We study the effects of finite volume on the two-particle decay rate of an unstable state with nonzero momentum. First, Lüscher’s field-theoretic relation between the infinite-volume scattering phase shifts and the quantized energy levels of a finite-volume, two-particle system is generalized to the case of nonzero total momentum, confirming earlier results of Rummukainen and Gottlieb. We then use this result and the method of Lellouch and Lüscher to determine the corrections needed for a finite-volume calculation of a two-particle decay amplitude when the decaying particle has nonvanishing center-of-mass momentum.

We present results from the first large-scale study of two-flavor QCD using domain wall fermions (DWF), a chirally symmetric fermion formulation which has been proven to be very effective in the quenched approximation. We work on lattices of size ${16}^3\times 32$, with a lattice cutoff of $a^{-1}\approx 1.7\mathrm{GeV}$ and dynamical (or sea) quark masses in the range $m_{\mathrm{strange}}/2\lesssim m_{\mathrm{sea}}\lesssim m_{\mathrm{strange}}$. After discussing the algorithmic and implementation issues involved in simulating dynamical DWF, we report on the low-lying hadron spectrum, decay constants, static quark potential, and the important kaon weak matrix element describing indirect $CP$ violation in the standard model, $B_K$. In the latter case we include the effect of nondegenerate quark masses ($m_s\ne m_u=m_d$), finding $B_K^{\overline{MS}}(2\mathrm{GeV})=0.495(18)$.

We reanalyze the $\gamma {\gamma }^{*}\to {\pi }^0$ transition form factor $F_{\pi \gamma }(Q^2)$ within the QCD light-cone sum rules method with the twist-4 accuracy. In computations, the pion leading twist distribution amplitude (DA) with two nonasymptotic terms and the renormalon method-inspired twist-4 DAs are used. The latters allow us to estimate the impact of effects due to higher conformal spin components in the pion twist-4 DAs on the form factor $F_{\pi \gamma }(Q^2)$. Obtained theoretical predictions are employed to deduce constraints on the pion DAs from CELLO and CLEO data.

In the general-mass variable-flavor-number scheme, the “heavy-quark mechanisms” of $B_c(B_c^{*})$ meson hadroproduction via the subprocesses $g+c\to B_c(B_c^{*})+\cdots$ and $g+\overline{b}\to B_c(B_c^{*})+\cdots$ are investigated. In the scheme, possible double counting from these mechanisms and the “light mechanisms” (the gluon-gluon fusion and quark-antiquark annihilation mechanisms) is subtracted properly. The numerical results show that the transverse-momentum, $p_t$, distribution of the produced $B_c(B_c^{*})$ from the “intrinsic heavy-quark mechanisms” (i.e. the heavy-quark mechanisms in which the double-counting components have been subtracted accordingly) declines faster with the increment of the $p_t$ than that from the light mechanisms, and only in the small $p_t$ region ($p_t\lesssim 7.0\mathrm{GeV}$) the intrinsic heavy-quark mechanisms themselves may make remarkable contributions. The combined contributions from the intrinsic heavy-quark mechanisms and the light mechanisms to the production are compared with that obtained by most of the calculations in the literature, which in some sense are within the fixed flavor number scheme at leading order, and we find that the production by virtue of the general-mass variable-flavor-number scheme is more or less the same as the one in the literature, except in the small $p_t$ region.

The observed pattern of neutrino mixing may be the result of a 2-3$(\mu -\tau )$ symmetry in the leptonic sector. We consider a two Higgs doublet model with a 2-3 symmetry in the down-type quark and the charged lepton sector. The breaking of the 2-3 symmetry by the strange quark mass and the muon mass leads to flavor changing neutral currents in the quark sector and the charged lepton sector that are suppressed by $m_s/m_b$ and $m_{\mu }/m_{\tau }$ in addition to the mass of the heavy Higgs boson of the second Higgs doublet. A Higgs boson mass of $m_H\sim 600–900\mathrm{GeV}$ can explain the deviation from the standard model reported in several rare $B$ decays. Predictions for other $B$ decays are made, and a new $CP$ phase is predicted in $B_s-{\overline{B}}_s$ mixing. The lepton flavor violating decays $\tau \to \mu \overline{l}(\overline{q})l(q)$ are below the experimental limits. The breaking of 2-3 symmetry in the lepton sector can lead to deviations of the atmospheric neutrino mixing angle from the maximal value by $\sim 2$ degrees.

Finite expressions for the mean value of the stress tensor corresponding to a scalar field with a generalized dispersion relation in a Friedmann-Robertson-Walker universe are obtained using adiabatic renormalization. Formally divergent integrals are evaluated by means of dimensional regularization. The renormalization procedure is shown to be equivalent to a redefinition of the cosmological constant and the Newton constant in the semiclassical Einstein equations.

Asymmetric brane worlds with dS expansion and static double kink topology are obtained from a recently proposed method and their properties are analyzed. These domain walls interpolate between two spacetimes with different cosmological constants. In the dynamic case, the vacua correspond to dS and AdS geometry, unlike the static case where they correspond to AdS background. We show that it is possible to confine gravity on such branes. In particular, the double-brane world hosts two different walls, so that the gravity is localized on one of them.

Causal radial geodesics with a positive interval in the Schwarzschild metric include a subset of trajectories completely confined behind a horizon, which compose a thermal statistical ensemble with the Hawking-Gibbons temperature. The Bekenstein-Hawking entropy is given by an action at corresponding geodesics of particles with a summed mass equal to that of the black hole in the limit of a large mass. The entropy of a charged black hole is calculated in this way by using the partition function evaluated at radial geodesics confined behind horizons. We establish two quantum phase states inside the black hole and a transition between them. For the Kerr-Newman black hole we specify an angular motion on geodesics to reduce the problem to the case of radial motion elaborated on in previous papers. An appropriate value of entropy for a charged and rotating black hole is obtained by calculating the partition function on thermal geodesics confined behind horizons. The quantum aggregation is classified in a similar way to the Reissner-Nordstrøm black hole.

The Faddeev model is a second class constrained system. Here we construct its nilpotent BRST operator and derive the ensuing manifestly BRST invariant Lagrangian. Our construction employs the structure of Stückelberg fields in a nontrivial fashion.

An almost-stationary gauge condition is proposed with a view to numerical relativity applications. The time lines are defined as the integral curves of the timelike solutions of the harmonic almost-Killing equation. This vector equation is derived from a variational principle, by minimizing the deviations from isometry. The corresponding almost-stationary gauge condition allows us to put the field equations in hyperbolic form, both in the free-evolution ADM and in the Z4 formalisms.

Inflation is known to produce both gravitational waves and seed magnetic fields on scales well beyond the size of the horizon. The general relativistic study of the interaction between these two sources after the end of inflation, showed a significant amplification of the initial magnetic seed which brought the latter within the currently accepted dynamo limits. In the present article we revisit this gravitomagnetic interaction and argue that the observed strong growth of the field is the result of resonance. More specifically, we show that the maximum magnetic boost always occurs when the wavelength of the inducing gravitational radiation and the scale of the original seed field coincide. We also look closer at the physics of the proposed Maxwell-Weyl coupling, consider the implications of finite electrical conductivity for the efficiency of the amplification mechanism and clarify further the mathematics of the analysis.

Topological defects may play the role of the curvatons. I propose a new mechanism of generating density perturbations from cosmological defects in inflationary models. I show several examples in which defects play crucial role in generating density perturbations.

Magnetic fields of unknown origin appear to permeate the Universe on all large scales. We suggest that the winds and cosmic rays, which are produced by the spherical ejecta and jets from supernova explosions, magnetize the interstellar medium in galaxies, the intracluster medium in galaxy clusters, and the intergalactic space. We show that, if the cosmic rays generate magnetic fields in rough energy equipartition with the cosmic rays, the predicted magnetic-field strengths coincide with the ones observed.

We calculate the SUSY-QCD corrections to the inclusive total cross sections of the associated production processes $pp\to W^{\pm }{H}^{\mp }+X$ in the Minimal Supersymmetric Standard Model(MSSM) at the CERN Large Hadron Collider(LHC). The SUSY-QCD corrections can increase and decrease the total cross sections depending on the choice of the SUSY parameters. When $\mu <0$ the SUSY-QCD corrections increase the leading-order (LO) total cross sections significantly for large tan$\beta$ ($\sim 40$), which can exceed $10\%$ and have the opposite sign with respect to the QCD and the SUSY-EW corrections, and thus cancel with them to some extent. Moreover, we also investigate the effects of the SUSY-QCD on the differential distribution of cross sections in transverse momentum $p_T$ and rapidity Y of W-boson, and the invariant mass $M_{W^{+}{H}^{-}}$.

We present a general numerical method for computing precisely the false vacuum decay rate, including the prefactor due to quantum fluctuations about the classical bounce solution, in a self-interacting scalar field theory modeling the process of nucleation in four-dimensional space-time. This technique does not rely on the thin-wall approximation. The method is based on the Gelfand-Yaglom approach to determinants of differential operators, suitably extended to higher dimensions using angular momentum cutoff regularization. A related approach has been discussed recently by Baacke and Lavrelashvili, but we implement the regularization and renormalization in a different manner, and compare directly with analytic computations made in the thin-wall approximation. We also derive a simple new formula for the zero mode contribution to the fluctuation prefactor, expressed entirely in terms of the asymptotic behavior of the classical bounce solution.

We study the pair creation of point particles and strings in a time-dependent, weak gravitational field. We find that, for massive string states, there are surprising and significant differences between the string and point-particle results. Central to our approach is the fact that a weakly curved spacetime can be represented by a coherent state of gravitons, and therefore we employ standard techniques in string perturbation theory. String and point-particle pairs are created through tree-level interactions between the background gravitons. In particular, we focus on the production of excited string states and perform explicit calculations of the production of a set of string states of arbitrary excitation level. The differences between the string and point-particle results may contain important lessons for the pair production of strings in the strong gravitational fields of interest in cosmology and black hole physics.

Recently, many dark energy models whose equation-of-state parameter can cross the phantom divide $w_{\mathrm{de}}=-1$ have been proposed. In a previous paper [H. Wei, R. G. Cai, and D. F. Zeng, Classical Quantum Gravity 22, 3189 (2005)], we suggest such a model named hessence, in which a noncanonical complex scalar field plays the role of dark energy. In this work, the cosmological evolution of the hessence dark energy is investigated. We consider two cases: one is the hessence field with an exponential potential, and the other is with a (inverse) power-law potential. We separately investigate the dynamical system with four different interaction forms between hessence and background perfect fluid. It is found that the big rip never appears in the hessence model, even in the most general case, beyond particular potentials and interaction forms.