We present the complete analytical result for the two-loop logarithmically enhanced contributions to the high-energy asymptotic behavior of the vector form factor and the four-fermion cross section in a spontaneously broken $SU(2)$ gauge model. On the basis of this result we derive the dominant two-loop electroweak corrections to the neutral current four-fermion processes at high energies.

We present an analysis of exclusive charmless semileptonic $B$-meson decays based on $83\times {10}^6$ $B\overline{B}$ pairs recorded with the BABAR detector at the ${\rm Y}(4S)$ resonance. Using isospin symmetry, we measure branching fractions $\mathcal{B}(B^0\to {\pi }^{-}{\ell }^{+}\nu )=(1.38\pm 0.10\pm 0.16\pm 0.08)\times {10}^{-4}$ and $\mathcal{B}(B^0\to {\rho }^{-}{\ell }^{+}\nu )=(2.14\pm 0.21\pm 0.48\pm 0.28)\times {10}^{-4}$, where the errors are statistical, experimental systematic, and due to form-factor shape uncertainties. We compare the measured distribution in $q^2$, the momentum-transfer squared, with theoretical predictions for the form factors from lattice QCD and light-cone sum rules, and extract the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $|V_{ub}|=(3.82\pm 0.14\pm 0.22\pm {0.11}_{-0.52}^{+0.88})\times {10}^{-3}$ from $B\to \pi \ell \nu$, where the fourth error reflects the uncertainty of the form-factor normalization.

High-energy neutrino astronomy will be capable of observing particles at both extremely high energies and over extremely long baselines. These features make such experiments highly sensitive to the effects of $CPT$ and Lorentz violation. In this article, we review the theoretical foundation and motivation for $CPT$ and Lorentz violating effects, and then go on to discuss the related phenomenology within the neutrino sector. We describe several signatures which might be used to identify the presence of $CPT$ or Lorentz violation in next generation neutrino telescopes and cosmic ray experiments. In many cases, high-energy neutrino experiments can test for $CPT$ and Lorentz violation effects with much greater precision than other techniques.

We give the equations of motion for a self-gravitating Dirac $p$-brane embedded in an even codimension spacetime. The dynamics of the bulk are dictated by Lovelock gravity and permit matching conditions, even when the codimension is strictly greater than 2. We show that the equations of motion involve both induced Lovelock densities on the brane and regular extrinsic curvature terms. The brane dynamics can be derived from an exact $(p+1)$-dimensional induced action. The Dirac charge is carried by an overall (solid) angle defect which sets the Planck scale on the brane. In particular, if the codimension is greater than the world-volume dimension of the $p$-brane, we show that the extrinsic curvature terms cancel, leaving an exact induced Lovelock theory. For example, a 3-brane embedded in 8 or 10 dimensions obeys Einstein’s equations with a cosmological constant.

The neutral $Z$ boson pair production due to radion resonance at the Large Hadron Collider (LHC) is an interesting process to explore the notion of warped geometry (Randall-Sundrum model). Because of the enhanced coupling of radion with a pair of gluons due to trace anomaly and top(quark) loop, the radion can provide a larger event rate possibility as compared to any new physics effect. Using the proper radion-top-antitop (with the quarks being off-shell) coupling, we obtain the correct radion production rate at LHC and explore several features of a heavier radion decaying into a pair of real $Z$ bosons which subsequently decays into charged $4l(l=e,\mu )$ leptons (the gold-plated mode). Using the signal and the background event rate, we obtain bounds on radion mass $m_{\varphi }$ and radion vacuum expectation value $⟨\varphi ⟩$ at the $5\sigma$, $10\sigma$ discovery level.

In the strongly correlated environment of high-temperature cuprate superconductors, the spin and charge degrees of freedom of an electron seem to separate from each other. A similar phenomenon may be present in the strong coupling phase of Yang-Mills theories, where a separation between the color charge and the spin of a gluon could play a role in a mass-gap formation. Here we study the phase structure of a decomposed SU(2) Yang-Mills theory in a mean-field approximation, by inspecting quantum fluctuations in the condensate which is formed by the color-charge component of the gluon field. Our results suggest that the decomposed theory has an involved phase structure. In particular, there appears to be a phase which is quite reminiscent of the superconducting phase in cuprates. We also find evidence that this phase is separated from the asymptotically-free theory by an intermediate pseudogap phase.

The global counterpart of infinitesimal symmetries of noncommutative space-time is discussed.

Loop quantization of diagonalized Bianchi class A models, leads to a partial difference equation as the Hamiltonian constraint at the quantum level. A criterion for testing a viable semiclassical limit has been formulated in terms of existence of the so-called preclassical solutions. We demonstrate the existence of preclassical solutions of the quantum equation for the vacuum Bianchi I model. All these solutions avoid the classical singularity at vanishing volume.

It has been known that the dynamics of $k$ coincident D-branes in string theory is described effectively by $\mathrm{U}(k)$ Yang-Mills theory at low energy. While these configurations appear as classical solutions in matrix models, it was not clear whether it is possible to realize the $k\ne 1$ case as the true vacuum. The massive Yang-Mills–Chern-Simons matrix model has classical solutions corresponding to all the representations of the SU(2) algebra, and provides an opportunity to address the above issue on a firm ground. We investigate the phase structure of the model, and find, in particular, that there exists a parameter region where $\mathrm{O}(N)$ copies of the spin-$1/2$ representation appear as the true vacuum, thus realizing a nontrivial gauge group dynamically. Such configurations are analogous to the ones that are interpreted in the Berenstein-Maldacena-Nastase (BMN) matrix model as coinciding transverse 5-branes in M-theory.

We study the effect of dense quarks in a $SU(N)$ matrix model of deconfinement. For three or more colors, the quark contribution to the loop potential is complex. After adding the charge conjugate loop, the measure of the matrix integral is real, but not positive definite. In a matrix model, quarks act like a background $Z(N)$ field; at nonzero density, the background field also has an imaginary part, proportional to the imaginary part of the loop. Consequently, while the expectation values of the loop and its complex conjugate are both real, they are not equal. These results suggest a possible approach to the fermion sign problem in lattice QCD.

We construct the action and transformation laws for bulk five-dimensional AdS supergravity coupled to one or two brane-localized Goldstone fermions. The resulting bulk-plus-brane system gives a model-independent description of brane-localized supersymmetry breaking in the Randall-Sundrum scenario. We explicitly reduce the action and transformation laws to spontaneously broken four-dimensional supergravity (in AdS, Minkowski or dS space).

In this article we investigate exact cylindrically symmetric solutions to the modified Einstein field equations in the braneworld gravity scenarios. It is shown that for the special choice of the equation of state $2U+P=0$ for the dark energy and dark pressure, the solutions found could be considered formally as solutions of the Einstein-Maxwell equations in 4-D general relativity.

Extra dimensions offer new ways to address long-standing problems in beyond-the-standard-model particle physics. In some classes of extra-dimensional models, the lightest Kaluza-Klein particle is a viable dark matter candidate. In this work, we study indirect detection of Kaluza-Klein dark matter via its annihilation into antiprotons. We use a sophisticated galactic cosmic ray diffusion model whose parameters are fully constrained by an extensive set of experimental data. We find that models with universal extra dimensions remain unconstrained by cosmic ray antiprotons while low-mass weakly interacting massive particle candidates of a few tens of GeV that arise in Randall-Sundrum geometries can be probed.

We have found a simple exact solution of spherically symmetrical Einstein equations describing a wormhole for an inhomogeneous distribution of the phantom energy. The equation of state is linear but highly anisotropic: while the radial pressure is negative, the transversal one is positive. At infinity the spacetime is not asymptotically flat and possesses on each side of the bridge a regular cosmological Killing horizon with an infinite area, impenetrable for any particles. This horizon does not arise if the wormhole region is glued to the Schwarzschild region. In doing so, the wormhole can enclose an arbitrary amount of the phantom energy. The configuration under discussion has a limit in which the phantom energy turns into the string dust, the areal radius tends to the constant. In this limit, the strong gravitational mass defect is realized in that the gravitational active mass is finite and constant while the proper mass integrated over the total manifold is infinite.

In the framework of the littlest Higgs (LH) model, we study single production of the standard model gauge boson $W_s^{-}$ and the heavy gauge boson $W_H^{-}$ via polarized $e^{-}\gamma$ collisions. We find that the corrections of the LH model to the cross section $\sigma (W_s^{-})$ might be observed only for the scale parameter $f\le 1.5\mathrm{TeV}$ and the mixing parameter $c^{\prime }\ge 0.4$ in future high-energy linear $e^{+}{e}^{-}$ collider (LC) experiments with the center-of-mass energy $\sqrt{s}=500\mathrm{GeV}$ and a yearly integrated luminosity $\mathcal{L}=100{\mathrm{fb}}^{-1}$. However, with a suitably chosen polarization of the initial electron and positron beams, the possible signals of the heavy gauge boson $W_H^{-}$ can be easily detected via $e^{-}\gamma$ collisions in future LC experiments with $\sqrt{s}=3\mathrm{TeV}$ and $\mathcal{L}=500{\mathrm{fb}}^{-1}$.

Within the framework of an $R$-parity violating minimal supergravity model, at least three relatively large lepton number violating ${\lambda }^{\prime }$ type trilinear couplings at the grand unified theory scale, not directly related to neutrino physics, can naturally generate via renormalization group evolution and/or CKM rotation, the highly suppressed bilinear and trilinear parameters at the weak scale required to explain the neutrino oscillation data. The structure of the renormalization group equations and the CKM matrix restrict the choices of the three input couplings to only eight possible combinations, each with its own distinctive experimental signature. The relatively large input couplings may lead to spectacular low-energy signatures like rare weak decays of the $\tau$ lepton and $K$ mesons, direct lepton number violating decays of several sparticles, and unconventional decay modes (and reduced lifetime) of the lightest neutralino, assumed to be the lightest supersymmetric particle, all with sizable branching ratios. Several low background signals at the Tevatron and CERN LHC have been suggested and their sizes are estimated to be at the observable level. From the particle content of the signal and the relative rate of different final states the input couplings at the grand unified theory scale, i.e., the origin of neutrino masses and mixing angles, can be identified.

We report on a program to compute the electromagnetic form factors of mesons. We discuss the techniques used to compute the pion form factor and present results computed with domain-wall valence fermions on MILC asqtad lattices, as well as with Wilson fermions on quenched lattices. We find that the full-QCD form factor is well described by a VMD picture, with the pole mass in the chiral limit $m_{\mathrm{VMD}}=0.868(65)\mathrm{GeV}$. However, the quenched Wilson fermion results are suggestive of large scaling violations.

Nonlinear susceptibilities up to the eighth order have been constructed in QCD with two flavors of dynamical quarks. Beyond leading order, they exhibit peaks at the crossover temperature, $T_c$. By analyzing their behavior in detail, we find that the dominant contributions near $T_c$ come from a set of operators with a remarkably simple topology. Any effective theory of QCD near $T_c$ must be able to explain these regularities.

We present an explicit example of a gauge symmetry breaking phase transition in heterotic models, the dynamics of which are not thermal and can be described in a well controlled manner throughout. The phase transition is driven by the evolution of bundle moduli—moduli associated with gauge field vacuum expectation values in the hidden dimensions. We present the necessary parts of the four dimensional effective theory including moduli which describe the embedding of the gauge bundle within the gauge group. We then present exact cosmological solutions to the system before going on to use them to describe the phase transition. The explicit nature of our description enables us to plot how the gauge bosons associated with the symmetries which are broken in the transition gain masses with time. This is in contrast to the use, for example, of a brane collision as a modulus driven phase transition. In the course of this work we find a number of other interesting results. We observe that the Kähler potential of the system is given by the logarithm of the volume of the compact space even when bundle moduli are included. We also note that the dynamics of the gauge bundle mean that small instanton transitions are classically forbidden for all but a set of measure zero of the initial conditions of the system. The paper is written in such a manner that the cosmological description of the phase transition can be read independently of the derivation of the four dimensional theory.

We perform a holographic renormalization of cascading gauge theories. Specifically, we find the counterterms that need to be added to the gravitational action of the backgrounds dual to the cascading theory of Klebanov and Tseytlin, compactified on an arbitrary four-manifold, in order to obtain finite correlation functions (with a limited set of sources). We show that it is possible to truncate the action for deformations of this background to a five-dimensional system coupling together the metric and four scalar fields. Somewhat surprisingly, despite the fact that these theories involve an infinite number of high-energy degrees of freedom, we find finite answers for all one-point functions (including the conformal anomaly). We compute explicitly the renormalized stress tensor for the cascading gauge theories at high temperature and show how our finite answers are consistent with the infinite number of degrees of freedom. Finally, we discuss ambiguities appearing in the holographic renormalization we propose for the cascading gauge theories; our finite results for the one-point functions have some ambiguities in curved space (including the conformal anomaly) but not in flat space.