Within the framework of the standard model, the exclusive decay mode $\overrightarrow{B}\pi \gamma \gamma$ is studied. Although the usual short distance contribution is small compared to that of the similar $\overrightarrow{B}K\gamma \gamma$ mode, the process offers the possibility of studying CP violation, a feature absent in the $\overrightarrow{B}K$ counterpart.

We reanalyze the mass matrix model of quarks and leptons that gives a unified description of quark and lepton mass matrices with the same texture form. By investigating possible types of assignment for the texture’s components of this mass matrix form, we find that a different assignment for up quarks than for down quarks can lead to consistent values of the CKM mixing matrix. This finding overcomes a weak point in a previous analysis of the model. We also obtain some relations among the CKM mixing matrix parameters, which are independent of evolution effects.

We investigate Higgs boson pair production at hadron colliders for Higgs boson masses $m_H<~140\mathrm{GeV}$ and the rare decay of one of the two Higgs bosons. While in the standard model the number of events is quite low at the CERN Large Hadron Collider (LHC), a first, albeit not very precise, measurement of the Higgs boson self-coupling is possible in the $g\overrightarrow{g}H\overrightarrow{H}b\overline{b}\gamma \gamma$ channel. A luminosity-upgraded LHC could improve this measurement considerably. A 200 TeV very large hadron collider could make a measurement of the Higgs self-coupling competitive with a next-generation linear collider. In the minimal supersymmetric standard model (MSSM) we find a significant region with observable Higgs boson pair production in the small $\tan \beta$ regime, where resonant production of two light Higgs bosons might be the only hint at the LHC of a MSSM Higgs sector.

We present a complete treatment in the strong field limit of gravitational retrolensing by a static spherically symmetric compact object having a photon sphere. The results are compared with those corresponding to ordinary lensing in similar strong field situations. As examples of the application of the formalism, a supermassive black hole at the Galactic center and a stellar mass black hole in the Galactic halo are studied as retrolenses, in both cases using Schwarzschild and Reissner-Nordström geometries.

We use the two-dimensional Kolmogorov-Smirnov (KS) test to study the correlation between the 60 cosmic ray events above $4\times {10}^{19}\mathrm{eV}$ from the Akeno Giant Air Shower Array (AGASA) experiment and the positions of infrared luminous galaxies from the IRAS Point Source Catalog. These galaxies are expected to be hosts to gamma ray bursts (GRB’s) and magnetars, both of which are associated with core collapse supernovae and have been proposed as possible acceleration sites for ultrahigh energy cosmic rays. We find consistency between the models and the AGASA events to have been drawn from the same underlying distribution of positions on the sky with KS probabilities ≳50%. Application of the same test to the 11 highest AGASA events above ${10}^{20}\mathrm{eV},$ however, yields a KS probability of <0.5%, rejecting the models at 99.5% significance level. Taken at face value, these highest energy results suggest that the existing cosmic ray events above ${10}^{20}\mathrm{eV}$ do not owe their origin to long burst GRB’s, rapidly rotating magnetars, or any other events associated with core collapse supernovae. The larger data set expected from the AUGER experiment will test whether this conclusion is real or is a statistical fluke that we estimate to be at the 2σ level.

We derive a set of necessary and sufficient conditions for obtaining $\mathcal{N}=1\mathrm{}$ backgrounds of M theory and type IIA strings in the presence of fluxes. Our metrics are warped products of four-dimensional Minkowski space-time with a curved internal manifold. We classify the different solutions for irreducible internal manifolds as well as for manifolds with $S^1$ isometries by employing the formalism of group structures and intrinsic torsion. We provide examples within these various classes along with general techniques for their construction. In particular, we generalize the Hitchin flow equations so that one can explicitly build irreducible 7-manifolds with a 4-form flux. We also show how several of the examples found in the literature fit in our framework and suggest possible generalizations.

We derive the effective potentials for composite operators in a Nambu–Jona–Lasinio model at zero and finite temperature and show that in each case they are equivalent to the corresponding effective potentials based on an auxiliary scalar field. Both effective potentials could lead to the same possible spontaneous breaking and restoration of symmetries including chiral symmetry if the momentum cutoff in the loop integrals is large enough, and can be transformed to each other when the Schwinger-Dyson equation of the dynamical fermion mass from the fermion-antifermion vacuum (or thermal) condensates is used. The results also generally indicate that two effective potentials with the same single order parameter but rather different mathematical expressions can still be considered physically equivalent if the Schwinger-Dyson equation corresponding to the extreme value conditions of the two potentials have the same form.

Using the Nahm transform we investigate doubly periodic charge-one SU(2) instantons with radial symmetry. Two special points where the Nahm zero modes have softer singularities are identified as the locations of instanton core constituents. For a square torus this constituent picture is closely reflected in the action density. In rectangular tori with large aspect ratios the cores merge to form monopolelike objects. For particular values of the parameters the torus can be cut in half, yielding two copies of a twisted charge-$\frac{1}{2}$ instanton. These findings are illustrated with plots of the action density within a two-dimensional slice containing the constituents.

There are a number of completely integrable gravity theories in two dimensions. We study the metric-affine approach in a two-dimensional spacetime and display a new integrable model. Its properties are described and compared with the known results of Poincaré gauge gravity.

Using the methods developed by Fewster and colleagues, we derive a quantum inequality for the free massive spin-$\frac{3}{2}$ Rarita-Schwinger fields in four dimensional Minkowski spacetime. Our quantum inequality bound for the Rarita-Schwinger fields is weaker, by a factor of 2, than that for the spin-$\frac{1}{2}$ Dirac fields. This fact along with other quantum inequalities obtained by various other authors for the fields of integer spin (bosonic fields) using similar methods lead us to conjecture that, in flat spacetime, separately for bosonic and fermionic fields, the quantum inequality bound gets weaker as the number of degrees of freedom of the field increases. A plausible physical reason might be that the more field degrees of freedom, the more freedom one has to create negative energy, therefore the weaker the quantum inequality bound.

In light of Wilkinson Microwave Anisotropy Probe (WMAP) results, we examine the observational constraint on the P-term inflation. With the tunable parameter f, P-term inflation contains richer physics than D-term and F-term inflationary models. We find the logarithmic derivative spectral index with $n>\mathrm{}1\mathrm{}$ on large scales and $n<\mathrm{}1\mathrm{}$ on small scales in agreement with observation. We obtain a reasonable range for the choice of the gauge coupling constant g in order to meet the requirements of WMAP observation and the expected number of the e-foldings. Although tuning f and g we can have larger values for the logarithmic derivative of the spectral index, it is not possible to satisfy all observational requirements for both the spectral index and its logarithmic derivative at the same time.

We consider a novel contribution to the polarization of the cosmic microwave background induced by vector and tensor modes generated by the nonlinear evolution of primordial scalar perturbations. Our calculation is based on relativistic second-order perturbation theory and allows us to estimate the effects of these secondary modes on the polarization angular power spectra. We show that a nonvanishing B-mode polarization unavoidably arises from pure scalar initial perturbations, thus limiting our ability to detect the signature of primordial gravitational waves generated during inflation. This secondary effect dominates over that of primordial tensors for an inflationary tensor-to-scalar ratio $r<\mathrm{}{10}^{-6}.$ The magnitude of the effect is smaller than the contamination produced by the conversion of polarization of type E into type B, by weak gravitational lensing. However, the lensing signal can be cleaned, making the secondary modes discussed here the actual background limiting the detection of small amplitude primordial gravitational waves.

Various authors have investigated the problem of light deflection by radially moving gravitational lenses, but the results presented so far do not appear to agree on the expected deflection angles. Some publications claim a scaling of deflection angles with $1-v$ to first order in the radial lens velocity $v,$ while others obtained a scaling with $1-2v.$ In this paper we generalize the calculations for arbitrary lens velocities and show that the first result is the correct one. We discuss the seeming inconsistency of relativistic light deflection with the classical picture of moving test particles by generalizing the lens effect to test particles of arbitrary velocity, including light as a limiting case. We show that the effect of radial motion of the lens is very different for slowly moving test particles and light and that a critical test particle velocity exists for which the motion of the lens has no effect on the deflection angle to first order. An interesting and not immediately intuitive result is obtained in the limit of a highly relativistic motion of the lens towards the observer, where the deflection angle of light reduces to zero. This phenomenon is elucidated in terms of moving refractive media. Furthermore, we discuss the dragging of inertial frames in the field of a moving lens and the corresponding Lense-Thirring precession, in order to shed more light on the geometrical effects in the surroundings of a moving mass. In a second part we discuss the effect of transversal motion on the observed redshift of lensed sources. We demonstrate how a simple kinematic calculation explains the effects for arbitrary velocities of the lens and test particles. Additionally we include the transversal motion of the source and observer to show that all three velocities can be combined into an effective relative transversal velocity similar to the approach used in microlensing studies.

We discuss the finite volume corrections to $f_K$ and $B_K$ by using one-loop chiral perturbation theory in full, quenched, and partially quenched QCD. We show that the finite volume corrections to these quantities dominate the physical (infinite volume) chiral logarithms.

In the framework of QCD factorization, we study the B-meson exclusive decays $\overrightarrow{B}{\chi }_{\mathrm{cJ}}K$ where the spin-triplet P-wave charmonium states ${\chi }_{\mathrm{cJ}}\mathrm{}(J=0,1,2\mathrm{})\mathrm{}$ are described by the color-singlet nonrelativistic wave functions. We find that for these decays (except ${\chi }_{c1\mathrm{}})$ there are infrared divergences arising from nonfactorizable vertex corrections as well as logarithmic end-point singularities arising from nonfactorizable spectator interactions at leading-twist order. The infrared divergences due to vertex corrections will explicitly break down QCD factorization within the color-singlet model for charmonia. Unlike in the inclusive decays where the higher Fock states with a color-octet $c\overline{c}$ pair and soft gluon can make contributions to remove the infrared divergences, their contributions cannot be accommodated in the exclusive two-body decays. As a result, the infrared divergences encountered in exclusive processes involving charmonia may raise a new question about QCD factorization and nonrelativistic QCD factorization in B exclusive decays.

In this paper we consider all possible $1D$ and $2P$ $c\overline{c}$ assignments for the recently discovered $X\left(3872\right).$ Taking the experimental mass as input, we give numerical results for the $E1\mathrm{}$ radiative widths as well as the three principal types of strong decays; open-charm, $c\overline{c}$ annihilation and closed-charm hadronic transitions. We find that many assignments may be immediately eliminated due to the small observed total width. The remaining viable $c\overline{c}$ assignments are $1{}^3{D}_3,$ $1{}^3{D}_2,$ $1{}^1{D}_2,$ $2{}^3{P}_1$ and $2{}^1{P}_1.$ A search for the mode $J/\psi {\pi }^0{\pi }^0$ can establish the C parity of the $X\left(3872\right),$ which will eliminate many of these possibilities. Radiative transitions can then be used to test the remaining assignments, as they populate characteristic final states. The $1{}^3{D}_2$ and $1{}^1{D}_2$ states are predicted to have large (ca. 50%) radiative branching fractions to ${\chi }_{c1\mathrm{}}\gamma$ and $h_c\gamma ,$ respectively. We predict that the $1{}^3{D}_3$ will also be relatively narrow and will have a significant (ca. 10%) branching fraction to ${\chi }_{c2\mathrm{}}\gamma ,$ and should also be observable in B decay. Tests for non-$c\overline{c}X\left(3872\right)\mathrm{}$ assignments are also discussed.

We replace the color singlet chain connection in the event generator JETSET with the color separate state one as the interface between the hard and soft sectors of hadronic processes. The modified generator is applied to produce the hadronic events in $e^{+}{e}^{-}$ annihilation. It describes the experimental data at the same level as the original JETSET with default parameters. This should be understood as a demonstration that the color singlet chain is not a unique color connection. We also search for the difference in special sets of three-jet events arising from different color connections, which could be subjected to further experimental tests.

We discuss a model for the study of quark-hadron duality in inclusive electron scattering based on solving the Dirac equation numerically for a scalar confining linear potential and a vector color Coulomb potential. We qualitatively reproduce the features of quark-hadron duality for all potentials considered, and discuss the similarities and differences to previous models that simplified the situation by treating either the quarks or all particles as scalars. We discuss the scaling results for the plane-wave impulse approximation and final-state interactions, and the approach to scaling using the analog of the Callan-Gross relation for y scaling.

We study the effects of the MSSM contribution on $\overrightarrow{B}\phi K$ decays using the perturbative QCD approach. In this approach, strong phases can be calculated, so that we can predict the values of CP asymmetries with the MSSM contribution. We predict a large relative strong phase between the penguin amplitude and the chromomagnetic penguin amplitude. If there is a new CP violating phase in the chromomagnetic penguin amplitude, then the CP asymmetries may change significantly from the SM prediction. We parametrize the new physics contributions that appear in the Wilson coefficients. We maximize the new physics parameters up to the point where it is limited by experimental constraints. In the case of the LR insertion, we find that the direct CP asymmetries can reach about 85% and the indirect CP asymmetry can reach about $-30\%.$

We study the effective chiral Lagrangian in the chiral limit from the instanton vacuum. Starting from the nonlocal effective chiral action, we derive the effective chiral Lagrangian, using the derivative expansion to order ${O(p}^4)$ in the chiral limit. The low energy constants $L_1,$ $L_2,$ and $L_3$ are determined and compared with various models and the corresponding empirical data. The results are in a good agreement with the data. We also discuss the upper limit of the sigma meson, based on the present results.