We study the scaling behavior of the quark propagator on two lattices with similar physical volume in Landau gauge with $2+1$ flavors of dynamical quarks in order to test whether we are close to the continuum limit for these lattices. We use configurations generated with an improved staggered (“Asqtad”) action by the MILC collaboration. The calculations are performed on ${28}^3\times 96$ lattices with lattice spacing $a=0.09\mathrm{fm}$ and on ${20}^3\times 64$ lattices with lattice spacing $a=0.12\mathrm{fm}$. We calculate the quark mass function, $M(q^2)$, and the wave-function renormalization function, $Z(q^2)$, for a variety of bare quark masses. Comparing the behavior of these functions on the two sets of lattices we find that both $Z(q^2)$ and $M(q^2)$ show little sensitivity to the ultraviolet cutoff.

We compute the $I=2$ $\pi \pi$ scattering length at pion masses of $m_{\pi }\sim 294$, 348, and 484 MeV in fully-dynamical lattice QCD using Lüscher’s finite-volume method. The calculation is performed with domain-wall valence-quark propagators on asqtad-improved MILC configurations with staggered sea quarks at a single lattice spacing, $b\sim 0.125\mathrm{fm}$. Chiral perturbation theory is used to perform the extrapolation of the scattering length from lattice quark masses down to the physical value, and we find $m_{\pi }{a}_2=-0.0426\pm 0.0006\pm 0.0003\pm 0.0018$, in good agreement with experiment. The $I=2$ $\pi \pi$ scattering phase shift is calculated to be $\delta =-43\pm 10\pm 5°$ at $|\mathbf{p}|\sim 544\mathrm{MeV}$ for $m_{\pi }\sim 484\mathrm{MeV}$.

We study magnetic dipole (M1) transitions between two quarkonia in the framework of nonrelativistic effective field theories of QCD. Relativistic corrections of relative order $v^2$ are investigated in a systematic fashion. Nonperturbative corrections due to color-octet effects are considered for the first time and shown to vanish at relative order $v^2$. Exact, all order expressions for the relevant $1/m$ and $1/m^2$ magnetic operators are derived. The results allow us to scrutinize several potential model claims. In particular, we show that QCD excludes both contributions to the anomalous magnetic moment of the quarkonium induced by low-energy fluctuations and contributions to the magnetic dipole operators of the type induced by a scalar potential. Finally, we apply our results to the transitions $J/\psi \to {\eta }_c\gamma$, ${\rm Y}(1S)\to {\eta }_b\gamma$, ${\rm Y}(2S)\to {\eta }_b(2S)\gamma$, ${\rm Y}(2S)\to {\eta }_b\gamma$, ${\eta }_b(2S)\to {\rm Y}(1S)\gamma$, $h_b(1P)\to {\chi }_{b0,1}(1P)\gamma$, and ${\chi }_{b2}(1P)\to h_b(1P)\gamma$ by assuming these quarkonium states in the weak-coupling regime. Our analysis shows that the $J/\psi \to {\eta }_c\gamma$ width is consistent with a weak-coupling treatment of the charmonium ground state, while such a treatment for the hindered transition ${\rm Y}(2S)\to {\eta }_b\gamma$ appears difficult to accommodate within the CLEO III upper limit.

We present a generalization of the hyperspherical harmonic formalism to study systems made of quarks and antiquarks of the same flavor. This generalization is based on the symmetrization of the $N$-body wave function with respect to the symmetric group using the Barnea and Novoselsky algorithm. The formalism is applied to study four-quark systems by means of a constituent quark model successful in the description of the two- and three-quark systems. The results are compared to those obtained by means of variational approaches. Our analysis shows that four-quark systems with exotic $0^{+-}$ and nonexotic $2^{++}$ quantum numbers may be bound independently of the mass of the quark. $2^{+-}$ and $1^{+-}$ states become attractive only for larger mass of the quarks.

We construct a chiral Lagrangian for doubly heavy baryons and heavy mesons that is invariant under heavy quark-diquark symmetry at leading order and includes the leading $O(1/m_Q)$ symmetry violating operators. The theory is used to predict the electromagnetic decay width of the $J=\frac{3}{2}$ member of the ground state doubly heavy baryon doublet. Numerical estimates are provided for doubly charm baryons. We also calculate chiral corrections to doubly heavy baryon masses and strong decay widths of low lying excited doubly heavy baryons.

We investigate a simple model of neutrino mass based on $\mathrm{SU}(3{)}_C\otimes \mathrm{SU}(3{)}_L\otimes \mathrm{U}(1{)}_X$ gauge unification. The Yukawa coupling of the model has automatic lepton-number symmetry which is broken only by the self-couplings of the Higgs boson. At tree level, the neutrino spectrum contains three Dirac fermions, one massless and two degenerate in mass. At the two-loop level, neutrinos obtain Majorana masses and correct the tree-level result which naturally gives rise to an inverted hierarchy mass pattern and interesting mixing which can fit the current data with minor fine-tuning. In another scenario, one can pick the scales such that the loop-induced Majorana mass matrix is bigger than the Dirac one and thus reproduces the usual seesaw mechanism.

Using ${\chi }_{c_J}\to 2({\pi }^{+}{\pi }^{-})p\overline{p}$ decays from $14\times {10}^6\psi (2S)$ events accumulated by the BESII detector at the BEPC, the intermediate states ${\Xi }^{-}{\overline{\Xi }}^{+}$, $\Lambda \overline{\Lambda }{\pi }^{+}{\pi }^{-}$, and $K_S^0{K}_S^{0}p\overline{p}$ are studied, and their branching ratios or upper limits are measured.

Galaxy cluster counts at high redshift, binned into spatial pixels and binned into ranges in an observable proxy for mass, contain a wealth of information on both the dark energy equation of state and the mass selection function required to extract it. The likelihood of the number counts follows a Poisson distribution whose mean fluctuates with the large-scale structure of the universe. We develop a joint likelihood method that accounts for these distributions. Maximization of the likelihood over a theoretical model that includes both the cosmology and the observable-mass relations allows for a joint extraction of dark energy and cluster structural parameters.

We argue that the holographic description of four-dimensional Bogomol’nyi-Prasad-Sommerfield black holes naturally includes multicenter solutions. This suggests that the holographic dual to the gauge theory is not a single $\mathrm{Ad}{\mathrm{S}}_2\times S^2$ but a coherent ensemble of them. We verify this in a particular class of examples, where the two-dimensional Yang-Mills theory gives a holographic description of the black holes obtained by branes wrapping Calabi-Yau cycles. Using the free fermionic formulation, we show that $O(e^{-N})$ nonperturbative effects entangle the two Fermi surfaces. In an Euclidean description, the wave function of the multicenter black holes gets mapped to the Hartle-Hawking wave function of baby universes. This provides a concrete realization, within string theory, of effects that can be interpreted as the creation of baby universes. We find that, at least in the case we study, the baby universes do not lead to a loss of quantum coherence, in accord with general arguments.

We study a method to obtain invariants under area-preserving diffeomorphisms associated to closed curves in the plane from classical Yang-Mills theory in two dimensions. Taking as starting point the Yang-Mills field coupled to nondynamical particles carrying chromo-electric charge, and by means of a perturbative scheme, we obtain the first two contributions to the on-shell action, which are area-invariants. A geometrical interpretation of these invariants is given.

We consider nonsupersymmetric two-dimensional $CP(N-1)$ model deformed by a term presenting the bosonic part of the twisted-mass deformation of $\mathcal{N}=2$ supersymmetric version of the model. Our deformation has a special form preserving a $Z_N$ symmetry at the Lagrangian level. In the large mass limit the model is weakly coupled. Its dynamics is described by the Higgs phase, with $Z_N$ spontaneously broken. At small masses it is in the strong coupling Coulomb/confining phase. The $Z_N$ symmetry is restored. Two phases are separated by a phase transition. We find the phase transition point in the large-$N$ limit. It lies at strong coupling. As was expected, the phase transition is related to broken versus unbroken $Z_N$ symmetry in these two respective phases. The vacuum energies for these phases are determined too.

We study the possible black-string black-hole transition by analyzing the structure of the apparent horizon for a large family of time-symmetric initial data. We observe that, as judged by the apparent horizon, it is possible to generate arbitrarily deformed black strings at a moment of time symmetry. A similar study for hyperspherical black holes reveals that although arbitrarily deformed hyperspherical black holes can be constructed, the proper distance between the north and south poles along the extra direction has an upper limit.

We investigate the gravitational implosion of magnetized matter by studying the inhomogeneous collapse of a weakly magnetized Tolman-Bondi spacetime. The role of the field is analyzed by looking at the convergence of neighboring particle world lines. In particular, we identify the magnetically related stresses in the Raychaudhuri equation and use the Tolman-Bondi metric to evaluate their impact on the collapsing dust. We find that, despite the low energy level of the field, the Lorentz force dominates the advanced stages of the collapse, leading to a strongly anisotropic contraction. In addition, of all the magnetic stresses, those that resist the collapse are found to grow faster.

We study stationary and axially symmetric two solitonic solutions of five dimensional vacuum Einstein equations by using the inverse scattering method developed by Belinski and Zakharov. In this generation of the solutions, we use five dimensional Minkowski spacetime as a seed. It is shown that if we restrict ourselves to the case of one angular momentum component, the generated solution coincides with a black ring solution with a rotating two sphere which was found by Mishima and Iguchi recently.

Vacuum fluctuations in the inflaton field driving chaotic inflation with a quadratic potential give a red spectrum of primordial density perturbations, $n=0.97$. However angular fluctuations in an $\mathrm{O}(\mathrm{N})$-symmetric quadratic potential have a very nearly scale-invariant spectrum, $n=0.9998$. We investigate the possibility that these isocurvature field perturbations could give the dominant contribution to the primordial density perturbation after inflation.

The discrete quantum geometric effects play an important role in dynamical evolution in the loop quantum cosmology. These effects which are significant at the high energies lead to the quadratic energy density modifications to the Friedmann equation, as in the Randall-Sundrum braneworld scenarios but with a negative sign. We investigate the scalar field dynamics in this scenario and show the existence of a phase of superinflation independent of the inverse scale factor modifications as found earlier. In this regime the scalar field mimics the dynamics of a phantom field and vice versa. We also find various symmetries between the expanding phase, the contracting phase and the phantom phase in the loop quantum cosmology. We then construct the scaling solutions in the loop quantum cosmology and show their dual relationship with those of the Randall-Sundrum cosmology.

Magnetic fields in various astrophysical settings may be helical and, in the cosmological context, may provide a measure of primordial $CP$ violation during baryogenesis. Yet it is difficult, even in principle, to devise a scheme by which magnetic helicity may be detected, except in some very special systems. We propose that charged cosmic rays originating from known sources may be useful for this purpose. We show that the correlator of the arrival momenta of the cosmic rays is sensitive to the helicity of an intervening magnetic field. If the sources themselves are not known, the method may still be useful provided we have some knowledge of their spatial distribution.

Sterile neutrinos, fermions with no standard model couplings [SU(2) singlets], are predicted by most extensions of the standard model, and may be the dark matter. I describe the nonthermal production and linear perturbation evolution in the early universe of this dark matter candidate. I calculate production of sterile neutrino dark matter including effects of Friedmann dynamics dictated by the quark-hadron transition and particle population, the alteration of finite temperature effective mass of active neutrinos due to the presence of thermal leptons, and heating of the coupled species due to the disappearance of degrees of freedom in the plasma. These effects leave the sterile neutrinos with a nontrivial momentum distribution. I also calculate the evolution of sterile neutrino density perturbations in the early universe through the linear regime and provide a fitting function form for the transfer function describing the suppression of small-scale fluctuations for this warm dark matter candidate. The results presented here differ quantitatively from previous work due to the inclusion of the relevant physical effects during the production epoch.

The thermal leptogenesis in brane world cosmology is studied. In brane world cosmology, the expansion law is modified from the four-dimensional standard cosmological one at high temperature regime in the early universe. As a result, the well-known upper bound on the lightest light neutrino mass induced by the condition for the out-of-equilibrium decay of the lightest heavy neutrino, ${\tilde{m}}_1\lesssim {10}^{-3}\mathrm{eV}$, can be moderated to be ${\tilde{m}}_1\lesssim {10}^{-3}\mathrm{eV}\times (M_1/T_t{)}^2$ in the case of $T_t\le M_1$ with the lightest heavy neutrino mass ($M_1$) and the “transition temperature” ($T_t$), at which the modified expansion law in brane world cosmology is smoothly connecting with the standard one. This implies that the degenerate mass spectrum of the light neutrinos can be consistent with the thermal leptogenesis scenario. Furthermore, as recently pointed out, the gravitino problem in supersymmetric case can be solved if the transition temperature is low enough $T_t\lesssim {10}^{6–7}\mathrm{GeV}$. Therefore, even in the supersymmetric case, thermal leptogenesis scenario can be successfully realized in brane world cosmology.

We have used our new technique for fully numerical evolutions of orbiting black-hole binaries without excision to model the last orbit and merger of an equal-mass black-hole system. We track the trajectories of the individual apparent horizons and find that the binary completed approximately one and a third orbits before forming a common horizon. Upon calculating the complete gravitational radiation waveform, horizon mass, and spin, we find that the binary radiated $3.2\%$ of its mass and 24% of its angular momentum. The early part of the waveform, after a relatively short initial burst of spurious radiation, is oscillatory with increasing amplitude and frequency, as expected from orbital motion. The waveform then transitions to a typical “plunge” waveform; i.e. a rapid rise in amplitude followed by quasinormal ringing. The plunge part of the waveform is remarkably similar to the waveform from the previously studied “ISCO” configuration. We anticipate that the plunge waveform, when starting from quasicircular orbits, has a generic shape that is essentially independent of the initial separation of the binary.