Drell-Yan lepton pairs are produced in the process $p\overline{p}\to {\mu }^{+}{\mu }^{-}+X$ through an intermediate ${\gamma }^{*}/Z$boson. The forward-backward asymmetry in the polar-angle distribution of the ${\mu }^{-}$ as a function of the invariant mass of the ${\mu }^{+}{\mu }^{-}$ pair is used to obtain the effective leptonic determination ${\sin }^2{\theta }_{\text{eff}}^{\text{lept}}$ of the electroweak-mixing parameter ${\sin }^2{\theta }_W$, from which the value of ${\sin }^2{\theta }_W$ is derived assuming the standard model. The measurement sample, recorded by the Collider Detector at Fermilab (CDF), corresponds to $9.2{\mathrm{fb}}^{-1}$ of integrated luminosity from $p\overline{p}$ collisions at a center-of-momentum energy of 1.96 TeV, and is the full CDF Run II data set. The value of ${\sin }^2{\theta }_{\text{eff}}^{\text{lept}}$ is found to be $0.2315\pm 0.0010$, where statistical and systematic uncertainties are combined in quadrature. When interpreted within the context of the standard model using the on-shell renormalization scheme, where ${\sin }^2{\theta }_W=1-M_W^2/M_Z^2$, the measurement yields ${\sin }^2{\theta }_W=0.2233\pm 0.0009$, or equivalently a $W$-boson mass of $80.365\pm 0.047\mathrm{GeV}/c^2$. The value of the $W$-boson mass is in agreement with previous determinations in electron-positron collisions and at the Tevatron collider.

We study the behavior of out of equilibrium retarded, advanced and correlated Green’s functions within the context of an exactly soluble (quenched) model. We show, to the lowest order, that even though the pinch singularities cancel, there is a residual linear dependence on the time interval (after the quench) in the correlated Green’s function which may invalidate perturbation theory. We sum the perturbation series to all orders in this simple model and show explicitly that the complete Green’s functions are well behaved even for large time intervals. The exact form of the correlated Green’s function allows us to extract a manifestly positive distribution function, for large times after the quench, which has a memory of the frequency of the initial system before the quench.

In this work we probe the anisotropy of gauge theory plasma at strong coupling regime within the framework of holographic AdS/CFT correspondence. To be specific, we compute the Chern-Simons diffusion rate in an anisotropic, strongly coupled $\mathcal{N}=4$ super-Yang-Mills plasma by working with its supergravity dual in an anisotropic spacetime. The Chern-Simons diffusion rate is an important observable in CP-odd phenomena, which may happen in the quark-gluon plasma. We worked out a generically analytic formula for the Chern-Simons diffusion rate using both linear hydrodynamic expansion and holographic renormalization group flow equation methods. In the high temperature phase (compared to the spatial anisotropy), we found that the anisotropy will decrease the Chern-Simons diffusion rate. We also used the generic formula to extract the stringy/higher order gravity corrections to the Chern-Simons diffusion rate.

We study the Regge and hard-scattering limits of the one-loop amplitude for massless open string states in the type I theory in flat space. For hard scattering we find the exact kinematic dependence in terms of the scattering angle of the factor multiplying the known exponential falloff, without relying on a saddle point approximation for the integration over the cross ratio. This bypasses the issues of estimating the contributions from flat directions as well as those that arise from fluctuations of the Gaussian integration about the saddle point. This result allows for a straightforward computation of the small-angle behavior of the hard-scattering regime and we find complete agreement with the Regge limit at high momentum transfer, as expected.

It is known that by introducing the Yukawa coupling between the fermion and the background scalar field, a bulk spin-half fermion can be localized on general Randall-Sundrum braneworlds generated by a kinklike background scalar. However, this localization mechanism does not work anymore for Randall-Sundrum braneworlds generated by a scalar whose configuration is an even function of the extra dimension. In this paper, we present a new localization mechanism for spin-half fermions for such a class of braneworld models, in which extra dimension has the topology $S^1/Z_2$. By two examples, it is shown that the new localization mechanism produces interesting results. In the first model with the brane generated by two scalars, the zero mode of the left-handed fermion is localized on the brane and there is a mass gap between the fermion zero mode and excited KK modes. In the second model with the brane generated by a dilaton scalar, the zero mode of the left- or right-chiral fermion can be localized on the brane and there is no mass gap.

Vacuum properties of quantum chromodynamics in strong magnetic and finite electric fields are investigated. We show that when a uniform electric field is instantaneously applied in the parallel direction to a strong magnetic field, it induces temporal oscillation of the scalar and pseudoscalar condensates. This is a temporal analog to the chiral spiral. The oscillation originates with the propagation of the collective mode, which is protected by the axial anomaly and thus is nondissipative.

Noncommutative (NC) quantum field theory is the subject of many analyses on formal and general aspects looking for deviations and, therefore, potential noncommutative spacetime effects. Within of this large class, we may now pay some attention to the quantization of NC field theory on lower dimensions and look closely at the issue of dynamical mass generation to the gauge field. This work encompasses the quantization of the two-dimensional massive quantum electrodynamics and three-dimensional topologically massive quantum electrodynamics. We begin by addressing the problem on a general dimensionality making use of the perturbative Seiberg-Witten map to, thus, construct a general action, to only then specify the problem to two and three dimensions. The quantization takes place through the Källén-Lehmann spectral representation and Yang-Feldman-Källén formulation, where we calculate the respective spectral density function to the gauge field. Furthermore, regarding the photon two-point function, we discuss how its infrared behavior is related to the term generated by quantum corrections in two dimensions, and, moreover, in three dimensions, we study the issue of nontrivial $\theta$-dependent corrections to the dynamical mass generation.

The actual value of the quantum vacuum energy density is generally regarded as irrelevant in nongravitational physics. However, this paper presents a nongravitational system where this value does have physical significance. The system is a mirror with an internal degree of freedom that interacts with a scalar field. We find that the force exerted on the mirror by the field vacuum undergoes wild fluctuations with a magnitude proportional to the value of the vacuum energy density, which is mathematically infinite. This infinite fluctuating force gives infinite instantaneous acceleration of the mirror. We show that this infinite fluctuating force and infinite instantaneous acceleration make sense because they will not result in infinite fluctuation of the mirror’s position. On the contrary, the mirror’s fluctuating motion will be confined in a small region due to two special properties of the quantum vacuum: (1) the vacuum friction that resists the mirror’s motion and (2) the strong anticorrelation of vacuum fluctuations that constantly changes the direction of the mirror’s infinite instantaneous acceleration and thus cancels the effect of infinities to make the fluctuation of the mirror’s position finite.

In the present work, we discuss certain characteristic features encoded in some of the fundamental QCD Green’s functions, for which the origin can be traced back to the nonperturbative masslessness of the ghost field, in the Landau gauge. Specifically, the ghost loops that contribute to these Green’s functions display infrared divergences, akin to those encountered in the perturbative treatment, in contradistinction to the gluonic loops, for which perturbative divergences are tamed by the dynamical generation of an effective gluon mass. In $d=4$, the aforementioned divergences are logarithmic, thus causing a relatively mild impact, whereas in $d=3$ they are linear, giving rise to enhanced effects. In the case of the gluon propagator, these effects do not interfere with its finiteness, but make its first derivative diverge at the origin, and introduce a maximum in the region of infrared momenta. The three-gluon vertex is also affected, and the induced divergent behavior is clearly exposed in certain special kinematic configurations, usually considered in lattice simulations; the sign of the corresponding divergence is unambiguously determined. The main underlying concepts are developed in the context of a simple toy model, which demonstrates clearly the interconnected nature of the various effects. The picture that emerges is subsequently corroborated by a detailed nonperturbative analysis, combining lattice results with the dynamical integral equations governing the relevant ingredients, such as the nonperturbative ghost loop and the momentum-dependent gluon mass.

Four-dimensional supergravities may be the right framework to describe particle physics at low energies. Its connection to the underlying string theory can be implemented through higher dimensional supergravities which bear special characteristics. Their reduction to four dimensions breaks supersymmetry whose magnitude depends both on the compactifying manifold and the mechanism that generates the breaking. In particular compactifications, notably on a $S_1/Z_2$ orbifold, the breaking of supersymmetry occurring on a hidden brane, residing at one end of $S_1/Z_2$, is communicated to the visible brane which lies at the other end, via gravitational interactions propagating in the bulk. This scenario has been exemplified in the framework of the $N=2$, $D=5$ supergravity. In this paper, motivated by the recent developments in the field, related to the six-dimensional description of the supergravity theory, we study the $N=2$, $D=5$ supergravity theory as originating from a $D=6$ supergravity which, in addition to the gravity, includes a number of tensor multiplets. This reduces to $N=1$, $D=4$ supergravity in a two step manner, first by a Kaluza-Klein reduction followed by a $S_1/Z_2$ orbifold compactification. The resulting theory has striking similarities with the one that follows from the single stand alone $N=2$, $D=5$ supergravity, with no reference to the underlying higher dimensional $D=6$ supergravity, and a structure that makes the supersymmetry breaking mechanisms studied in the past easily incorporated in higher dimensional schemes.

In this paper, the main properties of ($3+1$)-dimensional $U(1)$ gauged $Q$ balls are examined. In particular, it is shown that the relation $\frac{dE}{dQ}=\omega$ holds for such gauged $Q$ balls in the general case. As a consequence, it is shown that the well-known estimate for the maximal charge of stable gauged $Q$ balls was derived by means of an inconsistent procedure and cannot be considered as correct. A simple method for obtaining the main characteristics of gauged $Q$ balls using only the nongauged background solution for the scalar field in the case, when the backreaction of the gauge field on the scalar field is small and the linearized theory can be used, is proposed. The criteria of applicability of the linearized theory, which do not reduce to the demand of the smallness of the coupling constant, are established. Some interesting properties of gauged $Q$ balls, as well as the advantages of the proposed method, are demonstrated by the example of two models, admitting, in the linear approximation in the perturbations, exact analytic solutions for gauged $Q$ balls.

Gravitational lens models with negative convergence inspired by modified gravity theories, exotic matter, and energy have been recently examined in such a way that a static and spherically symmetric modified spacetime metric depends on the inverse distance to the $n$th power ($n=1$ for Schwarzschild metric, $n=2$ for Ellis wormhole, and $n\ne 1$ for an extended spherical distribution of matter such as an isothermal sphere) in the weak-field approximation. Some of the models act as if a convex lens, whereas the others are repulsive on light rays like a concave lens. The present paper considers microlensed image centroid motions by the exotic lens models. Numerical calculations show that, for large $n$ cases in the convex-type models, the centroid shift from the source position might move on a multiply connected curve like a bow tie, while it is known to move on an ellipse for the $n=1$ case and to move on an oval curve for $n=2$. The distinctive feature of the microlensed image centroid may be used for searching (or constraining) localized exotic matter or energy with astrometric observations. It is shown also that the centroid shift trajectory for concave-type repulsive models might be elongated vertically to the source motion direction like a prolate spheroid, whereas that for convex-type models such as the Schwarzschild one is tangentially elongated like an oblate spheroid.

We study stars in M theory. First, we obtain the analog of Oppenheimer-Volkoff equations in a suitably general setup. We obtain analytically the asymptotic solutions to these equations when the equations of state are linear. We study perturbations around such solutions in several examples and, following a standard method, use their behavior to determine whether an instability is present or not. In this way, we obtain a generalization of the corresponding results of Chavanis. We also find that stars in M theory have instabilities. Therefore, if sufficiently massive, such stars will collapse. We discuss the significance of these (in)stabilities within the context of Mathur’s fuzzball proposal.

We consider neutron-star-plus-wormhole configurations supported by a massless ghost scalar field. The neutron fluid is modeled by an anisotropic equation of state. When the central energy density of the fluid is of comparable magnitude to the one of the scalar field, configurations with an equator at the center and a double throat arise. These double-throat wormholes can be either partially or completely filled by the neutron fluid. In the latter case, the passage of light—radiated by the neutron matter—through these wormholes is studied. A stability analysis indicates that all considered configurations are unstable with respect to linear perturbations, independent of whether the fluid is isotropic or anisotropic.

We investigate the Lagrangian perturbation theory of general dark energy models with a constant equation of state, $\omega$, and derive the fitting form of the fastest growing mode solutions up to third order. These fitting forms are less than a few percent error compared to the numerical calculation. We also correct the solutions of Einstein–de Sitter and the open universe with the proper initial conditions and the correct consideration for the growing mode solutions in order to compare with the general dark energy models. Even though these fitting forms are limited to the constant equation of state models, one can apply these to the time-varying $\omega$ by interpolating between models with the constant $\omega$. These fitting forms can be used for the correct prediction for the two point correlation function and can give the proper predictions for the different dark energy models.

A theory of massive gravity depends on a nondynamical “reference metric” $f_{\mu \nu }$ which is often taken to be the flat Minkowski metric. In this paper we examine the theory of perturbations on a background with metric ${\overline{g}}_{\mu \nu }$ which does not coincide with the reference metric $f_{\mu \nu }$. We derive the mass term for general perturbations on this background and show that it generically is not of the form of the Fierz-Pauli mass term. We explicitly compute it for some cosmological situations and show that it generically leads to instabilities.

We perform accurate calculations of the energy-, momentum-, and charge-emission rates of a charged scalar field in the background of the Kerr-Newman black hole at the range of parameters for which the effect is not negligibly small and, at the same time, the semiclassical regime is, at least marginally, valid. For black holes with charge below or not much higher than the charge accretion limit $Q\sim \mu M/e$ (where $e$ and $\mu$ are the electron’s mass and charge), the time between the consequent emitting of two charged particles is very large. For primordial black holes the transition between the increasing and decreasing of the ratio $Q/M$ occurs around the charge accretion limit. The rotation increases the intensity of radiation up to three orders, while the effect of the field’s mass strongly suppresses the radiation.

We derive the tensor gravitational waveform generated by a binary of nonspinning compact objects (black holes or neutron stars) in a general class of scalar-tensor theories of gravity. The waveform is accurate to second post-Newtonian order beyond the leading order quadrupole approximation. We use the direct integration of the relaxed Einstein equations formalism, appropriately adapted to scalar-tensor theories, along with previous results for the equations of motion in these theories. The self-gravity of the compact objects is treated with an approach developed by Eardley. The scalar field causes deviations from the general relativistic waveform that depend only on a small number of parameters. Among the effects of the scalar field are new hereditary terms which depend on the past history of the source. One of these, a dipole-dipole coupling, produces a zero-frequency “gravitational-wave memory” equivalent to the Christodoulou memory of general relativity. In the special case of two black holes, the waveform reduces to the general relativistic waveform. For a mixed (black hole-neutron star) system, the waveform is identical to that of Einstein’s theory to first post-Newtonian order, with deviations at higher order depending only on a single parameter. The behavior in these cases matches that found for the equations of motion.

We consider the semiclassical Einstein equations (SEE) in the presence of a quantum scalar field with self-interaction $\lambda {\varphi }^4$. Working in the Hartree truncation of the two-particle irreducible effective action, we compute the vacuum expectation value of the energy-momentum tensor of the scalar field, which acts as a source of the SEE. We obtain the renormalized SEE by implementing a consistent renormalization procedure. We apply our results to find self-consistent de Sitter solutions to the SEE in situations with or without spontaneous breaking of the $Z_2$-symmetry.

The aim of this article is to introduce a Lagrangian formulation of relativistic non-Abelian spinning fluids in group theory language. The corresponding Mathisson-Papapetrou equation for spinning fluids in terms of the reduction limit of the de Sitter group has been proposed. The equation we find correctly boils down to the one for nonspinning fluids. Two alternative approaches based on a group theoretical formulation of particle dynamics are also explored.