The Schrödinger wave functional $\psi =\exp (-S\{{\mathcal{A}}_i^a(\overrightarrow{x})\})$ for the $d=3+1$ QCD vacuum is a partition function constructed in $d=4$; the exponent $2S$ [in $|\psi {|}^2=\exp (-2S)$] plays the role of a $d=3$ Euclidean action. We start from a simple conjecture for $S$ based on dynamical generation of a gluon mass $M$ in $d=4$, then use earlier techniques of the author to extend (in principle) the conjectured form to full non-Abelian gauge invariance. We argue that the exact leading term, of $\mathcal{O}(M)$, in an expansion of $S$ in inverse powers of $M$ is a $d=3$ gauge-invariant mass term (gauged nonlinear sigma model); the next-leading term, of $\mathcal{O}(1/M)$, is a conventional Yang-Mills action. The $d=3$ action that is (twice) the sum of these two terms has center vortices as classical solutions. The $d=3$ gluon mass $m_3$, which we constrain to be the same as $M$, and $d=3$ coupling $g_3^2$ are related through the conjecture to the $d=4$ coupling strength, but at the same time the dimensionless ratio $m_3/g_3^2$ can be estimated from $d=3$ dynamics. This allows us to estimate the $d=4$ coupling ${\alpha }_s(M^2)$ in terms of the strictly $d=3$ ratio $m_3/g_3^2$; we find a value of about 0.4, in good agreement with an earlier theoretical value but somewhat low compared to the QCD phenomenological value of $0.7\pm 0.3$. The wave functional for $d=2+1$ QCD has an exponent that is a $d=2$ infrared-effective action having both the gauge-invariant mass term and the field-strength squared term, and so differs from the conventional QCD action in two dimensions, which has no mass term. This conventional $d=2$ QCD would lead in $d=3$ to confinement of all color-group representations. But with the mass term (again leading to center vortices), only $N\mathrm{\text{−}}\mathrm{ality}\not\equiv 0$ mod $N$ representations can be confined [for gauge group $SU(N)$], as expected.

We place observational constraints on a coupling between dark energy and dark matter by using 71 Type Ia supernovae (SNe Ia) from the first year of the five-year Supernova Legacy Survey (SNLS), the cosmic microwave background (CMB) shift parameter from the three-year Wilkinson Microwave Anisotropy Probe (WMAP), and the baryon acoustic oscillation (BAO) peak found in the Sloan Digital Sky Survey (SDSS). The interactions we study are (i) constant coupling $\delta$ and (ii) varying coupling $\delta (z)$ that depends on a redshift $z$, both of which have simple parametrizations of the Hubble parameter to confront with observational data. We find that the combination of the three databases marginalized over a present dark energy density gives stringent constraints on the coupling, $-0.08<\delta <0.03$ (95% C.L.) in the constant coupling model and $-0.4<{\delta }_0<0.1$ (95% C.L.) in the varying coupling model, where ${\delta }_0$ is a present value. The uncoupled $\Lambda \mathrm{CDM}$ model ($w_X=-1$ and $\delta =0$) still remains a good fit to the data, but the negative coupling ($\delta <0$) with the equation of state of dark energy $w_X<-1$ is slightly favored over the $\Lambda \mathrm{CDM}$ model.

A new cosmological variable is introduced to characterize the degree of departure from Einstein’s general relativity with a cosmological constant. The new parameter, $\varpi$, is the cosmological analog of $\gamma$, the parametrized post-Newtonian variable which measures the amount of spacetime curvature per unit mass. In the cosmological context, $\varpi$ measures the difference between the Newtonian and longitudinal potentials in response to the same matter sources, as occurs in certain scalar-tensor theories of gravity. Equivalently, $\varpi$ measures the scalar shear fluctuation in a dark-energy component. In the context of a vanilla, cosmological constant-dominated universe, a nonzero $\varpi$ signals a departure from general relativity or a fluctuating cosmological constant. Using a phenomenological model for the time evolution $\varpi ={\varpi }_0{\rho }_{\mathrm{DE}}/{\rho }_{\mathrm{M}}$ which depends on the ratio of energy density in the cosmological constant to the matter density at each epoch, it is shown that the observed cosmic microwave background temperature anisotropies limit the overall normalization constant to be $-0.4<{\varpi }_0<0.1$ at the 95% confidence level. Existing measurements of the cross-correlations of the cosmic microwave background with large-scale structure further limit ${\varpi }_0>-0.2$ at the 95% CL. In the future, integrated Sachs-Wolfe and weak lensing measurements can more tightly constrain ${\varpi }_0$, providing a valuable clue to the nature of dark energy and the validity of general relativity.

Singlet Higgs bosons present in extensions of the minimal supersymmetric standard model (MSSM) can have sizable Yukawa couplings to the $b$ quark and the $\tau$ lepton for large values of $\tan \beta$ at the 1-loop level. We present an effective Lagrangian which incorporates these $\tan \beta$-enhanced Yukawa couplings and which enables us to study their effect on singlet Higgs-boson phenomenology within the context of both the minimal nonminimal supersymmetric SM (mnSSM) and the next-to-minimal supersymmetric SM (NMSSM). In particular, we find that the loop-induced coupling can be a significant effect for the singlet pseudoscalar, and may dominate its decay modes. Further implications of the $\tan \beta$-enhanced Yukawa couplings for the phenomenology of the singlet Higgs bosons are briefly discussed.

We generalize the notion of the Jarlskog invariant to supersymmetric models with right-handed neutrinos. This allows us to formulate basis-independent necessary and sufficient conditions for $CP$ conservation in such models.

We present a measurement of the shape of the boson rapidity distribution for $p\overline{p}\to Z/{\gamma }^{*}\to e^{+}{e}^{-}+X$ events at a center-of-mass energy of 1.96 TeV. The measurement is made for events with electron-positron mass $71<M_{ee}<111\mathrm{GeV}$ and uses $0.4{\mathrm{fb}}^{-1}$ of data collected at the Fermilab Tevatron collider with the D0 detector. This measurement significantly reduces the uncertainties on the rapidity distribution in the forward region compared with previous measurements. Predictions of next-to-next-to-leading order (NNLO) QCD are found to agree well with the data over the full rapidity range.

For cosmologically interesting $f(R)$ gravity models, we derive the complete set of the linearized field equations in the Newtonian gauge, under environments of the solar system, galaxies, and clusters, respectively. Based on these equations, we confirm the previous $\gamma =1/2$ solution in the solar system. However, $f(R)$ gravity models can be strongly environment dependent and the high density (comparing to the cosmological mean) solar system environment can excite a viable $\gamma =1$ solution for some $f(R)$ gravity models. Although for $f(R)\propto -1/R$, it is not the case; for $f(R)\propto -\exp (-R/{\lambda }_2{H}_0^2)$, such a $\gamma =1$ solution does exist. This solution is virtually indistinguishable from that in general relativity (GR) and the value of the associated curvature approaches the GR limit, which is much higher than the value in the $\gamma =1/2$ solution. We show that for some forms of $f(R)$ gravity, this solution is physically stable in the solar system and can smoothly connect to the surface of the Sun. The derived field equations can be applied directly to gravitational lensing of galaxies and clusters. We find that, despite a significant difference in the environments of galaxies and clusters comparing to that of the solar system, gravitational lensing of galaxies and clusters can be virtually identical to that in GR, for some forms of $f(R)$ gravity. Fortunately, galaxy rotation curve and intracluster gas pressure profile may contain valuable information to distinguish these $f(R)$ gravity models from GR.

We compute the black hole horizon entanglement entropy $S_E$ for a massless scalar field, first with a hard cutoff and then with high frequency dispersion, both imposed in a frame that falls freely across the horizon. Using WKB methods, we find that $S_E$ is finite for a hard cutoff or superluminal dispersion, because the mode oscillations do not diverge at the horizon and the contribution of high transverse momenta is cut off by the angular momentum barrier. For subluminal dispersion, the entropy depends on the behavior at arbitrarily high transverse momenta. In all cases it scales with the horizon area. For the hard cutoff it is linear in the cutoff, rather than quadratic. This discrepancy from the familiar result arises from the difference between the free-fall frame and the static frame in which a cutoff is usually imposed. In the superluminal case the entropy scales with a fractional power of the cutoff that depends on the index of the dispersion relation. Implications for the possible relation between regularized entanglement entropy and the Bekenstein-Hawking entropy are discussed. An appendix provides an explicit derivation of the entangled, thermal nature of the near-horizon free-fall vacuum for a dispersive scalar field in four dimensions.

Generalizing a previous work concerning cosmological linear tensor perturbations, we show that the Lagrangians and Hamiltonians of cosmological linear scalar and vector perturbations can be put in simple form through the implementation of canonical transformations and redefinitions of the lapse function, without ever using the background classical equations of motion. A similar result was obtained by Langlois in the case of a scalar field, but we generalize it for any perfect fluid. In such case, i.e., when the matter content of the Universe is a perfect fluid, we can go further and show that the Hamiltonian of scalar perturbations can be reduced, as usual, to a Hamiltonian of a scalar field with variable mass depending on background functions, independently of the fact that these functions satisfy the background Einstein classical equations. These simple Lagrangians and Hamiltonians can then be used in situations where the background metric is also quantized, hence providing a substantial simplification over the direct approach originally developed by Halliwell and Hawking.

We present results for light meson masses and pseudoscalar decay constants from the first of a series of lattice calculations with $2+1$ dynamical flavors of domain wall fermions and the Iwasaki gauge action. The work reported here was done at a fixed lattice spacing of about 0.12 fm on a ${16}^3\times 32$ lattice, which amounts to a spatial volume of $(2\mathrm{fm}{)}^3$ in physical units. The number of sites in the fifth dimension is 16, which gives $m_{\mathrm{res}}=0.00308(4)$ in these simulations. Three values of input light sea quark masses, $m_l^{\mathrm{sea}}\approx 0.85m_s$, $0.59m_s$ and $0.33m_s$ were used to allow for extrapolations to the physical light quark limit, while the heavier sea quark mass was fixed to approximately the physical strange quark mass $m_s$. The exact rational hybrid Monte Carlo algorithm was used to evaluate the fractional powers of the fermion determinants in the ensemble generation. We have found that $f_{\pi }=127(4)\mathrm{MeV}$, $f_K=157(5)\mathrm{MeV}$ and $f_K/f_{\pi }=1.24(2)$, where the errors are statistical only, which are in good agreement with the experimental values.

In this fourth paper of the series, I clarify the somewhat mysterious relation between the large class of orientation orbifolds (with twisted open-string conformal field theories (CFT’s) at $\widehat{c}=52$) and orientifolds (with untwisted open strings at $c=26$), both of which have been associated to division by world sheet orientation-reversing automorphisms. In particular—following a spectral clue in the previous paper—I show that, even as an interacting string system, a certain half-integer-moded orientation orbifold-string system is in fact equivalent to the archetypal orientifold. The subtitle of this paper, that orientation orbifolds include and generalize standard orientifolds, then follows because there are many other orientation orbifold-string systems—with higher fractional moding—which are not equivalent to untwisted string systems.

Cosmological hydrodynamics and magnetohydrodynamics may be set in a quasi-Newtonian form except for the presence of several terms related to the cosmological scale factor. This relative simplicity enables us to study the asymptotic form of velocity and magnetic field when one assumes that the distribution of matter tends to a final state. Some reasonable hypotheses on the smoothness of solutions for all time yield the specific rate of decrease of these magnitudes. This turns out to depend on a simple form on the universal expansion parameter.

The continuous improvement in localization errors (sky position and distance) in real time as LISA observes the gradual inspiral of a supermassive black hole binary can be of great help in identifying any prompt electromagnetic counterpart associated with the merger. We develop a new method, based on a Fourier decomposition of the time-dependent, LISA-modulated gravitational-wave signal, to study this intricate problem. The method is faster than standard Monte Carlo simulations by orders of magnitude. By surveying the parameter space of potential LISA sources, we find that counterparts to supermassive black hole binary mergers with total mass $M\sim {10}^5–{10}^7{\mathrm{M}}_{\odot }$ and redshifts $z\lesssim 3$ can be localized to within the field of view of astronomical instruments ($\sim {\mathrm{deg}}^2$) typically hours to weeks prior to coalescence. This will allow a triggered search for variable electromagnetic counterparts as the merger proceeds, as well as monitoring of the most energetic coalescence phase. A rich set of astrophysical and cosmological applications would emerge from the identification of electromagnetic counterparts to these gravitational-wave standard sirens.

We show that the recently proposed minimal walking technicolor theory together with a small modification of the standard model fermionic matter content leads to an excellent degree of unification of the gauge couplings. We compare the degree of unification with various time-honored technicolor models and the minimal supersymmetric extension of the standard model. We find that, at the one-loop level, the new theory provides a degree of unification higher than any of the other extensions above. The phenomenology of the present model is very rich with various potential dark matter candidates.

We present a numerical simulation of the Gross-Neveu model on the lattice using a new representation in terms of fermion loops. In the loop representation all signs due to Pauli statistics are eliminated completely and the partition function is a sum over closed loops with only positive weights. In the loop representation a different type of boundary condition appears: sectors of constant winding number. We demonstrate that the new formulation allows one to simulate volumes which are 2 orders of magnitude larger than those accessible with standard methods.

In lattice gauge theory (LGT) equilibrium simulations of QCD are usually performed with periodic boundary conditions (BCs). In contrast, deconfined regions created in heavy ion collisions are bordered by the confined phase. Here we discuss BCs in LGT with respect to their suitability to model a cold exterior of the lattice volume. Subsequently, we perform Monte Carlo (MC) simulations of pure SU(3) LGT with a thus inspired simple change of BCs using volumes of a size comparable to those typically encountered in the BNL relativistic heavy ion collider (RHIC) experiment. Corrections to the usual LGT results survive in the finite volume continuum limit. We estimate them as a function of the volume size for the temporal extensions $N_{\tau }=4$ and 6 of the lattice and find that the results collapse to one curve when the previously established SU(3) scaling relation for the Wilson action is used. In magnitude the corrections found are comparable to those of including quarks. As observables we use a pseudocritical temperature, which rises opposite to the effect of quarks, and the width of the transition, which broadens similar to the effect of quarks.

We consider a possible interpretation of the new charm-strange meson $D_{s0}^{*}(2317)$ as a hadronic molecule—a bound state of $D$ and $K$ mesons. Using an effective Lagrangian approach, we calculate the strong $D_{s0}^{*}\to D_s{\pi }^0$ and radiative $D_{s0}^{*}\to D_s^{*}\gamma$ decays. A new impact related to the $DK$ molecular structure of the $D_{s0}^{*}(2317)$ meson is that the presence of $u(d)$ quarks in the $D$ and $K$ mesons gives rise to a direct strong isospin-violating transition $D_{s0}^{*}\to D_s{\pi }^0$ in addition to the decay mechanism induced by $\eta -{\pi }^0$ mixing considered previously. We show that the direct transition dominates over the $\eta -{\pi }^0$ mixing transition in the $D_{s0}^{*}\to D_s{\pi }^0$ decay. Our results for the partial decay widths are consistent with previous calculations.

We evaluate the top-quark FCNC productions induced by the topcolor-assisted technicolor (TC2) model at the LHC. These productions proceed, respectively, through the parton-level processes $gg\to t\overline{c}$, $cg\to t$, $cg\to tg$, $cg\to tZ$, and $cg\to t\gamma$. We show the dependence of the production rates on the relevant TC2 parameters and compare the results with the predictions in the minimal supersymmetric model. We find that for each channel the TC2 model allows for a much larger production rate than the supersymmetric model. All these rare productions in the TC2 model can be enhanced above the $3\sigma$ sensitivity of the LHC. Since in the minimal supersymmetric model only $cg\to t$ is slightly larger than the corresponding LHC sensitivity, the observation of these processes will favor the TC2 model over the supersymmetric model. In case of unobservation, the LHC can set meaningful constraints on the TC2 parameters.

The left-right symmetric extension of the standard model with Higgs isospin triplets can provide neutrino masses via a TeV scale seesaw mechanism. The doubly charged Higgs bosons $H_L^{\pm \pm }$ and $H_R^{\pm \pm }$ induce lepton flavor violating decays ${\tau }^{\pm }\to lll$ at tree level via a coupling which is related to the Maki-Nakagawa-Sakata matrix $(V_{\mathrm{MNS}})$. We study the magnitude and correlation of ${\tau }^{\pm }\to lll$ and $\mu \to e\gamma$ with specific assumptions for the origin of the large mixing in $V_{\mathrm{MNS}}$ while respecting the stringent bound for $\mu \to eee$. It is also shown that an angular asymmetry for ${\tau }^{\pm }\to lll$ is sensitive to the relative strength of the $H_L^{\pm \pm }$ and $H_R^{\pm \pm }$ mediated contributions and provides a means of distinguishing models with doubly charged Higgs bosons.

Several exclusive $B_s^0$ decays are studied using a $1.86{\mathrm{fb}}^{-1}$ data sample collected at the ${\rm Y}(5S)$ resonance with the Belle detector at the KEKB asymmetric energy $e^{+}{e}^{-}$ collider. In the $B_s^0\to D_s^{-}{\pi }^{+}$ decay mode we find 10 $B_s^0$ candidates and measure the corresponding branching fraction. Combining the $B_s^0\to D_s^{(*)-}{\pi }^{+}$, $B_s^0\to D_s^{(*)-}{\rho }^{+}$, $B_s^0\to J/\psi \varphi$, and $B_s^0\to J/\psi \eta$ decay modes, a significant $B_s^0$ signal is observed. The ratio $\sigma (e^{+}{e}^{-}\to B_s^{*}{\overline{B}}_s^{*})/\sigma (e^{+}{e}^{-}\to B_s^{(*)}{\overline{B}}_s^{(*)})=({93}_{-9}^{+7}\pm 1)\%$ is obtained at the ${\rm Y}(5S)$ energy, indicating that $B_s^0$ meson production proceeds predominantly through the creation of $B_s^{*}{\overline{B}}_s^{*}$ pairs. The $B_s^0$ and $B_s^{*}$ meson masses are measured to be $M(B_s^0)=(5370\pm 1\pm 3)\mathrm{MeV}/c^2$ and $M(B_s^{*})=(5418\pm 1\pm 3)\mathrm{MeV}/c^2$. Upper limits on the $B_s^0\to \gamma \gamma$, $B_s^0\to \varphi \gamma$, $B_s^0\to K^{+}{K}^{-}$, and $B_s^0\to D_s^{(*)+}{D}_s^{(*)-}$ branching fractions are also reported.