The Lorentz contraction of bound states in field theory is often appealed to in qualitative descriptions of high energy particle collisions. Surprisingly, the contraction has not been demonstrated explicitly even in simple cases such as the hydrogen atom. It requires a calculation of wave functions evaluated at equal (ordinary) time for bound states in motion. Such wave functions are not obtained by kinematic boosts from the rest frame. Starting from the exact Bethe-Salpeter equation we derive the equal-time wave function of a fermion-antifermion bound state in QED, i.e., positronium or the hydrogen atom, in any frame to leading order in $\alpha$. We show explicitly that the bound state energy transforms as the fourth component of a vector and that the wave function of the fermion-antifermion Fock state contracts as expected. Transverse photon exchange contributes at leading order to the binding energy of the bound state in motion. We study the general features of the corresponding fermion-antifermion-photon Fock states, and show that they do not transform by simply contracting. We verify that the wave function reduces to the light-front one in the infinite momentum frame.

We demonstrate how a one parameter family of interacting noncommuting Hamiltonians, which are physically equivalent, can be constructed in noncommutative quantum mechanics. This construction is carried out exactly (to all orders in the noncommutative parameter) and analytically in two dimensions for a free particle and a harmonic oscillator moving in a constant magnetic field. We discuss the significance of the Seiberg-Witten map in this context. It is shown for the harmonic oscillator potential that an approximate duality, valid in the low-energy sector, can be constructed between the interacting commutative and a noninteracting noncommutative Hamiltonian. This approximation holds to order $1/B$ and is therefore valid in the case of strong magnetic fields and weak Landau-level mixing.

We consider $n$-dimensional asymptotically anti-de Sitter spacetimes in higher curvature gravitational theories with $n\ge 4$, by employing the conformal completion technique. We first argue that a condition on the Ricci tensor should be supplemented to define an asymptotically anti-de Sitter spacetime in higher curvature gravitational theories and propose an alternative definition of an asymptotically anti-de Sitter spacetime. Based on that definition, we then derive a conservation law of the gravitational field and construct conserved quantities in two classes of higher curvature gravitational theories. We also show that these conserved quantities satisfy a balance equation in the same sense as in Einstein gravity and that they reproduce the results derived elsewhere. These conserved quantities are shown to be expressed as an integral of the electric part of the Weyl tensor alone and hence they vanish identically in the pure anti-de Sitter spacetime as in the case of Einstein gravity.

First the second-order perturbations of nonzero-$\Lambda$ cosmological models are derived explicitly with an arbitrary potential function of spatial coordinates, using the nonlinear version of Lifshitz’s method in the synchronous gauge. Their expression is the generalization (to the nonzero-$\Lambda$ case) of second-order perturbations in the Einstein–de Sitter model which were derived previously by the present author. Next the second-order temperature anisotropies of cosmic microwave background radiation are derived using the gauge-invariant formula which was given by Mollerach and Matarrese. Moreover, the corresponding perturbations in the Poisson gauge are derived using the second-order gauge transformations formulated by Bruni et al. In the second order it is found in spite of gauges that tensor (gravitational-wave) perturbations and vector (shear) perturbations without vorticity are induced from the first-order scalar perturbations. These results will be useful to analyze the nonlinear effect of local inhomogeneities on cosmic microwave background anisotropies.

Dark matter particles annihilating in the Galactic halo can provide a flux of positrons potentially observable in upcoming experiments, such as PAMELA and AMS-02. We discuss the spectral features which may be associated with dark matter annihilation in the positron spectrum and assess the prospects for observing such features in future experiments. Although we focus on some specific dark matter candidates, neutralinos and Kaluza-Klein states, we carry out our study in a model independent fashion.

We study the variation of the effective fine-structure constant alpha for Dirac-Born-Infeld (DBI) type dark energy models. The DBI action based on string theory naturally gives rise to a coupling between gauge fields and a scalar field responsible for accelerated expansion of the universe. This leads to the change of alpha due to a dynamical evolution of the scalar field, which can be compatible with the recently observed cosmological data around the redshift $\tilde{z}\lesssim 3$. We place constraints on several different DBI models including exponential, inverse power-law and rolling massive scalar potentials. We find that these models can satisfy the varying alpha constraint provided that mass scales of the potentials are fine-tuned. When we adopt the mass scales which are motivated by string theory, both exponential and inverse power-law potentials give unacceptably large change of alpha, thus ruled out from observations. On the other hand the rolling massive scalar potential is compatible with the observationally allowed variation of alpha. Therefore the information of varying alpha provides a powerful way to distinguish between a number of string-inspired DBI dark energy models.

We present an attempt to constrain deviations from the gravitational inverse-square law on large-scale structure scales. A perturbed law modifies the Poisson equation, which implies a scale-dependent growth of overdensities in the linear regime and thus modifies the power spectrum shape. We use two large-scale structure surveys (the Sloan Digital Sky survey and the Anglo-Australian two-degree field galaxy redshift survey) to constrain the parameters of two simple modifications of the inverse-square law. We find no evidence for deviations from normal gravity on the scales probed by these surveys ($\sim {10}^{23}\mathrm{m}$).

Several earth-based gravitational-wave (GW) detectors are actively pursuing the quest for placing observational constraints on models that predict the behavior of a variety of astrophysical and cosmological sources. These sources span a wide gamut, ranging from hydrodynamic instabilities in neutron stars (such as $\mathrm{r}$-modes) to particle production in the early Universe. Signals from a subset of these sources are expected to appear in these detectors as stochastic GW backgrounds (SGWBs). The detection of these backgrounds will help us in characterizing their sources. Accounting for these backgrounds will also be required by some detectors, such as the proposed space-based detector LISA, so that they can detect other GW signals. Here, we formulate the problem of constructing a bank of search templates that discretely span the parameter space of a generic SGWB. We apply it to the specific case of a class of cosmological SGWBs, known as the broken power-law models. We derive how the template density varies in their three-dimensional parameter space and show that for the LIGO 4 km detector pair, with LIGO-I sensitivities, a few hundred templates will suffice to detect such a background while incurring a loss in signal-to-noise ratio of no more than 3%.

Isolated horizon conditions specialized to spherical symmetry can be imposed directly at the quantum level. This answers several questions concerning horizon degrees of freedom, which are seen to be related to orientation, and its fluctuations at the kinematical as well as dynamical level. In particular, in the absence of scalar or fermionic matter the horizon area is an approximate quantum observable. Including different kinds of matter fields allows to probe several aspects of the Hamiltonian constraint of quantum geometry that are important in inhomogeneous situations.

We study $I{J}^P=0{\frac{3}{2}}^{\pm }$ and $1{\frac{3}{2}}^{\pm }$ pentaquark states with $S=+1$ in the QCD sum rule approach. The QCD sum rule for positive parity states and that for negative parity are independently derived. The sum rule suggests that there exist the $0{\frac{3}{2}}^{-}$ and the $1{\frac{3}{2}}^{-}$ states. These states may be observed as extremely narrow peaks since they can be much below the $S$-wave threshold and since the only allowed decay channels are $NK$ in $D$ wave, whose centrifugal barriers are so large that the widths are strongly suppressed. The $0{\frac{3}{2}}^{-}$ state may be assigned to the observed ${\Theta }^{+}(1540)$ and the $1{\frac{3}{2}}^{-}$ state can be a candidate for ${\Theta }^{++}$.

We show that in a decay of the form $B_d$ or $B_s\to P_1{P}_2\gamma$ (where $P_1$ and $P_2$ are pseudoscalar mesons), through a flavor changing dipole transition, time dependent oscillations can reveal the presence of physics beyond the standard model. If $P_1$ and $P_2$ are $CP$ eigenstates (e.g. as in $B_d\to K_S{\pi }^0\gamma$), then to leading order in the effective Hamiltonian, the oscillation is independent of the resonance structure. Thus data from resonances as well as from nonresonant decays can be included. This may significantly enhance the sensitivity to new physics of the method. If $P_1$ is a charged particle, and $P_2$ its antiparticle (e.g. as in $B_d\to {\pi }^{+}{\pi }^{-}\gamma$), one has the additional advantage that both the magnitude and the weak phase of any new physics contribution can be determined from a study of the angular distribution. These signals offer excellent ways to detect new physics because they are suppressed in the standard model. We also show that the potential contamination of these signals originating from the standard model annihilation diagram gives rise to photons with, to a very good approximation, the same helicity as the dominant penguin graph and thus causes no serious difficulty. The formalism which applies to the case where $P_1$ and $P_2$ are $C$ eigenstates also further generalizes to the case of final states containing multiple $C$ eigenstates and a photon. This suggests several additional channels to search for new physics, such as $K_S{\eta }^{\prime }(\eta )\gamma$, $\varphi K_S\gamma$ etc. We also emphasize that the contribution of nondipole interactions can be monitored by the dependence of the mixing-induced $CP$ asymmetry of nonresonant modes on the Dalitz variables. Furthermore, using a number of different final states can also provide important information on the contribution from nondipole effects.

The Pontecorvo-Maki-Nakagawa-Sakata neutrino mixing matrix is given, in general, by the product of two unitary matrices associated with the diagonalization of the charged lepton and neutrino mass matrices. Assuming that the active flavor neutrinos possess a Majorana mass matrix which is diagonalized by a bimaximal mixing matrix, we give the allowed forms of the charged lepton mixing matrix and the corresponding implied forms of the charged lepton mass matrix. We then assume that the origin of bimaximal mixing is a weakly broken flavor symmetry corresponding to the conservation of the nonstandard lepton charge $L^{\prime }=L_e-L_{\mu }-L_{\tau }$. The latter does not predict, in general, the atmospheric neutrino mixing to be maximal. We study the impact of this fact on the allowed forms of the charged lepton mixing matrix and on the neutrino mixing observables, analyzing the case of $CP$ violation in detail. When compared with the case of exact bimaximal mixing, the deviations from zero $U_{e3}$ and from maximal atmospheric neutrino mixing are typically more sizable if one assumes just $L^{\prime }$ conservation. In fact, $|U_{e3}{|}^2$ can be as small as 0.007 and atmospheric neutrino mixing can take any value inside its currently allowed range. We discuss under which conditions the atmospheric neutrino mixing angle is larger or smaller than $\pi /4$. We present also a simple seesaw realization of the implied light neutrino Majorana mass matrix and consider leptogenesis in this scenario.

A measurement of direct photons in $p+p$ collisions at $\sqrt{s}=200\mathrm{GeV}$ is presented. A photon excess above background from ${\pi }^0\to \gamma +\gamma$, $\eta \to \gamma +\gamma$ and other decays is observed in the transverse momentum range $5.5<p_{\mathrm{T}}<7\mathrm{GeV}/c$. The result is compared to a next-to-leading-order perturbative QCD calculation. Within errors, good agreement is found between the QCD calculation and the measured result.

We derive corrections to the JIMWLK equation in the regime where the charge density in the hadronic wave function is small. We show that the framework of the JIMWLK equation has to be significantly modified at small densities in order to properly account for the noncommutativity of the charge density operators. In particular the weight function for the calculation of averages can not be real, but is shown to contain the Wess-Zumino term. The corrections to the kernel of the JIMWLK evolution which are leading at small density are resummed into a path ordered exponential of the functional derivative with respect to the charge density operator, thus hinting at intriguing duality between the high and the low density regimes.

Type-I proton superconducting cores of neutron stars break up in a magnetic field into alternating domains of superconducting and normal fluids. We examine two channels of superfluid-normal fluid friction where (i) rotational vortices are decoupled from the nonsuperconducting domains and the interaction is due to the strong force between protons and neutrons; (ii) the nonsuperconducting domains are dynamically coupled to the vortices and the vortex motion generates transverse electric fields within them, causing electronic current flow and Ohmic dissipation. The obtained dissipation coefficients are consistent with the Eulerian precession of neutron stars.

We study possible contribution of the Majorana neutrino mass eigenstate ${\nu }_h$, dominated by a sterile neutrino component, to neutrinoless double beta ($0\nu \beta \beta$) decay. A special emphasis is made on accurate calculation of the corresponding nuclear matrix elements. From the current experimental lower bound on the $0\nu \beta \beta$-decay half-life of $76$ Ge we derive stringent constraints on the ${\nu }_h-{\nu }_e$ mixing in a wide region of the values of ${\nu }_h$ mass. We discuss cosmological and astrophysical status of ${\nu }_h$ in this mass region.

We propose a mass matrix model that gives a unified description of a quark and lepton with the same texture form based on a flavor $2\leftrightarrow 3$ symmetry. The model is in contrast with the conventional picture that the mass matrix forms in the quark sector will take somewhat different structures from those in the lepton sector. By investigating possible types of assignment for masses, we find that our quark mass matrices can lead to small CKM quark mixings which are consistent with experimental values. We also find some phase-parameter-independent relations among CKM quark mixing matrix elements.

Anomaly-mediated supersymmetry breaking in the context of 4D conformally sequestered models is combined with Poppitz-Trivedi D-type gauge-mediation. The implementation of the two mediation mechanisms naturally leads to visible soft masses at the same scale so that they can cooperatively solve the $\mu$ and flavor problems of weak scale supersymmetry, as well as the tachyonic-slepton problem of pure anomaly-mediation. The tools are developed in a modular fashion for more readily fitting into the general program of optimizing supersymmetric dynamics in hunting for the most attractive weak scale phenomenologies combined with Planck-scale plausibility.

We revisit the problem of parameter estimation of gravitational-wave chirp signals from inspiralling nonspinning compact binaries in the light of the recent extension of the post-Newtonian (PN) phasing formula to order $(v/c{)}^7$ beyond the leading Newtonian order. We study in detail the implications of higher post-Newtonian orders from 1PN up to 3.5PN in steps of 0.5PN ($\sim v/c$), and examine their convergence. In both initial and advanced detectors the estimation of the chirp mass ($\mathcal{M}$) and symmetric mass ratio ($\eta$) improve at higher PN orders but oscillate with every half-a-PN order. In initial LIGO, for a $10M_{\odot }–10M_{\odot }$ binary at a signal-to-noise ratio (SNR) of 10, the improvement in the estimation of $\mathcal{M}$ ($\eta$) at 3.5PN relative to 2PN is $\sim 19\%$ (52%). We compare parameter estimation in different detectors and assess their relative performance in two different ways: at a fixed SNR, with the aim of understanding how the bandwidth improves parameter estimation, and for a fixed source, to gauge the importance of sensitivity. Errors in parameter estimation at a fixed SNR are smaller for VIRGO than for both initial and advanced LIGO. This is because of the larger bandwidth over which it observes the signals. However, for sources at a fixed distance it is advanced LIGO that achieves the lowest errors owing to its greater sensitivity. Finally, we compute the amplitude corrections due to the “frequency-sweep” in the Fourier domain representation of the waveform within the stationary phase approximation and discuss its implication on parameter estimation. We find that the amplitude corrections change the errors in $\mathcal{M}$ and $\eta$ by less than 10% for initial LIGO at a signal-to-noise ratio of 10. Our analysis makes explicit the significance of higher PN order modeling of the inspiralling compact binary on parameter estimation.

We present a generic form of the covariant nonlocal action for infrared modifications of Einstein theory recently suggested within the weak-field curvature expansion. In the lowest order it is determined by two nonlocal operators—kernels of Ricci tensor and scalar quadratic forms. In models with a low strong-coupling scale, this action also incorporates the strongly coupled mode which cannot be perturbatively integrated out in terms of the metric field. This mode enters the action as a Lagrange multiplier for the constraint on metric variables which reduces to the curvature scalar and enforces the latter to vanish on shell. Generic structure of the action is demonstrated on the examples of the Fierz-Pauli and Dvali-Gabadadze-Porrati models and their extensions. The gauge-dependence status of the strong-coupling and van Dam-Veltman-Zakharov problems is briefly discussed along with the manifestly gauge-invariant formalism of handling the braneworld gravitational models at classical and quantum levels.