The formation of positronium in our Galaxy is well measured, and has led to important and unanswered questions on the origin of the positrons. In principle it should be possible to form analogous systems from $\mu$ and $\tau$ leptons, viz. true muonium and true tauonium. However the probability of formation for these systems is greatly reduced due to the intrinsically short lifetimes of the $\mu$ and $\tau$ leptons. Likewise, the decay of the atoms is hastened by the high probability of the constituent particles decaying. Nevertheless, if sufficient numbers of $\mu$ and $\tau$ pairs are produced in high energy astrophysical environments there may be significant production of true muonium and true tauonium, despite the small probabilities. This paper addresses this possibility. We have calculated the pair production spectra of $\mu$ and $\tau$ leptons from photon-photon annihilation and electron-positron annihilation in astrophysical environments. We have computed the cross sections for radiative recombination and direct annihilation of the pairs, and the decay constants for the various allowable decays, and the wavelengths and energies of the recombination and annihilation signatures. In this way we have calculated the probabilities for the formation of true muonium and true tauonium, and the branching ratios for the various observable signatures. We have estimated the expected fluxes from accretion disks around microquasars and active galactic nuclei, and from interactions of jets with clouds and stars. We find that accretion disks around stellar mass black holes in our own Galaxy should have observable signatures at x-ray and $\gamma$-ray energies that are in principle observable with current observatories.

We investigate the dimension two condensate $⟨{\overline{\varphi }}_i^{ab}{\varphi }_i^{ab}-{\overline{\omega }}_i^{ab}{\omega }_i^{ab}⟩$ within the Gribov-Zwanziger approach to Euclidean Yang-Mills theories in the Coulomb gauge, in both 3 and 4 dimensions. An explicit calculation shows that, at the first order, the condensate $⟨{\overline{\varphi }}_i^{ab}{\varphi }_i^{ab}-{\overline{\omega }}_i^{ab}{\omega }_i^{ab}⟩$ is plagued by a nonintegrable IR divergence in $3D$, while in $4D$ it exhibits a logarithmic UV divergence, being proportional to the Gribov parameter ${\gamma }^2$. These results indicate that in 3D the transverse spatial Coulomb gluon two-point correlation function exhibits a scaling behavior, in agreement with Gribov’s expression. In 4D, however, they suggest that, next to the scaling behavior, a decoupling solution might emerge too.

It is the goal of the so-called “Yukawaon” model to give a unified description of masses, mixing, and $CP$ violation parameters of quarks and leptons without using any hierarchical (family number-dependent) parameters besides the charged lepton masses. However, in the conventional model so far, we have compelled ourselves to introduce a phase matrix $P=\text{daig}(e^{i{\varphi }_1},e^{i{\varphi }_2},e^{i{\varphi }_3})$ with the phase parameters $({\varphi }_1,{\varphi }_2,{\varphi }_3)$ as family number-dependent parameters other than the observed charged lepton mass values $m_{ei}$. In this paper, we present a revised model in which we are successful in describing the $CP$ violating phase parameters ${\varphi }_i$ in terms of $m_{ei}$. In the present model, by using the parameter values slightly changed from the previous version, we predict a value ${\delta }_{CP}^{\ell }\simeq -76°$ for the $CP$ violating phase ${\delta }_{CP}^{\ell }$ in the standard expression of the lepton mixing matrix $U_{\mathrm{PMNS}}$, and ${\delta }_{CP}^q\simeq 72°$ for that of the quark mixing matrix.

We analyze fermion masses and mixing in a general warped extra dimensional model, where all the Standard Model (SM) fields, including the Higgs, are allowed to propagate in the bulk. In this context, a slightly broken flavor symmetry imposed universally on all fermion fields, without distinction, can generate the full flavor structure of the SM, including quarks, charged leptons and neutrinos. For quarks and charged leptons, the exponential sensitivity of their wave functions to small flavor breaking effects yield hierarchical masses and mixing as it is usual in warped models with fermions in the bulk. In the neutrino sector, the exponential wave-function factors can be flavor blind and thus insensitive to the small flavor symmetry breaking effects, directly linking their masses and mixing angles to the flavor symmetric structure of the five-dimensional neutrino Yukawa couplings. The Higgs must be localized in the bulk and the model is more successful in generalized warped scenarios where the metric background solution is different than five-dimensional anti–de Sitter (${\mathrm{AdS}}_5$). We study these features in two simple frameworks, flavor complimentarity and flavor democracy, which provide specific predictions and correlations between quarks and leptons, testable as more precise data in the neutrino sector becomes available.

We study the mixing structure of isospin-singlet scalars, the light quarkonium ($\overline{q}q$) and glueball ($gg$) in two-flavor QCD, based on a holographic model of bottom-up hard-wall type. In the model the pure quarkonium and glueball states are unambiguously defined in terms of the different $U(1{)}_A$ charges in the restoration limit of the chiral $U(2{)}_L\times U(2{)}_R$ symmetry, in which the quarkonium becomes massless as the chiral partner of the pion. Hence the $\overline{q}q\text{−}gg$ mixing arises in the presence of the nonzero chiral condensate or pion decay constant. At the realistic point where the pion decay constant and other hadron masses reach the observed amount, we predict a tiny mixing between the lightest quarkonia and glueball: the smallness of the mixing is understood by the slightly small ratio of the chiral and gluon condensate scales. The low-lying two scalar masses are calculated to be $\simeq 1.25\mathrm{GeV}$ and $\simeq 1.77\mathrm{GeV}$, which are compared with the masses of $f_0(1370)$ and $f_0(1710)$. Our result implies that $f_0(1710)$ predominantly consists of the glueball.

Inclusive production of $J/\psi$ mesons, especially at forward rapidities, is an important probe of small-$x$ gluons in protons and nuclei. In this paper we reevaluate the production cross sections in the color glass condensate framework, where the process is described by a large $x$ gluon from the probe splitting into a quark pair and eikonally interacting with the target proton or nucleus. Using a standard collinear gluon distribution for the probe and an up-to-date dipole cross section fitted to HERA data to describe the target we achieve a rather good description of the cross section in proton-proton collisions, although with a rather large normalization uncertainty. More importantly, we show that generalizing the dipole cross section to nuclei in the Glauber approach results in a nuclear suppression of $J/\psi$ production that is much closer to the experimental data than claimed in previous literature.

We investigate the properties of mesons with the exotic $J^{PC}=1^{-+}$ quantum numbers. Starting out from the light-quark domain, where the ${\pi }_1$ states are used as references, we predict the masses of analogous quarkonia for $c\overline{c}$ and $b\overline{b}$ configurations. We employ a covariant Dyson-Schwinger–Bethe-Salpeter-equation approach with a rainbow-ladder truncated model of quantum chromodynamics.

I provide a calculation at full two-loop order of the complex pole squared mass of the $W$ boson in the Standard Model in the pure $\overline{\text{MS}}$ renormalization scheme, with Goldstone boson mass effects resummed. This approach is an alternative to earlier ones that use on-shell or hybrid renormalization schemes. The renormalization scale dependence of the real and imaginary parts of the resulting pole mass is studied. Both deviate by about $\pm 4\mathrm{MeV}$ from their median values as the renormalization scale is varied from 50 to 200 GeV, but the theory error is likely larger. A surprising feature of this scheme is that the two-loop QCD correction has a larger scale dependence, but a smaller magnitude, than the two-loop non-QCD correction, unless the renormalization scale is chosen very far from the top-quark mass.

We study the effect of stimulated photon emission from the vacuum in strong space-time-dependent electromagnetic fields. We emphasize the viewpoint that the vacuum subjected to macroscopic electromagnetic fields with at least one nonzero electromagnetic field invariant, as, e.g., attainable by superimposing two laser beams, can represent a source term for outgoing photons. We believe that this view is particularly intuitive and allows for a straightforward and intuitive study of optical signatures of quantum vacuum nonlinearity in realistic experiments involving the collision of high-intensity laser pulses, and exemplify this view for the vacuum subjected to a strong standing electromagnetic wave as generated in the focal spot of two counterpropagating, linearly polarized, high-intensity laser pulses. Focusing on a comparably simple electromagnetic field profile, which should nevertheless capture the essential features of the electromagnetic fields generated in the focal spots of real high-intensity laser beams, we provide estimates for emission characteristics and the numbers of emitted photons attainable with present and near future high-intensity laser facilities.

Some physical effects of time averaged quantum electric field fluctuations are discussed. The one loop radiative corrections to potential scattering are approximately derived from simple arguments which invoke vacuum electric field fluctuations. For both above barrier scattering and quantum tunneling, this effect increases the transmission probability. It is argued that the shape of the potential determines a sampling function for the time averaging of the quantum electric field operator. We also show that there is a nonperturbative enhancement of the transmission probability which can be inferred from the probability distribution for time averaged electric field fluctuations. The same method should be useful in understanding the effects of large quantum stress tensor fluctuations, which cannot be treated in perturbation theory.

Non-Abelian flux-tube (string) solutions carrying global currents are found in the bosonic sector of four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories. The specific model considered here possesses ${U(2)}_{\text{local}}\times {\mathrm{SU}(2)}_{\text{global}}$ symmetry, with two scalar doublets in the fundamental representation of SU(2). We construct string solutions that are stationary and translationally symmetric along the $x^3$ direction, and they are characterized by a matrix phase between the two doublets, referred to as “twist.” Consequently, twisted strings have nonzero (global) charge, momentum, and in some cases even angular momentum per unit length. The planar cross section of a twisted string corresponds to a rotationally symmetric, charged non-Abelian vortex, satisfying first-order Bogomolny-type equations and second-order Gauss constraints. Interestingly, depending on the nature of the matrix phase, some of these solutions even break cylindrical symmetry in ${\mathbb{R}}^3$. Although twisted vortices have higher energy than the untwisted ones, they are expected to be linearly stable since one can keep their charge (or twist) fixed with respect to small perturbations.

In this work we investigate the renormalization group flow of the cosmological constant $\mathrm{\Lambda }$ induced by the change in space-time curvature in the electroweak vacuum. We calculate the generic magnitude resulting from running in the standard model in a subtraction scheme that respects the Appelquist-Carazzone decoupling theorem. Interestingly, we find in this prescription that for a nonminimal coupling $\xi \lesssim 10^4$ the magnitude of the generated contribution remains below the value consistent with observations.

Quantum field theory in curved space-times is a well developed area in mathematical physics which has had important phenomenological applications to the very early universe. However, it is not commonly appreciated that on time-dependent space-times—including the simplest cosmological models—dynamics of quantum fields is not unitary in the standard sense. This issue is first explained with an explicit example, and it is then shown that a generalized notion of unitarity does hold. The generalized notion allows one to correctly pass to the Schrödinger picture starting from the Heisenberg picture used in the textbook treatments. Finally, we indicate how these considerations can be extended from simple cosmological models to general globally hyperbolic space-times.

We consider a novel approach to address the black hole information paradox. The idea is based on adapting, to the situation at hand, the modified versions of quantum theory involving spontaneous stochastic dynamical collapse of quantum states, which have been considered in attempts to deal with shortcomings of the standard Copenhagen interpretation of quantum mechanics, in particular, the issue known as “the measurement problem.” The new basic hypothesis is that the modified quantum behavior is enhanced in the region of high curvature so that the information encoded in the initial quantum state of the matter fields is rapidly erased as the black hole singularity is approached. We show that in this manner the complete evaporation of the black hole via Hawking radiation can be understood as involving no paradox. Calculations are performed using a modified version of quantum theory known as “continuous spontaneous localization” (CSL), which was originally developed in the context of many-particle nonrelativistic quantum mechanics. We use a version of CSL tailored to quantum field theory and applied in the context of the two -dimensional Callan-Giddings-Harvey-Strominger model. Although the role of quantum gravity in this picture is restricted to the resolution of the singularity, related studies suggest that there might be further connections.

Applying the Pomeransky inverse scattering method to the four-dimensional vacuum Einstein equation and using the Levi-Cività solution for a seed, we construct a cylindrically symmetric single-soliton solution. Although the Levi-Cività spacetime generally includes singularities on its axis of symmetry, it is shown that for the obtained single-soliton solution, such singularities can be removed by choice of certain special parameters. This single-soliton solution describes propagation of nonlinear cylindrical gravitational shock wave pulses rather than solitonic waves. By analyzing wave amplitudes and time dependence of polarization angles, we provide a physical description of the single-soliton solution.

We present a new five-parameter class of Ricci-flat solutions in four dimensions with a Euclidean signature. The solution is asymptotically locally flat (ALF) and contains a finite asymptotic Newman-Unti-Tamburino (NUT) charge. When this charge is sent to infinity, the solution becomes asymptotically locally Euclidean, and one in fact obtains the Ricci-flat Plebański-Demiański solution. The solution we have found can thus be regarded as an ALF generalization of the latter solution. We also show that it can be interpreted as a system consisting of two touching Kerr-NUTs: the south pole of one Kerr-NUT touches the north pole of the other. The total NUT charge of such a system is then identified with the asymptotic NUT charge. Setting the asymptotic NUT charge to zero gives a four-parameter asymptotically flat (AF) solution, and contained within this subclass is the completely regular two-parameter AF instanton previously discovered by the present authors. Various other limits are also discussed, including that of the triple-collinearly-centered Gibbons-Hawking solution, and an ALF generalization of the $C$-metric.

We propose a classical SU(2) gauge field in a flavor-space locked configuration as a species of radiation in the early Universe and show that it would have a significant imprint on a primordial stochastic gravitational wave spectrum. In the flavor-space locked configuration, the electric and magnetic fields of each flavor are parallel and mutually orthogonal to other flavors, with isotropic and homogeneous stress energy. Due to the non-Abelian coupling, the gauge field breaks the symmetry between left- and right-circularly polarized gravitational waves. This broken chiral symmetry results in a unique signal: nonzero cross-correlation of the cosmic microwave background temperature and polarization, $TB$ and $EB$, both of which should be zero in the standard, chiral symmetric case. We forecast the ability of current and future cosmic microwave background experiments to constrain this model. Furthermore, a wide range of behavior is shown to emerge, depending on the gauge field coupling, abundance, and allocation into electric and magnetic field energy density. The fluctuation power of primordial gravitational waves oscillates back and forth into fluctuations of the gauge field. In certain cases, the gravitational wave spectrum is shown to be suppressed or amplified by up to an order of magnitude depending on the initial conditions of the gauge field.

We consider an original variational approach for building new models of quintessence interacting with dark or baryonic matter. The coupling is introduced at the Lagrangian level using a variational formulation for relativistic fluids, where the interacting term generally depends on both the dynamical degrees of freedom of the theory and their spacetime derivatives. After deriving the field equations from the action, we consider applications in the context of cosmology. Two simple models are studied using dynamical system techniques showing the interesting phenomenology arising in this framework. We find that these models contain dark energy dominated late-time attractors with early-time matter dominated epochs and also obtain a possible dynamical crossing of the phantom barrier. The formulation and results presented here complete and expand the analysis exposed in the first part of this work, where only algebraic couplings, without spacetime derivatives, were considered.

We present a new approach to build models of quintessence interacting with dark or baryonic matter. We use a variational approach for relativistic fluids to realize an effective description of matter fields at the Lagrangian level. The coupling is introduced directly in the action by considering a single function mixing the dynamical degrees of freedom of the theory. The resulting gravitational field equations are derived by variations with respect to the independent variables. New interesting phenomenology can be obtained at both small scales, where new screening mechanisms for scalar fields can be realized, and large scales, where one finds an original and rich class of interacting quintessence models. The background cosmology of two of these models is studied in detail using dynamical system techniques. We find a variety of interesting results: for instance, these models contain dark energy dominated late-time attractors and scaling solutions, both with early-time matter dominated epochs and a possible inflationary origin. In general this new approach provides the starting point for future in-depth studies on new interacting quintessence models.