High-precision data from observation of the cosmic microwave background and the large scale structure of the universe provide very tight constraints on the effective parameters that describe cosmological inflation. Indeed, within a constrained class of $\Lambda \mathrm{CDM}$ models, the simple $\lambda {\varphi }^4$ chaotic inflation model already appears to be ruled out by cosmological data. In this paper, we compute constraints on inflationary parameters within a more general framework that includes other physically motivated parameters such as a nonzero neutrino mass. We find that a strong degeneracy between the tensor-to-scalar ratio $r$ and the neutrino mass prevents $\lambda {\varphi }^4$ from being excluded by present data. Reversing the argument, if $\lambda {\varphi }^4$ is the correct model of inflation, it predicts a sum of neutrino masses at $0.3\to 0.5\mathrm{eV}$, a range compatible with present experimental limits and within the reach of the next generation of neutrino mass measurements. We also discuss the associated constraints on the dark matter density, the dark energy equation of state, and spatial curvature, and show that the allowed regions are significantly altered. Importantly, we find an allowed range of $0.094<{\Omega }_c{h}^2<0.136$ for the dark matter density, a factor of 2 larger than that reported in previous studies. This expanded parameter space may have implications for constraints on SUSY dark matter models.

We discuss a robust data analysis method to detect a stochastic background of gravitational waves in the presence of non-Gaussian noise. In contrast to the standard cross-correlation (SCC) statistic frequently used in the stochastic background searches, we consider a generalized cross-correlation (GCC) statistic, which is nearly optimal even in the presence of non-Gaussian noise. The detection efficiency of the GCC statistic is investigated analytically, particularly focusing on the statistical relation between the false-alarm and the false-dismissal probabilities, and the minimum detectable amplitude of gravitational-wave signals. We derive simple analytic formulas for these statistical quantities. The robustness of the GCC statistic is clarified based on these formulas, and one finds that the detection efficiency of the GCC statistic roughly corresponds to the one of the SCC statistic neglecting the contribution of non-Gaussian tails. This remarkable property is checked by performing the Monte Carlo simulations and successful agreement between analytic and simulation results was found.

The amplitude for ordinary muon capture on the proton is evaluated, through the first four orders in the expansion parameter, in a manifestly Lorentz invariant form of baryon chiral perturbation theory. Expressions for the low energy constants in terms of physical quantities are obtained in each of the several renormalization schemes which have been proposed for forcing the relativistic approach to obey the same counting rules as obtained in heavy baryon chiral perturbation theory. The advantages and disadvantages of these schemes are discussed, using the muon capture results as an example, with the aim of gaining insight as to which scheme is preferable for practical calculations.

We propose a new set of observables that can be used as experimental null tests of the Standard Model in charged and neutral $B$ decays. The $CP$ asymmetries in hadronic decays of charged $B$ mesons into inclusive final states containing at least one of the following mesons: $K_{S,L}$, ${\eta }^{\prime }$, $c\overline{c}$ bound states or neutral $K^{*}$ or $D$ mesons, for all of which a $U$-spin rotation is equivalent to a $CP$ conjugation, are CKM suppressed and furthermore vanish in the exact $U$-spin limit. We show how this reduces the theoretical error by using Soft Collinear Effective Theory to calculate the $CP$ asymmetries for $K_{S,L}{X}_{s+d}$, $K^{*}{X}_{s+d}$ and ${\eta }^{\prime }{X}_{s+d}$ final states in the endpoint region. For these $CP$ asymmetries only the flavor and not the charge of the decaying $B$ meson needs to be tagged up to corrections of NLO in $1/m_b$, making the measurements more accessible experimentally.

The distributions of two-jet event shapes contain information on hadronization in QCD. Near the two-jet limit, these distributions can be described by convolutions of nonperturbative event shape functions with the same distributions calculated in resummed perturbation theory. The shape functions, in turn, are determined by correlations of momentum flow operators with each other and with lightlike Wilson lines, which describe the coupling of soft, wide-angle radiation to jets. We observe that leading power corrections to the mean values of event shapes are determined by the correlation of a single momentum flow operator with the relevant Wilson lines. This generalizes arguments for the universality of leading power corrections based on the low-scale behavior of the running coupling or resummation. We also show how a study of the angularity event shapes can provide information on correlations involving multiple momentum flow operators, giving a window to the system of QCD dynamics that underlies the variety of event shape functions. In deriving these results, we review, develop and compare factorization techniques in conventional perturbative QCD and soft-collinear effective theory (SCET). We give special emphasis to the elimination of double counting of momentum regions in these two formalisms.

The first observation of an azimuthal cross section asymmetry with respect to the charge of the incoming lepton beam is reported from a study of hard exclusive electroproduction of real photons. The data have been accumulated by the HERMES experiment at DESY, in which the HERA 27.6 GeV electron or positron beam scattered off an unpolarized hydrogen gas target. The observed asymmetry is attributed to the interference between the Bethe-Heitler process and the deeply virtual Compton scattering (DVCS) process. The interference term is sensitive to DVCS amplitudes, which provide the most direct access to generalized parton distributions.

For the weakly coupled heterotic string (WCHS) there is a well-known factor of 20 conflict between the minimum string coupling unification scale, ${\Lambda }_H\sim 5\times {10}^{17}\mathrm{GeV}$, and the projected minimal supersymmetric standard model (MSSM) gauge coupling unification scale, ${\Lambda }_U\sim 2.5\times {10}^{16}\mathrm{GeV}$, assuming an intermediate scale desert (ISD). From a bottom-up approach, renormalization effects of intermediate scale MSSM-charged exotics (ISME), which are endemic to quasirealistic string models, can resolve this issue by pushing the MSSM scale up to the string scale. However, for a generic string model, this implies that the projected ${\Lambda }_U$ unification under the ISD assumption is accidental. If the true unification scale is ${\Lambda }_H\gtrsim 5.0\times {10}^{17}\mathrm{GeV}$, is it possible that an illusionary unification at ${\Lambda }_U=2.5\times {10}^{17}\mathrm{GeV}$ in the ISD scenario is not accidental? (This is an issue recently raised again by Binétruy et al..) Optical unification suggests that ${\Lambda }_U$ might not be accidental. Through its ISME constraints, optical unification offers a mechanism whereby a generic MSSM scale ${\Lambda }_U<{\Lambda }_H$ is guaranteed. A WCHS model was recently constructed that could yield optical unification, depending on the availability of anomaly-cancelling $D$- and $F$-flat directions that meet optical unification ISME requirements. We report the results of a systematic investigation of the optical unification properties of a subset of flat directions of this model that are stringently flat. Stringent flat directions do not require significant fine-tuning and can be easily guaranteed to be $F$-flat to all finite order (or to at least a given finite order consistent with electroweak scale supersymmetry breaking). They are the likely roots of more complicated (and arguably, more finely tuned) flat directions. To realize optical unification, a flat direction must keep all exotic triplets and doublets massless down to an intermediate mass scale, except for three extra pairs of Higgs which must acquire MSSM (or higher) scale mass. Additionally, six out of seven pairs of exotic hypercharged non-Abelian singlets must acquire MSSM (or higher) scale mass, while the remaining pair remains massless down to the intermediate scale. Our investigation revealed that the best stringent directions could induce MSSM scale or higher mass to at most three of the six pairs of exotic singlets, and to only two out of three pairs of exotic Higgs. Each of these stringent flat directions keeps all of the exotic triplets and remaining exotic doublets massless down to an intermediate scale. Thus, some fine-tuning away from stringent flat directions is necessary, if it is possible for an additional three pairs of exotic hypercharged singlets and one more pair of extra Higgs to become MSSM scale massive. Future research may indicate if such flat directions exist. This paper is a product of the 2003-2004 NSF REU program at Baylor University.

We present a mechanism to localize zero mode non-Abelian gauge fields in a slice of ${\mathrm{AdS}}_5$. As in the U(1) case, bulk and boundary mass terms allow for a massless mode with an exponential profile that can be localized anywhere in the bulk. However in the non-Abelian extension, the cubic and quartic zero-mode gauge couplings do not match, implying a loss of 4D gauge invariance. We show that the symmetry can be restored at the nonlinear level by considering brane-localized interactions, which are added in a gauge invariant way using boundary kinetic terms. Possible issues related to the scalar sector of the theory, such as strong coupling and ghosts, are also discussed. Our approach is then compared with other localization mechanisms motivated by dilaton gravity and deconstruction. Finally, we show how to localize the scalar component $A_5$ zero mode anywhere in the bulk which could be relevant in gauge-Higgs unification models.

Loop quantum cosmology (LQC) homogeneous models with a massless scalar field show that the big-bang singularity can be replaced by a big quantum bounce. To gain further insight on the nature of this bounce, we study the semidiscrete loop quantum gravity Hamiltonian constraint equation from the point of view of numerical analysis. For illustration purposes, we establish a numerical analogy between the quantum bounces and reflections in finite difference discretizations of wave equations triggered by the use of nonuniform grids or, equivalently, reflections found when solving numerically wave equations with varying coefficients. We show that the bounce is closely related to the method for the temporal update of the system and demonstrate that explicit time-updates in general yield bounces. Finally, we present an example of an implicit time-update devoid of bounces and show back-in-time, deterministic evolutions that reach and partially jump over the big-bang singularity.

Gravitational interactions of higher spin fields are generically plagued by inconsistencies. There exists however, a simple framework that couples higher spins to a broad class of gravitational backgrounds (including Ricci flat and Einstein) consistently at the classical level. The model is the simplest example of a Yang-Mills detour complex and has broad mathematical applications, especially to conformal geometry. Even the simplest version of the theory, which couples gravitons, vectors and scalar fields in a flat background is rather rich, providing an explicit setting for detailed analysis of ghost excitations. Its asymptotic scattering states consist of a physical massless graviton, scalar, and massive vector along with a degenerate pair of zero norm photon excitations. Coherent states of the unstable sector do have positive norms, but their evolution is no longer unitary and amplitudes grow with time. The class of models proposed is extremely general and of considerable interest for ghost condensation and invariant theory.

We express Einstein’s field equations for a spherically symmetric ball of general fluid such that they are conducive to an initial value problem. We show how the equations reduce to the Vaidya spacetime in a non-null coordinate frame, simply by designating specific equations of state. Furthermore, this reduces to the Schwarzschild spacetime when all matter variables vanish. We then describe the formulation of an initial value problem, whereby a general fluid ball with vacuum exterior is established on an initial spacelike slice. As the system evolves, the fluid ball collapses and emanates null radiation such that a region of Vaidya spacetime develops. Therefore, on any subsequent spacelike slice there exists three regions; general fluid, Vaidya and Schwarzschild, all expressed in a single coordinate patch with two free-boundaries determined by the equations. This implies complicated matching schemes are not required at the interfaces between the regions, instead, one simply requires the matter variables tend to the appropriate equations of state. We also show the reduction of the system of equations to the static cases, and show staticity necessarily implies zero “heat flux.” Furthermore, the static equations include a generalization of the Tolman-Oppenheimer-Volkoff equations for hydrostatic equilibrium to include anisotropic stresses in general coordinates.

We carry out a model independent study of resonant photon scattering off dark matter (DM) particles. The DM particle ${\chi }_1$ can feature an electric or magnetic transition dipole moment which couples it with photons and a heavier neutral particle ${\chi }_2$. Resonant photon scattering then takes place at a special energy $E_{\gamma }^{\mathrm{res}}$ set by the masses of ${\chi }_1$ and ${\chi }_2$, with the width of the resonance set by the size of the transition dipole moment. We compute the constraints on the parameter space of the model from stellar energy losses, data from SN 1987A, the Lyman-$\alpha$ forest, big bang nucleosynthesis, electroweak precision measurements, and accelerator searches. We show that the velocity broadening of the resonance plays an essential role for the possibility of the detection of a spectral feature originating from resonant photon-DM scattering. Depending upon the particle setup and the DM surface mass density, the favored range of DM particle masses lies between tens of keV and a few MeV, while the resonant photon absorption energy is predicted to be between tens of keV and a few GeV.

The existence of chaotic behavior for the geodesics of the test particles orbiting compact objects is a subject of much current research. Some years ago, Guéron and Letelier [Phys. Rev. E 66, 046611 (2002)] reported the existence of chaotic behavior for the geodesics of the test particles orbiting compact objects like black holes induced by specific values of the quadrupolar deformation of the source using as models the Erez--Rosen solution and the Kerr black hole deformed by an internal multipole term. In this work, we are interested in the study of the dynamic behavior of geodesics around astrophysical objects with intrinsic quadrupolar deformation or nonisotropic stresses, which induces nonvanishing quadrupolar deformation for the nonrotating limit. For our purpose, we use the Tomimatsu-Sato spacetime [Phys. Rev. Lett. 29 1344 (1972)] and its arbitrary deformed generalization obtained as the particular vacuum case of the five parametric solution of Manko et  al. [Phys. Rev. D 62, 044048 (2000)] characterizing the geodesic dynamics throughout the Poincaré sections method. We found only regular motion for the geodesics in the Tomimatsu-Sato $\delta =2$ solution. Additionally, using the deformed generalization of Tomimatsu-Sato $\delta =2$ solution given by Manko et al. we found chaotic motion for oblate deformation instead of prolate deformation, which is in contrast to the results by Guéron and Letelier. It opens the possibility that the particles forming the accretion disk around a large variety of different astrophysical bodies (nonprolate, e.g., neutron stars) could exhibit chaotic dynamics. We also conjecture that the existence of an arbitrary deformation parameter is necessary for the existence of chaotic dynamics.

Recently, a more than $2\sigma$ discrepancy has been observed between the well measured inclusive value of $V_{ub}$ and the predicted value of $V_{ub}$ from the unitarity triangle fit using the world average value of $\sin 2\beta$. We attempt to resolve this tension in the context of grand unified SO(10) and SU(5) models where the neutrino mixing matrix is responsible for flavor changing neutral current at the weak scale and the models with nonproportional $A$-terms (can be realized simply in the context of intersecting D-brane models) and investigate the interplay between the constraints arising from $B_{s,d}\mathrm{\text{−}}{\overline{B}}_{s,d}$ mixings, ${ϵ}_K$, $\mathrm{Br}(\tau \to \mu \gamma )$, $\mathrm{Br}(\mu \to e\gamma )$ and a fit of this new discrepancy. We also show that the ongoing measurement of the phase of $B_s$ mixing will be able to identify the grand unified model. The measurement of $\mathrm{Br}(\tau \to e\gamma )$ will also be able to test these scenarios, especially the models with nonproportional $A$-terms.

Hadronic matrix elements of operators relevant to nucleon decay in grand unified theories are calculated numerically using lattice QCD. In this context, the domain-wall fermion formulation, combined with nonperturbative renormalization, is used for the first time. These techniques bring reduction of a large fraction of the systematic error from the finite lattice spacing. Our main effort is devoted to a calculation performed in the quenched approximation, where the direct calculation of the nucleon to pseudoscalar matrix elements as well as the indirect estimate of them from the nucleon to vacuum matrix elements are performed. First results, using two flavors of dynamical domain-wall quarks for the nucleon to vacuum matrix elements, are also presented to address the systematic error of quenching, which appears to be small compared to the other errors. Our results suggest that the representative values for the low-energy constants from the nucleon to vacuum matrix elements are given as $|\alpha |\simeq |\beta |\simeq 0.01{\mathrm{GeV}}^3$. For a more reliable estimate of the physical low-energy matrix elements, it is better to use the relevant form factors calculated in the direct method. The direct method tends to give a smaller value of the form factors, compared to the indirect one, thus enhancing the proton lifetime; indeed, for the ${\pi }^0$ final state the difference between the two methods is quite appreciable.

The invariant cross sections for direct photon production in hadron-hadron collisions are calculated for several initial energies (SPS, ISR, $\mathrm{S}p\overline{p}\mathrm{S}$, RHIC, Tevatron, LHC) including initial parton transverse momenta within the formalism of unintegrated parton distributions (UPDF). Different approaches from the literature are compared and discussed. A special emphasis is put on the Kimber-Martin-Ryskin (KMR) distributions and their extension into the soft region. Sum rules for UPDFs are formulated and discussed in detail. We find a violation of naive number sum rules for the KMR UPDFs. An interesting interplay of perturbative (large $k_t^2$) and nonperturbative (small $k_t^2$) regions of UPDFs in the production of both soft and hard photons is identified. The $k_t$-factorization approach with the KMR UPDFs is inconsistent with the collinear approach at large transverse momenta of photons. Kwieciński UPDFs provide very good description of all world data, especially at super proton synchrotron (SPS) and intersecting storage rings (ISR) energies. Off-shell effects are discussed and quantified. Predictions for the CERN LHC are given. Very forward/backward regions in rapidity at LHC energy are discussed and a possibility to test unintegrated gluon distributions (UGDF) is presented.

We consider the cross section of the deep inelastic pion electroproduction on a proton target at threshold for $Q^2$ in the region $5–10{\mathrm{GeV}}^2$. The corresponding amplitudes are described in terms of two form factors which we calculate using light-cone sum rules to leading order in QCD and including higher twist corrections. Our results suggest a considerable change from a small $Q^2$ region that can be treated in the soft-pion limit using current algebra. In particular, we obtain a ${\pi }^0$ to ${\pi }^{+}$ production ratio of order $1/3$ and significant nucleon helicity-flip contributions.

In this work a detailed spectral analysis for the periodicity search of the time series of the ${}^8\mathrm{B}$ solar neutrino flux released by the SNO Collaboration is presented. The data have been publicly released with truncation of the event times to the unit of day (1 day binning); they are thus suited to undergo the traditional Lomb-Scargle analysis for periodicity investigation, as well as an extension of such a method based on a likelihood approach. The results of the analysis presented here confirm the absence of modulation signatures in the SNO data. For completeness, a more refined “1 day binned” likelihood is also illustrated, which approximates the unbinned likelihood methodology, based upon the availability of the full time information, adopted by the SNO collaboration. Finally, this work is completed with two different joint analyses of the SNO and Super-Kamiokande data, respectively, over the common and the entire data taking periods. While both analyses reinforce the case of the constancy of the neutrino flux, the latter in addition provides evidence of the detection at the 99.7% confidence level of the annual modulation spectral line due to the Earth’s orbit eccentricity around the Sun.

The charged ${\Sigma }_b$ and ${\Sigma }_b^{*}$ states have recently been reported by the CDF Collaboration. The relation of their reported charge-averaged masses to expectations based on the quark model is reviewed briefly. A relation is proved among the $\Delta I=1$ electromagnetic mass differences ${\Sigma }_1\equiv M({\Sigma }^{+})-M({\Sigma }^{-})$, ${\Sigma }_1^{*}\equiv M({\Sigma }^{*+})-M({\Sigma }^{*-})$, ${\Sigma }_{b1}\equiv M({\Sigma }_b^{+})-M({\Sigma }_b^{-})$, and ${\Sigma }_{b1}^{*}\equiv M({\Sigma }_b^{*+})-M({\Sigma }_b^{*-})$. The relation is ${\Sigma }_{b1}^{*}-{\Sigma }_{b1}=(m_s/m_b)({\Sigma }_1^{*}-{\Sigma }_1)$, leading to the expectation ${\Sigma }_{b1}^{*}-{\Sigma }_{b1}=0.40\pm 0.07\mathrm{MeV}$.