross section of $e^{+}{e}^{-}\to t\overline{b}{H}^{-}$ and its charge-conjugate counterpart within the minimal supersymmetric extension of the standard model. This process is particularly important if $m_t<m_H{+m}_b$ and $\sqrt{s}<{2m}_H,$ so that $\overrightarrow{t}{\mathrm{bH}}^{+}$ and $e^{+}{e}^{-}\to H^{+}{H}^{-}$ are not allowed kinematically. Large logarithmic corrections that arise in the on-mass-shell scheme of quark mass renormalization, especially from the $t\overline{b}{H}^{-}$ Yukawa coupling for large values of $\tan \beta ,$ are resummed by adopting the modified minimal-subtraction scheme, so that the convergence behavior of the perturbative expansion is improved. The inclusion of the QCD corrections leads to a significant reduction of the theoretical uncertainties due to scheme and scale dependences.