In a recent publication, we suggested a mechanism for obtaining dynamical $CP$ violation in the early universe based on the out-of-equilibrium evolution of complex scalar fields. In this paper, we suggest several ways of transferring the $CP$ asymmetry from the scalar sector to the leptonic sector. In particular, we point out how a “transient Maki-Nakagawa-Sakata (Pontecorvo) matrix” can generate an asymmetry between fermions and antifermions directly.

We analyze the possibility of probing the supersymmetric flavor structure through the constraints of the $K$ and $B$ meson systems and those of the electric dipole moments. We show that combining these constraints would favor SUSY models with large flavor mixing either in $LR(RL)$ or $LL$ but with a very small $RR$ and intermediate/large $\tan \beta$. Large $LR$ mixing requires specific patterns for trilinear $A$ terms, while $LL$ mixing seems quite natural and easier to obtain. We present an example for this class of models and show how it can accommodate the current CP asymmetries experimental results.

In the scenario recently proposed by Arkani-Hamed and Dimopoulos, the supersymmetric scalar particles are all very heavy, at least of the order of ${10}^9\mathrm{GeV}$ but the gauginos, Higgsino, and one of the $CP$-even neutral Higgs bosons remain light under a TeV. In addition to gluino production, the first SUSY signature would be pair production of neutralinos and/or charginos. Here we study, with explicit $CP$ violation, the production of neutralinos and charginos at hadronic colliders as well as the possible decay modes. We notice that the branching ratio of the neutralino radiative decay can be sizable unlike the case with light sfermions. In particular, the decay of ${\tilde{\chi }}_3^0\to {\tilde{\chi }}_1^0\gamma$ has a branching ratio of the order $O(1)$ percent. In colliders, it would give rise to signatures of an isolated single photon plus missing energy.

The nonzero widths of heavy particles become significant when they appear in the final state of any decay occurring just around its kinematical threshold. To take into account such effects, a procedure, called the convolution method, was proposed by Altarelli, Conti, and Lubicz. We expand their study which included only threshold effects for $t\to bWZ$ in the standard model. We discuss finite width effects in the three-body decays $t\to cWW,cZZ$ and $A^0(h^0)\to tbW$ in the type III version of a two-Higgs doublet model. In particular, we find a substantial enhancement in the decay $t\to cZZ$, which brings its branching ratio to $\mathrm{BR}(t\to cZZ)\sim {10}^{-3}$, and in the decay $A^0\to tbW$, which, unlike the $h^0$ case, becomes competitive with the $A^0$ two-body decay modes.

We discuss a new method for obtaining the WKB approximation to the Dirac equation with a scalar potential and a timelike vector potential. We use the WKB solutions to investigate the scaling behavior of a confining model for quark-hadron duality. In this model, a light quark is bound to a heavy diquark by a linear scalar potential. Absorption of virtual photons promotes the quark to bound states. The analog of the parton model for this case is for a virtual photon to eject the bound, ground-state quark directly into free continuum states. We compare the scaling limits of the response functions for these two transitions.

Several positivity bounds are derived for generalized parton distributions (GPDs) with helicity flip.

We report on the calculation of virtual processes contributing to the production of a Higgs boson and two jets in hadron-hadron collisions. The coupling of the Higgs boson to gluons, via a virtual loop of top quarks, is treated using an effective theory, valid in the large top quark mass limit. The calculation is performed by evaluating one-loop diagrams in the effective theory. The primary method of calculation is a numerical evaluation of the virtual amplitudes as a Laurent series in $D-4$, where $D$ is the dimensionality of space-time. For the cases $H\to q\overline{q}q\overline{q}$ and $H\to q\overline{q}{q}^{\prime }{\overline{q}}^{\prime }$ we confirm the numerical results by an explicit analytic calculation.

The merging procedure of tree-level matrix elements and the subsequent parton shower as implemented in the new event generator SHERPA will be validated for the example of single gauge boson production at the CERN LHC. The validation includes consistency checks and comparisons to results obtained from other event generators. In particular, comparisons with full next-to-leading order QCD calculations prove SHERPA’s ability to correctly account for additional hard QCD radiation present in these processes.

We study the Berry phase in neutrino oscillations for both Dirac and Majorana neutrinos. In order to have a Berry phase, the neutrino oscillations must occur in a varying medium, the neutrino-background interactions must depend on at least two independent densities, and also there must be $CP$ violation. If the neutrino interactions with matter are mediated only by the standard model $W$ and $Z$ boson exchanges, these conditions imply that there must be at least three generations of neutrinos. The $CP$ violating Majorana phases do not play a role in generating a Berry phase. We show that a natural way to satisfy the conditions for the generation of a Berry phase is to have sterile neutrinos with active-sterile neutrino mixing, in which case at least two active and one sterile neutrinos are required. If there are additional new $CP$ violating flavor changing interactions, it is also possible to have a nonzero Berry phase with just two generations.

We show that the Hawking-Page phase transition of a conformal field theory on ${\mathrm{AdS}}_{d-1}$ weakly coupled to gravity has a dual bulk description in terms of a phase transition between a black string and a thermal gas on ${\mathrm{AdS}}_d$. At even lower temperatures the black string develops a Gregory Laflamme instability, which is dual to black hole evaporation in the boundary theory.

We study the scattering of low-energy tensor multiplet particles against a Bogomol’nyi-Prasad-Sommerfield (BPS)-saturated cosmic string. We show that the corresponding $S$ matrix is largely determined by symmetry considerations. We then apply a specific supersymmetric model of (2,0) theory and calculate the scattering amplitudes to lowest nontrivial order in perturbation theory. Our results are valid as long as the energy of the incoming particle is much lower than the square root of the string tension. The calculation involves the quantization of a (2,0) tensor multiplet and the derivation of an effective action describing the low-energy particles in the presence of a nearly BPS-saturated string.

We study in some detail the master equation, and its solution in a simplified case modelling flavor oscillations of a two-level system, stemming from the Liouville-string approach to quantum space-time foam. In this framework we discuss the appearance of diffusion terms and decoherence due to the interaction of low-energy string matter with space-time defects, such as D-particles in the specific model of “D-particle foam,” as well as dark-energy contributions. We pay particular attention to contrasting the decoherent role of a cosmological constant in inducing exponential quantum damping in the evolution of low-energy observables, such as the probability of flavor oscillations, with the situation where the dark-energy relaxes to zero for asymptotically large times, in which case such a damping is absent. Our findings may be of interest to (astrophysical) tests of quantum space-time foam models in the not-so-distant future.

We provide detailed evidence for the claim that nonperturbative quantum gravity, defined through state sums of causal triangulated geometries, possesses a large-scale limit in which the dimension of spacetime is four and the dynamics of the volume of the universe behaves semiclassically. This is a first step in reconstructing the universe from a dynamical principle at the Planck scale, and at the same time provides a nontrivial consistency check of the method of causal dynamical triangulations. A closer look at the quantum geometry reveals a number of highly nonclassical aspects, including a dynamical reduction of spacetime to two dimensions on short scales and a fractal structure of slices of constant time.

In the context of pure QED, we obtain analytic expressions for the contributions to the Bhabha scattering differential cross section at order ${\alpha }^4$, which originate from the interference of two-loop photonic vertices with tree-level diagrams and from the interference of one-loop photonic diagrams amongst themselves. The ultraviolet renormalization is carried out. The IR-divergent soft-photon emission corrections are evaluated and added to the virtual cross section. The cross section obtained in this manner is valid for on-shell electrons and positrons of finite mass and for arbitrary values of the center of mass energy and momentum transfer. We provide the expansion of our results in powers of the electron mass, and we compare them with the corresponding expansion of the complete order ${\alpha }^4$ photonic cross section, recently obtained by A. A. Penin [Phys. Rev. Lett. 95, 010408 (2005).]. As a by-product, we obtain the contribution to the Bhabha scattering differential cross section of the interference of the two-loop photonic boxes with the tree-level diagrams, up to terms suppressed by positive powers of the electron mass. We evaluate numerically the various contributions to the cross section, paying particular attention to the comparison between exact and expanded results.

We propose a method to calculate the Green’s function of a free massive scalar field on the lattice numerically to very high precision. For masses $m<2$ (in lattice units) the massive Green’s function can be expressed recursively in terms of the massless Green’s function and just two additional mass-independent constants.

We discuss the associated $W^{\pm }{H}^{\mp }$ production at the CERN large hadron collider. The dependence of the hadronic cross section on the Higgs sector parameters is investigated in detail in the framework of the general two Higgs doublet model (THDM). We study the possible enhancement of the THDM prediction for the cross section compared to the prediction of the minimal supersymmetric standard model (MSSM). We find regions in the THDM parameter space where the THDM prediction can exceed the one of the MSSM by 2 orders of magnitude. These regions of large cross section are in agreement with theoretical bounds on the model, derived from the requirement of vacuum stability and perturbative unitarity, and are not excluded by experimental constraints.

Effects of the 1-3 leptonic mixing on the solar neutrino observables are studied and the signatures of nonzero ${\theta }_{13}$ are identified. For this we have rederived the formula for $3\nu$-survival probability including all relevant corrections and constructed the isocontours of observables in the ${sin}^2{\theta }_{12}\mathrm{\text{−}}{sin}^2{\theta }_{13}$ plane. Analysis of the solar neutrino data gives ${sin}^2{\theta }_{13}={0.007}_{-0.007}^{+0.080}$ (90% C.L.) for $\Delta m^2=8\times {10}^{-5}{\mathrm{eV}}^2$. The combination of the ratio CC/NC at Sudbury Neutrino Observatory (SNO) and gallium production rate selects ${sin}^2{\theta }_{13}=0.017\pm 0.026$ ($1\sigma$). The global fit of all oscillation data leads to zero best value of ${sin}^2{\theta }_{13}$. The sensitivity ($1\sigma$ error) of future solar neutrino studies to ${sin}^2{\theta }_{13}$ can be improved down to 0.01–0.02 by precise measurements of the $pp$-neutrino flux and the CC/NC ratio as well as spectrum distortion at high ($E>4\mathrm{MeV}$) energies. Combination of experimental results sensitive to the low and high energy parts of the solar neutrino spectrum resolves the degeneracy of angles ${\theta }_{13}$ and ${\theta }_{12}$. Comparison of ${sin}^2{\theta }_{13}$ as well as ${sin}^2{\theta }_{12}$ measured in the solar neutrinos and in the reactor/accelerator experiments may reveal new effects which can not be seen otherwise.

We present a complete precision analysis of the sfermion pair production process $e^{+}{e}^{-}\to {\tilde{f}}_i{\overline{\tilde{f}}}_j(f=t,b,\tau ,{\nu }_{\tau })$ in the minimal supersymmetric standard model. Our results extend the previously calculated weak corrections by including all one-loop corrections together with higher order QED corrections. We present the details of the analytical calculation and discuss the renormalization scheme. The numerical analysis shows the results for total cross sections, forward-backward, and left-right asymmetries. It is based on the $\mathrm{SPS}1{\mathrm{a}}^{\prime }$ point from the SPA project. The complete corrections are about 10% and have to be taken into account in a high precision analysis.

We report the results for nucleon decay searches via modes favored by supersymmetric grand unified models in Super-Kamiokande. Using 1489 days of full Super-Kamiokande-I data, we searched for $p\to \overline{\nu }{K}^{+}$, $n\to \overline{\nu }{K}^0$, $p\to {\mu }^{+}{K}^0$, and $p\to e^{+}{K}^0$ modes. We found no evidence for nucleon decay in any of these modes. We set lower limits of partial nucleon lifetime $2.3\times {10}^{33}$, $1.3\times {10}^{32}$, $1.3\times {10}^{33}$, and $1.0\times {10}^{33}\mathrm{years}$ at 90% confidence level for $p\to \overline{\nu }{K}^{+}$, $n\to \overline{\nu }{K}^0$, $p\to {\mu }^{+}{K}^0$, and $p\to e^{+}{K}^0$ modes, respectively. These results give a strong constraint on supersymmetric grand unification models.