We analyze top-quark flavor violating decays into a charm quark and a gluon, photon, or $Z$ boson in a supersymmetric model incorporating left-right symmetry. We include loop calculations involving contributions from scalar quarks, gluinos, charginos, and neutralinos. We perform the calculations first assuming the minimal (flavor-diagonal) scalar quark scenario and then allowing for arbitrary mixing between the second and the third generation of scalar quarks, in both the up and the down sectors. In each case we present separately the contributions from gluino, chargino, and neutralino loops and compare their respective strengths. In the flavor-diagonal case, the branching ratio cannot exceed ${10}^{-5}$ (${10}^{-6}$) for the gluon (photon/$Z$ boson); while for the unconstrained (flavor-nondiagonal) case the same branching ratios can reach almost ${10}^{-4}$ for the gluon, ${10}^{-6}$ for the photon, and ${10}^{-5}$ for the $Z$ boson, all of which are slightly below the expected reach of LHC.

Long-range order of a specific kind has recently been found directly in configurations dominating the regularized QCD path integral. In particular, a low-dimensional global structure was identified in typical space-time distributions of topological charge defined via the overlap Dirac matrix. The presence of the order has been concluded from the fact that the structure disappears after random permutation of position coordinates in measured densities. Here we complete the argument for the reality of this structure (namely the conjecture that its existence is a consequence of QCD dynamics and not an artifact of the overlap-based definition of lattice topological field) by showing that the structure ceases to exist after randomizing the space-time coordinates of the underlying gauge field. This implies that the long-range order present in the overlap-based topological density is indeed a manifestation of the QCD vacuum, and that the notion of the fundamental structure (structure involving relevant features at all scales) is viable.

Exclusive electroproduction of hard dijets can be described within the collinear factorization. This process has clear experimental signature and provides one with an interesting alternative venue to test QCD description of hard diffractive processes and extract information on generalized nucleon parton distributions. In this work we present detailed leading-order QCD calculations of the relevant cross sections, including longitudinal momentum fraction distribution of the dijets and their azimuthal angle dependence.

An assumption of isospin symmetry permits the determination of $\sin (2\alpha )$ from the experimental study of $B\to \pi \pi$ decays. Isospin, however, is merely an approximate symmetry; its breaking predicates a theoretical systematical error ${\sigma }_{\alpha }^{\mathrm{IB}}$ in the extraction of $\alpha$. We focus on the impact of ${\pi }^0-\eta ,{\eta }^{\prime }$ mixing, as well as the manner in which it is amenable to empirical constraint, and determine that ${\sigma }_{\alpha }^{\mathrm{IB}}$ can potentially be controlled to $\mathcal{O}(1°)$.

We study the nonaquark states $S^0(3115)$ and $S^{+}(3140)$ which are reported by [T. Suzuki (KEK-PS), Phys. Lett. B 597, 236 (2004)M. Iwasaki et al., nucl-ex/0310018] by means of the quark model with diquark correlation. The nonaquark states form $\mathbf{1},\mathbf{8},\mathbf{10},\overline{\mathbf{10}},\mathbf{27},\overline{\mathbf{35}}$ SU(3) multiplets. The flavor wave functions of all the nonaquark states are constructed through the standard tensor technique. The mass spectrum is studied by using the Gell-Mann-Okubo mass formula. Some nonaquark mass sum rules are obtained. We further investigate the decay of $S^0(3115)$ and $S^{+}(3140)$ under the assumption of the “fall-apart” mechanism. It has been found that the main decay mode is $\Sigma NN$ rather than $\Lambda NN$ which is consistent with experiment. Also we have uniquely determined the flavor wave function of $S^0(3115)$ which belongs to the $\mathbf{27}$-plet with the quantum number $Y=2,I=1,I_z=-1$. Whereas the exotic states $S^{+}(3140)$ can belong to either the $\mathbf{27}$-plet or the $\overline{\mathbf{35}}$-plet. In the exact $\mathrm{SU}(3{)}^{\mathrm{flavor}}\times \mathrm{SU}(3{)}^{\mathrm{color}}\times \mathrm{SU}(2{)}^{\mathrm{spin}}$ limit, both $S^0(3115)$ and $S^{+}(3140)$ belong to the $\mathbf{27}$-plet with negative parity. We predict that its flavor structure can be determined by measuring the branch fractions of its decay channels. The experiments to check this prediction are as expected.

We compute the next-to-MHV one-loop $n$-gluon amplitudes in $\mathcal{N}=4$ super-Yang–Mills theory. These amplitudes contain three negative-helicity gluons and an arbitrary number of positive-helicity gluons, and are the first infinite series of amplitudes beyond the simplest, MHV, amplitudes. We also discuss some aspects of their twistor-space structure.

It is commonly accepted that the combination of quantum mechanics and general relativity gives rise to the emergence of a minimum uncertainty both in space and time. The arguments that support this conclusion are mainly based on perturbative approaches to the quantization, in which the gravitational interactions of the matter content are described as corrections to a classical background. In a recent paper, we analyzed the existence of a minimum time uncertainty in the framework of doubly special relativity. In this framework, the standard definition of the energy-momentum of particles is modified appealing to possible quantum gravitational effects, which are not necessarily perturbative. Demanding that this modification be completed into a canonical transformation determines the implementation of doubly special relativity in position space and leads to spacetime coordinates that depend on the energy-momentum of the particle. In the present work, we extend our analysis to the quantum length uncertainty. We show that, in generic cases, there actually exists a limit in the spatial resolution, both when the quantum evolution is described in terms of the auxiliary time corresponding to the Minkowski background or in terms of the physical time. These two kinds of evolutions can be understood as corresponding to perturbative and nonperturbative descriptions, respectively. This result contrasts with that found for the time uncertainty, which can be made to vanish in all models with unbounded physical energy if one adheres to a nonperturbative quantization.

We present a consistent low energy effective field theory framework for parametrizing the effects of novel short distance physics in inflation, and their possible observational signatures in the cosmic microwave background. We consider the class of general homogeneous, isotropic initial states for quantum scalar fields in Robertson-Walker (RW) spacetimes, subject to the requirement that their ultraviolet behavior be consistent with renormalizability of the covariantly conserved stress tensor which couples to gravity. In the functional Schrödinger picture such states are coherent, squeezed, mixed states characterized by a Gaussian density matrix. This Gaussian has parameters which approach those of the adiabatic vacuum at large wave number, and evolve in time according to an effective classical Hamiltonian. The one complex parameter family of $\alpha$ squeezed states in de Sitter spacetime does not fall into this UV allowed class, except for the special value of the parameter corresponding to the Bunch-Davies state. We determine the finite contributions to the inflationary power spectrum and stress tensor expectation value of general UV allowed adiabatic states, and obtain quantitative limits on the observability and backreaction effects of some recently proposed models of short distance modifications of the initial state of inflation. For all UV allowed states, the second order adiabatic basis provides a good description of particles created in the expanding RW universe. Because of the absence of particle creation for the massless, minimally coupled scalar field in de Sitter space, there is no phase decoherence in the simplest free field inflationary models. We apply adiabatic regularization to the renormalization of the decoherence functional in cosmology to corroborate this result.

Electroweak symmetry breaking may be a consequence of color sextet quark chiral symmetry breaking. A special solution of QCD is involved, with a high-energy S-Matrix that can be constructed “semiperturbatively” via the chiral anomaly and Reggeon diagrams. An infrared fixed point and color superconductivity are crucial components of the construction. Infinite-momentum physical states contain both quarks and a universal “anomalous wee gluon” component, and the spectrum is more limited than is required by confinement and chiral symmetry breaking. The Pomeron is approximately a Regge pole and the Critical Pomeron describes asymptotic cross sections. The strong coupling of the Pomeron to the electroweak sector could produce large $x$ and $Q^2$ events at HERA, and vector boson pairs at Fermilab. Further evidence for the sextet sector at Fermilab would be a large $E_T$ jet excess, due in part to the nonevolution of ${\alpha }_s$, and other phenomena related to the possibility that top quark production is due to the ${\eta }_6$. The sextet proton and neutron are the only new baryonic states. Sextet states dominate high-energy hadronic cross sections and stable sextet neutrons could produce both dark matter and ultrahigh energy cosmic rays. The cosmic ray spectrum knee suggests the effective sextet threshold is between Fermilab and LHC energies, with large cross-section effects expected at the LHC. Jet and vector boson cross sections will be very much larger than expected, and sextet baryons should also be produced. Double Pomeron produced states could provide definitive evidence for the existence of the sextet sector in the initial low luminosity running.

We discuss various issues concerning the behaviors near the boundary ($\sigma =0,\pi$) and the midpoint ($\sigma =\pi /2$) of the open string coordinate $X(\sigma )$ and its conjugate momentum $P(\sigma )=-i\delta /\delta X(\sigma )$ acting on the matter projectors of vacuum string field theory. Our original interest is in the dynamical change of the boundary conditions of the open string coordinate from the Neumann one in the translationally invariant backgrounds to the Dirichlet one in the D-brane backgrounds. We find that the Dirichlet boundary condition is realized on a lump solution only partially and only when its parameter takes a special value. On the other hand, the string midpoint has a mysterious property: it obeys the Neumann (Dirichlet) condition in the translationally invariant (lump) background.

We study the phase transition in gauge-Higgs unification at finite temperature. In particular, we obtain the strong first order electroweak phase transition for a simple matter content yielding the correct order of Higgs mass at zero temperature. Two stage phase transition is found for a particular matter content, which is the strong first order at each stage. We further study supersymmetric gauge models with the Scherk-Schwarz supersymmetry breaking. We again observe the first order electroweak phase transition and multistage phase transition.

It is well known that spherical D-branes are nucleated in the presence of an external RR electric field. Using the description of D-branes as solitons of the tachyon field on non-BPS D-branes, we show that the brane nucleation process can be seen as the decay of the tachyon false vacuum. This process can describe the decay of flux-branes in string theory or the decay of quintessence potentials arising in flux compactifications.

We consider the problem of asymptotic stability of a self-similar attractor for a simple semilinear radial wave equation which arises in the study of the Yang-Mills equations in $5+1$ dimensions. Our analysis consists of two steps. In the first step we determine the spectrum of linearized perturbations about the attractor using a method of continued fractions. In the second step we demonstrate numerically that the resulting eigensystem provides an accurate description of the dynamics of convergence towards the attractor.

We study the stability under linear perturbations of a class of static solutions of Einstein-Gauss-Bonnet gravity in $D=n+2$ dimensions with spatial slices of the form ${\Sigma }_{\kappa }^n\times {\mathbb{R}}^{+}$, ${\Sigma }_{\kappa }^n$ an $n$ manifold of constant curvature $\kappa$. Linear perturbations for this class of spacetimes can be generally classified into tensor, vector and scalar types. The analysis in this paper is restricted to tensor perturbations. We show that the evolution equations for tensor perturbations can be cast in Schrödinger form, and obtain the exact potential. We use $S$ deformations to analyze the Hamiltonian spectrum, and find an S-deformed potential that factors in a convenient way, allowing us to draw definite conclusions about stability in every case. It is found that there is a minimal mass for a $D=6$ black hole with a positive curvature horizon to be stable. For any $D$, there is also a critical mass above which black holes with negative curvature horizons are unstable.

“Einstein-Æther” theory, in which gravity couples to a dynamical, timelike, unit-norm vector field, provides a means for studying Lorentz violation in a generally covariant setting. Demonstrated here is the effect of a redefinition of the metric and “æther” fields in terms of the original fields and two free parameters. The net effect is a change of the coupling constants appearing in the action. Using such a redefinition, one of the coupling constants can be set to zero, simplifying studies of solutions of the theory.

Fits to high energy data alone cannot cleanly discriminate between asymptotic $\ln s$ and ${ln}^{2}s$ behavior of total hadronic cross sections. We demonstrate that this is no longer true when we require that these amplitudes also describe, on average, low energy data dominated by resonances. We simultaneously fit real analytic amplitudes to high energy measurements of: (i) the ${\pi }^{+}p$ and ${\pi }^{-}p$ total cross sections and $\rho$-values (ratio of the real to the imaginary portion of the forward scattering amplitude), for $\sqrt{s}\ge 6$ GeV, while requiring that the asymptotic fits smoothly join the ${\sigma }_{{\pi }^{+}p}$ and ${\sigma }_{{\pi }^{-}p}$ total cross sections at $\sqrt{s}=2.6$ GeV—both in magnitude and slope , and (ii) separately simultaneously fit the $\overline{p}p$ and $pp$ total cross sections and $\rho$-values for $\sqrt{s}\ge 6$ GeV, while requiring that their asymptotic fits smoothly join the the ${\sigma }_{\overline{p}p}$ and ${\sigma }_{pp}$ total cross sections at $\sqrt{s}=4.0$ GeV—again both in magnitude and slope. In both cases, we have used all of the extensive data of the Particle Data Group [K. Hagiwara et al. (Particle Data Group), Phys. Rev. D 66, 010001 (2002).]. However, we then subject these data to a screening process, the Sieve algorithm [M. M. Block, physics/0506010.], in order to eliminate outliers that can skew a ${\chi }^2$ fit. With the Sieve algorithm, a robust fit using a Lorentzian distribution is first made to all of the data to sieve out abnormally high $\Delta {\chi }_i^2$, the individual i$\mathrm{th}$ point’s contribution to the total ${\chi }^2$. The ${\chi }^2$ fits are then made to the sieved data. Both the $\pi p$ and nucleon-nucleon systems strongly favor a high energy ${ln}^{2}s$ fit of the form: ${\sigma }^{\pm }=c_0+c_1\ln (\frac{\nu }{m})+c_2{ln}^2(\frac{\nu }{m})+{\beta }_{{\mathcal{P}}^{\prime }}(\frac{\nu }{m}{)}^{\mu -1}\pm \delta (\frac{\nu }{m}{)}^{\alpha -1}$, basically excluding a $\ln s$ fit of the form: ${\sigma }^{\pm }=c_0+c_1\ln (\frac{\nu }{m})+{\beta }_{{\mathcal{P}}^{\prime }}(\frac{\nu }{m}{)}^{\mu -1}\pm \delta (\frac{\nu }{m}{)}^{\alpha -1}$. The upper sign is for ${\pi }^{+}p$ ($pp$) and the lower sign is for ${\pi }^{-}p$ ($\overline{p}p$) scattering, where $\nu$ is the laboratory pion (proton) energy, and $m$ is the pion (proton) mass.

We analyze the supersymmetric contributions to the direct and mixing $CP$ asymmetries and also to the branching ratios of the $B\to K\pi$ decays in a model independent way. We consider both gluino and chargino exchanges and emphasize that a large gluino contribution is essential for saturating the direct and mixing $CP$ asymmetries. We also find that combined contributions from the penguin diagrams with chargino and gluino in the loop could lead to a possible solution for the branching ratios puzzle and account for the results of $R_c$ and $R_n$ within $b\to s\gamma$ constraints. When all relevant constraints are satisfied, our result indicates that supersymmetry favors lower values of $R_c$. Finally, we study the correlations between the mixing $CP$ asymmetry $S_{K^0{\pi }^0}$ and mixing $CP$ asymmetries of the processes $B\to \varphi K$ and $B\to {\eta }^{\prime }K$. We show that it is quite possible for gluino exchanges to accommodate the results of the observables.

In this work we show that the implementation of spontaneous breaking of the lepton number in the 3-3-1 model with right-handed neutrinos gives rise to fast neutrino decay with Majoron emission and generates a bunch of new contributions to the neutrinoless double beta decay.

We investigate the generalized parton distributions (GPDs) with nonzero $\xi$ and ${\Delta }^{\perp }$ for a relativistic spin-$1/2$ composite system, namely, for an electron dressed with a photon, in light-front framework by expressing them in terms of overlaps of light-cone wave functions. The wave function provides a template for the quark spin-one diquark structure of the valence light-cone wave function of the proton. We verify the inequalities among the GPDs with different helicities and show the qualitative behavior of the fermion and gauge boson GPDs in the impact parameter space.