We provide quantitative evidence for our previous conjecture which states an equivalence of the partition function of a 3d $\mathcal{N}=2$ gauge theory on a duality wall and that of the $SL(2,\mathbb{R})$ Chern-Simons theory on a mapping torus, for a class of examples associated with once-punctured torus. In particular, we demonstrate that a limit of the 3d $\mathcal{N}=2$ partition function reproduces the hyperbolic volume and the Chern-Simons invariant of the mapping torus. This is shown by analyzing the classical limit of the trace of an element of the mapping class group in the Hilbert space of the quantum Teichmüller theory. We also show that the subleading correction to the partition function reproduces the Reidemeister torsion.

The $Z\to e^{+}{e}^{-}$ decay is studied based on the noncommutative standard model with the hybrid gauge transformation. It is shown that if the latter is not included, the noncommutative correction to the amplitude of the $Z\to e^{+}{e}^{-}$ appears only as a phase factor, so that there is no new physical effect on the decay width. However, when the hybrid gauge transformation is included, the noncommutative effect appears in the two-body decay process. The discrepancy between the experimental branch ratio and the standard model prediction allows us to set the bound on the noncommutative parameters.

We study the charge transports originating from triangle anomaly in out-of-equilibrium conditions in the framework of AdS/CFT correspondence at strong coupling, to gain useful insights on possible charge separation effects that may happen in the very early stages of heavy-ion collisions. We first construct a gravity background of a homogeneous mass shell with a finite (axial) charge density gravitationally collapsing to a charged black hole, which serves as a dual model for out-of-equilibrium charged plasma undergoing thermalization. We find that a finite charge density in the plasma slows down the thermalization. We then study the out-of-equilibrium properties of chiral magnetic effect and chiral magnetic wave in this background. As the medium thermalizes, the magnitude of chiral magnetic conductivity and the response time delay grow. We find a dynamical peak in the spectral function of retarded current correlator, which we identify as an out-of-equilibrium chiral magnetic wave. The group velocity of the out-of-equilibrium chiral magnetic wave is shown to receive a dominant contribution from a nonequilibrium effect, making the wave moving much faster than in the equilibrium, which may enhance the charge transports via triangle anomaly in the early stage of heavy-ion collisions.

We compute the soft contribution to the static energy of two heavy color sources interacting via a $\mathcal{N}=4$ supersymmetric Yang-Mills theory. Both singlet and octet color configurations are considered. Our calculations complete recent considerations of the ultrasoft contributions.

The proper-time 4D path integral is used as a starting point to derive the new explicit parametric form of the quark-antiquark Green’s function in gluonic and QED fields entering as a common Wilson loop. The subsequent vacuum averaging of the latter allows us to derive the instantaneous Hamiltonian. The explicit form and solutions are given in the case of the $q\overline{q}$ mesons in magnetic field.

We calculate the self-energy anomaly of a pointlike electric dipole located in a static ($2+1$)-dimensional curved spacetime. The energy functional for this problem is invariant under an infinite-dimensional (gauge) group of transformations parametrized by one scalar function of two variables. We demonstrate that the problem of the calculation of the self-energy anomaly for a pointlike dipole can be reduced to the calculation of quantum fluctuations of an effective two-dimensional Euclidean quantum field theory. We reduced the problem in question to the calculation of the conformal anomaly of an effective scalar field in two dimensions and obtained an explicit expression for the self-energy anomaly of an electric dipole in an asymptotically flat, regular ($2+1$)-dimensional spacetime, which may have electrically neutral black-hole-like metrics with regular Killing horizon.

In four-dimensional gravity theory, the Barbero-Immirzi parameter has a topological origin, and can be identified as the coefficient multiplying the Nieh-Yan topological density in the gravity Lagrangian, as proposed by Date et al. [Phys. Rev. D 79, 044008 (2009)]. Based on this fact, a first order action formulation for spacetimes with boundaries is introduced. The bulk Lagrangian, containing the Nieh-Yan density, needs to be supplemented with suitable boundary terms so that it leads to a well-defined variational principle. Within this general framework, we analyze spacetimes with and without a cosmological constant. For locally anti–de Sitter (or de Sitter) asymptotia, the action principle has nontrivial implications. It admits an extremum for all such solutions provided the SO(3,1) Pontryagin and Euler topological densities are added to it with fixed coefficients. The resulting Lagrangian, while containing all three topological densities, has only one independent topological coupling constant, namely, the Barbero-Immirzi parameter. In the final analysis, it emerges as a coefficient of the SO(3,2) [or SO(4,1)] Pontryagin density, and is present in the action only for manifolds for which the corresponding topological index is nonzero.

We study future singularity in teleparallel dark energy models, particularly its behavior and its (non)occurrence in the observationally viable models. For the models with a general self-potential of the scalar field, we point out that both at early times and in the future near the singularity the behavior of dark energy can be described by the analytic solutions of the scalar field we obtained for the model with no self-potential. As to the (non)occurrence in the viable models, we consider a natural binding-type self-potential, the quadratic potential, when fitting observational data, and illustrate the constraining region up to the $3\sigma$ confidence level as well as the region where a singularity will occur. As a result, the singularity region is outside the $3\sigma$ constraint. Thus, although the future singularity problem potentially exists in teleparallel dark energy models, the observationally viable models may not suffer this problem.

This work devises a formalism to obtain the equations of motion for a black hole-fluid configuration. Our approach is based on a post-Newtonian expansion and adapted to scenarios where obtaining the relevant dynamics requires long time-scale evolutions. These systems are typically studied with Newtonian approaches, which have the advantage that larger time steps can be employed than in full general-relativistic simulations but have the downside that important physical effects are not accounted for. The formalism presented here provides a relatively straightforward way to incorporate those effects in existing implementations, up to 2.5 post-Newtonian order, with lower computational costs than fully relativistic simulations.

Vacuum expectation values (VEVs) of the current densities for charged scalar and Dirac spinor fields are investigated in $(D+1)$-dimensional de Sitter (dS) spacetime with toroidally compactified spatial dimensions. Along compact dimensions we impose quasiperiodicity conditions with arbitrary phases. In addition, the presence of a classical constant gauge field is assumed. The VEVs of the charge density and of the components for the current density along noncompact dimensions vanish. The gauge field leads to Aharonov-Bohm-like oscillations of the components along compact dimensions as functions of the magnetic flux. For small values of the comoving length of a compact dimension, compared with the dS curvature scale, the current density is related to the corresponding current in the Minkowski spacetime by a conformal relation. For large values of the comoving length and for a scalar field, depending on the mass of the field, two different regimes are realized with the monotonic and oscillatory damping of the current density. For a massive spinor field, the decay of the current density is always oscillatory. In supersymmetric models on the background of Minkowski spacetime with equal number of scalar and fermionic degrees of freedom and with the same phases in the periodicity conditions, the total current density vanishes due to the cancellation between the scalar and fermionic parts. The background gravitational field modifies the current densities for scalar and fermionic fields in different ways, and for massive fields there is no cancellation in the dS spacetime.

It is well known that cosmic microwave background (CMB) temperature anisotropies and polarization can be used to probe the metric perturbations in the early universe. Presently, there exists no observational detection of tensor modes of primordial metric perturbations or of primordial non-Gaussianity. In such a scenario, the primordial power spectrum of scalar metric perturbations is the only correlation function of metric perturbations (presumably generated during inflation) whose effects can be directly probed through various observations. To explore the possibility of any deviations from the simplest picture of the era of cosmic inflation in the early universe, it thus becomes extremely important to uncover the amplitude and shape of this correlation sufficiently well. In the present work, we attempt to reconstruct the primordial power spectrum of scalar metric perturbations using the binned (uncorrelated) CMB temperature anisotropies data from WMAP 9-Year, using the maximum entropy method or MEM to solve the corresponding inverse problem. Our analysis shows that, given the current CMB data, there are no convincing reasons to believe that the primordial power spectrum of scalar metric perturbations has any significant features.

We consider the mixed inflaton-curvaton scenario in which quantum fluctuations of the curvaton field during inflation lead to a relatively large curvature perturbation spectrum at small scales. We use the model of chaotic inflation with quadratic potential including supergravity corrections leading to a large positive tilt in the power spectrum of the curvaton field. The model is characterized by the strongly inhomogeneous curvaton field in the Universe and large non-Gaussianity of curvature perturbations at small scales. We obtained the constraints on the model parameters considering the process of primordial black hole production in the radiation era.

Dissipative dark matter, such as mirror dark matter and related hidden-sector dark matter candidates, require an energy source to stabilize dark matter halos in spiral galaxies. It has been proposed previously that supernovae could be the source of this energy. Recently, it has been argued that this mechanism might explain two galactic scaling relations inferred from observations of spiral galaxies. One of these is that ${\rho }_0{r}_0$ is roughly constant, and the other relates the galactic luminosity to $r_0$. (${\rho }_0$ is the dark matter central density and $r_0$ is the core radius.) Here we derive equations for the heating of the halo via supernova energy, and the cooling of the halo via thermal bremsstrahlung. These equations are numerically solved to obtain constraints on the ${\rho }_0$, $r_0$ parameters appropriate for spiral galaxies. These constraints are in remarkable agreement with the aforementioned scaling relations.

As direct and indirect dark matter detection experiments continue to place stringent constraints on WIMP masses and couplings, it becomes imperative to expand the scope of the search for particle dark matter by looking in new and exotic places. One such place may be the core of active Galactic nuclei (AGN) where the density of dark matter is expected to be extremely high. Recently, several groups have explored the possibility of observing signals of dark matter from its interactions with the high-energy jets emanating from these galaxies. In this work, we build upon these analyses by including the other components of the WIMP-induced gamma ray spectrum of active Galactic nuclei; namely, (i) the continuum from WIMP annihilation into light standard model states which subsequently radiate and/or decay into photons and (ii) the direct (loop-induced) decay into photons. We work in the context of models of universal extra dimensions (in particular, a model with two extra dimensions) and compute all three components of the gamma ray spectrum and compare with current data. We find that the model with two extra dimensions exhibits several interesting features which may be observable with the Fermi gamma ray telescope. We also show that, in conjunction with other measurements, the gamma ray spectrum from AGN can be an invaluable tool for restricting WIMP parameter space.

In the present paper we address the interaction of pairs of charmed mesons with hidden charm in a finite box. We use the interaction from a recent model based on heavy-quark spin symmetry that predicts molecules of hidden charm in the infinite volume. The energy levels in the box are generated within this model, and from them some synthetic data are generated. These data are then employed to study the inverse problem of getting the energies of the bound states and phase shifts for $D\overline{D}$ or $D^{*}{\overline{D}}^{*}$. Different strategies are investigated using the lowest two levels for different values of the box size, and the errors produced are studied. Starting from the upper level, fits to the synthetic data are carried out to determine the scattering length and effective range plus the binding energy of the ground state. A similar strategy using the effective range formula is considered with a simultaneous fit to the two levels—one above and the other one below the threshold. This method turns out to be more efficient than the previous one. Finally, a method based on the fit to the data by means of a potential and a conveniently regularized loop function, turns out to be very efficient and allows us to produce accurate results in the infinite volume starting from levels of the box with errors far larger than the uncertainties obtained in the final results. A regularization method based on Gaussian wave functions turns out to be rather efficient in the analysis and as a byproduct a practical and fast method to calculate the Lüscher function with high precision is presented.

We extend our analysis of transverse single spin asymmetry in electroproduction of $J/\psi$ to include the effect of the scale evolution of the transverse momentum dependent (TMD) parton distribution functions and gluon Sivers function. We estimate single spin asymmetry for JLab, HERMES, COMPASS, and eRHIC energies using the color evaporation model of charmonium production, using an analytically obtained approximate solution of TMD evolution equations discussed in the literature. We find that there is a reduction in the asymmetry compared with our predictions for the earlier case considered by us, wherein the $Q^2$ dependence came only from DGLAP evolution of the unpolarized gluon densities and a different parametrization of the TMD Sivers function was used.

Analyses of the $J/\psi {\pi }^{+}{\pi }^{-}$ decay channel of the $X(3872)$ resonance by the CDF, Belle, and LHCb Collaborations have established its $J^{PC}$ quantum numbers as $1^{++}$. An analysis of the ${\pi }^{+}{\pi }^{-}{\pi }^0$ invariant mass distribution in the $J/\psi {\pi }^{+}{\pi }^{-}{\pi }^0$ decay channel by the BABAR Collaboration indicated a preference for $2^{-+}$ over $1^{++}$. We point out that a proper evaluation of the ${\chi }^2$ in that analysis increases the probability for $1^{++}$ from 7.1% to about 18.7%. In the case of quantum numbers $1^{++}$, where the $X$ has an $S$-wave coupling to $J/\psi \omega$, the proximity of the $J/\psi \omega$ threshold to $D^{*}\overline{D}$ thresholds and the narrow width of the $\omega$ suggest that the effects of scattering between $J/\psi \omega$ and charm meson pairs could be significant. We derive invariant mass distributions for $J/\psi {\pi }^{+}{\pi }^{-}{\pi }^0$ and ${\pi }^{+}{\pi }^{-}{\pi }^0$ that take into account $S$-wave scattering between the $D^{*0}{\overline{D}}^0$, $D^{*+}{D}^{-}$, and $J/\psi \omega$ channels. We also analyze the effects of scattering through the ${\chi }_{c1}(2P)$ charmonium resonance. We find that scattering effects are unable to produce significant changes in the shape of the ${\pi }^{+}{\pi }^{-}{\pi }^0$ invariant mass distribution.

Quarkonium production in hadron collisions at low transverse momentum $q_{\perp }\ll M$ with $M$ as the quarkonium mass can be used for probing transverse momentum dependent (TMD) gluon distributions. For this purpose, one needs to establish the TMD factorization for the process. We examine the factorization at the one-loop level for the production of ${\eta }_c$ or ${\eta }_b$. The perturbative coefficient in the factorization is determined at one-loop accuracy. Comparing the factorization derived at tree level and that beyond the tree level, a soft factor is, in general, needed to completely cancel soft divergences. We have also discussed possible complications of TMD factorization of p-wave quarkonium production.

We present a comprehensive analysis of $\gamma Z$ interference corrections to the weak charge of the proton measured in parity-violating electron scattering, including a survey of existing models and a critical analysis of their uncertainties. Constraints from parton distributions in the deep-inelastic region, together with new data on parity-violating electron scattering in the resonance region, result in significantly smaller uncertainties on the corrections compared to previous estimates. At the kinematics of the $Q_{\mathrm{weak}}$ experiment, we determine the $\gamma Z$ box correction to be $\Re e{\square }_{\gamma Z}^V=(5.57\pm 0.36)\times {10}^{-3}$. The new constraints also allow precise predictions to be made for parity-violating deep-inelastic asymmetries on the deuteron.

The measurement of the Higgs coupling to $W$ bosons is an important test of our understanding of the electroweak symmetry-breaking mechanism. We study the sensitivity of the International Linear Collider (ILC) to the presence of anomalous $H{W}^{+}{W}^{-}$ couplings using $ZH\to \nu \overline{\nu }W{W}^{*}\to \nu \overline{\nu }4j$ events. Using an effective Lagrangian approach, we calculate the differential decay rates of the Higgs boson including the effects of new dimension-five operators. We present a Monte Carlo simulation of events at the ILC, using a full detector simulation based on geant4 and a real event reconstruction chain. Expected constraints on the anomalous couplings are given.