We explore the discovery potential of $W^{\prime }$ and $Z^{\prime }$ boson searches for various $SU(2{)}_1\otimes SU(2{)}_2\otimes U(1{)}_X$ models at the Large Hadron Collider (LHC), after taking into account the constraints from low energy precision measurements and direct searches at both the Tevatron (1.96 TeV) and the LHC (7 TeV). In such models, the $W^{\prime }$ and $Z^{\prime }$ bosons emerge after the electroweak symmetry is spontaneously broken. Two patterns of the symmetry breaking are considered in this work: one is $SU(2{)}_L\otimes SU(2{)}_2\otimes U(1{)}_X\to SU(2{)}_L\otimes U(1{)}_Y$ (breaking pattern I), another is $SU(2{)}_1\otimes SU(2{)}_2\otimes U(1{)}_Y\to SU(2{)}_L\otimes U(1{)}_Y$ (breaking pattern II). Examining the single production channel of $W^{\prime }$ and $Z^{\prime }$ with their subsequent leptonic decays, we find that the probability of detecting $W^{\prime }$ and $Z^{\prime }$ bosons in the considered models at the LHC (with 14 TeV) is highly limited by the low energy precision data constraints. We show that observing $Z^{\prime }$ alone, without seeing a $W^{\prime }$, does not rule out new physics models with non-Abelian gauge extension, such as the phobic models in breaking pattern I. Models in breaking pattern II would predict the discovery of degenerate $W^{\prime }$ and $Z^{\prime }$ bosons at the LHC.

We demonstrate how the measurements of the Higgs-fermion and Higgs-gauge boson couplings can be interpreted in terms of physics beyond the Standard Model in a model-independent way. That is, we describe deviations from the Standard Model by effective $d=6$ operators made of Higgs fields and gauge fields, under the hypothesis that the new physics may show up in the Higgs sector only and the effective operators are generated at tree level. While the effective operator coefficients are independent in general, the completion of the theory at high energies will lead to specific correlations which will be recovered between Higgs-fermion and Higgs-gauge boson couplings. We demonstrate that the current measurement of these couplings in terms of tree-level new physics requires several new mediators with specific relationships among different couplings. New insights in the effective theory and mediator spaces can be expected for improved measurements from the inclusive $H\to \tau \tau$ and the exclusive vector boson fusion-dominated $H\to \gamma \gamma$ search channels, as well as the measurement of the Higgs self-couplings, including higher-order couplings which do not exist in the Standard Model.

We introduce a model independent method for the determination of the hadronic contribution to the QED running coupling, $\Delta {\alpha }_{\mathrm{HAD}}(M_Z^2)$, requiring no $e^{+}{e}^{-}$ annihilation data as input. This is achieved by calculating the heavy-quark contributions entirely in perturbative QCD, while the light-quark resonance piece is determined using available lattice QCD results. Future reduction in the current uncertainties in the latter shall turn this method into a valuable alternative to the standard approach. Subsequently, we find that the precision of current determinations of $\Delta {\alpha }_{\mathrm{HAD}}(M_Z^2)$ can be improved by some 20% by computing the heavy-quark pieces in perturbative QCD, while using $e^{+}{e}^{-}$ data only for the low-energy light-quark sector. We obtain in this case $\Delta {\alpha }_{\mathrm{HAD}}(M_Z^2)=275.7(0.8)\times {10}^{-4}$, which currently is the most precise value of $\Delta {\alpha }_{\mathrm{HAD}}(M_Z^2)$.

We interpret the new particle at the Large Hadron Collider as a $CP$-even scalar and investigate its electroweak quantum number. Assuming an unbroken custodial invariance as suggested by precision electroweak measurements, only four possibilities are allowed if the scalar decays to pairs of gauge bosons, as exemplified by a dilaton/radion, a nondilatonic electroweak singlet scalar, an electroweak doublet scalar, and electroweak triplet scalars. We show that current LHC data already strongly disfavor both the “plain-vanilla” dilatonic and nondilatonic singlet imposters. On the other hand, a generic Higgs doublet gives excellent fits to the measured event rates of the newly observed scalar resonance, while the Standard Model Higgs boson gives a slightly worse overall fit due to the lack of a signal in the $\tau \tau$ channel. The triplet imposter exhibits some tension with the data. The global fit indicates that the enhancement in the diphoton channel could be attributed to an enhanced partial decay width, while the production rates are consistent with the Standard Model expectations. We emphasize that more precise measurements of the ratio of event rates in the $WW$ over $ZZ$ channels, as well as the event rates in $b\overline{b}$ and $\tau \tau$ channels, are needed to further distinguish the Higgs doublet from the triplet imposter.

Unpolarized cross sections and double-helicity asymmetries of single-inclusive positive and negative charged hadrons at midrapidity from $p+p$ collisions at $\sqrt{s}=62.4\mathrm{GeV}$ are presented. The PHENIX measurement of the cross sections for $1.0<p_T<4.5\mathrm{GeV}/c$ are consistent with perturbative QCD calculations at next-to-leading order in the strong-coupling constant, ${\alpha }_s$. Resummed pQCD calculations including terms with next-to-leading-log accuracy, yielding reduced theoretical uncertainties, also agree with the data. The double-helicity asymmetry, sensitive at leading order to the gluon polarization in a momentum-fraction range of $0.05\lesssim x_{\mathrm{gluon}}\lesssim 0.2$, is consistent with recent global parametrizations disfavoring large gluon polarization.

We study a holographic description for correlation function of $1/4$ Bogomol’nyi-Prasad-Sommerfield (BPS) Wilson loop operator and $1/2$ BPS local operator carrying a large R charge of order $\sqrt{\lambda }$. We construct a rotating string solution that is extended in ${\mathrm{S}}^5$ as well as in ${\mathrm{AdS}}_5$. The string solution preserves the $1/8$ of the supersymmetry as expected from the gauge theory computation. By evaluating the string action including boundary terms, we show that the string solution reproduces correlation function in the large $J\sim \mathcal{O}(\sqrt{\lambda })$ limit. In addition, we found the second solution for which the “size” of the string becomes larger than the radius of ${\mathrm{S}}^5$. In the case $J=0$, this solution reduces to the previously known unstable string configuration. The gauge theory side also contains a saddle point that is not on the steepest descent path. We show that the saddle point value matches for this case as well.

We show that the double-copy structure of gravity forbids divergences in pure half-maximal (16 supercharge) supergravity at four and five points at one loop in $D<8$ and at two loops in $D<6$. We link the cancellations that render these supergravity amplitudes finite to corresponding ones that eliminate forbidden color factors from the divergences of pure nonsupersymmetric Yang-Mills theory. The vanishing of the two-loop four-point divergence in $D=5$ half-maximal supergravity is an example where a valid counterterm satisfying the known symmetries exists, yet is not present. We also give explicit forms of divergences in half-maximal supergravity at one loop in $D=8$ and at two loops in $D=6$.

Resonant $e^{+}{e}^{-}$ pair production by an electron in a magnetic field near the process threshold has been analytically studied. Using the Nikishov’s theorem, an estimation of the number of events has been made in the magnetic field equivalent to laser wave in the SLAC experiment, [D. Burke et al., Phys. Rev. Lett. 79, 1626 (1997)]. The obtained estimation is in reasonable agreement with the experimental data.

In a Euclidean path integral formulation of gauge theory and quantum mechanics, the $\theta$-term induces a sign problem, and relatedly, a complex phase for the fugacity of topological defects; whereas in Minkowskian formulation, it induces a topological (geometric) phase multiplying ordinary path-amplitudes. In an $SU(2)$ Yang-Mills theory which admits a semi-classical limit, we show that the complex fugacity generates interference between Euclidean path histories, i.e., monopole-instanton events, and radically alters the vacuum structure. At $\theta =0$, a mass gap is due to the monopole-instanton plasma, and the theory has a unique vacuum. At $\theta =\pi$, the monopole induced mass gap vanishes, despite the fact that monopole density is independent of $\theta$, due to destructive topological interference. The theory has two options: to remain gapless or to be gapped with a two-fold degenerate vacua. We show the latter is realized by the magnetic bion mechanism, and the two-vacua are realization of spontaneous $CP$-breaking. The effect of the $\theta$-term in the circle-compactified gauge theory is a generalization of Aharonov-Bohm effect, and the geometric (Berry) phase. As $\theta$ varies from 0 to $\pi$, the gauge theory interpolates between even- and odd-integer spin quantum anti-ferromagnets on two spatial dimensional bi-partite lattices, which have ground state degeneracies one and two, respectively, as it is in gauge theory at $\theta =0$ and $\theta =\pi$.

While $Q$-balls have been investigated intensively for many years, another type of nontopological solution, $Q$-tubes, have not been understood very well. In this paper we make a comparative study of $Q$-balls and $Q$-tubes. First, we investigate their equilibrium solutions for four types of potentials. We find, for example, that in some models the charge-energy relation is similar between $Q$-balls and $Q$-tubes while in other models the relation is quite different between them. To understand what determines the charge-energy relation, which is a key of stability of the equilibrium solutions, we establish an analytical method to obtain the two limit values of the energy and the charge. Our prescription indicates how the existent domain of solutions and their stability depend on their shape as well as potentials, which would also be useful for a future study of $Q$-objects in higher-dimensional spacetime.

Motivated by novel results in the theory of wave dynamics in black-hole spacetimes, we analyze the dynamics of a massive scalar field surrounding a rapidly rotating Kerr black hole. In particular, we report on the existence of stationary (infinitely long-lived) regular field configurations in the background of maximally rotating black holes. The effective height of these scalar “clouds” above the central black hole is determined analytically. Our results support the possible existence of stationary scalar field dark matter distributions surrounding rapidly rotating black holes.

Dense enough compact objects were recently shown to lead to an exponentially fast increase of the vacuum energy density for some free scalar fields properly coupled to the spacetime curvature as a consequence of a tachyonic-like instability. Once the effect is triggered, the star energy density would be overwhelmed by the vacuum energy density in a few milliseconds. This demands that eventually geometry and field evolve to a new configuration to bring the vacuum back to a stationary regime. Here, we show that the vacuum fluctuations built up during the unstable epoch lead to particle creation in the final stationary state when the tachyonic instability ceases. The amount of created particles depends mostly on the duration of the unstable epoch and final stationary configuration, which are open issues at this point. We emphasize that the particle creation coming from the tachyonic instability will occur even in the adiabatic limit, where the spacetime geometry changes arbitrarily slowly, and therefore is quite distinct from the usual particle creation due to the change in the background geometry.

In this paper, we first study spherically symmetric, stationary vacuum configurations in general covariant theory [$U(1)$ extension] of Hořava-Lifshitz gravity with the projectability condition and an arbitrary value of the coupling constant $\lambda$. We obtain all the solutions with the assumed symmetry in closed forms. If the gauge field $A$ and the Newtonian prepotential $\phi$ do not directly couple to matter fields, the theory is inconsistent with solar system tests for $\lambda \ne 1$, no matter how small $|\lambda -1|$ is. This is shown to be true also with the most general ansatz of spherically symmetric (but not necessarily stationary) configurations. Therefore, to be consistent with observations, one needs either to find a mechanism to restrict $\lambda$ precisely to its relativistic value ${\lambda }_{\mathrm{GR}}=1$, or to consider $A$ and/or $\phi$ as parts of the four-dimensional metric on which matter fields propagate. In the latter, requiring that the line element be invariant not only under the foliation-preserving diffeomorphism but also under the local $U(1)$ transformations, we propose the replacements, $N\to N-\upsilon (A-\mathcal{A})/c^2$ and $N^i\to N^i+N{\nabla }^i\phi$, where $\upsilon$ is a dimensionless coupling constant to be constrained by observations, $N$ and $N^i$ are, respectively, the lapse function and shift vector, and $\mathcal{A}\equiv -\dot{\phi }+N^i{\nabla }_i\phi +N({\nabla }_i\phi {)}^2/2$. With this prescription, we show explicitly that the aforementioned solutions are consistent with solar system tests for both $\lambda =1$ and $\lambda \ne 1$, provided that $|\upsilon -1|<{10}^{-5}$. From this result, the physical and geometrical interpretations of the fields $A$ and $\phi$ become clear. However, it still remains to be understood how to obtain such a prescription from the action principle.

The self-field of a charged particle has a singular component which diverges at the particle. We use both coordinate and covariant approaches to compute an expansion of this singular field for particles in generic geodesic orbits about a Schwarzschild black hole for scalar, electromagnetic and gravitational cases. We check that both approaches yield identical results and give, as an application, the calculation of previously unknown mode-sum regularization parameters. In the so-called mode-sum regularization approach to self-force calculations, each mode of the retarded field is finite, while their sum diverges. The sum may be rendered finite and convergent by the subtraction of appropriate regularization parameters. Higher-order parameters lead to faster convergence in the mode sum. To demonstrate the significant benefit which they yield, we use our newly derived parameters to calculate a highly accurate value of $F_r=0.000013784482575667959(3)$ for the self-force on a scalar particle in a circular orbit around a Schwarzschild black hole. Finally, as a second example application of our high-order expansions, we compute high-order expressions for use in the effective source approach to self-force calculations.

We present the detailed derivation of the recently announced most general cosmological solution with homogeneous and isotropic metric in the ghost-free massive gravity theory. We use the standard parametrization of the theory in terms of the matrix square root, and then show how the same results are recovered within the tetrad formulation. The solution obtained includes the matter source, it exists for generic values of the theory parameters, and it describes a universe that can be spatially open, closed, or flat, and that shows the late-time acceleration due to the effective cosmological term mimicked by the graviton mass. The Stückelberg fields are inhomogeneous, which could probably give rise to inhomogeneous perturbations of the homogeneous and isotropic backgrounds, although this effect should be suppressed by the smallness of the graviton mass.

We study the self-energy of a charged particle located in a static D-dimensional gravitational field. We show that the energy functional for this problem is invariant under an infinite dimensional (gauge) group of transformations parametrized by one scalar function of ($D-1$)—variables. We demonstrate that the problem of the calculation of the self-energy for a pointlike charge is equivalent to the calculation of the fluctuations $⟨{\psi }^2⟩$ for an effective ($D-1$)—dimensional Euclidean quantum field theory. Using point-splitting regularization we obtain an expression for the self-energy and show that it possesses anomalies. Explicit calculation of the self-energy and its anomaly is done for the higher dimensional Majumdar-Papapetrou spacetimes.

We investigate stationary rotating closed Nambu-Goto strings in five-dimensional flat spacetime. The stationary string is defined as a world sheet that is tangent to a timelike Killing vector. The Nambu-Goto equation of motion for the stationary string is reduced to the geodesic equation on the orbit space of the isometry group action generated by the Killing vector. We take a linear combination of a time-translation vector and space-rotation vectors as the Killing vector, and explicitly construct general solutions of stationary rotating closed strings in five-dimensional flat spacetime. We show a variety of their configurations and properties.

In the theories of generalized modified gravity, the acceleration equation is generally fourth order. So, it is hard to analyze the evolution of the Universe. In this paper, we present a class of generalized modified gravity theories which have the acceleration equation of a second-order derivative. Then both the cosmic evolution and the weak-field limit of the theories are easily investigated. We find that, not only the big bang singularity problem, but also that the current cosmic acceleration problem could be easily dealt with.

Chiral effective field theory provides a systematic expansion for the coupling of weakly interacting massive particles (WIMPs) to nucleons at the momentum transfers relevant to direct cold dark matter detection. We derive the currents for spin-dependent WIMP scattering off nuclei at the one-body level and include the leading long-range two-body currents, which are predicted in chiral effective field theory. As an application, we calculate the structure factor for spin-dependent WIMP scattering off ${}^{129,131}\mathrm{Xe}$ nuclei, using nuclear interactions that have been developed to study nuclear structure and double-beta decays in this region. We provide theoretical error bands due to the nuclear uncertainties of WIMP currents in nuclei.

We discuss the damping of tensor modes due to anisotropic stress in inflation. The effect is negligible in standard inflation and may be significantly large in inflation models which involve drastic production of free-streaming particles.