A misspelling error in the NUT is rectified.

During the last few years progress has been made on several fronts making it possible to revisit Cauchy-perturbative matching (CPM) in numerical relativity in a more robust and accurate way. This paper is the first in a series where we plan to analyze CPM in the light of these new results. One of the new developments is an understanding of how to impose constraint-preserving boundary conditions (CPBC); though most of the related research has been driven by outer boundaries, one can use them for matching interface boundaries as well. Another front is related to numerically stable evolutions using multiple patches, which in the context of CPM allows the matching to be performed on a spherical surface, thus avoiding interpolations between Cartesian and spherical grids. One way of achieving stability for such schemes of arbitrary high order is through the use of penalty techniques and discrete derivatives satisfying summation by parts (SBP). Recently, new, very efficient and high-order accurate derivatives satisfying SBP and associated dissipation operators have been constructed. Here we start by testing all these techniques applied to CPM in a setting that is simple enough to study all the ingredients in great detail: Einstein’s equations in spherical symmetry, describing a black hole coupled to a massless scalar field. We show that with the techniques described above, the errors introduced by Cauchy-perturbative matching are very small, and that very long-term and accurate CPM evolutions can be achieved. Our tests include the accretion and ring-down phase of a Schwarzschild black hole with CPM, where we find that the discrete evolution introduces, with a low spatial resolution of $\Delta r=M/10$, an error of 0.3% after an evolution time of $1,000,000M$. For a black hole of solar mass, this corresponds to approximately $5s$, and is therefore at the lower end of timescales discussed e.g. in the collapsar model of gamma-ray burst engines.

We investigate the nonlinear coupling between radial and nonradial oscillations of static spherically-symmetric neutron stars as a possible mechanism for the generation of gravitational waves that may lead to observable signatures. In this paper we concentrate on the axial sector of the nonradial perturbations. By using a multiparameter perturbative framework we introduce a complete description of the nonlinear coupling between radial and axial nonradial oscillations; we study the gauge-invariant character of the associated perturbative variables and develop a computational scheme to evolve the nonlinear coupling perturbations in the time domain. We present results of simulations corresponding to different physical situations and discuss the dynamical behavior of this nonlinear coupling. Of particular interest is the occurrence of signal amplifications in the form of resonance phenomena when a frequency associated with the radial pulsations is close to a frequency associated with one of the axial $w$-modes of the star. Finally, we mention possible extensions of this work and improvements towards more astrophysically motivated scenarios.

Modified gravity can be considered as an alternative to dark energy. In a generalized theory of gravity, the Universe may accelerate while containing only baryonic and dark matter. We study, in particular, the evolution of matter fluctuations in $f(R)$ models within the Palatini approach, and find that the resulting matter power spectrum is sensitive to a nonlinear dependence on the curvature scalar in the gravitational action. The constraints that arise from comparison to the form of the observed matter power spectrum tighten the previous constraints derived from background expansion by several orders of magnitude. Models in the allowed parameter space are practically indistinguishable from general relativity with a cosmological constant when the background expansion is considered.

We discuss the evolution of linear perturbations in a quintessence model in which the scalar field is nonminimally coupled to cold dark matter. We consider the effects of this coupling on both cosmic microwave background temperature anisotropies and matter perturbations. Because of the modification of the scale of cold dark matter as ${\rho }_c={\rho }_c^{(0)}{a}^{-3+\xi }$, we can shift the turnover in the matter power spectrum even without changing the present energy densities of matter and radiation. This can be used to constrain the strength of the coupling. We find that the phenomenology of this model is consistent with current observations up to the coupling power $n_c\le 0.01$ while adopting the current parameters measured by the Wilkinson Microwave Anisotropy Probe. Upcoming cosmic microwave background observations continuing to focus on resolving the higher peaks may put strong constraints on the strength of the coupling.

The effects of mass-varying neutrinos on cosmic microwave background (CMB) anisotropies and large scale structures (LSS) are studied. In these models, dark energy and neutrinos are coupled such that the neutrino masses are functions of the scalar field playing the role of dark energy. We begin by describing the cosmological background evolution of such a system. It is pointed out that, similar to models with a dark matter/dark energy interaction, the apparent equation of state measured with SNIa can be smaller than $-1$. We then discuss the effect of mass-varying neutrinos on the CMB anisotropies and the matter power spectrum. A suppression of power in the CMB power spectrum at large angular scales is usually observed. We give an explanation for this behavior and discuss different couplings and quintessence potentials to show the generality of the results obtained. We perform a likelihood analysis using wide-ranging SNIa, CMB, and LSS observations to assess whether such theories are viable. Treating the neutrino mass as a free parameter we find that the constraints on the coupling are weak, since CMB and LSS surveys give only upper bounds on the neutrino mass. However, fixing a priori the neutrino masses, we find that there is some evidence that the existence of such a coupling is actually preferred by current cosmological data over the standard $\Lambda \mathrm{CDM}$ cosmology.

One of the puzzles of the dark energy problem is the (first) cosmological coincidence problem, namely, why does our Universe begin the accelerated expansion recently? Why are we living in an epoch in which the dark energy density and the dust matter energy density are comparable? On the other hand, cosmological observations hint that the equation-of-state parameter (EoS) of dark energy crossed the phantom divide $w_{\mathrm{de}}=-1$ in the near past. Many dark energy models whose EoS can cross the phantom divide have been proposed. However, to our knowledge, these models with crossing the phantom divide only provide the possibility that $w_{\mathrm{de}}$ can cross $-1$. They do not answer another question, namely, why crossing the phantom divide occurs recently? Since in many existing models whose EoS can cross the phantom divide, $w_{\mathrm{de}}$ undulates around $-1$ randomly, why are we living in an epoch $w_{\mathrm{de}}<-1$? This can be regarded as the second cosmological coincidence problem. In this work, the cosmological evolution of the vectorlike dark energy interacting with background perfect fluid is investigated. We find that the first and second cosmological coincidence problems can be alleviated at the same time in this scenario.

The Drell-Yan process is analyzed in soft collinear effective theory near the end-point region. It is assumed that the relevant final-state hadron energy $Q(1-z)$ where $z$ is the momentum fraction transferred to the virtual photon is the typical hadronic scale $\sim \Lambda$, thus no intermediate scale exists. It is shown that this setup successfully reproduces the full theory results. We also discuss the factorized soft Wilson lines for the Drell-Yan process.

We study lepton flavor number violating rare $B$ decays, $b\to s{l}_h^{\pm }{l}_l^{\mp }$, in a seesaw model with low scale singlet Majorana neutrinos motivated by the resonant leptogenesis scenario. The branching ratios of inclusive decays $b\to s{l}_h^{\pm }{\overline{l}}_l^{\mp }$ with two almost degenerate singlet neutrinos at TeV scale are investigated in detail. We find that there exists a class of seesaw model in which the branching fractions of $b\to s\tau \mu$ and $\tau \to \mu \gamma$ can be as large as ${10}^{-10}$ and ${10}^{-9}$ within the reach of Super $B$ factories, respectively, without being in conflict with neutrino mixings and mass-squared difference of neutrinos from neutrino data, invisible decay width of $Z$, and the present limit of $\mathrm{Br}(\mu \to e\gamma )$. In the model, the lepton number asymmetries are vanishing.

We investigate chiral symmetry restoration in finite spatial volume and at finite temperature by calculating the dependence of the chiral phase transition temperature $T_c$ on the size of the spatial volume and the current-quark mass for the quark-meson model, using the proper-time renormalization group approach. We find that the critical temperature is weakly dependent on the size of the spatial volume for large current-quark masses, but depends strongly on it for small current-quark masses. In addition, for small volumes we observe a dependence on the choice of quark boundary conditions.

We show that topological semisuperfluid strings exist in the color-flavor locked (CFL) phase of color superconductors. These semisuperfluid strings carry quantized flux of ordinary and color magnetic fields. Away from the core the behavior of the string is that of a superfluid string. Using a Ginzburg-Landau free energy we find the configurations of these strings. These strings can form during the transition from the normal phase to the CFL phase at the core of very dense stars. We discuss an interesting scenario for a network of strings and its evolution at the core of dense stars.

The inverse eigenvalues of the Dirac operator in the Schwinger model satisfy the same Leutwyler-Smilga sum rules as in the case of QCD with one flavor. In this paper we give a microscopic derivation of these sum rules in the sector of arbitrary topological charge. We also show that the sum rules can be obtained from the clustering property of the scalar correlation functions. This argument holds for other theories with a mass gap and broken chiral symmetry such as QCD with one flavor. For QCD with several flavors a modified clustering property is derived from the low-energy chiral Lagrangian. We also derive sum rules for a fixed external gauge field. Both types of sum rules are obtained from the bosonized version of the Schwinger model. In the sector of topological charge $\nu$ the sum rules are consistent with a shift of the Dirac spectrum away from zero by $\nu /2$ average level spacings. This shift is also required to obtain a nonzero chiral condensate in the massless limit. Finally, we discuss the Dirac spectrum for a closely related two-dimensional theory with a gauge field action that is quadratic in the gauge field and has applications to the quantum Hall effect and $d$-wave superconductors.

We prove that taking correctly into account the lepton flavour dependence of the $CP$ asymmetries and washout processes, it is possible to obtain successful thermal leptogenesis from the decays of the second right-handed neutrino. The asymmetries in the muon and tau-flavour channels are then not erased by the inverse decays of the lightest right-handed neutrino $N_1$. In this way, we reopen the possibility of “thermal leptogenesis” in models with a strong hierarchy in the right-handed Majorana masses that is typically the case in models with up-quark neutrino-Yukawa unification.

The semileptonic decays ${\tau }^{-}\to {\mu }^{-}M(M={\pi }^0,\eta ,{\eta }^{\prime })$ could be sensitive probes for new physics scenarios with lepton flavor violation (LFV). Motivated by the recent Belle measurement, we investigate these decays in the type III two-Higgs-doublet model, $R$-parity violating supersymmetric models, and flavor changing $Z^{\prime }$ models with family nonuniversal couplings, respectively. In these new physics scenarios, there are LFV couplings at tree level. Our results have shown that the decays are very sensitive to the LFV couplings and could be enhanced to the present experimental sensitivities. We have derived tighter bounds on relevant couplings of these models, which may be useful for further relevant studies.

We describe searches for decays to two-body charmless final states ${\eta }^{\prime }\eta$, ${\eta }^{\prime }{\pi }^0$ and $\eta {\pi }^0$ of $B^0$ mesons produced in $e^{+}{e}^{-}$ annihilation. The data, collected with the BABAR detector at the Stanford Linear Accelerator Center, represent $232\times {10}^6$ produced $B\overline{B}$ pairs. The results for branching fractions are, in units of ${10}^{-6}$ (upper limits at 90% C.L.): $\mathcal{B}(B^0\to {\eta }^{\prime }\eta )={0.2}_{-0.5}^{+0.7}\pm 0.4(<1.7)$, $\mathcal{B}(B^0\to \eta {\pi }^0)={0.6}_{-0.4}^{+0.5}\pm 0.1(<1.3)$, and $\mathcal{B}(B^0\to {\eta }^{\prime }{\pi }^0)={0.8}_{-0.6}^{+0.8}\pm 0.1(<2.1)$. The first error quoted is statistical and the second systematic.

We have reinvestigated the collision of gluonic bubbles in an SU(2) model of QCD which was studied by Johnson, Choi, and Kisslinger in the context of the instanton-inspired model of QCD phase transition bubbles with plane-wave approximation. We discuss treacherous points of the instanton-inspired model that cause the violation of causality due to the presence of imaginary gluon fields. By constructing a new slightly modified Lorentzian model where we have three independent real gluon fields, we reanalyzed the process of bubble collisions. Our numerical results show some indication of forming a bubble wall in the colliding region.

Making use of the Nambu–Jona-Lasinio model and the multiple reflection expansion approximation, we study the phase transition of the finite size droplet with $u$ and $d$ quarks. We find that the dynamical masses of $u$, $d$ quarks are different, and the chiral symmetry can be restored at different critical radii for $u$, $d$ quarks. It provides a clue to understanding the effective nucleon mass splitting in nuclear matter. Meanwhile, it shows that the maximal isospin chemical potential at zero temperature is much smaller than the mass of pion in free space.

We study the quarkonia correlators above deconfinement using the potential model with screened temperature-dependent potentials. We find that while the qualitative features of the spectral functions, such as the survival of the 1S state, can be reproduced by potential models, the temperature dependence of the correlators disagree with the recent lattice data.

A modified formulation of the energy-momentum relation is proposed in the context of doubly special relativity. We investigate its impact on black hole physics. It turns out that such a modification will give corrections to both the temperature and the entropy of black holes. In particular, this modified dispersion relation also changes the picture of Hawking radiation greatly when the size of black holes approaches the Planck scale. It can prevent black holes from total evaporation, as a result providing a plausible mechanism to treat the remnant of black holes as a candidate for dark matter.

We formulate Lorentz covariance of a quantum field theory in terms of covariance of time-ordered products (or other Green’s functions). This formulation of Lorentz covariance implies spacelike local commutativity or anticommutativity of fields, sometimes called microscopic causality or microcausality. With this formulation microcausality does not have to be taken as a separate assumption.