The Raychaudhuri equation has seen extensive use in general relativity, most notably in the development of various singularity theorems. In this rather technical article we shall generalize the Raychaudhuri equation in several ways. First an improved version of the standard timelike Raychaudhuri equation is developed, where several key terms are lumped together as a divergence. This already has a number of interesting applications, both within the Arnowitt-Deser-Misner formalism and elsewhere. Second, a spacelike version of the Raychaudhuri equation is briefly discussed. Third, a version of the Raychaudhuri equation is developed that does not depend on the use of normalized congruences. This leads to useful formulae for the “diagonal” part of the Ricci tensor. Fourth, a “two vector” version of the Raychaudhuri equation is developed that uses two congruences to effectively extract “off-diagonal” information concerning the Ricci tensor.

We consider a simple modification of the amplitude defining the dynamics of loop quantum gravity, corresponding to the introduction of the cosmological constant, and possibly related to the $SL(2,\mathbb{C}{)}_q$ extension of the theory recently considered by Fairbairn-Meusburger and Han. We show that, in the context of spinfoam cosmology, this modification yields the de Sitter cosmological solution.

Recent searches of gravitational-wave data raise the question of what maximum gravitational-wave energies could be emitted during gamma-ray flares of highly magnetized neutron stars (magnetars). The highest energies ($\sim {10}^{49}\mathrm{erg}$) predicted so far come from a model [K. Ioka, Mon. Not. R. Astron. Soc. 327, 639 (2001), http://adsabs.harvard.edu/abs/2001MNRAS.327..639I] in which the internal magnetic field of a magnetar experiences a global reconfiguration, changing the hydromagnetic equilibrium structure of the star and tapping the gravitational potential energy without changing the magnetic potential energy. The largest energies in this model assume very special conditions, including a large change in moment of inertia (which was observed in at most one flare), a very high internal magnetic field, and a very soft equation of state. Here we show that energies of ${10}^{48}–{10}^{49}\mathrm{erg}$ are possible under more generic conditions by tapping the magnetic energy, and we note that similar energies may also be available through cracking of exotic solid cores. Current observational limits on gravitational waves from magnetar fundamental modes are just reaching these energies and will beat them in the era of advanced interferometers.

We use mathematical methods based on generating functions to study the statistical properties of the black hole degeneracy spectrum in loop quantum gravity. In particular we will study the persistence of the observed effective quantization of the entropy as a function of the horizon area. We will show that this quantization disappears as the area increases despite the existence of black hole configurations with a large degeneracy. The methods that we describe here can be adapted to the study of the statistical properties of the black hole degeneracy spectrum for all the existing proposals to define black hole entropy in loop quantum gravity.

In this paper, we investigate three important issues: stability, ghost, and strong coupling, in the Horava–Melby-Thompson setup of the Horava-Lifshitz theory with $\lambda \ne 1$, generalized recently by da Silva. We first develop the general linear scalar perturbations of the Friedmann-Robertson-Walker (FRW) universe with arbitrary spatial curvature and find that an immediate by-product of the setup is that, in all the inflationary models described by a scalar field, the FRW universe is necessarily flat. Applying them to the case of the Minkowski background, we find that it is stable, and, similar to the case $\lambda =1$, the spin-0 graviton is eliminated. The vector perturbations vanish identically in the Minkowski background. Thus, similar to general relativity, a free gravitational field in this setup is completely described by a spin-2 massless graviton, even with $\lambda \ne 1$. We also study the ghost problem in the FRW background and find explicitly the ghost-free conditions. To study the strong coupling problem, we consider two different kinds of spacetimes, all with the presence of matter: one is cosmological, and the other is static. We find that the coupling becomes strong for a process with energy higher than $M_{\mathrm{pl}}|c_{\psi }{|}^{5/2}$ in the flat FRW background and $M_{\mathrm{pl}}|c_{\psi }{|}^3$ in a static weak gravitational field, where $|c_{\psi }|\equiv |(1-\lambda )/(3\lambda -1){|}^{1/2}$.

A test particle of mass $\mu$ on a bound geodesic of a Kerr black hole of mass $M\gg \mu$ will slowly inspiral as gravitational radiation extracts energy and angular momentum from its orbit. This inspiral can be considered adiabatic when the orbital period is much shorter than the time scale on which energy is radiated, and quasicircular when the radial velocity is much less than the azimuthal velocity. Although the inspiral always remains adiabatic provided $\mu \ll M$, the quasicircular approximation breaks down as the particle approaches the innermost stable circular orbit (ISCO). In this paper, we relax the quasicircular approximation and solve the radial equation of motion explicitly near the ISCO. We use the requirement that the test particle’s 4-velocity remains properly normalized to calculate a new contribution to the difference between its energy and angular momentum. This difference determines how a black hole’s spin changes following a test-particle merger, and can be extrapolated to help predict the mass and spin of the final black hole produced in finite-mass-ratio black-hole mergers. Our new contribution is particularly important for nearly maximally spinning black holes, as it can affect whether a merger produces a naked singularity.

In this paper we study the effect of biasing on the power spectrum at large scales. We show that even though nonlinear biasing does introduce a white noise contribution on large scales, the $P(k)\propto k^n$ behavior of the matter power spectrum on large scales may still be visible and above the white noise for about one decade. We show, that the Kaiser biasing scheme which leads to linear bias of the correlation function on large scales, also generates a linear bias of the power spectrum on rather small scales. This is a consequence of the divergence on small scales of the pure Harrison-Zeldovich spectrum. However, biasing becomes $k$ dependent if we damp the underlying power spectrum on small scales. We also discuss the effect of biasing on the baryon acoustic oscillations.

The temperature fluctuations of the cosmic microwave background (CMB) are supposed to be distributed randomly in both magnitude and phase, following to the simplest model of inflation. In this paper, we look at the odd and even multipoles of the spherical harmonic decomposition of the CMB, and the different characteristics of these, giving rise to a parity asymmetry. We compare the even and odd multipoles in the CMB power spectrum, and also the even and odd mean angles. We find for the multipoles of the power spectrum that there is power excess in odd multipoles, compared to even ones, meaning that we have a parity asymmetry. Further, for the phases, we present a random walk for the mean angles, and find a significant separation for even/odd mean angles, especially so for galactic coordinates. This is further tested and confirmed with a directional parity test, comparing the parity asymmetry in galactic and ecliptic coordinates.

This brief note is devoted to reconcile the conclusions from a recent analysis of the IR solutions for the ghost propagator Dyson-Schwinger equations in Coulomb gauge with previous studies in Landau gauge.

We propose an approach for the calculation of the Yukawa coupling through the scalar decay constant and the chiral condensate in the context of the extended technicolor . We perform the nonperturbative computation of the Yukawa coupling based on the improved ladder Schwinger-Dyson equation. It turns out that the Yukawa coupling can be larger or smaller than the standard model value, depending on the number $N_D$ of the weak doublets for each technicolor (TC) index. It is thus nontrivial whether or not the huge enhancement of the production of the scalar via the gluon fusion takes place even for a walking TC model with a colored techni-fermion. For the typical one-family TC model near conformality, it is found that the Yukawa coupling is slightly larger than the standard model one, where the expected mass of the scalar bound state is around 500 GeV. In this case, the production cross section via the gluon fusion is considerably enhanced, as naively expected, and hence such a scalar can be discovered/excluded at the early stage of the LHC.

The recently evaluated two-pion contribution to the muon $g-2$ and the phase of the pion electromagnetic form factor in the elastic region, known from $\pi \pi$ scattering by Fermi-Watson theorem, are exploited by analytic techniques for finding correlations between the coefficients of the Taylor expansion at $t=0$ and the values of the form factor at several points in the spacelike region. We do not use specific parametrizations, and the results are fully independent of the unknown phase in the inelastic region. Using for instance, from recent determinations, $⟨r_{\pi }^2⟩=(0.435\pm 0.005){\mathrm{fm}}^2$ and $F(-1.6{\mathrm{GeV}}^2)={0.243}_{-0.014}^{+0.022}$, we obtain the allowed ranges $3.75{\mathrm{GeV}}^{-4}\lesssim c\lesssim 3.98{\mathrm{GeV}}^{-4}$ and $9.91{\mathrm{GeV}}^{-6}\lesssim d\lesssim 10.46{\mathrm{GeV}}^{-6}$ for the curvature and the next Taylor coefficient, with a strong correlation between them. We also predict a large region in the complex plane where the form factor cannot have zeros.

We examine many $SO(10)$ models for their viability or otherwise in explaining all the fermion masses and mixing angles. This study is carried out for both supersymmetric and nonsupersymmetric models and with minimal ($10+\overline{126}$) and nonminimal ($10+\overline{126}+120$) Higgs content. Extensive numerical fits to fermion masses and mixing are carried out in each case, assuming dominance of type-II or type-I seesaw mechanism. Required scale of the $B\mathrm{\text{−}}L$ breaking is identified in each case. In supersymmetric case, several sets of data at the GUT scale with or without inclusion of finite supersymmetric corrections are used. All the cases studied provide quite good fits if the type-I seesaw mechanism dominates. This is not the case in the minimal model based on several data sets and type-II seesaw mechanism. This can be traced to the absence of the $b\mathrm{\text{−}}\tau$ unification at the GUT scale in these cases. In contrast, the type-II seesaw mechanism works uniformly well in all the supersymmetric cases when 120 Higgs is also included. The minimal nonsupersymmetric model with type-I seesaw dominance gives excellent fits. In the presence of a ${45}_H$ and an intermediate scale, the model can also account for the gauge coupling unification making it potentially interesting model for the complete unification. Structure of the Yukawa coupling matrices obtained numerically in this specific case is shown to follow from a very simple $U(1)$ symmetry and a Froggatt-Nielsen singlet.

We develop a unitarized formalism to study tetraquarks using the triple flip-flop potential, which includes two meson-meson potentials and the tetraquark four-body potential. This can be related to the Jaffe-Wilczek and to the Karliner-Lipkin tetraquark models, where we also consider the possible open channels, since the four quarks and antiquarks may at any time escape to a pair of mesons. Here we study a simplified two-variable toy model and explore the analogy with a cherry in a glass, but a broken one where the cherry may escape from. It is quite interesting to have our system confined or compact in one variable and infinite in the other variable. In this framework we solve the two-variable Schrödinger equation in configuration space. With the finite difference method, we compute the spectrum, we search for localized states and we attempt to compute phase-shifts. We then apply the outgoing spherical wave method to compute in detail the phase-shifts and to determine the decay widths. We explore the model in the equal mass case, and we find narrow resonances. In particular the existence of two commuting angular momenta is responsible for our small decay widths.

Heavy hadron chiral perturbation theory ($\mathrm{HH}\chi \mathrm{PT}$) and XEFT are applied to the decays $X(3872)\to \psi (2S)\gamma$ and $\psi (4040)\to X(3872)\gamma$ under the assumption that the $X(3872)$ is a molecular bound state of neutral charm mesons. In these decays the emitted photon energies are 181 MeV and 165 MeV, respectively, so $\mathrm{HH}\chi \mathrm{PT}$ can be used to calculate the underlying $D^0{\overline{D}}^{0*}+{\overline{D}}^0{D}^{0*}\to \psi (2S)\gamma$ or $\psi (4040)\to (D^0{\overline{D}}^{0*}+{\overline{D}}^0{D}^{0*})\gamma$ transition. These amplitudes are matched onto XEFT to obtain decay rates. The decays receive contributions from both long-distance and short-distance processes. We study the polarization of the $\psi (2S)$ in the decay $X(3872)\to \psi (2S)\gamma$ and the angular distribution of $X(3872)$ in the decay $\psi (4040)\to X(3872)\gamma$ and find they can be used to differentiate between different decay mechanisms as well as discriminate between $2^{-+}$ and $1^{++}$ quantum number assignments of the $X(3872)$.

The $\Lambda \to {\Sigma }^0$ transition magnetic moment is computed in the QCD sum rules approach. Three independent tensor structures are derived in the external-field method using generalized interpolating fields. They are analyzed together with the $\Lambda$ and ${\Sigma }^0$ mass sum rules using a Monte-Carlo-based analysis, with attention to operator product expansion convergence, ground-state dominance, and the role of the transitions in the intermediate states. Relations between sum rules for magnetic moments of $\Lambda$ and ${\Sigma }^0$ and sum rules for transition magnetic moment of $\Lambda \to {\Sigma }^0$ are also examined. Our best prediction for the transition magnetic moment is ${\mu }_{{\Sigma }^0\Lambda }=1.60\pm 0.07{\mu }_N$. A comparison is made with other calculations in the literature.

We present precise tests of $CP$ and $CPT$ symmetry based on the full data set of $K\to \pi \pi$ decays collected by the KTeV experiment at Fermi National Accelerator Laboratory during 1996, 1997, and 1999. This data set contains $16\times {10}^6$ $K\to {\pi }^0{\pi }^0$ and $69\times {10}^6$ $K\to {\pi }^{+}{\pi }^{-}$ decays. We measure the direct $CP$ violation parameter $\mathrm{Re}({ϵ}^{\prime }/ϵ)=(19.2\pm 2.1)\times {10}^{-4}$. We find the $K_L-K_S$ mass difference $\Delta m=(5270\pm 12)\times {10}^6\hslash {\mathrm{s}}^{-1}$ and the $K_S$ lifetime ${\tau }_S=(89.62\pm 0.05)\times {10}^{-12}\mathrm{s}$. We also measure several parameters that test $CPT$ invariance. We find the difference between the phase of the indirect $CP$ violation parameter $ϵ$ and the superweak phase: ${\varphi }_{ϵ}-{\varphi }_{\mathrm{SW}}=(0.40\pm 0.56)°$. We measure the difference of the relative phases between the $CP$ violating and $CP$ conserving decay amplitudes for $K\to {\pi }^{+}{\pi }^{-}$ (${\varphi }_{+-}$) and for $K\to {\pi }^0{\pi }^0$ (${\varphi }_{00}$): $\Delta \varphi =(0.30\pm 0.35)°$. From these phase measurements, we place a limit on the mass difference between $K^0$ and ${\overline{K}}^0$: $\Delta M<4.8\times {10}^{-19}\mathrm{GeV}/c^2$ at 95% C.L. These results are consistent with those of other experiments, our own earlier measurements, and $CPT$ symmetry.

Superradiant instability turns rotating astrophysical black holes into unique probes of light axions. We consider what happens when a light axion is coupled to a strongly coupled hidden gauge sector. In this case superradiance results in an adiabatic increase of a hidden sector $CP$-violating $\theta$ parameter in a near horizon region. This may trigger a first order phase transition in the gauge sector. As a result a significant fraction of a black hole mass is released as a cloud of hidden mesons and can be later converted into electromagnetic radiation. This results in a violent electromagnetic burst. The characteristic frequency of such bursts may range from $\sim 100\mathrm{eV}$ to $\sim 100\mathrm{MeV}$.

We systematically study dijet production in various processes in the small-$x$ limit and establish an effective $k_t$-factorization for hard processes in a system with dilute probes scattering on a dense target. We find that the well-known Weizsäcker-Williams gluon distribution can be directly probed in the quark-antiquark jet correlation in deep inelastic scattering and the dipole gluon distribution can be directly measured in the direct photon-jet correlation in $pA$ collisions. In the large-$N_c$ limit, the unintegrated gluon distributions involved in other different dijet channels in $pA$ collisions are shown to be related to two widely proposed ones: the Weizsäcker-Williams gluon distribution and the dipole gluon distribution.

We revisit the “hybrid formalism” for particle production used recently to study saturation effects in single hadron multiplicities at forward rapidities at RHIC and LHC. We point out that at leading twist there is an extra contribution to the formulae used so far, which corresponds to particle production via inelastic scattering of the projectile partons on the target fields. This contribution is expected to be small due to kinematics at very forward rapidities/very high transverse momenta, but should be significant at high momenta and very high energies. This contribution is expected to be most affected by saturation effects, and is therefore an interesting object of study in the context of possible onset of saturation at high energies.

We study a noninteracting supersymmetric model in an expanding FRW spacetime. A soft supersymmetry breaking induces a nonzero contribution to the vacuum energy density. A short distance cutoff of the order of Planck length provides a scale for the vacuum energy density comparable with the observed cosmological constant. Assuming the presence of a dark energy substance in addition to the vacuum fluctuations of the field, an effective equation of state is derived in a self-consistent approach. The effective equation of state is sensitive to the choice of the cutoff but no fine-tuning is needed.