In the most minimal seesaw model with two heavy right-handed neutrinos, we generalize the Frampton-Glashow-Yanagida Ansatz for the $3\times 2$ Dirac neutrino mass matrix and show that the determinant of the $3\times 3$ light Majorana neutrino mass matrix M always vanishes. Parametrizing M in terms of three neutrino masses, three lepton mixing angles, and three $\mathrm{CP}$-violating phases, we examine all its possible one-zero textures with one vanishing mass eigenvalue. We find that three one-zero patterns of M with $m_1=0\mathrm{}$ and four one-zero patterns of M with $m_3=0\mathrm{}$ are compatible with current neutrino oscillation data. The implications of these phenomenological Ansätze on the neutrino mass spectrum and the neutrinoless double beta decay are also discussed.

The branching ratio of $J/\overrightarrow{\psi }{K}_S^0{K}_L^0$ is measured with improved precision to be $\mathcal{B}(J/\overrightarrow{\psi }{K}_S^0{K}_L^0)=(1.82\mathrm{}\pm 0.04\pm 0.13)\times {10}^{-4}$ using $J/\psi$ data collected with the Beijing Spectrometer (BESII) at the Beijing Electron-Positron Collider. This result is used to test the perturbative QCD prediction between $\psi \mathrm{}\left(2S\right)\mathrm{}$ and $J/\psi$ decays and to investigate the relative phase between the three-gluon and one-photon annihilation amplitudes in $J/\psi$ decays.

The neutrino sector in a left-right extension of the standard model depends on how ${\mathrm{SU}\left(2\right)\mathrm{}}_R$ is broken. I list all possible scenarios, including the ones where the Majorana ${\nu }_R$ mass is naturally much smaller than the ${\mathrm{SU}\left(2\right)\mathrm{}}_R$ breaking scale, which is desirable for generating the proper baryon asymmetry of the Universe. The best such choice is identified and discussed.

Renormalization-group (RG) flow equations have been derived for the generalized sine-Gordon model (GSGM) and the Coulomb gas (CG) in $d>~3$ of dimensions by means of the Wegner-Houghton method, and by way of the real-space RG approach. The UV scaling laws determined by the leading-order terms of the flow equations are in qualitative agreement for all dimensions $d>~3,$ independent of the dimensionality, and in sharp contrast to the special case $d=2.\mathrm{}$ For the 4-dimensional GSGM it is demonstrated explicitly (by numerical calculations) that the blocked potential tends to a constant effective potential in the infrared limit, satisfying the requirements of periodicity and convexity. The comparison of the RG flows for the three-dimensional GSGM, the CG, and the vortex-loop gas reveals a significant dependence on the renormalization schemes and the approximations used.

We investigate the appearance of closed timelike curves in quotients of plane waves along spacelike isometries. First we formulate a necessary and sufficient condition for a quotient of a general space-time to preserve stable causality. We explicitly show that the plane waves are stably causal; in passing, we observe that some pp waves are not even distinguishing. We then consider the classification of all quotients of the maximally supersymmetric ten-dimensional plane wave under a spacelike isometry, and show that the quotient will lead to closed timelike curves iff the isometry involves a translation along the u direction. The appearance of these closed timelike curves is thus connected to the special properties of the light cones in plane wave space-times. We show that all other quotients preserve stable causality.

We show that by imposing local $Z_{13}\otimes Z_3$ symmetries in an $\mathrm{SU}\left(2\right)\mathrm{}\otimes U\left(1\right)\mathrm{}$ electroweak model we can implement an invisible axion in such a way that (i) the Peccei-Quinn symmetry is an automatic symmetry of the classical Lagrangian, and (ii) the axion is protected from semiclassical gravitational effects. In order to be able to implement such a large discrete symmetry, and at the same time allow a general mixing in each charge sector, we introduce right-handed neutrinos and enlarge the scalar sector of the model. The domain wall problem is briefly considered.

We show that a minithermal inflation occurs naturally in a class of gauge mediation models of supersymmetry (SUSY) breaking, provided that the reheating temperature $T_R$ of the primary inflation is much higher than the SUSY-breaking scale, say $T_R>{10}^{10}\mathrm{GeV}.$ The reheating process of the thermal inflation produces an amount of entropy, which dilutes the number density of relic gravitinos. This dilution renders the gravitino to be the dark matter in the present Universe. The abundance of the gravitinos is independent of the reheating temperature $T_R,$ once the gravitinos are thermally produced after the reheating of the primary inflation. We find that the thermal leptogenesis takes place at $T_L\simeq {10}^{12}–{10}^{14}\mathrm{GeV}$ for $m_{3/2}\simeq 100\mathrm{keV}–10\mathrm{MeV}$ without any gravitino problem.

The requirement that the minimal supersymmetric standard model (MSSM) remain an acceptable effective field theory up to energies beyond the weak scale constrains the sparticle spectrum, and hence the permissible ranges of cold dark matter neutralino-proton cross sections. Specifically, squarks are generally much heavier than sleptons if no tachyons are to appear before the grand unified theory (GUT) scale $\sim {10}^{16}\mathrm{GeV},$ or even before 10 TeV. We display explicitly the allowed ranges of effective squark and slepton masses at the weak scale, and the cross-section ranges allowed if the MSSM is to remain valid without tachyons up to 10 TeV or the GUT scale. The allowed areas in the cross-section–mass plane for both spin-independent and spin-dependent scattering are significantly smaller than would be allowed if the MSSM were required to be valid only around the weak scale. In addition to a reduction in the maximum cross section, the upper limit on the neutralino mass is greatly reduced when tachyons are avoided, particularly for smaller values of the squark masses.

Motivated by the possible discrepancy between the observed $\mathrm{CP}$ asymmetry and that of the standard model expectation in the decay mode $B^0\to \phi K_S,$ we study the corresponding vector vector decay mode $B^0\to \phi K^{*0}.$ In order to obtain decisive information regarding the $\mathrm{CP}$ violation effect, we make an angular distribution analysis of the decay products, where both the outgoing vector mesons decay into two pseudoscalars. Furthermore, we study the possible effects of new physics using the angular distribution observables.

An updated analysis of all available neutrino oscillation evidence in reactor (Kamland, first 145 days of data) and solar experiments (SK day and night spectra, global rates from Homestake, SAGE, and GALLEX) including the SNOCC and NC data is presented. In the framework of two active neutrino oscillations we determine the allowed regions in neutrino parameter space; we obtain, from the Kamland spectral shape and global signal, the following antineutrino best solution parameters: $\Delta m_{\mathrm{kl}}^2=7.7\mathrm{}\times {10}^{-5}{\mathrm{eV}}^2,{\tan }^2{\theta }_{\mathrm{kl}}=\mathrm{0.98.}\mathrm{}$ The overall effect of the measured observed ratio $R\sim 0.6$ is that the large mixing angle (LMA) region remains the only one that is still favored. Combining Kamland and solar data and assuming CPT invariance, i.e., the same mass matrix for neutrinos and antineutrinos, we obtain the following antineutrino best solution parameters (LMAI solution): $\Delta m^2=7.1\mathrm{}\times {10}^{-5}{\mathrm{eV}}^2,{\tan }^2\theta =\mathrm{0.47.}\mathrm{}$ A second solution (LMAII) appears for values $\Delta m^2=1.5\mathrm{}\times {10}^{-4}{\mathrm{eV}}^2,{\tan }^2\theta =\mathrm{0.48.}\mathrm{}$ We determine additionally individual neutrino mixing parameters and their errors from fits to marginal likelihood distributions; the values are compatible with previous results. In both methods, ${\chi }^2$ minimization and marginal likelihood, the combined analysis of solar and Kamland data concludes that maximal mixing is not favored at the $\sim 3\sigma$ level at least.

The experimental discovery of large ${\nu }_{\mu }-{\nu }_{\tau }$ mixing indicates that analogous mixing in the charged lepton sector could be substantial. We consider the possibility that if a high intensity muon beam, perhaps at the early stages of a muon or neutrino factory, strikes a nuclear target, then conversion of some of the muons into tau leptons could occur (similar to the conversion of muons to electrons at MECO). Using current experimental limits on rare tau decays to bound the size of the relevant operators, we find that a 50 GeV muon beam, with ${10}^{20}$ muons on target per year, could yield as many as ${10}^7\mu +\overrightarrow{N}\tau +N$ events per year. Backgrounds could be substantial, and we comment on the possibility of detection of this process.

Supersymmetric Slavnov-Taylor and Ward identities are investigated in the presence of soft and spontaneous symmetry breaking. We consider an Abelian model where soft supersymmetry breaking yields a mass splitting between electron and selectron and triggers spontaneous symmetry breaking, and we derive the corresponding identities that relate the electron and selectron masses to the Yukawa coupling. We demonstrate that the identities are valid in dimensional reduction and invalid in dimensional regularization and compute the necessary symmetry-restoring counterterms.

In a scenario in which fourth generation fermions exist, we study the effects of new physics on the differential decay width, forward-backward asymmetry, and the integrated branching ratio for $\overrightarrow{B}{X}_s{\mathcal{l}}^{+}{\mathcal{l}}^{-}$ decay with $(\mathcal{l}=e,\mu ).\mathrm{}$ The prediction of the new physics on the mentioned quantities essentially differs from the standard model results in certain regions of parameter space; the enhancement of new physics on the above-mentioned physical quantities can yield values as large as 2 times that of the SM predictions, from which present limits of experimental measurements of the branching ratio are spanned, and constraints of the new physics can be extracted. For the fourth generation CKM factor $V_{t^{\prime }b}^{*}{V}_{t^{\prime }s}$ we use $\pm {10}^{-2}$ and $\pm {10}^{-3}$ ranges, take into consideration the possibility of a complex phase where it may bring sizable contributions, and obtain no significant dependence on the imaginary part of the new CKM factor. For the above-mentioned quantities with a new family, deviations from the SM are promising and can be used as a probe of new physics.

The structures of confining vortices which underlie pure $\mathrm{SU}\left(3\right)\mathrm{}$ Yang-Mills theory are studied by means of lattice gauge theory. Vortices and $Z_3$ monopoles are defined as dynamical degrees of freedom of the $Z_3$ gauge theory which emerges by center gauge fixing and by subsequent center projection. It is observed for the first time for the case of $\mathrm{SU}\left(3\right)\mathrm{}$ that these degrees of freedom are sensible in the continuum limit: the planar vortex density and the monopole density properly scales with the lattice spacing. By contrast to earlier findings concerning the gauge group $\mathrm{SU}\left(2\right),$ the effective vortex theory only reproduces 62% of the full string tension. On the other hand, however, the removal of the vortices from the lattice configurations yields ensembles with vanishing string tension. $\mathrm{SU}\left(3\right)\mathrm{}$ vortex matter which originates from Laplacian center gauge fixing is also discussed. Although these vortices recover the full string tension, they lack a direct interpretation as physical degrees of freedom in the continuum limit.

We determine the patterns of spontaneous symmetry breaking in strong-coupling lattice QCD in a fixed background baryon density. We employ a next-nearest-neighbor fermion formulation that possesses the ${SU(N}_f)\times {SU(N}_f)$ chiral symmetry of the continuum theory. We find that the global symmetry of the ground state varies with $N_f$ and with the background baryon density. In all cases the condensate breaks the discrete rotational symmetry of the lattice as well as part of the chiral symmetry group.

We study the SU(2) gauge-Higgs system in $D=4\mathrm{}$ dimensions, and analyze the influence of the fundamental-representation Higgs field on the vortex content of the gauge field. It is shown that center projected Polyakov lines, at low temperature, are finite in the infinite volume limit, which means that the center vortex distribution is consistent with color screening. In addition we confirm and further investigate the presence of a “Kertész line” in the strong-coupling region of the phase diagram, which we relate to the percolation properties of center vortices. It is shown that this Kertész line separates the gauge-Higgs phase diagram into two regions: a confinementlike region, in which center vortices percolate, and a Higgs region, in which they do not. The free energy of the gauge-Higgs system, however, is analytic across the Kertész line.

We present a leading-order PQCD factorization formula for the helicity-flip $\overrightarrow{\Delta }N{\gamma }^{*}$ matrix element $G_0$ (Coulomb quadrupole amplitude $C2),$ taking into account the transverse momenta of the quarks and the contribution from the gluons. In the large $Q^2$ limit, its scaling behavior acquires a double-logarithmic correction ${\log }^2{(Q}^2/{\Lambda }^2)$ compared with the standard scaling analysis, due to the contribution from the orbital motion of the small-x partons. Based on this and on the latest JLab experimental results of the $C2\mathrm{}-M1\mathrm{}$ ratio $R_{\mathrm{SM}}$ at $Q^2=3\mathrm{}–4{\mathrm{GeV}}^2,$ we make a phenomenological prediction for the latter at higher values of $Q^2.$

In the generic supersymmetric standard model which has no global symmetry enforced by hand, lepton number violation is a natural consequence. Supersymmetry, hence, can be considered the source of experimentally demanded properties for the neutrinos beyond the standard model. With an efficient formulation of the model, we perform a comprehensive detailed analysis of all (fermion-scalar) one-loop contributions to neutrino masses.

Recent experimental results on $\overrightarrow{B}\rho \rho$ decays indicate that the CP asymmetry $S_{{\rho }^{+}{\rho }^{-}}$ will give an interesting determination of $\alpha =\arg \left[-{(V}_{\mathrm{td}}{V}_{\mathrm{tb}}^{*}{)/(V}_{\mathrm{ud}}{V}_{\mathrm{ub}}^{*}\right)].$ In the limit when the $\rho$ width is neglected, the $\overrightarrow{B}\pi \pi$ isospin analysis can also be applied to $\overrightarrow{B}\rho \rho ,$ once an angular analysis is used to separate transversity modes. The present bound on the shift of $S_{{\rho }^{+}{\rho }^{-}}$ from the true $\sin 2\alpha$ is already stronger than it is for $S_{{\pi }^{+}{\pi }^{-}}.$ We point out a subtle violation of the isospin relations when the two $\rho$ mesons are observed with different invariant masses, and how to constrain this effect experimentally.

We study the phase structures of $\mathcal{N}=1\mathrm{}$ supersymmetric ${USp(2N}_c)$ gauge theory with $N_f$ flavors in the fundamental representation as we deform the $\mathcal{N}=2\mathrm{}$ supersymmetric QCD by adding the superpotential for an adjoint chiral scalar field. We determine the most general factorization curves for various breaking patterns, for example, the two different breaking patterns of the quartic superpotential. We observe all kinds of smooth transitions for the quartic superpotential. Finally, we discuss the intriguing role of $\mathrm{USp}\left(0\right)\mathrm{}$ in the phase structure and the possible connection with observations made recently by Aganagic, Intriligator, Vafa, and Warner, hep-th/0304271 and Cachazo, hep-th/0307063.