We derive, using the spherical collapse model, a generalized Layzer-Irvine equation which can be used to describe the gravitational collapse of cold dark matter in a dark energy background. We show that the usual Layzer-Irvine equation is valid if the dark matter and the dark energy are minimally coupled to each other and the dark energy distribution is homogeneous, independently of its equation of state. We compute the corrections to the standard Layzer-Irvine equation which arise in the presence of dark energy inhomogeneities assuming a minimal coupling between dark matter and dark energy. We show that, in the case of a dark energy component with a constant equation-of-state parameter consistent with the latest observational constraints, these corrections are expected to be small, even if the dark energy has a negligible sound speed. However, we find that, in more general models, the impact of dark energy perturbations on the dynamics of clusters of galaxies, which will be constrained by ESA’s Euclid mission with unprecedented precision, might be significant.

Identifying the source parameters from a gravitational-wave measurement alone is limited by our ability to discriminate signals from different sources and the accuracy of the waveform family employed in the search. Here we address both issues in the framework of an adapted coordinate system that allows for linear Fisher-matrix–type calculations of waveform differences that are both accurate and computationally very efficient. We investigate statistical errors by using principal component analysis of the post-Newtonian (PN) expansion coefficients, which is well conditioned despite the Fisher matrix becoming ill conditioned for larger numbers of parameters. We identify which combinations of physical parameters are most effectively measured by gravitational-wave detectors for systems of neutron stars and black holes with aligned spin. We confirm the expectation that the dominant parameter of the inspiral waveform is the chirp mass. The next dominant parameter depends on a combination of the spin and the symmetric mass ratio. In addition, we can study the systematic effect of various spin contributions to the PN phasing within the same parametrization, showing that the inclusion of spin-orbit corrections up to next-to-leading order, but not necessarily of spin-spin contributions, is crucial for an accurate inspiral waveform model. This understanding of the waveform structure throughout the parameter space is important to set up an efficient search strategy and correctly interpret future gravitational-wave observations.

So-called “dirty” black holes are those surrounded by nonzero stress energy, rather than vacuum. The presence of the nonzero stress energy modifies key features of the black hole, such as the surface gravity, Regge-Wheeler equation, linear stability, and greybody factors in a rather nontrivial way. Working within the inverse-Cowling approximation, (effectively the test-field limit), we shall present general forms for the Regge-Wheeler equation for linearized spin 0, spin 1, and axial spin 2 perturbations on an arbitrary static spherically symmetric background spacetime. Using very general features of the background spacetime, (in particular the classical energy conditions for the stress energy surrounding the black hole), we extract several interesting and robust bounds on the behavior of such systems, including rigorous bounds on the greybody factors for dirty black holes.

Two of the most commonly used tools to constrain the primordial non-Gaussianity are the bispectrum and the Minkowski functionals of cosmic microwave background temperature anisotropies. These two measures of non-Gaussianity in principle provide distinct (though correlated) information, but in the past constraints from them have only been loosely compared and not statistically combined. In this work we evaluate, for the first time, the covariance matrix between the local non-Gaussianity coefficient $f_{\mathrm{NL}}$ estimated through the bispectrum and Minkowski functionals. We find that the estimators are positively correlated, with correlation coefficient $r\simeq 0.3$. Using the WMAP7 data to combine the two measures and accounting for the point-source systematics, we find the combined constraint $f_{\mathrm{NL}}=37\pm 28$, which has a $\sim 20\%$ smaller error than either of the individual constraints.

We present an effective field theory method to determine secondary massive quark effects in jet production taking the thrust distribution for $e^{+}{e}^{-}$ collisions in the dijet limit as a concrete example. The method is based on the field theoretic treatment of collinear and soft mass modes which have to be separated coherently from the collinear and ultrasoft modes related to massless quarks and gluons. For thrust the structure of the conceptual setup is closely related to the production of massive gauge bosons and involves four different effective field theories to describe all possible kinematic situations. The effective field theories merge into one another continuously and thus allow for a continuous description from infinitely heavy to arbitrarily small masses keeping the exact mass dependence of the most singular terms treated through factorization. The mass mode field theory method we present here is in the spirit of the variable fermion number scheme originally proposed by Aivazis, Collins, Olness and Tung and can also be applied in hadron collisions.

After the discovery of a 126 GeV state at the LHC, it is imperative to establish whether this particle really is the Higgs boson of the standard model. The early measurements have not yet pinpointed any of the Higgs couplings to fermions, the Yukawa couplings of the standard model. In this paper we study the values of the top-quark–Higgs coupling, $g_{ht\overline{t}}$, that are still allowed by the one-loop couplings of the Higgs to two gluons or two photons. We first assume that both the gluon fusion production of the Higgs and its decay into two photons proceed through loops with standard model particles only, albeit with an arbitrary top-Higgs coupling. We find that the current Higgs data still allow for 20% deviations in $g_{ht\overline{t}}$ from its standard model value. We then investigate the effect of new particles contributing to the effective one-loop couplings. Specifically, we consider a color-octet electroweak doublet extension of the scalar sector and find that, in this case, $g_{ht\overline{t}}$ is allowed to deviate from its standard model value by 40% with the current data.

We present a measurement of $Z$ boson pair production in $p\overline{p}$ collisions at 1.96 TeV with 9.6 to $9.8{\mathrm{fb}}^{-1}$ of D0 data. We examine the final states $eeee$, $ee\mu \mu$, and $\mu \mu \mu \mu$. Based on selected data, the measured cross section in the mass region $M(Z/{\gamma }^{*})>30\mathrm{GeV}$ is $\sigma (p\overline{p}\to Z/{\gamma }^{*}Z/{\gamma }^{*})={1.26}_{-0.36}^{+0.44}(\mathrm{stat}{)}_{-0.15}^{+0.17}(\mathrm{syst})\pm 0.08(\mathrm{lumi})\mathrm{pb}$; after correcting for the expected ratio of $\sigma (p\overline{p}\to Z/{\gamma }^{*}Z/{\gamma }^{*})$ to $\sigma (p\overline{p}\to ZZ)$, we derive a cross section for $p\overline{p}\to ZZ$ production of ${1.05}_{-0.30}^{+0.37}(\mathrm{stat}{)}_{-0.12}^{+0.14}(\mathrm{syst})\pm 0.06(\mathrm{lumi})\mathrm{pb}$. This result is combined with a previous result from the $ZZ\to {\ell }^{+}{\ell }^{-}\nu \overline{\nu }$ channel resulting in a combined $p\overline{p}\to ZZ$ cross section measurement of ${1.32}_{-0.25}^{+0.29}(\mathrm{stat})\pm 0.12(\mathrm{syst})\pm 0.04(\mathrm{lumi})\mathrm{pb}$. These measurements are consistent with the standard model expectation of $1.43\pm 0.10\mathrm{pb}$. We extend this analysis to search for the standard model (SM) Higgs boson between 115 and 200 GeV. At a Higgs boson mass of 125 GeV, we expect to set a limit of 43 times the SM expectation at 95% C.L., and set a limit of 42 times the SM expectation at 95% C.L.

We study the new physics related to the recently discovered 125 GeV Higgs by employing an important subset of the standard model (SM) gauge-invariant dimension-6 operators constructed by the SM Higgs and gauge fields. Explicitly, we perform a model-independent study on the production and decays of the Higgs, the electric dipole moments (EDMs) of the neutron and the electron, and we take into account the anomalous magnetic dipole moments of the muon and electron as well. We find that, even if all Higgs decay channels agree with the SM predictions, the SM theoretical uncertainties provide a lot of room to host new phyiscs associated with the 125 GeV boson. A linear relation is revealed in our numerical study that ${\mu }_{ZZ}\simeq {\mu }_{WW}$ and $0.6\lesssim {\mu }_{ZZ,WW}\lesssim 1.4$ at 95% C.L. with or without the EDM constraints. The neutron and electron EDMs severely constrain the relevant Wilson coefficients. Therefore the $CP$-violating components in the $h\to WW$, $ZZ$ channels are too small, $\sim \mathcal{O}({10}^{-5})$, to be detected at the LHC. However, we point out that, even though the parity of the 125 GeV boson has been largely determined to be even in the $h\to ZZ$ channel, one should pay special attention to the potentially large $CP$ violation in the $h\to \gamma \gamma$ and $h\to \gamma Z$ channels. This should be seriously checked in the future spin correlation experiments.

We consider an extension of the Weyl-Cartan-Weitzenböck (WCW) and teleparallel gravity in which the Weitzenböck condition of the exact cancellation of curvature and torsion in a Weyl-Cartan geometry is inserted into the gravitational action via a Lagrange multiplier. In the standard metric formulation of the WCW model, the flatness of the space-time is removed by imposing the Weitzenböck condition in the Weyl-Cartan geometry, where the dynamical variables are the space-time metric, the Weyl vector and the torsion tensor, respectively. However, once the Weitzenböck condition is imposed on the Weyl-Cartan space-time, the metric is not dynamical, and the gravitational dynamics and evolution are completely determined by the torsion tensor. We show how to resolve this difficulty and generalize the WCW model by imposing the Weitzenböck condition on the action of the gravitational field through a Lagrange multiplier. The gravitational field equations are obtained which explicitly depend on the Lagrange multiplier. As a particular model we consider the case of the Riemann-Cartan space-times with zero nonmetricity which mimics the teleparallel theory. The Newtonian limit of the model is investigated and a generalized Poisson equation is obtained, with the weak field gravitational potential explicitly depending on the Lagrange multiplier and on the Weyl vector. The cosmological implications of the theory are also studied, and three classes of exact cosmological models are considered.

We propose a new mixing pattern for neutrinos with a nonzero mixing angle ${\theta }_{13}$. Under a simple form, it agrees well with current neutrino oscillation data and displays a number of intriguing features including the $\mu \mathrm{\text{−}}\tau$ interchange symmetry $|U_{\mu i}|=|U_{\tau i}|$, ($i=1$, 2, 3), the trimaximal mixing $|U_{\mathrm{e}2}|=|U_{\mu 2}|=|U_{\tau 2}|=1/\sqrt{3}$, the self-complementarity relation ${\theta }_1+{\theta }_3=45°$, together with the maximal Dirac $CP$ violation as a prediction.

The quantization condition for interacting energy eigenvalues of the two-nucleon system in a finite cubic volume is derived in connection to the nucleon-nucleon scattering amplitudes. This condition is derived using an auxiliary (dimer) field formalism that is generalized to arbitrary partial waves in the context of nonrelativistic effective field theory. The quantization condition presented gives access to the scattering parameters of the two-nucleon systems with arbitrary parity, spin, isospin, angular momentum and center-of-mass motion, from a lattice QCD calculation of the energy eigenvalues. In particular, as it includes all noncentral interactions, such as the two-nucleon tensor force, it makes explicit the dependence of the mixing parameters of nucleon-nucleon systems calculated from lattice QCD when there is a physical mixing among different partial waves, e.g. $S\mathrm{\text{−}}D$ partial wave mixing in the deuteron channel. We provide explicit relations among scattering parameters and their corresponding point group symmetry class eigenenergies with orbital angular momentum $l\le 3$, and for center-of-mass boost vectors of the form $\frac{2\pi }{L}(2n_1,2n_2,2n_3)$, $\frac{2\pi }{L}(2n_1,2n_2,2n_3+1)$ and $\frac{2\pi }{L}(2n_1+1,2n_2+1,2n_3)$. $L$ denotes the special extent of the cubic volume and $n_1$, $n_2$, $n_3$ are integers. Our results are valid below inelastic thresholds up to exponential volume corrections that are governed by the pion mass.

The Fermi Gamma-ray Space Telescope discovered two $\gamma$-ray emitting bubble-shaped structures that extend nearly symmetrically on either side of our Galaxy and appear morphologically connected to the Galactic center. The origin of the emission is still not entirely clear. It was recently shown that the spectral shape of the emission from the Fermi bubbles is well described by an approximately 50 GeV dark matter particle annihilating to $b\overline{b}$, with a normalization corresponding to a velocity average annihilation cross section $⟨{\sigma }_{b}v⟩\approx 8\times {10}^{-27}{\mathrm{cm}}^3/\mathrm{s}$. We study the minimal hidden sector recently introduced by Weinberg and examine to what extent its weakly interacting massive particles are capable of accommodating both the desired effective annihilation rate into quarks and the observed dark matter density.

We discuss the possibility that a $Z^{\prime }$ gauge boson, predicted by a large class of models in which the Higgs doublet is charged under $\mathrm{U}(1{)}^{\prime }$, can have a reduced gauge coupling and can therefore be quite light, even below the 1 TeV scale, avoiding present experimental constraints. This generic possibility is discussed within the framework of the class of supersymmetric ${\mathrm{E}}_6$-inspired models as an example. Since the $Z^{\prime }$ can be light, we refer to such models as Little $Z^{\prime }$ models. One of the main motivations for such models is to reduce the fine-tuning due to the current experimental limits on the $Z^{\prime }$ mass. As we point out, such fine-tuning arises when the Higgs doublets are charged under the extra $\mathrm{U}(1{)}^{\prime }$ gauge group leading to large additional D-terms in the Higgs potential. We show that reducing the value of the extra gauge coupling relaxes the experimental limits, leading to the possibility of low-mass $Z^{\prime }$ resonances, for example down to 200 GeV, which may yet appear in LHC searches. Although the source of tree-level fine-tuning due to the $Z^{\prime }$ mass is reduced, it typically does so at the expense of increasing the vacuum expectation value of the $\mathrm{U}(1{)}^{\prime }$-breaking standard model singlet field, reducing the fine-tuning to levels similar to that in the minimal supersymmetric standard model.

Recently evidence for gamma ray lines at energies of approximately 111 and 128 GeV has been found in Fermi-LAT data from the center of the Galaxy and from unassociated point sources. Many explanations in terms of dark matter particle pairs annihilating to $\gamma \gamma$ and $\gamma Z$ have been suggested, but these typically require very large couplings or mysterious coincidences in the masses of several new particles to fit the signal strength. We propose a simple novel explanation in which dark matter is part of a multiplet of new states which all have mass near 260 GeV as a result of symmetry. Two dark matter particles annihilate to a pair of neutral particles in this multiplet which subsequently decay to $\gamma \gamma$ and $\gamma Z$. For example, one may have a triplet of pseudo-Nambu-Goldstone bosons, ${\pi }_{\pm }^h$ and ${\pi }_0^h$, where ${\pi }_{\pm }^h$ are stabilized by their charge under a new U(1) symmetry and the slightly lighter neutral state ${\pi }_0^h$ decays to $\gamma \gamma$ and $\gamma Z$. The symmetry structure of such a model explains the near degeneracy in masses needed for the resulting photons to have a linelike shape and the large observed flux. The tunable lifetime of the neutral state allows such models to go unseen at direct detection or collider experiments that can constrain most other explanations. However, nucleosynthesis constraints on the ${\pi }_0^h$ lifetime fix a minimum necessary coupling between the new multiplet and the Standard Model. The spectrum is predicted to be not a line but a box with a width of order a few GeV, smaller than but on the order of the Fermi-LAT resolution.

We revisit the problem of new physics (NP) contribution to the branching ratio of the $B_s\to {\mu }^{+}{\mu }^{-}$ decay in light of the recent observation of this decay by LHCb. We consider R-parity violating (RPV) supersymmetric models as a primary example—recently one has reported stringent constraints on the products of the RPV coupling constants that account for the $B_s\to {\mu }^{+}{\mu }^{-}$ transition at the tree level. We argue that despite the fact that the LHCb measurement of the $B(B_s\to {\mu }^{+}{\mu }^{-})$ is in a remarkable agreement with the Standard Model (SM) prediction, there is still a room for a significant new physics contribution to the $B(B_s\to {\mu }^{+}{\mu }^{-})$, as the sign of the $B_s\to {\mu }^{+}{\mu }^{-}$ transition amplitude may be opposite to that of the Standard Model; alternatively the amplitude may have a large phase. We conduct our analysis mainly for the case of real RPV couplings. We find that taking into account the scenario with the sign flip of the $B_s\to {\mu }^{+}{\mu }^{-}$ amplitude (as compared to that of the SM) makes the bounds on the RPV coupling products significantly weaker. Also, we discuss briefly how our results are modified if the RPV couplings have large phases. In particular, we examine the dependence of the derived bounds on the phase of the NP amplitude.

We use modern jet-substructure techniques to propose LHC searches for multijet-resonance signals without leptons or missing energy. We focus on three-jet resonances produced by $R$-parity-violating decays of boosted gluinos, showing that shape analyses searching for a mass peak can probe such gluinos up to masses of $\sim 750\mathrm{GeV}$ (650 GeV) with $20{\mathrm{fb}}^{-1}$ ($5{\mathrm{fb}}^{-1}$) at the LHC at 8 TeV. This complements existing search strategies, which also include counting methods that are inherently more prone to systematic uncertainties. Since $R$-parity-violating gluinos lighter than all squarks hadronize before decaying, we introduce new color-flow variables, “radial pull” and “axis contraction,” which are sensitive to the color structure of the $R$-hadron’s decay. The former measures the inward pull of subjets in a fat jet, while the latter quantifies the inward drift of the $N$-subjettiness axes when changing the distance measure. We show that they can dramatically improve the discrimination of a boosted gluino signal vs QCD, $t\overline{t}$, and combinatoric background for $m_{\tilde{g}}\sim m_t$. Cuts on axis contraction also noticeably improve the resonance shape for heavy gluinos with $m_{\tilde{g}}\gtrsim 500\mathrm{GeV}$. With minor adaptations, these variables could find application in substructure searches for particles in different color representations or with other decay topologies. We also compare how several different Monte Carlo generators model the high-multiplicity QCD background. This provides evidence that the discriminating power of our color-flow observables are robust, and provides useful guidance for future substructure studies.

Based on $(106.41\pm 0.86)\times {10}^6$ $\psi (3686)$ events collected with the BESIII detector at the BEPCII collider, the branching fractions of $\psi (3686)\to {\pi }^{+}{\pi }^{-}J/\psi$, $J/\psi \to e^{+}{e}^{-}$, and $J/\psi \to {\mu }^{+}{\mu }^{-}$ are measured. We obtain $\mathcal{B}[\psi (3686)\to {\pi }^{+}{\pi }^{-}J/\psi ]=(34.98\pm 0.02\pm 0.45)\%$, $\mathcal{B}[J/\psi \to e^{+}{e}^{-}]=(5.983\pm 0.007\pm 0.037)\%$, and $\mathcal{B}[J/\psi \to {\mu }^{+}{\mu }^{-}]=(5.973\pm 0.007\pm 0.038)\%$. The measurement of $\mathcal{B}[\psi (3686)\to {\pi }^{+}{\pi }^{-}J/\psi ]$ confirms the CLEO-c measurement, and is apparently larger than the others. The measured $J/\psi$ leptonic decay branching fractions agree with previous experiments within one standard deviation. These results lead to $\mathcal{B}[J/\psi \to l^{+}{l}^{-}]=(5.978\pm 0.005\pm 0.040)\%$ by averaging over the $e^{+}{e}^{-}$ and ${\mu }^{+}{\mu }^{-}$ channels and a ratio of $\mathcal{B}[J/\psi \to e^{+}{e}^{-}]/\mathcal{B}[J/\psi \to {\mu }^{+}{\mu }^{-}]=1.0017\pm 0.0017\pm 0.0033$, which tests $e$-$\mu$ universality at the four tenths of a percent level. All the measurements presented in this paper are the most precise in the world to date.

In this paper, we systematically study gauge anomalies in bosonic and fermionic weak-coupling gauge theories with gauge group $G$ (which can be continuous or discrete) in $d$ space-time dimensions. We show a very close relation between gauge anomalies for gauge group $G$ and symmetry-protected trivial (SPT) orders (also known as symmetry-protected topological (SPT) orders) with symmetry group $G$ in one-higher dimension. The SPT phases are classified by group cohomology class ${\mathcal{H}}^{d+1}(G,\mathbb{R}/\mathbb{Z})$. Through a more careful consideration, we argue that the gauge anomalies are described by the elements in $\mathrm{\text{Free}}[{\mathcal{H}}^{d+1}(G,\mathbb{R}/\mathbb{Z})]\oplus {\dot{H_{\pi }}}^{d+1}(BG,\mathbb{R}/\mathbb{Z})$. The well known Adler-Bell-Jackiw anomalies are classified by the free part of ${\mathcal{H}}^{d+1}(G,\mathbb{R}/\mathbb{Z})$ (denoted as $\mathrm{\text{Free}}[{\mathcal{H}}^{d+1}(G,\mathbb{R}/\mathbb{Z})]$). We refer to other kinds of gauge anomalies beyond Adler-Bell-Jackiw anomalies as non-ABJ gauge anomalies, which include Witten $SU(2)$ global gauge anomalies. We introduce a notion of $\pi$-cohomology group, ${\dot{H_{\pi }}}^{d+1}(BG,\mathbb{R}/\mathbb{Z})$, for the classifying space $BG$, which is an Abelian group and include $\mathrm{Tor}[{\mathcal{H}}^{d+1}(G,\mathbb{R}/\mathbb{Z})]$ and topological cohomology group $H^{d+1}(BG,\mathbb{R}/\mathbb{Z})$ as subgroups. We argue that ${\dot{H_{\pi }}}^{d+1}(BG,\mathbb{R}/\mathbb{Z})$ classifies the bosonic non-ABJ gauge anomalies and partially classifies fermionic non-ABJ anomalies. Using the same approach that shows gauge anomalies to be connected to SPT phases, we can also show that gravitational anomalies are connected to topological orders (i.e., patterns of long-range entanglement) in one-higher dimension.