Exact solutions of the Poisson equation are found for multidimensional spaces with topology $M_{3+d}={\mathbb{R}}^3\times T^d$. These solutions describe smooth transitions from Newtonian behavior $1/r_3$ for distances bigger than the periods of the tori (the sizes of the extra dimensions) to multidimensional behavior $1/r_{3+d}^{1+d}$ in the small-distance limit. In the case of one extra dimension $d=1$, a compact and elegant formula for the gravitational potential is found. It is shown that corrections to the gravitational constant in Cavendish-type experiments can be within the measurement accuracy of Newton’s gravitational constant $G_N$. Models with test masses smeared over some (or all) extra dimensions are proposed. It is shown that in a 10-dimensional spacetime with three smeared extra dimensions the size of the remaining three extra dimensions can be enlarged up to submillimeter scales in case of a fundamental Planck scale $M_{\mathrm{Pl}(10)}\approx 1\mathrm{TeV}$. In models with all extra dimensions smeared, the gravitational potential coincides exactly with the Newtonian one. Nevertheless, the hierarchy problem can be solved in these models.

We prove that many cosmological models characterized by vectors nonminimally coupled to the curvature (such as the Turner-Widrow mechanism for the production of magnetic fields during inflation, and models of vector inflation or vector curvaton) contain ghosts. The ghosts are associated with the longitudinal vector polarization present in these models and are found from studying the sign of the eigenvalues of the kinetic matrix for the physical perturbations. Ghosts introduce two main problems: (1) they make the theories ill defined at the quantum level in the high energy/subhorizon regime (and create serious problems for finding a well-behaved UV completion), and (2) they create an instability already at the linearized level. This happens because the eigenvalue corresponding to the ghost crosses zero during the cosmological evolution. At this point the linearized equations for the perturbations become singular (we show that this happens for all the models mentioned above). We explicitly solve the equations in the simplest cases of a vector without a vacuum expectation value in a Friedmann-Robertson-Walker geometry, and of a vector with a vacuum expectation value plus a cosmological constant, and we show that indeed the solutions of the linearized equations diverge when these equations become singular.

Location of critical point and mapping the QCD phase boundary still exists as one of the most interesting and studied problems of heavy-ion physics. A new equation of state (EOS) for a gas of extended baryons and pointlike mesons is presented here which accounts for the repulsive hard-core interactions arising due to the geometrical size of the baryons. A first-order deconfining phase transition is obtained using Gibbs’ equilibrium criteria and a bag model EOS for the weakly interacting quark matter. It is interesting to find that the phase transition line ends at a critical point beyond which a crossover region exists between hot-dense meson gas and quark-antiquark gluon matter. Our curve closely resembles in shape the predictions of the available lattice gauge calculations and also reproduces the conjectured phase boundary.

The observed slow running of the gauge coupling in SU(3) lattice gauge theory with two flavors of color sextet fermions naturally suggests it is a theory with one relevant coupling, the fermion mass, and that at zero mass correlation functions decay algebraically. I perform a finite-size scaling study on simulation data at two values of the bare gauge coupling with this assumption and observe a common exponent for the scaling of the correlation length with the fermion mass, $y_m\sim 1.5$. An analysis of the scaling of valence Dirac eigenvalues at one of these bare couplings produces a similar number.

The distribution of gluon fields in hadrons is of fundamental interest in QCD. Using lattice QCD we have observed the formation of gluon flux tubes within three-quark (baryon) and quark plus antiquark (meson) systems for a wide variety of spatial distributions of the color sources. In particular we have investigated three-quark configurations where two of the quarks are close together and the third quark is some distance away, which approximates a quark plus diquark string. We find that the string tension of the quark-diquark string is the same as that of the quark-antiquark string on the same lattice. We also compare the longitudinal and transverse profiles of the gluon flux tubes for both sets of strings, and find them to be of similar radii and to have similar vacuum suppression.

We discuss precision measurements of the leading atmospheric parameters at a standard neutrino factory with a detector that is sensitive to muons alone. The oscillation of the muon and electron neutrinos in the neutrino factory beam to tau neutrinos adds to the muon events sample (both right sign and wrong sign) via leptonic decays of the taus produced through charge-current interactions in the detector. In particular, we study how this affects a precision measurement of the atmospheric mixing parameters and the deviation of ${\nu }_{\mu }\leftrightarrow {\nu }_{\tau }$ mixing from maximality. In spite of the enhancement of the number of events due to the additional tau contribution, the determination of the atmospheric mixing angle and the deviation from maximality will be poorer. We show that it is impossible to devise satisfactory cuts to remove this tau contamination. Neglect of these tau contributions will lead to an incorrect conclusion about the precision obtainable at a neutrino factory.

We study an extension of the standard model based on the flavor symmetry $A_4$ only. Neutrino Majorana mass terms arise from a dimension five operator and charged lepton masses from renormalizable Yukawa couplings. We introduce three Higgs doublets that belong to one triplet irreducible representation of $A_4$. We study the most general $A_4$-invariant scalar potential and the phenomenological consequences of the model. We find that the reactor angle could be as large as ${sin}^2{\theta }_{{13}_{\max }}\sim 0.03$, while the atmospheric mixing angle ${\theta }_{23}$ is close to maximal, ${sin}^2{\theta }_{23}=1/2$.

Analyzing $600{\mathrm{pb}}^{-1}$ of $e^{+}{e}^{-}$ collisions at 4170 MeV center-of-mass energy with the CLEO-c detector, we measure the branching fraction $\mathcal{B}(D_s^{+}\to {\tau }^{+}\nu )=(5.52\pm 0.57\pm 0.21)\%$ using the ${\tau }^{+}\to {\rho }^{+}\overline{\nu }$ decay mode. Combining with other CLEO measurements of $\mathcal{B}(D_s^{+}\to {\tau }^{+}\nu )$ we determine the pseudoscalar decay constant $f_{D_s}=(259.7\pm 7.8\pm 3.4)\mathrm{MeV}$ consistent with the value obtained from our $D_s^{+}\to {\mu }^{+}\nu$ measurement of $(257.6\pm 10.3\pm 4.3)\mathrm{MeV}$. Combining these measurements we find a value of $f_{D_s}=(259.0\pm 6.2\pm 3.0)\mathrm{MeV}$, that differs from the most accurate prediction based on unquenched lattice gauge theory of $(241\pm 3)\mathrm{MeV}$ by 2.4 standard deviations. We also present the first measurements of $\mathcal{B}(D_s^{+}\to K^0{\pi }^{+}{\pi }^0)=(1.00\pm 0.18\pm 0.04)\%$, and $\mathcal{B}(D_s^{+}\to {\pi }^{+}{\pi }^0{\pi }^0)=(0.65\pm 0.13\pm 0.03)\%$, and measure a new value for $\mathcal{B}(D_s^{+}\to \eta {\rho }^{+})=(8.9\pm 0.6\pm 0.5)\%$.

Using $24\times {10}^6$ ${\psi }^{\prime }\equiv \psi (2S)$ decays in CLEO-c, we have searched for higher multipole admixtures in electric-dipole-dominated radiative transitions in charmonia. We find good agreement between our data and theoretical predictions for magnetic quadrupole ($M2$) amplitudes in the transitions ${\psi }^{\prime }\to \gamma {\chi }_{c1,c2}$ and ${\chi }_{c1,c2}\to \gamma J/\psi$, in striking contrast to some previous measurements. Let $b_2^J$ and $a_2^J$ denote the normalized $M2$ amplitudes in the respective aforementioned decays, where the superscript $J$ refers to the angular momentum of the ${\chi }_{cJ}$. By performing unbinned maximum likelihood fits to full five-parameter angular distributions, we found the following values of $M2$ admixtures for $J_{\chi }=1$: $a_2^{J=1}=(-6.26\pm 0.63\pm 0.24)\times {10}^{-2}$ and $b_2^{J=1}=(2.76\pm 0.73\pm 0.23)\times {10}^{-2}$, which agree well with theoretical expectations for a vanishing anomalous magnetic moment of the charm quark. For $J_{\chi }=2$, if we fix the electric octupole ($E3$) amplitudes to zero as theory predicts for transitions between charmonium $S$ states and $P$ states, we find $a_2^{J=2}=(-9.3\pm 1.6\pm 0.3)\times {10}^{-2}$ and $b_2^{J=2}=(1.0\pm 1.3\pm 0.3)\times {10}^{-2}$. If we allow for $E3$ amplitudes we find, with a four-parameter fit, $a_2^{J=2}=(-7.9\pm 1.9\pm 0.3)\times {10}^{-2}$, $b_2^{J=2}=(0.2\pm 1.4\pm 0.4)\times {10}^{-2}$, $a_3^{J=2}=(1.7\pm 1.4\pm 0.3)\times {10}^{-2}$, and $b_3^{J=2}=(-0.8\pm 1.2\pm 0.2)\times {10}^{-2}$. We determine the ratios $a_2^{J=1}/a_2^{J=2}={0.67}_{-0.13}^{+0.19}$ and $a_2^{J=1}/b_2^{J=1}=-{2.27}_{-0.99}^{+0.57}$, where the theoretical predictions are independent of the charmed quark magnetic moment and are $a_2^{J=1}/a_2^{J=2}=0.676\pm 0.071$ and $a_2^{J=1}/b_2^{J=1}=-2.27\pm 0.16$.

We propose a new catalysis mechanism for nonperturbative vacuum electron-positron pair production, by superimposing a plane-wave x-ray probe beam with a strongly focused optical laser pulse, such as is planned at the Extreme Light Infrastructure (ELI) facility. We compute the absorption coefficient arising from vacuum polarization effects for photons below threshold in a strong electric field. This setup should facilitate the (first) observation of this nonperturbative QED effect with planned light sources such as ELI yielding an envisioned intensity of order ${10}^{26}\mathrm{W}/{\mathrm{cm}}^2$.

We explore extensions of the minimal supersymmetric standard model in which TeV scale vectorlike multiplets can mediate observable $n-\overline{n}$ oscillations, without causing conflict with the proton decay experiments, with a U(1) symmetry playing an important role. The colored vectorlike particles, in particular, may be found at the LHC through some decay modes arising from their direct couplings to quarks.

We compute the even part of the planar two-loop MHV amplitude in $\mathcal{N}=4$ supersymmetric Yang-Mills theory, for an arbitrary number of external particles. The answer is expressed as a sum of pseudoconformal integrals.

Employing standard results from spectral geometry, we provide strong evidence that in the classical limit the ground state of three-dimensional causal dynamical triangulations is de Sitter spacetime. This result is obtained by measuring the expectation value of the spectral dimension on the ensemble of geometries defined by these models, and comparing its large-scale behavior to that of a sphere (Euclidean de Sitter). From the same measurement we are also able to confirm the phenomenon of dynamical dimensional reduction observed in this and other approaches to quantum gravity—the first time this has been done for three-dimensional causal dynamical triangulations. In this case, the value for the short-scale limit of the spectral dimension that we find is approximately 2. We comment on the relevance of these results for the comparison to asymptotic safety and Hořava-Lifshitz gravity, among other approaches to quantum gravity.

Using a formulation of the post-Newtonian expansion in terms of Feynman graphs, we discuss how various tests of general relativity (GR) can be translated into measurement of the three- and four-graviton vertices. In problems involving only the conservative dynamics of a system, a deviation of the three-graviton vertex from the GR prediction is equivalent, to lowest order, to the introduction of the parameter ${\beta }_{\mathrm{PPN}}$ in the parametrized post-Newtonian formalism, and its strongest bound comes from lunar laser ranging, which measures it at the 0.02% level. Deviation of the three-graviton vertex from the GR prediction, however, also affects the radiative sector of the theory. We show that the timing of the Hulse-Taylor binary pulsar provides a bound on the deviation of the three-graviton vertex from the GR prediction at the 0.1% level. For coalescing binaries at interferometers we find that, because of degeneracies with other parameters in the template such as mass and spin, the effects of modified three- and four-graviton vertices is just to induce an error in the determination of these parameters and, at least in the restricted PN approximation, it is not possible to use coalescing binaries for constraining deviations of the vertices from the GR prediction.

We revisit the new type of $Q$ ball (the gravity-mediation type of the $Q$ ball in gauge mediation) in order to clarify its properties and correct some misunderstandings found in recent literature. In addition, we investigate the feature of the other kind of the hybrid-type of the $Q$ ball, which was considered in the context of the $Q$-ball capture by the neutron star.

We investigate a $f(R)$ modification of gravity that is exponential in the Ricci scalar $R$ to explain cosmic acceleration. The steepness of this dependence provides extra freedom to satisfy solar system and other curvature regime constraints. With a parameter to alleviate the usual fine-tuning of having the modification strengthen near the present, the total number of parameters is only one more than $\Lambda \mathrm{CDM}$. The resulting class of solutions asymptotes to $w=-1$ but has no cosmological constant. We calculate the dynamics in detail, examine the effect on the matter power spectrum, and provide a simple fitting form relating the two.

We show how to match the Isgur-Karl model to the spin-flavor quark operator expansion used in the $1/N_c$ studies of the nonstrange negative parity $L=1$ excited baryons. Using the transformation properties of states and interactions under the permutation group $S_3$ we are able to express the operator coefficients as overlap integrals, without making any assumption on the spatial dependence of the quark wave functions. The general mass operator leads to parameter free mass relations and constraints on the mixing angles that are valid beyond the usual harmonic oscillator approximation. The Isgur-Karl model with harmonic oscillator wave functions provides a simple counterexample that demonstrates explicitly that the alternative operator basis for the $1/N_c$ expansion for excited baryons recently proposed by Matagne and Stancu is incomplete.