An $\mathrm{SO}\left(10\right)\mathrm{}$ grand unified model considered previously by the authors featuring lopsided down quark and charged lepton mass matrices is successfully predictive and requires that the lightest two right-handed Majorana neutrinos be nearly degenerate in order to obtain the LMA solar neutrino solution. Here we use this model to test its predictions for baryogenesis through resonant-enhanced leptogenesis. With the conventional type I seesaw mechanism, the best predictions for baryogenesis appear to fall a factor of three short of the observed value. However, with a proposed type III seesaw mechanism leading to three pairs of massive pseudo-Dirac neutrinos, resonant leptogenesis is decoupled from the neutrino mass and mixing issues with successful baryogenesis easily obtained.

We assess how well next-generation neutrinoless double beta decay and normal neutrino beta decay experiments can answer four fundamental questions. (1) If neutrinoless double beta decay searches do not detect a signal, and if the spectrum is known to be inverted hierarchy, can we conclude that neutrinos are Dirac particles? (2) If neutrinoless double beta decay searches are negative and a next-generation ordinary beta decay experiment detects the neutrino mass scale, can we conclude that neutrinos are Dirac particles? (3) If neutrinoless double beta decay is observed with a large neutrino mass element, what is the total mass in neutrinos? (4) If neutrinoless double beta decay is observed, but next-generation beta decay searches for a neutrino mass only set a mass upper limit, can we establish whether the mass hierarchy is normal or inverted? We base our answers on the expected performance of next-generation neutrinoless double beta decay experiments and on simulations of the accuracy of calculations of nuclear matrix elements.

We compute the strange quark mass $m_s$ and the average of the u and d quark masses $\mathrm{m̂}$ using full lattice QCD with three dynamical quarks combined with the experimental values for the $\pi$ and K masses. The simulations have degenerate u and d quarks with masses $m_u{=m}_d\equiv \mathrm{m̂}$ as low as $m_s/8,$ and two different values of the lattice spacing. The bare lattice quark masses obtained are converted to the $\overline{\mathrm{MS}}$ scheme using perturbation theory at $\mathcal{O}\left({\alpha }_S\right).\mathrm{}$ Our results are $m_s^{\overline{\mathrm{MS}}}\left(2\mathrm{}\mathrm{GeV}\right)=76\mathrm{}\left(0\right)\mathrm{}\left(3\right)\mathrm{}\left(7\right)\mathrm{}\left(0\right)\mathrm{}\mathrm{MeV},$ $m^{\overline{\mathrm{MS}}}\left(2\mathrm{}\mathrm{GeV}\right)=2.8\mathrm{}\left(0\right)\mathrm{}\left(1\right)\mathrm{}\left(3\right)\mathrm{}\left(0\right)\mathrm{}$ MeV, and $m_s/\mathrm{m̂}=27.4\mathrm{}\left(1\right)\mathrm{}\left(4\right)\mathrm{}\left(0\right)\mathrm{}\left(1\right),$ where the errors are from statistics, simulation, perturbation theory, and electromagnetic effects, respectively.

Positive vacuum energy together with extra dimensions of space imply that our four-dimensional Universe is unstable, generically to decompactification of the extra dimensions. Either quantum tunneling or thermal fluctuations carry one past a barrier into the decompactifying regime. We give an overview of this process, and examine the subsequent expansion into the higher-dimensional geometry. This is governed by certain fixed-point solutions of the evolution equations, which are studied for both positive and negative spatial curvature. In the case where there is a higher-dimensional cosmological constant, we also outline a possible mechanism for compactification to a four-dimensional de Sitter cosmology.

For one and two dimensional field theory compactifications we compute in the DR scheme the full dependence on the momentum scale (q) of the one-loop radiative corrections to the 4D gauge coupling. Imposing the discrete shift symmetry of summing the infinite towers of associated Kaluza-Klein (KK) modes, it is shown that higher (dimension) derivative operators are radiatively generated as one-loop counterterms for the case of two (but not for one) compact dimension(s). They emerge as a “radiative mixing” of effects (Kaluza-Klein infinite sums) associated with both compact dimensions. Particular attention is paid to the link of the one-loop corrections with their counterparts computed in infrared regularized 4D N=1 heterotic string orbifolds with N=2 sectors. The correction from these sectors usually ignores higher order terms in the IR string regulator $({\lambda }_s\to 0)$ of type ${\lambda }_s\ln {\alpha }^{\prime }$ $\left({\alpha }^{\prime }\ne 0\right),$ but these become relevant in the field theory limit. Such terms ultimately re-emerge in pure field theory calculations of $\Pi {(q}^2)$ as higher dimension one-loop counterterms. We stress the importance of such terms for the unification of gauge couplings and for the predicted value of the string scale.

We argue that two-dimensional classical SU(2) Yang-Mills theory describes the embedding of Riemann surfaces in three-dimensional curved manifolds. Specifically, the Yang-Mills field strength tensor computes the Riemannian curvature tensor of the ambient space in a thin neighborhood of the surface. In this sense the two-dimensional gauge theory then serves as a source of three-dimensional gravity. In particular, if the three-dimensional manifold is flat it corresponds to the vacuum of the Yang-Mills theory. This implies that all solutions to the original Gauss-Codazzi surface equations determine two-dimensional integrable models with a SU(2) Lax pair. Furthermore, the three-dimensional SU(2) Chern-Simons theory describes the Hamiltonian dynamics of two-dimensional Riemann surfaces in a four-dimensional flat space-time.

In numerical evolution of Einstein’s equations for black hole spacetimes, it will be necessary to use approximate boundary conditions at a finite distance from the holes. One interesting feature of numerical evolutions is a “tail,” the inverse power-law decrease of the late-time field. Here we discuss and present numerical evidence about the effect of approximate boundary conditions on the late-time behavior of evolved fields.

We obtain conditions for the existence and stability of de Sitter attractors in the phase space of homogeneous and isotropic cosmology in generalized theories of gravity (including nonlinear and scalar-tensor theories). These conditions are valid for any form of the coupling functions of the theory. Stability with respect to inhomogeneous perturbations is analyzed using a covariant and gauge-invariant formalism. The relevance for inflationary scenarios of the early universe and for quintessence models of the present era is discussed.

We investigate the qualitative dynamical properties of a brane model for the flat isotropic universe with a single matter component represented by a scalar field. We study the flat and quadratic potential. Three classes of behaviors of the scale factor are determined. In particular, in the case of the brane with dark negative radiation, via a fine tuning, the existence of oscillatory solutions is shown, which is not possible in the traditional flat FRW model.

In the search for the nature of dark energy most cosmological probes measure simple functions of the expansion rate. While powerful, these all involve roughly the same dependence on the dark energy equation of state parameters, with anticorrelation between its present value $w_0$ and time variation $w_a.$ Quantities that have instead positive correlation and so a sensitivity direction largely orthogonal to, e.g., distance probes offer the hope of achieving tight constraints through complementarity. Such quantities are found in strong gravitational lensing observations of image separations and time delays. While degeneracy between cosmological parameters prevents full complementarity, strong lensing measurements to 1% accuracy can improve equation of state characterization by 15–50%. Next generation surveys should provide data on roughly ${10}^5$ lens systems, though systematic errors will remain challenging.

Models of multifield inflation exhibiting primordial non-Gaussianity have recently been introduced. This is the case, in particular, if the fluctuations of a light field scalar field, transverse to the inflaton direction, with quartic coupling can be transferred to the metric fluctuations. So far in those calculations only the ensemble statistical properties have been considered. We explore here how finite volume effects could affect those properties. We show that the expected non-Gaussian properties survive at a similar level when the finite volume effects are taken into account and also find that they can skew the metric distribution even though the ensemble distribution is symmetric.

We study signatures of a structured universe in the multi-pole moments, auto-correlation function, and cluster statistics of ultrahigh energy cosmic rays above ${10}^{19}\mathrm{eV}.$ We compare scenarios where the sources are distributed homogeneously or according to the baryon density distribution obtained from a cosmological large scale structure simulation. The influence of extragalactic magnetic fields is studied by comparing the case of negligible fields with fields expected to be produced along large scale shocks with a maximal strength consistent with observations. We confirm that strongly magnetized observers would predict considerable anisotropy on large scales, which is already in conflict with current data. In the best fit scenario only the sources are strongly magnetized, although deflection can still be considerable, of order $20°$ up to ${10}^{20}\mathrm{eV},$ and a pronounced GZK cutoff is predicted. We then discuss signatures for future large scale full-sky detectors such as the Pierre Auger and EUSO projects. Auto-correlations are sensitive to the source density only if magnetic fields do not significantly affect propagation. In contrast, for a weakly magnetized observer, degree scale auto-correlations below a certain level indicate magnetized discrete sources. It may be difficult even for next generation experiments to distinguish between structured and unstructured source distributions.

We report the results of a search for the decay $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ in the kinematic region with ${\pi }^{+}$ momentum $140<P<\mathrm{}195\mathrm{}\mathrm{MeV}/c$ using the data collected by the E787 experiment at BNL. No events were observed. When combined with our previous search in this region, one candidate event with an expected background of $1.22\pm 0.24$ events results in a 90% C.L. upper limit of $2.2\times {10}^{-9}$ on the branching ratio of $K^{+}\to {\pi }^{+}\nu \overline{\nu }.$ We also report improved limits on the rates of $K^{+}\to {\pi }^{+}{X}^0$ and $K^{+}\to {\pi }^{+}{X}^1{X}^2$ where $X^0{,X}^1{,X}^2$ are hypothetical, massless, long-lived neutral particles.

Monte Carlo simulations of finite density systems are often plagued by the complex action problem. We point out that there exists certain noncommutativity in the zero chemical potential limit and the thermodynamic limit when one tries to study such systems by reweighting techniques. This is demonstrated by explicit calculations in a Random Matrix Theory, which is thought to be a simple qualitative model for finite density QCD. The factorization method allows us to understand how the noncommutativity, which appears at the intermediate steps, cancels in the end results for physical observables. In the recent reweighting type of approaches to QCD in the small $\mu$ regime, we expect a transition when the volume reaches $V_{\mathrm{tr}}\simeq \mathrm{const}.\mathrm{}/{\mu }^2,$ which however may not be in the range of current lattice calculations.

We consider the production of neutralino pairs ${\tilde{\chi }}_i^0{\tilde{\chi }}_j^0$ at a high energy hadron collider, putting a special emphasis on the case where one of them is the lightest neutralino ${\tilde{\chi }}_1^0,$ possibly constituting the main dark matter component. At tree level, the only relevant subprocess is $q\overline{q}\to {\tilde{\chi }}_i^0{\tilde{\chi }}_j^0,$ while the subprocess $g\overrightarrow{g}{\tilde{\chi }}_i^0{\tilde{\chi }}_j^0$ first appears at the one loop level. Explicit expressions for the $q\overline{q}$-helicity amplitudes are presented, including the tree level contributions and the leading-log one loop radiative corrections. For the one-loop $g\overrightarrow{g}{\tilde{\chi }}_i^0{\tilde{\chi }}_j^0$ process, a numerical code named PLATONggnn is released, allowing the computation of $d\sigma /d\mathrm{t̂}$ in any MSSM model with real soft breaking parameters. It turns out that acceptable MSSM benchmark models exist for which the $q\overline{q}$ and the gluonic contributions may give comparable effects at LHC, due to the enhanced gluonic structure functions at low fractional momenta. Depending on the values of the MSSM parameters, we find that the LHC neutralino pair production may provide sensitive tests of SUSY models generating neutralino dark matter.

We consider neutrino oscillations in the minimal Standard-Model Extension describing general Lorentz and CPT violation. Among the models without neutrino mass differences is one with two degrees of freedom that reproduces most major observed features of neutrino behavior.

Dirac-Born-Infeld type effective actions reproduce many aspects of string theory classical tachyon dynamics of unstable $\mathrm{D}p$-branes. The inhomogeneous tachyon field rolling from the top of its potential forms topological defects of lower codimensions. In between them, as we show, the tachyon energy density fragments into a p-dimensional web-like high density network evolving with time. We present an analytic asymptotic series solution of the nonlinear equations for the inhomogeneous tachyon and its stress energy. The generic solution for a tachyon field with a runaway potential in arbitrary dimensions is described by the free streaming of noninteracting massive particles whose initial velocities are defined by the gradients of the initial tachyon profile. Thus, relativistic particle mechanics is a dual picture of the tachyon field effective action. Implications of this picture for inflationary models with a decaying tachyon field are discussed.

We perform a new study of future sensitivities of galaxy redshift surveys to the free-streaming effect caused by neutrino masses, adding the information on cosmological parameters from measurements of primary anisotropies of the cosmic microwave background (CMB). Our reference cosmological scenario has nine parameters and three different neutrino masses, with a hierarchy imposed by oscillation experiments. Within the present decade, the combination of the Sloan Digital Sky Survey (SDSS) and CMB data from the PLANCK experiment will have a $2\sigma$ detection threshold on the total neutrino mass close to 0.2 eV. This estimate is robust against the inclusion of extra free parameters in the reference cosmological model. On a longer term, the next generation of experiments may reach values of order $\sum m_{\nu }=0.1\mathrm{}\mathrm{eV}$ at $2\sigma ,$ or better if a galaxy redshift survey significantly larger than SDSS is completed. We also discuss how the small changes on the free-streaming scales in the normal and inverted hierarchy schemes are translated into the expected errors from future cosmological data.

We present a supersymmetric model of space-time foam with two stacks of eight D8-branes with equal string tensions, separated by a single bulk dimension containing D0-brane particles that represent quantum fluctuations in the space-time foam. The ground-state configuration with static D-branes has zero vacuum energy. However, gravitons and other closed-string states propagating through the bulk may interact with the D0-particles, causing them to recoil and the vacuum energy to become non-zero. This provides a possible origin of dark energy. Recoil also distorts the background metric felt by energetic massless string states, which travel at less than the usual (low-energy) velocity of light. On the other hand, the propagation of chiral matter fields anchored on the D8-branes is not affected by such space-time foam effects.

We study stationary string configurations in a space-time of a higher-dimensional rotating black hole. We demonstrate that the Nambu-Goto equations for a stationary string in the 5D (five-dimensional) Myers-Perry metric allow a separation of variables. We present these equations in the first-order form and study their properties. We prove that the only stationary string configuration that crosses the infinite redshift surface and remains regular there is a principal Killing string. A worldsheet of such a string is generated by a principal null geodesic and a timelike at infinity Killing vector field. We obtain principal Killing string solutions in the Myers-Perry metrics with an arbitrary number of dimensions. It is shown that due to the interaction of a string with a rotating black hole, there is an angular momentum transfer from the black hole to the string. We calculate the rate of this transfer in a space-time with an arbitrary number of dimensions. This effect slows down the rotation of the black hole. We discuss possible final stationary configurations of a rotating black hole interacting with a string.