We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by diagrams with one-loop radiative photon insertions both in the electron and muon lines. An analytic result for these nonlogarithmic corrections of order $\alpha (Z^2\alpha )(Z\alpha )(m/M){\tilde{E}}_F$ is obtained. This result constitutes a next step in the implementation of the program of reduction of the theoretical uncertainty of hyperfine splitting below 10 Hz.

An effective local quantum field theory with UV and IR cutoffs correlated in accordance with holographic entropy bounds is capable of rendering the cosmological constant (CC) stable against quantum corrections. By setting an IR cutoff to length scales relevant to cosmology, one easily obtains the currently observed ${\rho }_{\Lambda }\simeq {10}^{-47}{\mathrm{G}\mathrm{e}\mathrm{V}}^4$ thus alleviating the CC problem. It is argued that scaling behavior of the CC in these scenarios implies an interaction of the CC with matter sector or a time-dependent gravitational constant to accommodate the observational data.

We study a class of dilatonic deformations of asymptotically ${\mathrm{A}\mathrm{d}\mathrm{S}}_5\times S^5$ geometry analytically and numerically. The spacetime is nonsupersymmetric and suffers from a naked singularity. We propose that the causality bound may serve as a criterion for such a geometry with a naked singularity to still make sense in the AdS/CFT correspondence. We show that the static string, the one corresponding to a large Wilson loop in the dual gauge theory, reveals confinement in a certain range of parameters of our solutions, where the singularity exhibits the repulsion that can well cloak the singularity from the static string probe. In particular, we find the exact expression for the tension of the QCD strings. We also discuss a possible interpretation of our solution in terms of unstable branes and their tachyon matter.

We present a Kähler potential for four-dimensional heterotic M-theory which includes moduli describing a gauge five-brane living on one of the orbifold fixed planes. This result can also be thought of as describing compactifications of either of the weakly coupled heterotic strings in the presence of a gauge five-brane. This is the first example of a Kähler potential in these theories which includes moduli describing background gauge field configurations. Our results are valid when the solitons width is much smaller than the size scale of the Calabi-Yau threefold and can be used to provide a more complete description of some moving brane scenarios. We point out that, in general, it is not consistent to truncate away the gauge five-brane moduli in a simple manner.

A supersymmetric (SUSY) model of radius stabilization is constructed for the $S^1/Z_2$ warped compactifications with a hypermultiplet in five dimensions. Requiring the continuity of scalar field across the boundaries, we obtain radius stabilization preserving SUSY, realizing the SUSY extension of the Goldberger-Wise mechanism. Even if we allow discontinuity of the $Z_2$ odd field across the boundary, we always obtain SUSY preservation but obtain the radius stabilization only when the discontinuity is fixed by other mechanisms.

We study a noncommutative nonrelativistic theory in $2+1$ dimensions of a scalar field coupled to the Chern-Simons field. In the commutative situation this model has been used to simulate the Aharonov-Bohm effect in the field theory context. We verified that, contrary to the commutative result, the inclusion of a quartic self-interaction of the scalar field is not necessary to secure the ultraviolet renormalizability of the model. However, to obtain a smooth commutative limit the presence of a quartic gauge invariant self-interaction is required. For small noncommutativity we fix the corrections to the Aharonov-Bohm scattering and prove that up to one loop the model is free from dangerous infrared/ultraviolet divergences.

A field-theoretical model for nonsingular global cosmic strings is presented. The model is a nonlinear sigma model with a potential term for a self-gravitating complex scalar field. Nonsingular stationary solutions with angular momentum and possibly linear momentum are obtained by assuming an oscillatory dependence of the scalar field on $t$, $\phi$, and $z$. This dependence has an effect similar to gauging the global U(1) symmetry of the model, which is actually a Kaluza-Klein reduction from four to three spacetime dimensions. The method of analysis can be regarded as an extension of the gravito-electromagnetism formalism beyond the weak field limit. Some $D=3$ self-dual solutions are also discussed.

We propose a new method for obtaining the position space of nonlinear relativity, i.e., the dual of its usual momentum space formulation. We require that plane waves still be solutions to free field theory. This is equivalent to postulating the invariance of the linear contraction between position and momentum spaces, and dictates a set of energy-dependent space-time Lorentz transformations. In turn this leads to an energy-dependent metric. An alternative, more problematic approach, would allow for position and momentum space to acquire independent nonlinear representations of the Lorentz group ; this requires a nonlinear contraction between momentum and position spaces. We discuss a variety of physical implications of these approaches and show how they point to two rather distinct formulations of theories of gravity with an invariant energy and/or length scale.

We formulate a theory of gravity with a matrix-valued complex vierbein based on the $SL(2N,\mathbb{C})\otimes SL(2N,\mathbb{C})$ gauge symmetry. The theory is metric independent, and before symmetry breaking all fields are massless. The symmetry is broken spontaneously and all gravitons corresponding to the broken generators acquire masses. If the symmetry is broken to $SL(2,\mathbb{C})$, then the spectrum would correspond to one massless graviton coupled to $2N^2-1$ massive gravitons. A novel feature is the way the fields corresponding to noncompact generators acquire kinetic energies with correct signs. Equally surprising is the way Yang-Mills gauge fields acquire their correct kinetic energies through the coupling to the nondynamical antisymmetric components of the vierbeins.

The spectrum of primordial fluctuations from inflation can be obtained using a mathematically controlled, and systematically extendable, uniform approximation. Closed-form expressions for power spectra and spectral indices may be found without making explicit slow-roll assumptions. Here we provide details of our previous calculations, extend the results beyond leading-order in the approximation, and derive general error bounds for power spectra and spectral indices. Already at next-to-leading-order, the errors in calculating the power spectrum are less than a percent. This meets the accuracy requirement for interpreting next-generation cosmic microwave background observations.

We study the simplest class of Bekenstein-type, varying $\alpha$ models, in which the two available free functions (potential and gauge kinetic function) are Taylor-expanded up to linear order. Any realistic model of this type reduces to a model in this class for a certain time interval around the present day. Nevertheless, we show that no such model is consistent with all existing observational results. We discuss possible implications of these findings, and, in particular, clarify the ambiguous statement (often found in the literature) that “the Webb results are inconsistent with Oklo.”

Many recent analyses have indicated that large scale Wilkinson Microwave Anisotropy Probe (WMAP) data display anomalies that appear inconsistent with the standard cosmological paradigm. However, the effects of foreground contamination, which require elimination of some fraction of the data, have not been fully investigated due to the complexity in the analysis. Here we develop a general formalism of how to incorporate these effects into any analysis of this type. Our approach is to compute the full multidimensional probability distribution function of all possible sky realizations that are consistent with the data and with the allowed level of contamination. Any statistic can be integrated over this probability distribution to assess its significance. As an example we apply this method to compute the joint probability distribution function for the possible realizations of quadrupole and octopole using the WMAP data. This 12 dimensional distribution function is explored using the Markov Chain Monte Carlo technique. The resulting chains are used to assess the statistical significance of the low quadrupole using frequentist methods, which we find to be $3-4\%$. Octopole is normal and the probability of it being anomalously low or as low as WMAP reported value is very small. We address the quadrupole-octopole alignment using several methods that have been recently used to argue for anomalies, such as angular momentum dispersion, multipole vectors and a new method based on feature matching. While we confirm that the full-sky map Internal Linear Combination Map (ILC) suggest an alignment, we find that removing the most contaminated part of the data also removes any evidence of alignment: the probability distributions strongly disfavor the alignment. This suggests that most of the evidence for it comes from non-Gaussian features in the part of the data most contaminated by the foregrounds. We also present an example, that of octopole alignment with the ecliptic, where the statistical significance can be enhanced by removing the contamination.

The topological susceptibility of the vacuum in quantum chromodynamics has been simulated numerically using the Asqtad improved staggered fermion formalism. At nonzero lattice spacing, the residual fermion doublers (fermion tastes) in the staggered fermion formalism give contributions to the susceptibility that deviate from conventional continuum chiral perturbation theory. In this brief report, we estimate the taste-breaking artifact and compare it with results of recent simulations, finding that it accounts for roughly half of the scaling violation.

We consider the supersymmetric extension of the 3-3-1 model with right-handed neutrinos. We study the mass spectra in the scalar and pseudoscalar sectors, and for a given set of the input parameters, we find that the lightest scalar in the model has a mass of 130 GeV and the lightest pseudoscalar has mass of 5 GeV. However, this pseudoscalar decouples from the $Z^0$ at high energy scales since it is almost a singlet under $\mathrm{S}\mathrm{U}(2{)}_L\otimes \mathrm{U}(1{)}_Y$.

We extend the study of the light hadron spectrum and the quark mass in two-flavor QCD to smaller sea quark mass, corresponding to $m_{PS}/m_V=0.60–0.35$. Numerical simulations are carried out using the RG-improved gauge action and the meanfield-improved clover quark action at $\beta =1.8$ ($a=0.2\mathrm{f}\mathrm{m}$ from $\rho$ meson mass). We observe that the light hadron spectrum for small sea quark mass does not follow the expectation from chiral extrapolations with quadratic functions made from the region of $m_{PS}/m_V=0.80–0.55$. Whereas fits with either polynomial or continuum chiral perturbation theory (ChPT) fail, the Wilson ChPT (WChPT) that includes $a^2$ effects associated with explicit chiral symmetry breaking successfully fits the whole data: In particular, WChPT correctly predicts the light quark mass spectrum from simulations for medium heavy quark mass, such as $m_{PS}/m_V\gtrsim 0.5$. Reanalyzing the previous data with the use of WChPT, we find the mean up and down quark mass being smaller than the previous result from quadratic chiral extrapolation by approximately 10%, $m_{ud}^{\overline{\mathrm{M}\mathrm{S}}}(\mu =2\mathrm{G}\mathrm{e}\mathrm{V})=3.11(17)[\mathrm{M}\mathrm{e}\mathrm{V}]$ in the continuum limit.

Renormalization constants ($Z$-factors ) of vector and axial-vector currents are determined nonperturbatively in quenched QCD for a renormalization group improved gauge action and a tadpole-improved clover quark action using the Schrödinger functional method. Nonperturbative values of $Z$-factors turn out to be smaller than 1-loop perturbative values by $O$(15%) at a lattice spacing of $a^{-1}\approx$ 1 GeV. The pseudoscalar and vector meson decay constants calculated with the nonperturbative $Z$-factors show a much better scaling behavior compared to previous results obtained with tadpole-improved one-loop $Z$-factors. In particular, the nonperturbative $Z$-factors normalized at infinite physical volume show that the scaling violations of the decay constants are within about 10% up to the lattice spacing $a^{-1}\sim 1$ GeV. The continuum estimates obtained from data in the range $a^{-1}\sim$ 1–2 GeV agree with those determined from finer lattices ($a^{-1}\sim 2-4$ GeV) with the standard action.

Density and thermal corrections to the mass of the pions are studied in the framework of the $SU(2)$ low-energy effective chiral lagrangian, in terms of the isospin chemical potential ${\mu }_I$. We concentrate the discussion in the region where the isospin chemical potential (absolute value) becomes bigger than the pion mass at zero temperature and density, i.e., in the phase where the condensed ${\pi }^{-}$ phase appears (for negative chemical potential). We are able to calculate the thermal and density evolution of masses in the limits where $|{\mu }_I|\gg m$ and where $|{\mu }_I|\gtrsim m$. We also identified the phase transition curve.

The flavor changing neutral current (FCNC) transitions $t\to q^{\prime }H$ and $t\to q^{\prime }{V}_i$ $(V_i=\gamma ,g,Z)$ are studied in the context of the effective Lagrangian approach. We focus on the scenario in which these decays are predominantly induced by new physics effects arising from the Yukawa sector extended with dimension-six ${\mathrm{S}\mathrm{U}}_L(2)\times {\mathrm{U}}_Y(1)$-invariant operators, which generate the most general $CP$-even and $CP$-odd $t{q}^{\prime }H$ vertex at the tree level. For the unknown coefficients, we assume a slightly modified version of the Cheng-Sher ansatz. We found that the branching ratio for the Higgs-mediated FCNC $t\to q^{\prime }{V}_i$ decays are enhanced by two or 3 orders of magnitude with respect to the results expected in models with extended Higgs sectors, such as the general two-Higgs doublet model. We discuss the possibilities of detecting this class of decays at the large hadron collider (LHC).

We calculate the hadronic tensor for inclusive semileptonic $B\to X_c\ell \overline{\nu }$ decay to $\mathcal{O}({\alpha }_s)$. This allows $\mathcal{O}({\alpha }_s{\Lambda }_{\mathrm{Q}\mathrm{C}\mathrm{D}}/m_b)$ corrections to hadronic invariant mass observables to be directly evaluated with experimentally required cuts on phase space. Several moments of phenomenological interest are presented to order $\mathcal{O}({\alpha }_s{\Lambda }_{\mathrm{Q}\mathrm{C}\mathrm{D}}/m_b)$ and $\mathcal{O}({\Lambda }_{\mathrm{Q}\mathrm{C}\mathrm{D}}^3/m_b^3)$, allowing a consistent extraction of the heavy quark effective theory parameters up to $\mathcal{O}({\Lambda }_{\mathrm{Q}\mathrm{C}\mathrm{D}}^3/m_b^3)$ and the $b$ quark mass with theoretical error $\sim 50\mathrm{M}\mathrm{e}\mathrm{V}$. The hadronic invariant mass spectrum is examined with a general moment to obtain observables that test the theoretical error estimate assigned to these parameters; in particular, fractional moments that directly test the operator product expansion for inconsistencies in the hadronic invariant mass spectrum are reported. The $m_b{\Lambda }_{\mathrm{Q}\mathrm{C}\mathrm{D}}/m_c^2$ expansion present for fractional moments of the hadronic invariant mass spectrum is discussed and shown to introduce a numerically suppressed uncertainty of $\mathcal{O}(m_b^4{\Lambda }_{\mathrm{Q}\mathrm{C}\mathrm{D}}^4/m_c^8)$.

Using data collected by the CLEO III detector at CESR, we report on measurements of ${\rm Y}(1S)$ decays to charmonium final states. The data sample used for this analysis consists of $21.2\times {10}^6$ ${\rm Y}(1S)$ decays, representing about 35 times more data than previous CLEO ${\rm Y}(1S)$ data samples. We present substantially improved measurements of the branching fraction $\mathcal{B}({\rm Y}(1S)\to J/\psi +X)$ using $J/\psi \to {\mu }^{+}{\mu }^{-}$ and $J/\psi \to e^{+}{e}^{-}$ decays. The branching fractions for these two modes are averaged, thereby obtaining: $\mathcal{B}({\rm Y}(1S)\to J/\psi +X)=(6.4\pm 0.4(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.6(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}))\times {10}^{-4}$. A greatly improved measurement of the $J/\psi$ momentum distribution is presented and indicates a spectrum which is much softer than predicted by the color-octet model and somewhat softer than the color-singlet model. First measurements of the $J/\psi$ polarization and production angle are also presented. In addition, we report on the first observation of ${\rm Y}(1S)\to \psi (2S)+X$ and evidence for ${\rm Y}(1S)\to {\chi }_{cJ}+X$. Their branching fractions are measured relative to $\mathcal{B}({\rm Y}(1S)\to J/\psi +X)$ and are found to be $\{[\mathcal{B}({\rm Y}(1S)\to \psi (2S)+X)]/[\mathcal{B}({\rm Y}(1S)\to J/\psi +X)]\}=0.41\pm 0.11(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.08(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})$, $\{[\mathcal{B}({\rm Y}(1S)\to {\chi }_{c1}+X)]/[\mathcal{B}({\rm Y}(1S)\to J/\psi +X)]\}=0.35\pm 0.08(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.06(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})$, $\{[\mathcal{B}({\rm Y}(1S)\to {\chi }_{c2}+X)]/[\mathcal{B}({\rm Y}(1S)\to J/\psi +X)]\}=0.52\pm 0.12(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.09(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})$, and $\{[\mathcal{B}({\rm Y}(1S)\to {\chi }_{c0}+X)]/[\mathcal{B}({\rm Y}(1S)\to J/\psi +X)]\}<7.4$ at 90% confidence level. The resulting feed-down contributions to $J/\psi$ are $[24\pm 6(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 5(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})]\%$ for $\psi (2S)$, $[11\pm 3(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 2(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})]\%$ for ${\chi }_{c1}$, $[10\pm 2(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 2(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})]\%$ for ${\chi }_{c2}$, and $<8.2\%$ at 90% confidence level for ${\chi }_{c0}$. These measurements (apart from ${\chi }_{c0}$) are about a factor of 2 larger than expected based on the color-octet model.