The Planck Collaboration has recently published maps of the cosmic microwave background radiation with the highest precision. In the standard flat $\Lambda$ cold dark matter framework, Planck data show that the Hubble constant $H_0$ is in tension with that measured by the several direct probes on $H_0$. In this paper, we perform a global analysis from the current observational data in the general dark energy models and find that resolving this tension requires the dark energy model with its equation of state (EOS) $w\ne -1$. Firstly, assuming the $w$ to be a constant, the Planck data favor $w<-1$ at about $2\sigma$ confidence level when combining with the supernovae “supernova legacy survey” compilation. Consequently the value derived on $H_0$, $H_0=71.3\pm 2.0\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$ (68% C.L.) is consistent with that from direct $H_0$ probes. We then investigate the dark energy model with a time-evolving $w$, and obtain the 68% C.L. constraints $w_0=-0.81\pm 0.19$ and $w_a=-1.9\pm 1.1$ from the Planck data and the “supernova legacy survey” compilation. Current data still slightly favor the quintom dark energy scenario with EOS across the cosmological constant boundary $w\equiv -1$.

Scalar fields confined either by a mass term or by a mirrorlike boundary condition have unstable modes in the background of a Kerr black hole. Assuming a time dependence as $e^{-i\omega t}$, the growth time scale of these unstable modes is set by the inverse of the (positive) imaginary part of the frequency, $\mathrm{Im}(\omega )$, which reaches a maximum value of the order of $\mathrm{Im}(\omega )M\sim {10}^{-5}$, attained for a mirrorlike boundary condition, where $M$ is the black hole mass. In this paper we study the minimally coupled Klein-Gordon equation for a charged scalar field in the background of a Reissner-Nordström black hole and show that the unstable modes, due to a mirrorlike boundary condition, can grow several orders of magnitude faster than in the rotating case: we have obtained modes with up to $\mathrm{Im}(\omega )M\sim 0.07$. We provide an understanding, based on an analytic approximation, of why the instability in the charged case has a shorter time scale than in the rotating case. This faster growth, together with the spherical symmetry, makes the charged case a promising model for studies of the fully nonlinear development of superradiant instabilities.

We derive the metric on the parameter space of 3.5 post-Newtonian (3.5PN) stationary phase compact binary inspiral waveforms for a single detector, neglecting spin, eccentricity, and finite-body effects. We demonstrate that this leads to better template placement than the current practice of using the 2PN metric to place 3.5PN templates: The recovered event rate is improved by about 10% at a cost of nearly doubling the number of templates. The cross correlations between mass parameters are also more accurate, which will result in better coincidence tests.

A phase of strong interacting matter with deconfined quarks is expected in the core of massive neutron stars. In this article, we perform a study of the hadron-quark phase transition in cold ($T=0$) neutron star matter and we calculate various structural properties of hybrid stars. For the quark phase, we make use of an equation of state (EOS) derived with the field correlator method (FCM) recently extended to the case of nonzero baryon density. For the hadronic phase, we consider both pure nucleonic and hyperonic matter, and we derive the corresponding EOS within a relativistic mean field approach. We make use of measured neutron star masses, and particularly the mass $M=1.97\pm 0.04M_{\odot }$ of PSR $\mathrm{J}1614-2230$ to constrain the values of the gluon condensate $G_2$, which is one of the EOS parameters within the FCM. We find that the values of $G_2$ extracted from the mass measurement of PSR $\mathrm{J}1614-2230$ are consistent with the values of the same quantity derived within the FCM from recent lattice QCD calculations of the deconfinement transition temperature at zero baryon chemical potential. The FCM thus provides a powerful tool to link numerical calculations of QCD on a space-time lattice with measured neutron star masses.

We extend the adiabatic regularization method to spin-$1/2$ fields. The ansatz for the adiabatic expansion for fermionic modes differs significantly from the WKB-type template that works for scalar modes. We give explicit expressions for the first adiabatic orders and analyze particle creation in de Sitter spacetime. As for scalar fields, the adiabatic method can be distinguished by its capability to overcome the UV divergences of the particle number operator. We also test the consistency of the extended method by working out the conformal and axial anomalies for a Dirac field in a Friedmann-Lemaître-Robertson-Walker spacetime, in exact agreement with those obtained from other renormalization prescriptions. We finally show its power by computing the renormalized stress-energy tensor for Dirac fermions in de Sitter space.

The evolution equations of the Yukawa couplings and quark mixings are derived for the one-loop renormalization group equations in six-dimensional models, compactified in different possible ways to yield standard four space-time dimensions. Different possibilities for the matter fields are also discussed, such as the case of bulk propagating or brane localized fields. We discuss in both cases the evolution of the Yukawa couplings, the Jarlskog parameter and the Cabibbo-Kobayashi-Maskawa matrix element, and find that for both scenarios, as we run up to the unification scale, significant renormalization group corrections are present. We also discuss the results of different observables of the five-dimensional universal extra dimension model in comparison with these six-dimensional models and the model dependence of the results.

Using the example of the two-dimensional (2D) Ising model, we show that in contrast to what can be done in configuration space, the tensor renormalization group formulation allows one to write exact, compact, and manifestly local blocking formulas and exact coarse-grained expressions for the partition function. We argue that similar results should hold for most models studied by lattice gauge theorists. We provide exact blocking formulas for several 2D spin models [the $O(2)$ and $O(3)$ sigma models and the SU(2) principal chiral model] and for the three-dimensional gauge theories with groups $Z_2$, U(1) and SU(2). We briefly discuss generalizations to other groups, higher dimensions and practical implementations.

In this article we study the finite temperature and chemical potential effects in a nonlocal Nambu-Jona-Lasinio model in the real time formalism. We make the usual Wick rotation to get from imaginary to real time formalism. In doing so, we need to define our regulator in the complex plane $q^2$. This definition will be crucial in our later analysis. We study the poles in the propagator of this model and conclude that only some of them are of interest to us. Once we have a well-defined model in a real time formalism, we look at the chiral condensate to find the temperature at which chiral symmetry restoration will occur. We find a second-order phase transition that turns to a first-order one for high enough values of the chemical potential.

Signals broadly compatible with light (7–10 GeV) dark matter have been reported in three direct detection experiments: CoGeNT, DAMA/LIBRA, and CDMS-II silicon. These possible signals have been interpreted in the context of spin-independent interactions between the target nuclei and dark matter, although there is tension with null results, particularly from xenon-based experiments. In this paper, we demonstrate that the CoGeNT and CDMS-II silicon results are also compatible assuming a spin-dependent neutron interaction, though this is in tension with xenon-based experiments and PICASSO. The tension with the null results from XENON100 and XENON10 is approximately the same as for the spin-independent coupling. All three experimental signals can be made compatible through a combination of spin-dependent interactions with both the proton and neutron, although such a scenario increases the conflict with the null results of other experiments.

The semileptonic $B_s\to \varphi \nu \overline{\nu }$, and $B_s\to \varphi l^{+}{l}^{-}$, $l=\tau$, $\mu$, $e$ transitions are investigated in the framework of the three-point QCD sum rules in the standard model. These rare decays take place at loop level by electroweak penguin and weak box diagrams in the standard model via the flavor-changing neutral current transition of $b\to s$. Considering the quark condensate contributions, the relevant form factors as well as the branching fractions of these transitions are calculated. The longitudinal lepton polarization and forward-backward asymmetries are also investigated.

We study—at leading order in the large number of colors expansion and within the resonance chiral theory framework—the odd-intrinsic-parity $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}({\pi }^0,\eta )$ cross sections in the energy regime populated by hadron resonances, namely $3m_{\pi }\lesssim E\lesssim 2\mathrm{GeV}$. In addition, we implement our results in the Monte Carlo generator phokhara 7.0 and we simulate hadron production through the radiative return method.

Dark matter particles captured by the Sun through scattering may annihilate and produce neutrinos, which escape. Current searches are for the few high-energy neutrinos produced in the prompt decays of some final states. We show that interactions in the solar medium lead to a large number of pions for nearly all final states. Positive pions and muons decay at rest, producing low-energy neutrinos with known spectra, including ${\overline{\nu }}_e$ through neutrino mixing. We demonstrate that Super-Kamiokande can thereby provide a new probe of the spin-dependent WIMP-proton cross section. Compared to other methods, the sensitivity is competitive and the uncertainties are complementary.

We reevaluate prospects for supersymmetry (SUSY) at the proposed International Linear $e^{+}{e}^{-}$ Collider (ILC) in light of the first two years of serious data taking at LHC: LHC7 with $\sim 5{\mathrm{fb}}^{-1}$ of $pp$ collisions at $\sqrt{s}=7\mathrm{TeV}$ and LHC8 with $\sim 20{\mathrm{fb}}^{-1}$ at $\sqrt{s}=8\mathrm{TeV}$. Strong new limits from LHC8 SUSY searches, along with the discovery of a Higgs boson with $m_h\simeq 125\mathrm{GeV}$, suggest a paradigm shift from previously popular models to ones with new and compelling signatures. After a review of the current status of supersymmetry, we present a variety of new ILC benchmark models, including natural SUSY, radiatively driven natural SUSY, NUHM2 with low $m_A$, a focus point case from mSUGRA/CMSSM, nonuniversal gaugino mass model, $\tilde{\tau }$ coannihilation, Kallosh-Linde/spread SUSY model, mixed gauge-gravity mediation, normal scalar mass hierarchy, and one example with the recently discovered Higgs boson being the heavy $CP$-even state $H$. While all these models at present elude the latest LHC8 limits, they do offer intriguing case study possibilities for ILC operating at $\sqrt{s}\simeq 0.25–1\mathrm{TeV}$. The benchmark points also present a view of the widely diverse SUSY phenomena which might still be expected in the post-LHC8 era at both LHC and ILC.

Motivated by results from short-baseline neutrino oscillation data, we study neutrino masses and mixing in $U(1{)}^{\prime }$ supersymmetric models with $R$-parity breaking. Whether $R$-parity is broken spontaneously or through (effective) bilinear terms in the Lagrangian, the breaking terms induce mixing between the neutralinos and neutrinos, creating a scenario in which some neutralinos can be heavy and some light. Both the right-handed neutrino and the singlino (fermionic partner of the additional singlet Higgs field) can be light and act as sterile neutrinos, which reconcile some of the anomalies observed in solar baseline and reactor experiments. We show that, scanning a large range of the parameter space satisfying solar and atmospheric neutrino constraints, the mass and mixing parameters of the sterile neutrinos are very restrictive, leading to some predictive features for the $U(1{)}^{\prime }$ scenarios.

The scattering of longitudinally polarized electroweak bosons is likely to play an important role in the elucidation of the fundamental nature of the electroweak symmetry breaking sector and in determining the Higgs interactions with this sector. In this paper, by making use of the equivalence theorem, we determine the renormalization properties of the electroweak effective theory parameters in a model with generic Higgs couplings to the $W$ and $Z$ bosons. When the couplings between the Higgs and the electroweak gauge bosons deviate from their Standard Model values, additional counterterms of $O(p^4)$ in the usual chiral counting are required. We also determine in the same approximation the full radiative corrections to the $W_L{W}_L\to Z_L{Z}_L$ process in this type of model. Assuming custodial invariance, all the related processes can be easily derived from this amplitude.

We study “gluonic effects” (gluon condensation effects) on the hadronic leading order (HLO) contributions to the anomalous magnetic moment ($g-2$) of leptons, based on a holographic model having explicit gluonic mode introduced for consistency with the operator product expansion of QCD. We find gluonic enhancement of HLO contributions to the muon $g-2$ by about 6%, which nicely fills in the gap between the holographic estimate without gluonic effects and the phenomenological one using the experimental data as inputs. Similar calculations including the gluonic effects for the electron and the tau lepton $g-2$ are also carried out in good agreement with the phenomenological estimates. We then apply our holographic estimate to the walking technicolor (WTC) where large technigluonic effects were shown to be vital for the technidilaton, (pseudo)Nambu-Goldstone boson of the (approximate) scale symmetry of WTC, to be naturally as light as 125 GeV. It is shown that the value of the techni-HLO contributions to the muon $g-2$ is 10–100 times enhanced by inclusion of the same amount of the gluonic effects as that realizing the 125 GeV technidilaton, although such an enhanced techni-HLO contribution is still negligibly small compared with the current deviation of the standard model prediction of the muon $g-2$ from the experiments. The techni-HLO contributions to the tau lepton $g-2$ is also discussed, suggesting a possible phenomenological relevance to be tested by the future experiments.

We give analytical and numerical solutions for the zero modes of the Dirac operator in topological $SU(2)$ gauge backgrounds at nonzero chemical potential. Continuation from imaginary to real chemical potential is used to systematically derive analytical zero modes for calorons at arbitrary holonomy and, in particular limits, for instantons and dyons (magnetic monopoles). For the latter a spherical ansatz is explored as well. All the zero modes exhibit stronger peaks at the core and negative regions in their densities. We discuss the structure of the corresponding overlap matrix elements. For discretized calorons on the lattice we consider the staggered operator and show that it does possess (quartet quasi)zero modes, whose eigenmodes agree very well with the continuum profiles, for zero as well as nonzero chemical potential.

The parton densities of the proton are of fundamental importance not only for our description of hadronic and nuclear structure, but also for reliable predictions for new heavy-particle searches at colliders. At the large partonic momentum fractions required for the production of these particles, the parton distribution functions—in particular, that of the gluon—are unfortunately still badly constrained. In this paper, we investigate the possibility to improve on their determination with new data coming from electroweak vector boson production at large transverse momenta at the LHC with center-of-mass energies of 7, 8, or 14 TeV. We demonstrate that this process is dominated by quark-gluon scattering, that theoretical predictions can be reliably made on the basis of next-to-leading order perturbation theory and its resummation, and that these data should thus be used in global fits. We also point out that the nonperturbative parameters determined from Tevatron Run 1 $Z$-boson data at low $p_T$ describe very well the new LHC data at $\sqrt{s}=7\mathrm{TeV}$.

We determine the values of the one- and two-loop low energy constants appearing in the SU(2) Chiral Perturbation Theory calculation of pion-pion scattering. For this we use a recent and precise sum rule determination of some scattering lengths and slopes that appear in the effective range expansion. In addition we provide sum rules for these coefficients up to third order in the expansion. Our results when using only the scattering lengths and slopes of the $S$, $P$, $D$, and $F$ waves are consistent with previous determinations but seem to require higher order contributions if they are to accommodate the third order coefficients of the effective range expansion.

We consider the tunneling processes induced by two-particle collisions. The result derived by the thermal bath approach is reproduced by the classical configurations. The Coulomb and Yukawa corrections for the rate of the processes are found.