A geometric formulation of the Lax pair equation on a curved manifold is studied using the phase-space formalism. The corresponding (covariantly conserved) Lax tensor is defined and the method of generation of constants of motion from it is discussed. It is shown that when the Hamilton equations of motion are used, the conservation of the Lax tensor translates directly to the well-known Lax pair equation, with one matrix identified with components of the Lax tensor and the other matrix constructed from the (metric) connection. A generalization to Clifford objects is also discussed. Nontrivial examples of Lax tensors for geodesic and charged particle motion are found in spacetimes admitting a hidden symmetry of Killing-Yano tensors.

Numerical-relativity simulations for the merger of binary neutron stars are performed for a variety of equations of state (EOSs) and for a plausible range of the neutron-star mass, focusing primarily on the properties of the material ejected from the system. We find that a fraction of the material is ejected as a mildly relativistic and mildly anisotropic outflow with the typical and maximum velocities $\sim 0.15–0.25c$ and $\sim 0.5–0.8c$ (where $c$ is the speed of light), respectively, and that the total ejected rest mass is in a wide range ${10}^{-4}–{10}^{-2}{M}_{\odot }$, which depends strongly on the EOS, the total mass, and the mass ratio. The total kinetic energy ejected is also in a wide range between ${10}^{49}$ and ${10}^{51}\mathrm{ergs}$. The numerical results suggest that for a binary of canonical total mass $2.7M_{\odot }$, the outflow could generate an electromagnetic signal observable by the planned telescopes through the production of heavy-element unstable nuclei via the $r$-process [6,20,21] or through the formation of blast waves during the interaction with the interstellar matter [7], if the EOS and mass of the binary are favorable ones.

We explore the four-dimensional Einstein-Maxwell landscape as a toy model in which we can formulate a sphere compactification stabilized by an electromagnetic field. Replacing the compactification sphere by $J$ spheres, we obtain a simple sector of the ($2J+2$)-dimensional Einstein-Maxwell landscape. In this toy model, we analyze some properties which are very difficult to uncover in the string theory landscape, including complete moduli stabilization, stability conditions, and state counting. We also show how to construct anthropic states in this model. A detailed comparison between the main features of this landscape and the Bousso-Polchinski landscape is given. We finally speculate on the impact of these phenomena in the string theory landscape.

We analyze the dynamical system defined by a universe filled with a barotropic fluid plus a scalar field with modified kinetic term of the form $\mathcal{L}=F(X)-V(\varphi )$. After a suitable choice of variables that allows us to study the phase space of the system, we obtain the critical points and their stability. We find that some of them reduce to the ones defined for the canonical case when $F(X)=X$. We also study the field energy conditions to have a nonsingular bounce.

The aim of this paper is to answer the following two questions: (1) Given cosmological observations of the expansion history and linear perturbations in a range of redshifts and scales as precise as is required, which of the properties of dark energy could actually be reconstructed without imposing any parameterization? (2) Are these observables sufficient to rule out not just a particular dark energy model, but the entire general class of viable models comprising a single scalar field? This paper bears both good and bad news. On one hand, we find that the goal of reconstructing dark energy models is fundamentally limited by the unobservability of the present values of the matter density ${\Omega }_{\mathrm{m}0}$, the perturbation normalization ${\sigma }_8$ as well as the present matter power spectrum. On the other, we find that, under certain conditions, cosmological observations can nonetheless rule out the entire class of the most general single scalar-field models, i.e., those based on the Horndeski Lagrangian.

Using a nonlocal extension of the SU(3) Nambu–Jona-Lasinio model, which reproduces several of the key features of quantum chromodynamics, we show that mixed phases of deconfined quarks and confined hadrons (quark-hybrid matter) may exist in the cores of neutron stars as massive as around $2.1M_{\odot }$. The radii of these objects are found to be in the canonical range of $\sim 12–13\mathrm{km}$. According to our study, the transition to pure quark matter does not occur in stable neutron stars, but is shifted to neutron stars which are unstable against radial oscillations. The implications of our study for the recently discovered, massive neutron star PSR J1614–2230, whose gravitational mass is $1.97\pm 0.04M_{\odot }$, are that this neutron star may contain an extended region of quark-hybrid matter at it center, but no pure quark matter.

We propose simple forms of the neutrino mixing matrix in analogy with the Wolfenstein parametrization of the quark mixing matrix by adopting the smallest mixing angle ${\theta }_{13}$ as a measure of expansion parameters with the tribimaximal pattern as the base matrix. The triminimal parametrization technique is utilized to expand the mixing matrix under two schemes, i.e., the standard Chau-Keung scheme and the original Kobayashi-Maskawa scheme. The new parametrizations have their corresponding Wolfenstein-like parametrizations of the quark mixing matrix, and therefore they share the same intriguing features of the Wolfenstein parametrization. The newly introduced expansion parameters for neutrinos are connected to the Wolfenstein parameters for quarks via the quark-lepton complementarity.

Existing analyses of baryon semileptonic decays indicate the presence of a small $SU(3)$ symmetry breaking effect in hyperon semileptonic decays. However, to provide evidence for $SU(3)$ symmetry breaking, one needs a relation similar to the Gell-Mann–Okubo baryon mass formula satisfied to within a few percent, showing evidence for $SU(3)$ symmetry breaking in the divergence of the vector current matrix element. In this paper, we shall present a similar Gell-Mann–Okubo relation for the hyperon semileptonic decay axial vector form factors. Using these relations and the measured axial vector current for vector current form factor ratios, we show that the amount of $SU(3)$ symmetry breaking in hyperon semileptonic decaysis 5–11%.

We analyze the properties of four-quark condensates and scalar susceptibilities in the meson gas, within finite temperature chiral perturbation theory (ChPT). The breaking of the factorization hypothesis does not allow for a finite four-quark condensate and its use as an order parameter, except in the chiral limit. This is rigorously obtained within ChPT and is therefore a model-independent result. Factorization only holds formally in the large $N_c$ limit and breaks up at finite temperature even in the chiral limit. Nevertheless, the factorization breaking terms are precisely those needed to yield a finite scalar susceptibility, deeply connected to chiral symmetry restoration. Actually, we provide the full result for the $SU(3)$ quark condensate to next-to-next-to- leading order in ChPT, thus extending previous results to include kaon and eta interactions. This allows us to check the effect of those corrections compared to previous approaches and the uncertainties due to low-energy constants. We provide a detailed analysis of scalar susceptibilities in the $SU(3)$ meson gas, including a comparison between the pure ChPT approach and the virial expansion, where the unitarization of pion scattering is crucial to achieve a more reliable prediction. Through the analysis of the interactions within this approach, we have found that the role of the $\sigma$ resonance is largely canceled with the scalar isospin two-channel interaction, leaving the $\rho (770)$ as the main contribution. Special attention is paid to the evolution towards chiral restoration, as well as to the comparison with recent lattice analysis.

The Lee-Wick (LW) formulation of higher-derivative theories can be extended from one in which the extra degrees of freedom are represented as a single, heavy, negative-norm partner for each known particle ($N=2$), to one in which a second, positive-norm partner appears ($N=3$). We explore the extent to which the presence of these additional states in a LW Standard Model affect precision electroweak observables, and find that they tend to have either a marginal effect (e.g., quark partners on $T$) or a substantial beneficial effect (e.g., Higgs partners on the $Zb\overline{b}$ couplings). We find that precision constraints allow LW partners to exist in broad regions of mass parameter space accessible at the LHC, making LW theories a viable Beyond Standard Model candidate.

The framework for soft leptogenesis minimally extended with a dark matter (DM) sector is studied. A heavy singlet neutrino superfield acts as the source for (s)lepton asymmetry and by coupling to the singlet DM superfield it produces a DM particle density through decays. The nature of DM generated is twofold depending on whether the Yukawa and DM couplings are either small or large. With sufficiently small Yukawa and DM couplings DM annihilations into minimal supersymmetric standard model particles are slow and as a consequence all DM particles form the DM component. The solutions to Boltzmann equations are given and the dependence between the DM masses and coupling are presented in this weak coupling regime. Also, the behavior of the efficiency of producing asymmetric DM is determined with weak couplings. We note that a different outcome arises if the couplings are larger because then the asymmetric DM component is dominant due to the effectiveness of DM decays into the minimal supersymmetric standard model sector.

Effective supersymmetry (SUSY), where the stop is the lightest squark, may run into a two-loop tachyonic problem in some $Z^{\prime }$ mediation models. In addition, a large $A$ term and/or a large stop mass are needed to have a $\sim 126\mathrm{GeV}$ Higgs boson with three families of quarks and leptons. Thus, we suggest an inverted effective SUSY (IeffSUSY) where the stop mass is larger compared to those of the first two families. In this case, it is possible to have a significant correction to the anomalous magnetic moment of the muon. A three-family IeffSUSY in a $Z^{\prime }$ mediation scenario is explicitly studied with the $Z^{\prime }$ quantum number related to $B-L$. Here we adopt both the $Z^{\prime }$ mediation and gravity mediation, where the $Z^{\prime }$ mediation is the dominant one for the stop, while the gravity mediation is the dominant one for the muonic leptons and Higgs multiplets. We present a numerical study based on a specific anomaly-free model, and show the existence of the parameter region where all the phenomenological conditions are satisfied.

We show that an enhanced two-photon signal of the Higgs boson, $h$, observed with 125 GeV mass by the ATLAS and CMS collaborations, can be obtained if it is identified principally with the neutral $H_u^0$ of the two Higgs doublets of minimal supersymmetry. We focus on sparticles and the pseudoscalar Higgs $A$ with TeV masses. The off-diagonal element of the ($H_u^0$,$H_d^0$) mass matrix in the flavor basis must be suppressed, and this requires a large Higgsino mass parameter, $\mu \sim \mathrm{TeV}$, and large $\tan \beta$. A minimal supersymmetric Standard Model sum rule is derived that relates $\gamma \gamma$ and $b\overline{b}$ rates, and a $\gamma \gamma$ enhancement relative to the SM predicts $b\overline{b}$ reduction. On the contrary, natural supersymmetry requires $|\mu |<\sim 0.5\mathrm{TeV}$, for which $\gamma \gamma$ is reduced and $b\overline{b}$ is enhanced. This conclusion is independent of the $m_A$ value and the supersymmetry quantum correction ${\Delta }_b$. Relative $\tau \overline{\tau }$ to $b\overline{b}$ rates are sensitive to ${\Delta }_b$.

We present an alternative formulation of the left-right symmetric theory where the scalar sector consists of two Higgs doublets. This formulation differs from the standard version of the left-right model that makes use of $L$- and $R$- Higgs triplets and a Higgs bidoublet. The basic idea is to consider a few extra charged isosinglet fields; the fermion masses can be realized by integrating out these heavy isosinglet fields. We also give a detailed discussion on neutrinoless double beta decay in this particular left-right symmetric theory where the right-handed (RH) Majorana neutrino can be of MeV range. With this RH Majorana mass around the MeV scale, the contribution to neutrinoless double beta decay coming from the right-handed current can be comparable to the contributions coming from the standard left-handed sector only if the right-handed gauge boson mass is around 5 TeV. With this operative scale of $W_R$ around a few TeV, it is possible to probe at the LHC. We have briefly commented on cosmological constraints from the big-bang nucleosynthesis and Universe cosmology on the RH neutrinos involved in this discussion.

Inspired by a recently proposed model of millicharged atomic dark matter (MADM), we analyze several classes of light dark matter models with respect to CoGeNT modulated and unmodulated data, and constraints from CDMS, XENON10 and XENON100. After removing the surface contaminated events from the original CoGeNT data set, we find an acceptable fit to all these data (but with the modulating part of the signal making a statistically small contribution), using somewhat relaxed assumptions about the response of the null experiments at low recoil energies, and postulating an unknown modulating background in the CoGeNT data at recoil energies above 1.5 keVee. We compare the fits of MADM—an example of inelastic magnetic dark matter—to those of standard elastically and inelastically scattering light weakly interacting massive particles. The inelastic dark matter model gives the best fit, with MADM close behind. The dark matter interpretation of the DAMA annual modulation cannot be made compatible with these results however. We find that the inclusion of a tidal debris component in the dark matter phase space distribution improves the fits or helps to relieve tension with XENON constraints.

Properties of $2^{-+}$ charmonium ${\eta }_{c2}$ are investigated in quenched lattice QCD. The mass of ${\eta }_{c2}$ is determined to be 3.80(3) GeV, which is close to the mass of $D$-wave charmonium $\psi (3770)$ and in agreement with quark model predictions. The transition width of ${\eta }_{c2}\to \gamma J/\psi$ is also obtained with a value of $\Gamma =3.8(9)\mathrm{keV}$. Since the possible $2^{-+}$ assignment to $X(3872)$ has not been ruled out by experiments, our results help to clarify the nature of $X(3872)$.

We discuss the pion and nucleon form factors and generalized form factors within the large-$N_c$ approach in the spacelike region. We estimate their theoretical uncertainties through the use of the half-width rule, amounting to taking the half width of the resonances as the deviation of their mass parameters. The approach embodies the meson dominance of form factors and the high-energy constraints from perturbative QCD. We compare the results with the available experimental data and lattice simulations. The meson-dominance form factors are generally comparable to the available experimental data within the half-width-rule uncertainties. Our errors are comparable to the experimental uncertainties, but are smaller than the lattice errors.

The $t\overline{t}$ asymmetry measured at the Tevatron continues to disagree with Standard Model predictions at the 3 sigma level. We update the status of the phenomenological light axigluon model in explaining the asymmetry data, taking into account constraints from the charge asymmetry at the LHC and the $t\overline{t}$ cross section at both the Tevatron and LHC. We find that an axigluon with a mass between 100 and 400 GeV provides an excellent fit to the data. Recent searches by ATLAS and CMS for pair production of heavy resonances which decay to dijets rule out axigluons with large branching fractions to dijets. However, axigluons which predominantly decay to multijets via intermediate resonances are still a possibility. We outline four distinct scenarios which cover the most important decay topologies and discuss how one might exclude or discover axigluons as multijet resonances at the LHC. MadGraph implementations for each of the scenarios are provided.

After constructing the possible $J^P=0^{-}$, $0^{+}$, $1^{-}$, and $1^{+}$ $QQ\overline{q}\overline{q}$ tetraquark interpolating currents in a systematic way, we investigate the two-point correlation functions and extract the corresponding masses with the QCD sum rule approach. We study the $QQ\overline{q}\overline{q}$, $QQ\overline{q}\overline{s}$, and $QQ\overline{s}\overline{s}$ systems with various isospins $I=0$, $1/2$, 1. Our numerical analysis indicates that the masses of doubly bottomed tetraquark states are below the threshold of the two-bottom mesons, two-bottom baryons, and one doubly bottomed baryon plus one antinucleon. Very probably these doubly bottomed tetraquark states are stable.

We present completely general next-to-leading order predictions for squark and gluino production at the LHC, based on the fully automated MadGolem tool. Without any assumptions on the mass spectrum we predict production rates and examine the structure of the massless and massive QCD and SUSY-QCD quantum corrections. This allows us to quantify theory uncertainties induced by the spectrum assumptions commonly made. Going beyond total rates we compare general fixed-order distributions to resummed predictions from jet merging. As part of this comprehensive study we present the MadGolem treatment of ultraviolet, infrared, and on-shell divergences.