It is well known that in Lorentz-invariant quantum field theories in flat space the commutator of spacelike separated local operators vanishes (microcausality). We provide two different arguments showing that this is a consequence of the causal structure of the classical theory, rather than of Lorentz invariance. In particular, microcausality holds in arbitrary curved space-times, where Lorentz invariance is explicitly broken by the background metric. As illustrated by an explicit calculation on a cylinder this property is rather nontrivial at the level of Feynman diagrams.

We study the properties of the merger of black hole–neutron star (BH-NS) binaries in fully general relativistic simulation, focusing on the case that the NS is tidally disrupted. We prepare BH-NS binaries in a quasicircular orbit as the initial condition in which the BH is modeled by a nonspinning moving puncture. For modeling the NS, we adopt the $\Gamma$-law equation of state with $\Gamma =2$ and the irrotational velocity field. We change the BH mass in the range $M_{\mathrm{BH}}\approx 3.3M_{\odot }–4.6M_{\odot }$, while the rest mass of the NS is fixed to be $M_{*}=1.4M_{\odot }$ (i.e., the NS mass $M_{\mathrm{NS}}\approx 1.3M_{\odot }$). The radius of the corresponding spherical NS is set in the range $R_{\mathrm{NS}}\approx 12–15\mathrm{km}$ (i.e., the compactness $G{M}_{\mathrm{NS}}/R_{\mathrm{NS}}{c}^2\approx 0.13–0.16$). We find for all the chosen initial conditions that the NS is tidally disrupted near the innermost stable circular orbit. The numerical results indicate that, for the model of $R_{\mathrm{NS}}=12\mathrm{km}$, more than $\sim 95\%$ of the rest mass is quickly swallowed by the BH and the resultant torus mass surrounding the BH is less than $\sim 0.05M_{\odot }$. For the model of $R_{\mathrm{NS}}\approx 14.7\mathrm{km}$, by contrast, the torus mass is $\sim 0.15M_{\odot }$ for the BH mass $\approx 4M_{\odot }$. The thermal energy of the material in the torus increases due to the shock heating that occurs in the collision between the spiral arms, resulting in the temperature ${10}^{10}–{10}^{11}\mathrm{K}$. Our results indicate that the merger between a low-mass BH and its companion NS may form a central engine of short gamma-ray bursts of the total energy of order ${10}^{49}\mathrm{ergs}$ if the compactness of the NS is fairly small, $\lesssim 0.145$. However, for the canonical values $M_{\mathrm{NS}}=1.35M_{\odot }$ and $R_{\mathrm{NS}}=12\mathrm{km}$, the merger results in small torus mass, and hence it can be a candidate only for the low-energy, short gamma-ray bursts of total energy of order ${10}^{48}\mathrm{ergs}$. We also present gravitational waveforms during the inspiral, tidal disruption of the NS, and subsequent evolution of the disrupted material. We find that the amplitude of gravitational waves quickly decreases after the onset of tidal disruption. Although the quasinormal mode is excited, its gravitational wave amplitude is much smaller than that of the late inspiral phase. This is reflected in the fact that the spectrum amplitude sharply falls above a cutoff frequency which is determined by the tidal disruption process. We also find that the cutoff frequency is 1.25–1.4 times larger than the frequency predicted by the study for the sequence of the quasicircular orbits, and this factor of the deviation depends on the compactness of the NS.

We study the classical stability of an anisotropic space-time seeded by a spacelike, fixed-norm, dynamical vector field in a vacuum-energy-dominated inflationary era. It serves as a model for breaking isotropy during the inflationary era. We find that, for a range of parameters, the linear differential equations for small perturbations about the background do not have a growing mode. We also examine the energy of fluctuations about this background in flat space. If the kinetic terms for the vector field do not take the form of a field strength tensor squared, then there is a negative energy mode and the background is unstable. For the case where the kinetic term is of the form of a field strength tensor squared, we show that classical solutions to the equations of motion that are close to the background solution have energy greater than or equal to zero. This suggests that the background is metastable.

In this paper we study the use of cross correlations between multiple gravitational wave (GW) data streams for detecting long-lived periodic signals. Cross-correlation searches between data from multiple detectors have traditionally been used to search for stochastic GW signals, but recently they have also been used in directed searches for periodic GWs. Here we further adapt the cross-correlation statistic for periodic GW searches by taking into account both the nonstationarity and the long-term-phase coherence of the signal. We study the statistical properties and sensitivity of this search and its relation to existing periodic wave searches, and describe the precise way in which the cross-correlation statistic interpolates between semicoherent and fully coherent methods. Depending on the maximum duration over which we wish to preserve phase coherence, the cross-correlation statistic can be tuned to go from a standard cross-correlation statistic using data from distinct detectors, to the semicoherent time-frequency methods with increasing coherent time baselines, and all the way to a full coherent search. This leads to a unified framework for studying periodic wave searches and can be used to make informed trade-offs between computational cost, sensitivity, and robustness against signal uncertainties.

We present results from numerical relativity simulations of equal-mass, nonspinning binary-black-hole inspirals and mergers with initial eccentricities $e\le 0.8$ and coordinate separations $D\ge 12M$ of up to 9 orbits (18 gravitational wave cycles). We extract the mass $M_{\mathrm{f}}$ and spin $a_{\mathrm{f}}$ of the final black hole and find, for eccentricities $e\lesssim 0.4$, that $a_{\mathrm{f}}/M_{\mathrm{f}}\approx 0.69$ and $M_{\mathrm{f}}/M_{\mathrm{adm}}\approx 0.96$ are independent of the initial eccentricity, suggesting that the binary has circularized by the merger time. For $e\gtrsim 0.5$, the black holes plunge rather than orbit, and we obtain a maximum spin parameter $a_{\mathrm{f}}/M_{\mathrm{f}}\approx 0.72$ around $e=0.5$.

The group $E_6$ for grand unification is combined with the generation symmetry group $SO(3{)}_g$. The coupling matrices in the Yukawa interaction are identified with the vacuum expectation values of scalar fields which are representations of the generation symmetry. These values determine the hierarchy of the fermions as well as their mixings and $CP$ violation. This generation mixing appears in conjunction with the mixing of the standard model fermions with the heavy fermions present in the lowest representation of $E_6$. A close connection between charged and neutral fermions is observed relating for instance the Cabibbo-Kobayashi-Maskawa (CKM) mixings with the mass splittings of the light neutrinos. Numerical fits with only a few parameters reproduce quantitatively all known fermion properties. The model predicts an inverted neutrino hierarchy and gives rather strict values for the light and heavy neutrino masses as well as for the $0\nu 2\beta$ decay parameter. It also predicts that the masses of the two lightest of six “right handed” neutrinos lie in the low TeV region.

In unparticle physics, operators of the conformal sector have self-interactions, and these are unsuppressed for strong coupling. The 3-point interactions are completely determined by conformal symmetry, up to a constant. We do not know of any theoretical upper bounds on this constant. Imposing current experimental constraints, we find that these interactions mediate spectacular collider signals, such as $pp\to \mathcal{U}\to \mathcal{U}\mathcal{U}\to \gamma \gamma \gamma \gamma$, $\gamma \gamma ZZ$, $ZZZZ$, $\gamma \gamma l^{+}{l}^{-}$, $ZZ{l}^{+}{l}^{-}$, and $4l$, with cross sections of picobarns or larger at the large hadron collider. Self-interactions may therefore provide the leading discovery prospects for unparticle physics.

Weak scale supersymmetry provides elegant solutions to many of the problems of the standard model, but it also generically gives rise to excessive flavor and $CP$ violation. We show that, if the mechanism that suppresses the Yukawa couplings also suppresses flavor changing interactions in the supersymmetry breaking parameters, essentially all the low energy flavor and $CP$ constraints can be satisfied. The standard assumption of flavor universality in the supersymmetry breaking sector is not necessary. We study signatures of this framework at the LHC. The mass splitting among different generations of squarks and sleptons can be much larger than in conventional scenarios, and even the mass ordering can be changed. We find that there is a plausible scenario in which the next-to-lightest superparticle is a long-lived right-handed selectron or smuon which decays into the lightest superparticle, a gravitino. This leads to the spectacular signature of monochromatic electrons or muons in a stopper detector, providing strong evidence for the framework.

The $B_c\to J/\psi \pi$, ${\eta }_c\pi$ decays are studied in the scheme of the QCD factorization approach. The branching ratios are calculated with the asymptotic distribution amplitude of the pion. The charm quark mass effect is considered. We find that the mass effect on the branching ratios is small.

It was argued long ago that ${\eta }_b$ could be observed through the ${\eta }_b\to J/\psi (\to {\mu }^{+}{\mu }^{-})J/\psi (\to {\mu }^{+}{\mu }^{-})$ decay chain. Recent calculations indicate that the width of ${\eta }_b$ into two $J/\psi$ is almost 3 orders of magnitude smaller than the one into the $D{\overline{D}}^{*}$. We study the effects of final-state interactions due to the $D{\overline{D}}^{*}$ intermediate state on the $J/\psi J/\psi$ final state. We find that the inclusion of this contribution may enhance the short-distance branching ratio up to about 2 orders of magnitude.

In the past few years, a great deal of evidence has accumulated which indicates that the gluon polarization inside the nucleon is likely to be small at least at the low renormalization scales. On the other hand, the recent lattice QCD analyses suggest that the net orbital angular momentum carried by the quarks is nearly zero. There is also some indication, noted by Brodsky and Gardner based on the COMPASS observation of small single-spin asymmetry on the isoscalar deuteron target, that the gluon orbital angular momentum inside the nucleon is likely to be small. Naively combining all these observations, we are led to a rather embarrassing conclusion that the nucleon constituents altogether do not carry an adequate amount of angular momentum saturating the total nucleon spin. We show that this somewhat confused state of affairs can be cleared up only by paying careful attention to the scale dependencies of the nucleon spin decomposition.

This paper describes the first measurement of $b$-quark fragmentation fractions into bottom hadrons in Run II of the Tevatron Collider at Fermilab. The result is based on a $360{\mathrm{pb}}^{-1}$ sample of data collected with the CDF II detector in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$. Semileptonic decays of ${\overline{B}}^0$, $B^{-}$, and ${\overline{B}}_s^0$ mesons, as well as ${\Lambda }_b^0$ baryons, are reconstructed. For an effective bottom hadron $p_T$ threshold of $7\mathrm{GeV}/c$, the fragmentation fractions are measured to be $f_u/f_d=1.054\pm 0.018(\mathrm{stat}{)}_{-0.045}^{+0.025}(\mathrm{sys})\pm 0.058(\mathcal{B})$, $f_s/(f_u+f_d)=0.160\pm 0.005(\mathrm{stat}{)}_{-0.010}^{+0.011}(\mathrm{sys}{)}_{-0.034}^{+0.057}(\mathcal{B})$, and $f_{{\Lambda }_b}/(f_u+f_d)=0.281\pm 0.012(\mathrm{stat}{)}_{-0.056}^{+0.058}(\mathrm{sys}{)}_{-0.087}^{+0.128}(\mathcal{B})$, where the uncertainty $\mathcal{B}$ is due to uncertainties on measured branching ratios. The value of $f_s/(f_u+f_d)$ agrees within one standard deviation with previous CDF measurements and the world average of this quantity, which is dominated by LEP measurements. However, the ratio $f_{{\Lambda }_b}/(f_u+f_d)$ is approximately twice the value previously measured at LEP. The approximately $2\sigma$ discrepancy is examined in terms of kinematic differences between the two production environments.

We consider a scenario where the dynamics of a scalar field is ruled by an exponential potential, such as those arising from some quintessence-type models, and aim at obtaining phenomenological manifestations of this entity within our Solar System. To do so, we assume a perturbative regime, derive the perturbed Schwarzschild metric, and extract the relevant post-Newtonian parameters.

We study the properties of Wilson loops in three-dimensional noncompact $U(1)$ gauge theories with global Abelian symmetries. We use duality in the continuum and on the lattice to argue that, close to the critical point between the Higgs and Coulomb phases, all correlators of the Wilson loops are periodic functions of the Wilson loop charge, $Q$. The period depends on the global symmetry of the theory, which determines the magnetic flux carried by the dual particles. For single flavor scalar electrodynamics, the emergent period is $Q=1$. In the general case of $N$ complex scalars with a $U(1{)}^{N-1}$ global symmetry, the period is $Q=N$. We also give some arguments why this phenomenon does not generalize to theories with a full non-Abelian $SU(N)$ symmetry, where no periodicity in $Q$ is expected. Implications for lattice simulations, as well as for physical systems, such as easy-plane antiferromagnets and disordered superfluids, are noted.

We study the noncommutative massless Kalb-Ramond gauge field coupled to a dynamical $U(1)$ gauge field in the adjoint representation together with a compensating vector field. We derive the Seiberg-Witten map and obtain the corresponding mapped action to first order in $\theta$. The (emergent) gravity structure found in other situations is not present here. The off-shell dual scalar theory is derived and it does not coincide with the Seiberg-Witten mapped scalar theory. Dispersion relations are also discussed. The $p$-form generalization of the Seiberg-Witten map to order $\theta$ is also derived.

Using a Lagrangian formalism, a three-parameter nonminimal Einstein-Maxwell theory is established. The three parameters $q_1$, $q_2$, and $q_3$ characterize the cross-terms in the Lagrangian, between the Maxwell field and terms linear in the Ricci scalar, Ricci tensor, and Riemann tensor, respectively. Static spherically symmetric equations are set up, and the three parameters are interrelated and chosen so that effectively the system reduces to a one parameter only, $q$. Specific black hole and other type of one-parameter solutions are studied. First, as a preparation, the Reissner-Nordström solution, with $q_1=q_2=q_3=0$, is displayed. Then, we search for solutions in which the electric field is regular everywhere as well as asymptotically Coulombian, and the metric potentials are regular at the center as well as asymptotically flat. In this context, the one-parameter model with $q_1\equiv -q$, $q_2=2q$, $q_3=-q$, called the Gauss-Bonnet model, is analyzed in detail. The study is done through the solution of the Abel equation (the key equation), and the dynamical system associated with the model. There is extra focus on an exact solution of the model and its critical properties. Finally, an exactly integrable one-parameter model, with $q_1\equiv -q$, $q_2=q$, $q_3=0$, is considered also in detail. A special submodel, in which the Fibonacci number appears naturally, of this one-parameter model is shown, and the corresponding exact solution is presented. Interestingly enough, it is a soliton of the theory, the Fibonacci soliton, without horizons and with a mild conical singularity at the center.

We exploit a previous computation of the self-mass-squared from quantum gravity to include quantum corrections to the scalar evolution equation. The plane wave mode functions are shown to receive no significant one loop corrections at late times. This result probably applies as well to the inflaton of scalar-driven inflation. If so, there is no significant correction to the $\phi \phi$ correlator that plays a crucial role in computations of the power spectrum.

Detecting the parity-odd, or B-mode, polarization pattern in the cosmic microwave background radiation due to primordial gravity waves is considered to be the final observational key to confirming the inflationary paradigm. The search for viable models of inflation from particle physics and string theory has (re)discovered another source for B-modes: cosmic strings. Strings naturally generate as much vector-mode perturbation as they do scalar, producing B-mode polarization with a spectrum distinct from that expected from inflation itself. In a large set of models, B-modes arising from cosmic strings are more prominent than those expected from primordial gravity waves. In light of this, we study the physical underpinnings of string-sourced B-modes and the model dependence of the amplitude and shape of the $C_l^{\mathrm{BB}}$ power spectrum. Observational detection of a string-sourced B-mode spectrum would be a direct probe of post-inflationary physics near the grand unified theory (GUT) scale. Conversely, nondetection would put an upper limit on a possible cosmic string tension of $G\mu \lesssim {10}^{-7}$ within the next three years.

A closed integral expression for the chiral susceptibility at finite temperature is derived. The corresponding disconnected part, which proves to be of major physical relevance and free from the additive quadratic ultraviolet divergence, is identified. Then a calculation based on an effective model gluon propagator is conducted within the framework of the Dyson-Schwinger equations for two flavors in the chiral limit. A narrow, divergent peak is observed as temperature varies, and its implications are discussed.