We construct chiral effective Lagrangian for two lattice theories: one with Wilson fermions and the other with Wilson sea fermions and Ginsparg-Wilson valence fermions. For each of these theories we construct the Symanzik action through $\mathcal{O}{(a}^2).\mathrm{}$ The chiral Lagrangian is then derived, including terms of $\mathcal{O}{(a}^2),$ which have not been calculated before. We find that there are only few new terms at this order. Corrections to existing coefficients in the continuum chiral Lagrangian are proportional to $a^2$ and appear in the Lagrangian at $\mathcal{O}{(a}^2{p}^2)$ or higher. Similarly, O(4) symmetry-breaking terms enter the Symanzik action at $\mathcal{O}{(a}^2),$ but contribute to the chiral Lagrangian at $\mathcal{O}{(a}^2{p}^4)$ or higher. We calculate the light meson masses in chiral perturbation theory for both lattice theories. At next-to-leading order, we find that there are no $\mathcal{O}{(a}^2)$ corrections to the valence-valence meson mass in the mixed theory due to the enhanced chiral symmetry of the valence sector.

Inclusive $J/\psi$ production in $e^{+}{e}^{-}$ annihilation is studied in the framework of NRQCD. We first review the leading-order calculations of the cross sections for $e^{+}{e}^{-}\to J/\psi c\overline{c}$ and $e^{+}{e}^{-}\to J/\psi \mathrm{gg}$ and find that their ratio is about 1:1.5 at $\sqrt{s}\simeq 10\mathrm{GeV}.$ This result is in conflict with the current measurements by the Belle Collaboration, which finds that the process $e^{+}{e}^{-}\to J/\psi c\overline{c}$ accounts for about 2/3 of all the prompt $J/\psi ’s.\mathrm{}$ We find that the discrepancy problems in the total rate as well as in the $J/\psi$ momentum distributions can be resolved by postulating a large renormalization K factor $\left(K\simeq 4\right)$ for the $J/\psi c\overline{c}$ cross section and by taking into account collinear suppression in the end-point energy region of $J/\psi \mathrm{gg}$ production. Detailed studies of the model predictions in terms of the density matrix are performed and various momentum and angular distributions are presented as functions of the K factors. These distributions can be used to determine the normalizations of each subprocess provided that the production and decay angular distributions do not alter much by higher-order corrections.

The Kwieciński equations for QCD evolution of unintegrated parton distributions in transverse-coordinate space (b) are analyzed with the help of the Mellin-transform method. The equations are solved numerically in the general case, as well as in a small-b expansion which converges fast for $b{\Lambda }_{\mathrm{QCD}}$ sufficiently small. We also discuss the asymptotic limit of large $\mathrm{bQ}$ and show that the distributions generated by the evolution decrease with b according to a power law. Numerical results are presented for the pion distributions with a simple valencelike initial condition at the low scale, following from chiral large-$N_c$ quark models. We use two models: the spectral quark model and the Nambu–Jona-Lasinio model. Formal aspects of the equations, such as the analytic form of the b-dependent anomalous dimensions, their analytic structure, as well as the limits of unintegrated parton densities at $\overrightarrow{x}0,$ $\overrightarrow{x}1,$ and at large b, are discussed in detail. The effect of the spreading of the transverse momentum with increasing scale is confirmed, with $〈k_{\perp }^2〉$ growing asymptotically as $Q^2\alpha {(Q}^2).\mathrm{}$ Approximate formulas for $〈k_{\perp }^2〉$ for each parton species are given, which may be used in practical applications.

We discuss quark-antiquark leptoproduction within a QCD two-gluon exchange model at small x. The double spin asymmetries for longitudinally polarized leptons and transversely polarized protons in diffractive $Q\overline{Q}$ production are analyzed at eRHIC energies. The predicted $A_{\mathrm{lT}}$ asymmetry is large and can be used to obtain information on the polarized generalized gluon distributions in the proton.

We present a next-to-leading order QCD calculation for single-inclusive high-$p_T$ jet production in longitudinally polarized pp collisions within the “small-cone” approximation. The fully analytical expressions obtained for the underlying partonic hard-scattering cross sections greatly facilitate the analysis of upcoming BNL-RHIC data on the double-spin asymmetry $A_{\mathrm{LL}}^{\mathrm{jet}}$ for this process in terms of the unknown polarization of gluons in the nucleon. We simultaneously rederive the corresponding QCD corrections to unpolarized scattering and confirm the results existing in the literature. We also numerically compare to results obtained with Monte Carlo methods and assess the range of validity of the “small-cone” approximation for the kinematics relevant at BNL-RHIC.

In this paper, we calculate the decay rate and CP asymmetry of the $B_s\to {\pi }^{+}{\pi }^{-}$ decay in the perturbative QCD approach with Sudakov resummation. Since none of the quarks in final states is the same as those of the initial $B_s$ meson, this decay can occur only via annihilation diagrams in the standard model. Besides the current-current operators, the contributions from the QCD and electroweak penguin operators are also taken into account. We find that (a) the branching ratio is about $4\times {10}^{-7};$ (b) the penguin diagrams dominate the total contribution; and (c) the direct CP asymmetry is small in size: no more than 3%; but the mixing-induced CP asymmetry can be as large as 10% testable in the near future LHC-b experiments.

We use various methods of Borel integration to calculate the binding ground energies and masses of $b\overline{b}$ and $t\overline{t}$ quarkonia. The methods take into account the leading infrared renormalon structure of the $(\mathrm{hard}+)$soft part of the binding energies $E\left(s\right),$ and of the corresponding quark pole masses $m_q,$ where the contributions of these singularities in ${M\left(s\right)=2m}_q+E\left(s\right)\mathrm{}$ cancel. Beforehand, we carry out the separation of the binding energy into its $(\mathrm{hard}+)$soft and ultrasoft parts. The resummation formalisms are applied to expansions of $m_q$ and $E\left(s\right)\mathrm{}$ in terms of quantities which do not involve renormalon ambiguity, such as $\overline{\mathrm{MS}}$ mass $m_q$ and ${\alpha }_s\left(\mu \right).\mathrm{}$ The renormalization scales $\mu$ are different in calculations of $m_q,$ $E\left(s\right)\mathrm{}$ and $E\left(\mathrm{us}\right).$ The mass $m_b$ is extracted, and the binding energies $E_{t\overline{t}}$ and the peak (resonance) energies $E_{\mathrm{res}.\mathrm{}}$ for $t\overline{t}$ production are obtained.

A semiclassical electroweak generalization of the Weizsäcker-Williams method was formulated in a previous paper, with equivalent boson masses and the minimum impact parameter left as free parameters. These two quantities are derived and examined in great detail here. The mass of an equivalent boson is found to be determined by the mass and the electroweak charges of the parent fermion. It is shown that equivalent photons are massless, and the W and Z equivalent bosons have roughly the same mass. Formulas for the minimum impact parameter are also derived for various cases of interest. Using these results, the generalized number spectrum functions for point particles and nuclei are compared to similar functions found in other theories. Excellent agreement is found in all applications of the method.

The $A_4$ model of leptons was proposed originally for nearly degenerate neutrino masses. With minimal modification, it is shown to accommodate as well the cases of normal hierarchy and inverted hierarchy. In all cases, this new model predicts ${\sin }^{2}2{\theta }_{\mathrm{atm}}=1\mathrm{}$ and ${\tan }^2{\theta }_{\mathrm{sol}}=0.5\mathrm{}$ for $U_{e3\mathrm{}}=0.\mathrm{}$ It also predicts their deviations from 1 and 0.5 respectively for $U_{e3\mathrm{}}\ne 0.$

A massless scalar field is quantized in the background of a spinning string with cosmic dislocation. By increasing the spin density toward the dislocation parameter, a region containing closed timelike curves (CTCs) eventually forms around the defect. Correspondingly, the propagator tends to the ordinary cosmic string propagator, leading therefore to a mean-square field fluctuation, which remains well behaved throughout the process, unlike the vacuum expectation value of the energy-momentum tensor, which diverges due to a subtle mechanism. These results suggest that back reaction leads to the formation of a “horizon” that protects from the appearance of CTCs.

We study the low energy dynamics of pions in a gravity dual of chiral symmetry breaking. The string theory construction consists of a probe D7 brane in the Constable-Myers nonsupersymmetric background, which has been shown to describe chiral symmetry breaking in the pattern of QCD. We expand the D7 brane’s Dirac-Born-Infeld action for fluctuations that correspond to the Goldstone mode and show that they take the form of a nonlinear chiral Lagrangian. We numerically compute the quark condensate, pion decay constant, and higher order Gasser-Leutwyler coefficients. We find their form is consistent with naive dimensional analysis estimates. We also explore the gauging of the quark’s chiral symmetries and the vector meson spectrum.

We propose an exactly solvable model of the quantum oscillator on the class of Kähler spaces (with conic singularities), connected with two-dimensional complex projective spaces. Its energy spectrum is nondegenerate in the orbital quantum number, when the space has nonconstant curvature. We reduce the model to a three-dimensional system interacting with the Dirac monopole. Owing to noncommutativity of the reduction and quantization procedures, the Hamiltonian of the reduced system gets nontrivial quantum corrections. We transform the reduced system into a MIC-Kepler-like one and find that quantum corrections arise only in its energy and coupling constant. We present the exact spectrum of the generalized MIC-Kepler system. The one-(complex) dimensional analog of the suggested model is formulated on the Riemann surface over the complex projective plane and could be interpreted as a system with fractional spin.

So far it has been found by using lattice techniques that in the anisotropic five-dimensional Abelian Higgs model, a layered Higgs phase exists in addition to the expected five-dimensional one. The exploration of the phase diagram has shown that the two Higgs phases are separated by a phase transition from the confining phase. This transition is known to be first order. In this paper we explore the possibility of finding a second-order transition point in the critical line that separates the first-order phase transition from the crossover region. This is shown to be the case only for the four-dimensional Higgs layered phase while the phase transition to the five-dimensional broken phase remains first order. The layered phase serves as the possible realization of four-dimensional spacetime dynamics, which is embedded in a five-dimensional spacetime. These results are due to gauge and scalar field localization by confining interactions along the extra fifth direction.

The late-time tails of a massive scalar field in the spacetime of black holes are studied numerically. Previous analytical results for a Schwarzschild black hole are confirmed: The late-time behavior of the field as recorded by a static observer is given by $\psi \mathrm{}\left(t\right)\mathrm{}\sim t^{-5/6}\sin \left[\omega \mathrm{}\right(t)\mathrm{}\times t],$ where $\omega \mathrm{}\left(t\right)\mathrm{}$ depends weakly on time. This result is carried over to the case of a Kerr black hole. In particular, it is found that the power-law index of $-5/6$ depends on neither the multipole mode $\mathcal{l}$ nor on the spin rate of the black hole $a/M.\mathrm{}$ In all black hole spacetimes, massive scalar fields have the same late-time behavior irrespective of their initial data (i.e., angular distribution). Their late-time behavior is universal.

We consider cosmological particle production in 1+1 dimensional string theory. The process is described most efficiently in terms of anomalies, but we also discuss the explicit mode expansions. In matrix cosmology the usual vacuum ambiguity of quantum fields in time-dependent backgrounds is resolved by the underlying matrix model. This leads to a finite energy density for the “in” state which cancels the effect of anomalous particle production.

We study the pp limit of ${\mathrm{AdS}}_3\times S^3$ at the interaction level. We find the interacting Hamiltonian for the bosonic fields of $D=6\mathrm{}$ SUGRA in the pp-wave background, and compare it to the cubic couplings of the full ${\mathrm{AdS}}_3\times S^3.$ We show how the pp-wave theory vertex arises in the large J limit. Our analysis also provides some insight into the origin of specific “prefactors” which appear in the pp-wave interaction.

We propose a dual thermodynamic description of a classical instability of generalized black hole spacetimes. From a thermodynamic perspective, the instability is due to negative compressibility in regions where the Casimir pressure is large. The argument indicates how the correspondence between thermodynamic and classical instability for horizons may be extended to cases without translational invariance.

In this paper we consider nonlinear interaction between gravitational and electromagnetic waves in a strongly magnetized plasma. More specifically, we investigate the propagation of gravitational waves with the direction of propagation perpendicular to a background magnetic field and the coupling to compressional Alfvén waves. The gravitational waves are considered in the high-frequency limit and the plasma is modeled by a multifluid description. We make a self-consistent, weakly nonlinear analysis of the Einstein-Maxwell system and derive a wave equation for the coupled gravitational and electromagnetic wave modes. A WKB-approximation is then applied and as a result we obtain the nonlinear Schrödinger equation for the slowly varying wave amplitudes. The analysis is extended to 3D wave pulses, and we discuss the applications to radiation generated from pulsar binary mergers. It turns out that the electromagnetic radiation from a binary merger should experience a focusing effect, that in principle could be detected.

We construct a model of inflation in string theory after carefully taking into account moduli stabilization. The setting is a warped compactification of type IIB string theory in the presence of D3- and anti-D3-branes. The inflaton is the position of a D3-brane in the internal space. By suitably adjusting fluxes and the location of symmetrically placed anti-D3-branes, we show that at a point of enhanced symmetry, the inflaton potential V can have a broad maximum, satisfying the condition $V^{″}/V\ll 1$ in Planck units. On starting close to the top of this potential the slow-roll conditions can be met. Observational constraints impose significant restrictions. As a first pass we show that these can be satisfied and determine the important scales in the compactification to within an order of magnitude. One robust feature is that the scale of inflation is low, $H=\mathcal{O}{(10\mathrm{}}^{10})\mathrm{GeV}.$ Removing the observational constraints makes it much easier to construct a slow-roll inflationary model. Generalizations and consequences including the possibility of eternal inflation are also discussed. A more careful study, including explicit constructions of the model in string theory, is left for the future.

Primordial vector modes describe vortical fluid perturbations in the early Universe. A regular solution exists with constant nonzero radiation vorticities on superhorizon scales. Baryons are tightly coupled to the photons, and the baryon velocity only decays by an order unity factor by recombination, leading to an observable CMB anisotropy signature via the Doppler effect. There is also a large B-mode CMB polarization signal, with significant power on scales larger than $l\sim 2000.$ This B-mode signature is distinct from that expected from tensor modes or gravitational lensing, and makes a primordial vector to scalar mode power ratio $\sim {10}^{-6}$ detectable. Future observations aimed at detecting large scale B modes from gravitational waves will also be sensitive to regular vector modes at around this level.