The existing bounds from CDF on the masses of the fourth generation quarks, $t^{\prime }$ and $b^{\prime }$, are reexamined. The bound of 256 GeV on the $t^{\prime }$ mass assumes that the primary decay of the $t^{\prime }$ is into $q+W$, which is not the case for a substantial region of parameter space. The bound of 268 GeV on the $b^{\prime }$ mass assumes that the branching ratio for $b^{\prime }\to b+Z$ is very large, which is not only not true for much of parameter space, but is never true for $b^{\prime }$ masses above 255 GeV. In addition, it is assumed that the heavy quarks decay within the silicon vertex detector, and for small mixing angles this will not be the case. The experimental bounds, including all of these effects, are found as a function of the other heavy quark mass and the mixing angle.

We discuss the properties of a model incorporating both a scalar electroweak Higgs doublet and an electroweak Higgs triplet. We construct the low-energy effective theory for the light Higgs doublet in the limit of small (but nonzero) deviations in the $\rho$ parameter from one, a limit in which the triplet states become heavy. For $\Delta \rho >0$, perturbative unitarity of $WW$ scattering breaks down at a scale inversely proportional to the renormalized vacuum expectation value of the triplet field (or, equivalently, inversely proportional to the square root of $\Delta \rho$). This result imposes an upper limit on the mass scale of the heavy triplet bosons in a perturbative theory; we show that this upper bound is consistent with dimensional analysis in the low-energy effective theory. Recent articles have shown that the triplet bosons do not decouple, in the sense that deviations in the $\rho$ parameter from one do not necessarily vanish at one-loop in the limit of large triplet mass. We clarify that, despite the nondecoupling behavior of the Higgs triplet, this model does not violate the decoupling theorem since it incorporates a large dimensionful coupling. Nonetheless, we show that if the triplet-Higgs boson masses are of order the grand unified theory scale, perturbative consistency of the theory requires the (properly renormalized) Higgs-triplet vacuum expectation value to be so small as to be irrelevant for electroweak phenomenology.

Working with a large basis of covariant derivative-based meson interpolating fields we demonstrate the feasibility of reliably extracting multiple excited states using a variational method. The study is performed on quenched anisotropic lattices with clover quarks at the charm mass. We demonstrate how a knowledge of the continuum limit of a lattice interpolating field can give additional spin-assignment information, even at a single lattice spacing, via the overlap factors of interpolating field and state. Excited state masses are systematically high with respect to quark-potential model predictions and, where they exist, experimental states. We conclude that this is most likely a result of the quenched approximation.

We present a detailed study of a linear sigma model containing one chiral nonet transforming under $\mathrm{U}(1{)}_{\mathrm{A}}$ as a quark-antiquark composite and another chiral nonet transforming as a diquark-antidiquark composite (or, equivalently from a symmetry point of view, as a two meson molecule). The model provides an intuitive explanation of a current puzzle in low energy QCD: Recent work has suggested the existence of a lighter than 1 GeV nonet of scalar mesons which behave like four quark composites. On the other hand, the validity of a spontaneously broken chiral symmetric description would suggest that these states be chiral partners of the light pseudoscalar mesons, which are two quark composites. The model solves the problem by starting with the two chiral nonets mentioned and allowing them to mix with each other. The input of physical masses in the SU(3) invariant limit for two scalar octets and an excited pion octet results in a mixing pattern wherein the light scalars have a large four quark content while the light pseudoscalars have a large two quark content. One light isosinglet scalar is exceptionally light. In addition, the pion pion scattering is also studied and the current algebra theorem is verified for massless pions which contain some four quark admixture.

The Bakamjian-Thomas relativistic quark model provides a Poincaré representation of bound states with a fixed number of constituents and, in the heavy quark limit, form factors of currents satisfy covariance and Isgur-Wise scaling. We compute the light cone distribution amplitudes (LCDA) of $B$ mesons ${\phi }_{\pm }^B(\omega )$ as well as the shape function $S(\omega )$, that enters in the decay $B\to X_s\gamma$, that are also covariant in this class of models. The LCDA and the shape function are related through the quark model wave function. The former satisfy, in the limit of vanishing constituent light quark mass, the integral relation given by QCD in the valence sector of Fock space. Using a Gaussian wave function, the obtained $S(\omega )$ is identical to the so-called roman shape function. From the parameters for the latter that fit the $B\to X_s\gamma$ spectrum we predict the behavior of ${\phi }_{\pm }^B(\omega )$. We discuss the important role played by the constituent light quark mass. In particular, although ${\phi }_{-}^B(0)\ne 0$ for vanishing light quark mass, a nonvanishing mass implies the unfamiliar result ${\phi }_{-}^B(0)=0$. Moreover, we incorporate the short distance behavior of QCD to ${\phi }_{+}^B(\omega )$, which has sizeable effects at large $\omega$. We obtain the values for the parameters $\overline{\Lambda }\cong 0.35\mathrm{GeV}$ and ${\lambda }_B^{-1}\cong 1.43{\mathrm{GeV}}^{-1}$. We compare with other theoretical approaches and illustrate the great variety of models found in the literature for the functions ${\phi }_{\pm }^B(\omega )$; hence the necessity of imposing further constraints as in the present paper. We briefly review also the different phenomena that are sensitive to the LCDA. The value that we find for ${\lambda }_B^{-1}$ fulfills the upper bound recently measured by BABAR.

A quasiparticle model of the quark-gluon plasma is compared with lattice QCD data for purely imaginary chemical potential. Net quark number density, susceptibility as well as the deconfinement border line in the phase diagram of strongly interacting matter are investigated. In addition, the impact of baryochemical potential dependent quasiparticle masses is discussed. This accomplishes a direct test of the model for nonzero baryon density. The found results are compared with lattice QCD data for real chemical potential by means of analytic continuation and with a different (independent) set of lattice QCD data at zero chemical potential.

Since $Z^{+}(4430)$ lies very close to the threshold of $D^{*}{\overline{D}}_1$, we investigate whether $Z^{+}(4430)$ could be a loosely bound S-wave state of $D^{*}{\overline{D}}_1$ or $D^{*}{\overline{D}}_1^{\prime }$ with $J^P=0^{-},1^{-},2^{-}$, i.e., a molecular state arising from the one-pion-exchange potential. The potential from the crossed diagram is much larger than that from the diagonal scattering diagram. With various trial wave functions, we notice that the attraction from the one-pion-exchange potential alone is not strong enough to form a bound state with realistic pionic coupling constants deduced from the decay widths of $D_1$ and $D_1^{\prime }$.

The chiral symmetry of QCD shows up in the linear Weyl-Wigner mode at short Euclidean distances or at high temperatures. On the other hand, low-lying hadronic states exhibit the nonlinear Nambu-Goldstone mode. An interesting question was raised as to whether the linear realization of the chiral symmetry is asymptotically restored for highly excited states. We address it in a number of ways. On the phenomenological side we argue that to the extent the meson Regge trajectories are observed to be linear and equidistant, the Weyl-Wigner mode is not realized. This picture is supported by quasiclassical arguments implying that the quark spin interactions in high excitations are weak, the trajectories are linear, and there is no chiral symmetry restoration. Then we use the string/gauge duality. In the top-down Sakai-Sugimoto construction the nonlinear realization of the chiral symmetry is built in. In the bottom-up AdS/QCD construction by Erlich et al. and Karch et al. the situation is more ambiguous. However, in this approach linearity and equidistance of the Regge trajectories can be naturally implemented, with the chiral symmetry in the Nambu-Goldstone mode. Asymptotic chiral symmetry restoration might be possible if a nonlinearity (convergence) of the Regge trajectories in an “intermediate window” of $n$, $J$, beyond the explored domain, takes place. This would signal the failure of the quasiclassical picture.

Ultrahigh-energy string scattering is investigated to clarify the relative role of string and gravitational effects, and their possible contributions to nonlocal behavior. Different regimes can be characterized by varying the impact parameter at fixed energy. In the regime where momentum transfers reach the string scale, string effects appear subdominant to higher-loop gravitational processes, approximated via the eikonal. At smaller impact parameters, “diffractive” or “tidal” string excitation leads to processes dominated by highly excited strings. However, new evidence is presented that these excitation effects do not play a direct role in black-hole formation, which corresponds to the breakdown of gravitational perturbation theory and appears to dominate at sufficiently small impact parameters. The estimated amplitudes violate expected bounds on high-energy behavior for local theories.

The light-cone gauge allows one to single out a set of transverse fields (TF), whose Green functions are free from UV divergences in SYM $\mathcal{N}=4$. Green functions with external lines involving the remaining fields do instead exhibit divergences: indeed those fields can be expressed, by solving their equations of motion, as composite operators in terms of transverse fields. A set of exact identities (bridge identities) automatically realize their insertions in a path-integral formulation.

We construct new models of black hole-neutron star binaries in quasiequilibrium circular orbits by solving Einstein’s constraint equations in the conformal thin-sandwich decomposition together with the relativistic equations of hydrostationary equilibrium. We adopt maximal slicing, assume spatial conformal flatness, and impose equilibrium boundary conditions on an excision surface (i.e., the apparent horizon) to model the black hole. In our previous treatment we adopted a “leading-order” approximation for a parameter related to the black hole spin in these boundary conditions to construct approximately nonspinning black holes. Here we improve on the models by computing the black hole’s quasilocal spin angular momentum and setting it to zero. As before, we adopt a polytropic equation of state with adiabatic index $\Gamma =2$ and assume the neutron star to be irrotational. In addition to recomputing several sequences for comparison with our earlier results, we study a wider range of neutron star masses and binary mass ratios. To locate the innermost stable circular orbit we search for turning points along both the binding energy and total angular momentum curves for these sequences. Unlike for our previous approximate boundary condition, these two minima now coincide. We also identify the formation of cusps on the neutron star surface, indicating the onset of tidal disruption. Comparing these two critical binary separations for different mass ratios and neutron star compactions we distinguish those regions that will lead to a tidal disruption of the neutron star from those that will result in the plunge into the black hole of a neutron star more or less intact, albeit distorted by tidal forces.

We derive the semiclassical evolution of massless conformally coupled scalar matter in the de Sitter space-time from the Born-Oppenheimer reduction of the Wheeler-DeWitt equation. We find a remarkable difference with respect to the minimally coupled case: the effect of the quantum gravitational corrections does not depend on the momentum of the scalar mode up to second order in the Planck length and, therefore, there are no relevant corrections to the dispersion relation.

We study the evolution in axisymmetry of accretion disks formed self-consistently through collapse of magnetized hypermassive neutron stars to black holes. Such stars can arise following the merger of binary neutron stars. They are differentially rotating, dynamically stable, and have rest masses exceeding the mass limit for uniform rotation. However, hypermassive neutron stars are secularly unstable to collapse due to MHD-driven angular momentum transport. The rotating black hole which forms in this process is surrounded by a hot, massive, magnetized torus and a magnetic field collimated along the spin axis. This system is a candidate for the central engine of a short-hard gamma-ray burst (GRB). Our code integrates the coupled Einstein-Maxwell-MHD equations and is used to follow the collapse of magnetized hypermassive neutron star models in full general relativity until the spacetime settles down to a quasistationary state. We then employ the Cowling approximation, in which the spacetime is frozen, to track the subsequent evolution of the disk. This approximation allows us to greatly extend the disk evolutions and study the resulting outflows, which may be relevant to the generation of a GRB. We find that outflows are suppressed when a stiff equation of state is assumed for low-density disk material and are sensitive to the initial magnetic field configuration.

The majority of models of inflation in string theory predict an absence of measurable gravitational waves, $r<<{10}^{-3}$. The most promising proposals for making string theoretic models that yield measurable tensor fluctuations involve axion fields with slightly broken shift symmetry. We consider such models in detail, with a particular focus on the $N$-flation scenario and on axion valley/natural inflation models. We find that in Calabi-Yau threefold compactifications with logarithmic Kähler potentials $K$ it appears to be difficult to meet the conditions required for axion inflation in the supergravity regime. However, in supergravities with an (approximately) quadratic shift-symmetric $K$, axion inflation may be viable. Such Kähler potentials do arise in some string models, in specific limits of the moduli space. We describe the most promising classes of models; more detailed study will be required before one can conclude that working models exist.

It is well established that neutrinos have mass, yet it is very difficult to measure those masses directly. Within the standard model of particle physics, neutrinos will have an intrinsic magnetic moment proportional to their mass. We examine the possibility of detecting the magnetic moment using a conducting loop. According to Faraday’s law of induction, a magnetic dipole passing through a conducting loop induces an electromotive force in the loop. We compute this electromotive force for neutrinos in several cases, based on a fully covariant formulation of the problem. We discuss prospects for a real experiment, as well as the possibility to test the relativistic formulation of intrinsic magnetic moments.

We calculate, using a generalized parton distribution based formalism, the nonlinearity of the Rosenbluth plots that arise from hard two-photon exchange corrections that are not included in the classic calculations of the radiative corrections to electron-proton elastic scattering.

We consider direct experimental verification of warped models, based on the Randall-Sundrum (RS) scenario, that explain gauge and flavor hierarchies, assuming that the gauge fields and fermions of the standard model (SM) propagate in the 5D bulk. Most studies have focused on the bosonic Kaluza-Klein (KK) signatures and indicate that discovering gauge KK modes is likely possible, yet challenging, while graviton KK modes are unlikely to be accessible at the CERN LHC, even with a luminosity upgrade. We show that direct evidence for bulk SM fermions, i.e. their KK modes, is likely also beyond the reach of a luminosity-upgraded LHC. Thus, neither the spin-2 KK graviton, the most distinct RS signal, nor the KK SM fermions, direct evidence for bulk flavor, seem to be within the reach of the LHC. We then consider hadron colliders with $\sqrt{s}=21$, 28, and 60 TeV. We find that discovering the first KK modes of SM fermions and the graviton typically requires the Next Hadron Collider (NHC) with $\sqrt{s}\approx 60\mathrm{TeV}$ and $\mathcal{O}(1){\mathrm{ab}}^{-1}$ of integrated luminosity. If the LHC yields hints of these warped models, establishing that nature is described by them, or their 4D conformal field theory duals, requires an NHC-class machine in the post-LHC experimental program.

We study the photon induced $\Lambda (1520)$ production in the effective Lagrangian method near threshold, $E_{\gamma }^{\mathrm{LAB}}\le 2\mathrm{GeV}$, and in the quark-gluon string model at higher energies $3\mathrm{GeV}\le E_{\gamma }^{\mathrm{LAB}}\le 5\mathrm{GeV}$. In particular, we study the role of the $K^{*}$ exchange for the production of $\Lambda (1520)$ within the SU(6) Weinberg-Tomozowa chiral unitary model proposed by García-Recio, Nieves, and Salcedo [Phys. Rev. D 74, 034025 (2006)]. The coupling of the $\Lambda (1520)$ resonance to the $N{\overline{K}}^{*}$ pair, which is dynamically generated, turns out to be relatively small and, thus, the $K$ exchange mechanism dominates the reaction. In the higher energy region, where experimental data are available, the quark-gluon string mechanism with the $K$ Regge trajectory reproduces both the energy and the angular distribution dependences of the $\Lambda (1520)$ photoproduction reaction.

We derive an explicit form of the family of four-point Neveu-Schwarz blocks with $\widehat{c}=1$, external weights ${\Delta }_i=\frac{1}{8}$ and arbitrary intermediate weight $\Delta$. The derivation is based on analytic properties of correlation functions of Ramond fields in the free superscalar theory.

We discuss the effects that a noncommutative geometry induced by a Drinfeld twist has on physical theories. We systematically deform all products and symmetries of the theory. We discuss noncommutative classical mechanics, in particular its deformed Poisson bracket and hence time evolution and symmetries. The twisting is then extended to classical fields, and then to the main interest of this work: quantum fields. This leads to a geometric formulation of quantization on noncommutative space-time, i.e., we establish a noncommutative correspondence principle from $\star$-Poisson brackets to $\star$ commutators. In particular commutation relations among creation and annihilation operators are deduced.