The set of 63 real generalized Pauli matrices of three-qubits can be factored into two subsets of 35 symmetric and 28 antisymmetric elements. This splitting is shown to be completely embodied in the properties of the Fano plane; the elements of the former set being in a bijective correspondence with the 7 points, 7 lines, and 21 flags, whereas those of the latter set having their counterparts in 28 antiflags of the plane. This representation naturally extends to the one in terms of the split Cayley hexagon of order two. Sixty three points of the hexagon split into 9 orbits of 7 points (operators) each under the action of an automorphism of order 7. Sixty three lines of the hexagon carry three points each and represent the triples of operators such that the product of any two gives, up to a sign, the third one. Since this hexagon admits a full embedding in a projective 5-space over $GF(2)$, the 35 symmetric operators are also found to answer to the points of a Klein quadric in such space. The 28 antisymmetric matrices can be associated with the 28 vertices of the Coxeter graph, one of two distinguished subgraphs of the hexagon. The $PS{L}_2(7)$ subgroup of the automorphism group of the hexagon is discussed in detail and the Coxeter subgeometry is found to be intricately related to the $E_7$-symmetric black-hole entropy formula in string theory. It is also conjectured that the full geometry/symmetry of the hexagon should manifest itself in the corresponding black-hole solutions. Finally, an intriguing analogy with the case of Hopf sphere fibrations and a link with coding theory are briefly mentioned.

We use the effective field theory for gravitational bound states, proposed by Goldberger and Rothstein, to compute the interaction Lagrangian of a binary system at the second post-Newtonian order. Throughout the calculation, we use a metric parametrization based on a temporal Kaluza-Klein decomposition and test the claim by Kol and Smolkin that this parametrization provides important calculational advantages. We demonstrate how to use the effective field theory method efficiently in precision calculations, and we reproduce known results for the second post-Newtonian order equations of motion in harmonic gauge in a straightforward manner.

We propose the lightest supersymmetric particle (LSP) as a well-suited candidate for superheavy dark matter (SHDM). Various production mechanisms at the end of inflation can produce SHDM with the correct abundance, ${\Omega }_{\mathrm{LSP}}{h}^2\sim 0.1$, if its mass is sufficiently high. In particular, gravitational production requires that the mass $m_{\mathrm{LSP}}$ of the LSP is above $3\times {10}^{11}\mathrm{GeV}$. Weak interactions remain perturbative despite the large mass hierarchy, $m_{\mathrm{LSP}}\gg m_Z$, because of the special decoupling properties of supersymmetry. As a result the model is predictive and we discuss the relevant cosmological processes for the case of a superheavy neutralino within this scheme.

There exist new polarized structure functions in a spin-one hadron. In deep inelastic electron scattering from a spin-one hadron, there are eight structure functions $F_1$, $F_2$, $g_1$, $g_2$, $b_1$, $b_2$, $b_3$, and $b_4$. We derive projections to these eight functions from the hadron tensor $W^{\mu \nu }$ by combinations of the hadron momentum and its polarization vectors.

I apply a recently developed algorithm for reweighting simulations of lattice QCD from one quark mass to another to simulations performed with overlap fermions in the epsilon regime. I test it by computing the condensate from distributions of the low-lying eigenvalues of the Dirac operator. Results seem favorable, when the difference of squared masses is small.

We study two different initial conditions for fermions for the problem of pair production of fermions coupled to a classical electromagnetic field with backreaction in ($1+1$)-dimensional boost-invariant coordinates. Both of these conditions are consistent with fermions initially in a vacuum state. We present results for the proper-time evolution of the electric field $E$, the current $J$, the matter energy density $\epsilon$, and the pressure $p$ as a function of the proper time for these two cases. We also determine the interpolating number density as a function of the proper time. We find that when we use a “first-order adiabatic” vacuum initial condition or a “free-field” initial condition for the fermion field, we obtain essentially similar behavior for physically measurable quantities. The second method is computationally simpler, it is twice as fast and involves half the storage required by the first method.

We investigate the parameter space of the minimal supersymmetric standard model where the gluino and squark masses are much above 1 TeV but the remaining part of the sparticle spectrum is accessible to the Large Hadron Collider at CERN. After pointing out that such a scenario may constitute an important benchmark of gaugino/scalar nonuniversality, we find that hadronically quiet trileptons are rather useful signals for it. Regions of the parameter space, where the signal is likely to be appreciable, are identified through a detailed scan. The advantage of hadronically quiet trileptons over other types of signals is demonstrated.

We study the properties and production mechanisms of color-octet scalars at the Large Hadron Collider. We focus on the single production of both charged and neutral members of an $(\mathbf{8},\mathbf{2}{)}_{1/2}$ doublet through bottom-quark initial states. These channels provide a window to the underlying Yukawa structure of the scalar sector. Color-octet scalars naturally appear in grand unified theories based on the $SU(5)$ gauge symmetry. In the context of adjoint $SU(5)$ these fields are expected to be light to satisfy constraints coming from unification and proton decay, and may have TeV-scale masses. One combination of their couplings is defined by the relation between the down-quark and charged-lepton Yukawa couplings. Observation of these states at the LHC gives an upper bound on the proton lifetime if they truly arise from this grand unified theory. We demonstrate that TeV-mass scalars can be observed over background at the LHC using boosted top-quark final states, and study how well the scalar Yukawa parameters can be measured.

We estimate the accuracy with which the coefficient of the $CP$ even dimension-six operators involving Higgs and two vector bosons ($HVV$) can be measured at linear $e^{+}{e}^{-}$ colliders. Using the optimal observables method for the kinematic distributions, our analysis is based on the five different processes. First is the $WW$ fusion process in the $t$-channel ($e^{+}{e}^{-}\to {\overline{\nu }}_e{\nu }_{e}H$), where we use the rapidity $y$ and the transverse momentum $p_{\mathrm{T}}$ of the Higgs boson as observables. Second is the $ZH$ pair production process in the $s$ channel, where we use the scattering angle of the $Z$ and the $Z$ decay angular distributions, reproducing the results of the previous studies. Third is the $t$-channel $ZZ$, fusion processes ($e^{+}{e}^{-}\to e^{+}{e}^{-}H$), where we use the energy and angular distributions of the tagged $e^{+}$ and $e^{-}$. In the fourth, we consider the rapidity distribution of the untagged $e^{+}{e}^{-}H$ events, which can be approximated well as the $\gamma \gamma$ fusion of the bremsstrahlung photons from $e^{+}$ and $e^{-}$ beams. As the last process, we consider the single-tagged $e^{+}{e}^{-}H$ events, which probe the $\gamma e^{\pm }\to H{e}^{\pm }$ process. All the results are presented in such a way that statistical errors of the constraints on the effective couplings and their correlations are read off when all of them are allowed to vary simultaneously, for each of the above processes, for $m_H=120\mathrm{GeV}$, at $\sqrt{s}=250\mathrm{GeV}$, 350 GeV, 500 GeV, and 1 TeV, with and without $e^{-}$ beam polarization of 80%. We find, for instance, that the $HZZ$ and $HWW$ couplings can be measured with 0.6% and 0.9% accuracy, respectively, for the integrated luminosity of $L=100{\mathrm{fb}}^{-1}$ at $\sqrt{s}=250\mathrm{GeV}$, 350 GeV, and $L=500{\mathrm{fb}}^{-1}$ at $\sqrt{s}=500\mathrm{GeV}$, 1 TeV, for the luminosity uncertainty of 1% at each energy. We find that the luminosity uncertainty affects only one combination of the nonstandard couplings, which are proportional to the standard $HWW$ and $HZZ$ couplings, while it does not affect the errors of the other independent combinations of the couplings. As a consequence, we observe that a few combinations of the eight dimension-six operators can be constrained as accurately as the two operators, which have been constrained by the precision measurements of the $Z$ and $W$ boson properties.

We have simulated QCD using $2+1$ flavors of domain wall quarks and the Iwasaki gauge action on a $(2.74\mathrm{fm}{)}^3$ volume with an inverse lattice scale of $a^{-1}=1.729(28)\mathrm{GeV}$. The up and down (light) quarks are degenerate in our calculations and we have used four values for the ratio of light quark masses to the strange (heavy) quark mass in our simulations: 0.217, 0.350, 0.617, and 0.884. We have measured pseudoscalar meson masses and decay constants, the kaon bag parameter $B_K$, and vector meson couplings. We have used SU(2) chiral perturbation theory, which assumes only the up and down quark masses are small, and SU(3) chiral perturbation theory to extrapolate to the physical values for the light quark masses. While next-to-leading order formulas from both approaches fit our data for light quarks, we find the higher-order corrections for SU(3) very large, making such fits unreliable. We also find that SU(3) does not fit our data when the quark masses are near the physical strange quark mass. Thus, we rely on SU(2) chiral perturbation theory for accurate results. We use the masses of the $\Omega$ baryon, and the $\pi$ and $K$ mesons to set the lattice scale and determine the quark masses. We then find $f_{\pi }=124.1(3.6{)}_{\mathrm{stat}}(6.9{)}_{\mathrm{syst}}\mathrm{MeV}$, $f_K=149.6(3.6{)}_{\mathrm{stat}}(6.3{)}_{\mathrm{syst}}\mathrm{MeV}$, and $f_K/f_{\pi }=1.205(0.018{)}_{\mathrm{stat}}(0.062{)}_{\mathrm{syst}}$. Using nonperturbative renormalization to relate lattice regularized quark masses to regularization independent momentum scheme masses, and perturbation theory to relate these to $\overline{\mathrm{MS}}$, we find $m_{ud}^{\overline{\mathrm{MS}}}(2\mathrm{GeV})=3.72(0.16{)}_{\mathrm{stat}}(0.33{)}_{\mathrm{ren}}(0.18{)}_{\mathrm{syst}}\mathrm{MeV}$, $m_s^{\overline{\mathrm{MS}}}(2\mathrm{GeV})=107.3(4.4{)}_{\mathrm{stat}}(9.7{)}_{\mathrm{ren}}(4.9{)}_{\mathrm{syst}}\mathrm{MeV}$, and ${\tilde{m}}_{ud}:{\tilde{m}}_s=1:28.8(0.4{)}_{\mathrm{stat}}(1.6{)}_{\mathrm{syst}}$. For the kaon bag parameter, we find $B_K^{\overline{\mathrm{MS}}}(2\mathrm{GeV})=0.524(0.010{)}_{\mathrm{stat}}(0.013{)}_{\mathrm{ren}}(0.025{)}_{\mathrm{syst}}$. Finally, for the ratios of the couplings of the vector mesons to the vector and tensor currents ($f_V$ and $f_V^T$, respectively) in the $\overline{\mathrm{MS}}$ scheme at 2 GeV we obtain $f_{\rho }^T/f_{\rho }=0.687(27)$; $f_{K^{*}}^T/f_{K^{*}}=0.712(12)$, and $f_{\varphi }^T/f_{\varphi }=0.750(8)$.

The weak decays of ${\Lambda }_b\to \Lambda l^{+}{l}^{-}$ ($l=e$, $\mu$) are investigated in the minimal supersymmetric standard model (MSSM) and also in supersymmetric (SUSY) SO(10) grand unified models. In the MSSM special attention is paid to the neutral Higgs bosons (NHBs) as they make quite a large contribution in exclusive $B\to X_s{l}^{+}{l}^{-}$ decays at large $\tan \beta$ regions of parameter space of SUSY models, since part of SUSY contributions is proportional to ${tan}^3\beta$. The analysis of decay rate, forward-backward asymmetries, lepton polarization asymmetries, and the polarization asymmetries of the $\Lambda$ baryon in ${\Lambda }_b\to \Lambda l^{+}{l}^{-}$ show that the values of these physical observables are greatly modified by the effects of NHBs. In the SUSY SO(10) grand unified theory model, the new physics contribution comes from the operators which are induced by the NHBs’ penguins and also from the operators having chirality opposite to that of the corresponding standard model (SM) operators. SUSY SO(10) effects show up only in the decay ${\Lambda }_b\to \Lambda +{\tau }^{+}{\tau }^{-}$ where the longitudinal and transverse lepton polarization asymmetries deviate significantly from the SM value while the effects in the decay rate, forward-backward asymmetries, and polarization asymmetries of final state $\Lambda$ baryon are very mild. The transverse lepton polarization asymmetry in ${\Lambda }_b\to \Lambda +{\tau }^{+}{\tau }^{-}$ is almost zero in the SM and in the MSSM model. However, it can reach to $-0.1$ in the SUSY SO(10) grand unified theory model and could be seen at the future colliders; hence this asymmetry observable will provide us useful information to probe new physics and discriminate between different models.

We consider $CP$-violating effects in $\tau \to K\pi \pi {\nu }_{\tau }$, assuming that a charged Higgs boson provides a new amplitude that can interfere with the usual standard model amplitude. We consider four $CP$-odd observables—the regular rate asymmetry, two modified rate asymmetries and a triple-product asymmetry. The regular rate asymmetry is expected to be small because it requires the interference of the new physics amplitude with the standard model amplitude containing the hadronic scalar form factor. The other $CP$ asymmetries may be more promising in terms of their new physics reach. Numerical estimates indicate that the maximum obtainable values for the modified and triple-product asymmetries are on the order of a percent.

I describe how superstring theory may violate spin statistics in an experimentally observable manner. Reviewing the basics of superstring interactions and how to utilize these to produce a statistical phase, I then apply these ideas to two specific examples. The first is the case of heterotic world sheet linkings, whereby one small closed string momentarily enlarges sufficiently to pass over another, producing such a statistical phase. The second is the braneworld model with noncommutative geometry, whereby matter composed of open strings may couple to a background in which spacetime coordinates do not commute, modifying the field (anti)commutator algebra. I conclude with ways to sharpen and experimentally test these exciting avenues to possibly verify superstring theory.

The $1/N$ expansion of the two-particle irreducible effective action offers a powerful approach to study quantum field dynamics far from equilibrium. We investigate the effective convergence of the $1/N$ expansion in the $O(N)$ model by comparing results obtained numerically in $1+1$ dimensions at leading, next-to-leading and next-to-next-to-leading order in $1/N$ as well as in the weak coupling limit. A comparison in classical statistical field theory, where exact numerical results are available, is made as well. We focus on early-time dynamics and quasiparticle properties far from equilibrium and observe rapid effective convergence already for moderate values of $1/N$ or the coupling.

Model waveforms are used in gravitational wave data analysis to detect and then to measure the properties of a source by matching the model waveforms to the signal from a detector. This paper derives accuracy standards for model waveforms which are sufficient to ensure that these data analysis applications are capable of extracting the full scientific content of the data, but without demanding excessive accuracy that would place undue burdens on the model waveform simulation community. These accuracy standards are intended primarily for broadband model waveforms produced by numerical simulations, but the standards are quite general and apply equally to such waveforms produced by analytical or hybrid analytical-numerical methods.

Using the teleparallel equivalent of general relativity formulated in Weitzenböck spacetime, we thoroughly explore a kind of Born-Infeld regular gravity leading to second order field equations for the vielbein components. We explicitly solve the equations of motion for two examples: the extended Bañados-Teitelboim-Zanelli black hole, which exists even if the cosmological constant is positive, and a cosmological model with matter, where the scale factor is well behaved, thus giving a singularity-free solution.

Employing the perturbative treatment of gravitational clustering, we discuss possible effects of primordial non-Gaussianity on the matter power spectrum. As gravitational clustering develops, the coupling between different Fourier modes of density perturbations becomes important and the primordial non-Gaussianity which intrinsically possesses a nontrivial mode correlation can affect the late-time evolution of the power spectrum. We quantitatively estimate the non-Gaussian effect on the power spectrum from the perturbation theory. The potential impact on the cosmological parameter estimation using the power spectrum are investigated based on the Fisher-matrix formalism. In addition, on the basis of the local biasing prescription, non-Gaussian effects on the galaxy power spectrum are considered, showing that the scale-dependent biasing arises from a local-type primordial non-Gaussianity. On the other hand, an equilateral-type non-Gaussianity does not induce such scale dependence because of weaker mode correlations between small and large Fourier modes.

Scalar wavelets have been used extensively in the analysis of cosmic microwave background (CMB) temperature maps. Spin needlets are a new form of (spin) wavelets which were introduced in the mathematical literature by Geller and Marinucci (2008) as a tool for the analysis of spin random fields. Here we adopt the spin needlet approach for the analysis of CMB polarization measurements. The outcome of experiments measuring the polarization of the CMB are maps of the Stokes $Q$ and $U$ parameters which are spin two quantities. Here we discuss how to transform these spin two maps into spin two needlet coefficients and outline briefly how these coefficients can be used in the analysis of CMB polarization data. We review the most important properties of spin needlets, such as localization in pixel and harmonic space and asymptotic uncorrelation. We discuss several statistical applications, including the relation of angular power spectra to the needlet coefficients, testing for non-Gaussianity on polarization data, and reconstruction of the $E$ and $B$ scalar maps.

Gamma-ray bursts (GRB) are the most energetic events in the Universe and provide a complementary probe of dark energy by allowing the measurement of cosmic expansion history that extends to redshifts greater than 6. Unlike type Ia supernovae (SNe Ia), GRBs must be calibrated for each cosmological model considered, because of the lack of a nearby sample of GRBs for model-independent calibration. For a flat universe with a cosmological constant, we find ${\Omega }_m={0.25}_{-0.11}^{+0.12}$ from 69 GRBs alone. We show that the current GRB data can be summarized by a set of model-independent distance measurements, with negligible loss of information. We constrain a dark energy equation of state linear in the cosmic scale factor using these distance measurements from GRBs, together with the “Union” compilation of SNe Ia, WMAP five-year observations, and the SDSS (Sloan Digital Sky Survey) baryon acoustic oscillation scale measurement. We find that a cosmological constant is consistent with current data at 68% confidence level for a flat universe. Our results provide a simple and robust method to incorporate GRB data in a joint analysis of cosmological data to constrain dark energy.

We use the Szekeres inhomogeneous relativistic models in order to fit supernova combined data sets. We show that with a choice of the spatial curvature function that is guided by current observations, the models fit the supernova data almost as well as the Lambda-CDM model without requiring a dark energy component. The Szekeres models were originally derived as an exact solution to Einstein’s equations with a general metric that has no symmetries, and they are regarded as good candidates to model the true lumpy universe that we observe. The null geodesics in these models are not radial. The best fit model found is also consistent with the requirement of spatial flatness at cosmic microwave background scales. The first results presented here seem to encourage further investigations of apparent acceleration using various inhomogeneous models, and other constraints from cosmic microwave background and large structure need to be explored next.