We study the impact of the QCD Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution on the geometric scaling of gluon distributions that is expected to hold at small x within the saturation models. With this aim we solve the DGLAP evolution equations with the initial conditions provided along the critical line $Q^2{=Q}_s^2\mathrm{}\left(x\right)\mathrm{}$ with $Q_s^2\mathrm{}\left(x\right)\mathrm{}\sim x^{-\lambda }$ and satisfying geometric scaling. Both fixed and running coupling cases are studied. We show that in the fixed coupling case the geometric scaling at low x is stable against the DGLAP evolution for sufficiently large values of the parameter $\lambda ,$ and in the double logarithmic approximation of the DGLAP evolution this happens for $\lambda >~{4N}_c{\alpha }_s/\pi .$ In the running coupling case geometric scaling is found to be approximately preserved at very small x. The residual geometric scaling violation in this case can be approximately factored out and the corresponding form factor controlling this violation is found.

No spin-singlet $b\overline{b}$ quarkonium state has yet been observed. In this paper we discuss the production of the singlet P-wave $b\overline{b}$ and $c\overline{c}$ ${}^1{P}_1$ states $h_b$ and $h_c.$ We consider two possibilities. In the first the ${}^1{P}_1$ states are produced via the electromagnetic cascades ${\rm Y}\mathrm{}\left(3S\right)\mathrm{}\to {\eta }_b\mathrm{}\left(2S\right)+\overrightarrow{\gamma }{h}_b+\gamma \overrightarrow{\gamma }{\eta }_b+\gamma \gamma \gamma$ and ${\psi }^{\prime }\to {\eta }_c^{\prime }+\overrightarrow{\gamma }{h}_c+\gamma \overrightarrow{\gamma }{\eta }_c+\gamma \gamma \gamma .$ A more promising process consists of single pion transition to the ${}^1{P}_1$ state followed by the radiative transition to the $1{}^1{S}_0$ state: ${\rm Y}\mathrm{}\left(3S\right)\mathrm{}\to h_b+{\pi }^0\to {\eta }_b+{\pi }^0+\gamma$ and ${\psi }^{\prime }\to h_c+{\pi }^0\to {\eta }_c+{\pi }^0+\gamma .$ For a million ${\rm Y}\mathrm{}\left(3S\right)\mathrm{}$ or ${\psi }^{\prime }’\mathrm{s}$ produced we expect these processes to produce several hundred events.

We present a phenomenological application of the joint resummation formalism to electroweak annihilation processes at a measured boson momentum $Q_T.$ This formalism simultaneously resums at next-to-leading logarithmic accuracy large threshold and recoil corrections to partonic scattering. We invert the impact parameter transform using a previously described analytic continuation procedure. This leads to a well-defined, resummed perturbative cross section for all nonzero $Q_T,$ which can be compared to resummation carried out directly in $Q_T$ space. From the structure of the resummed expressions, we also determine the form of nonperturbative corrections to the cross section and implement these into our analysis. We obtain a good description of the transverse momentum distribution of Z bosons produced at the Fermilab Tevatron collider.

For any perturbative series that is known to k-subleading orders of perturbation theory, we utilize the process-appropriate renormalization-group (RG) equation in order to obtain all-orders summation of series terms proportional to ${\alpha }^n{\log }^{n-k}\left({\mu }^2\right)$ with $k=\{0,1,2,3\},$ corresponding to the summation to all orders of the leading and subsequent-three-subleading logarithmic contributions to the full perturbative series. These methods are applied to the perturbative series for semileptonic b decays in both $\overline{\mathrm{MS}}$ and pole-mass schemes, and they result in RG-summed series for the decay rates which exhibit greatly reduced sensitivity to the renormalization scale μ. Such summation via RG methods of all logarithms accessible from known series terms is also applied to perturbative QCD series for vector- and scalar-current correlation functions, the perturbative static potential function, the (single-doublet standard-model) Higgs decay amplitude into two gluons, as well as the Higgs-mediated high-energy cross section for $W^{+}{W}^{-}\to \mathrm{ZZ}$ scattering. The resulting RG-summed expressions are also found to be much less sensitive to the renormalization scale than the original series for these processes.

We perform a comprehensive study of a number of rare charm decays, incorporating the first evaluation of the QCD corrections to the short distance contributions, as well as examining the long range effects. For processes mediated by the $\overrightarrow{c}{\mathrm{ul}}^{+}{l}^{-}$ transitions, we show that sensitivity to short distance physics exists in kinematic regions away from the vector meson resonances that dominate the total rate. In particular, we find that $\overrightarrow{D}\pi l^{+}{l}^{-}$ and $\overrightarrow{D}\rho l^{+}{l}^{-}$ are sensitive to nonuniversal soft-breaking effects in the minimal supersymmetric standard model with R-parity conservation. We separately study the sensitivity of these modes to R-parity violating effects and derive new bounds on R-parity violating couplings. We also obtain predictions for these decays within extensions of the standard model, including extensions of the Higgs, gauge and fermion sectors, as well as models of dynamical electroweak symmetry breaking.

Motivated in part by recent demonstrations that electroweak unification into a simple group may occur at a low scale, we detail the requirements on the Higgs boson mass if the unification is to be perturbative. We do this for the standard model effective theory, minimal supersymmetry, and next-to-minimal supersymmetry with an additional singlet field. Within the standard model framework, we find that perturbative unification with ${\sin }^2{\theta }_W=1/4\mathrm{}$ occurs at $\Lambda =3.8\mathrm{}\hspace{0.5em}\mathrm{TeV}$ and requires $m_h\lesssim 460\hspace{0.5em}\mathrm{GeV},$ whereas perturbative unification with ${\sin }^2{\theta }_W=3/8\mathrm{}$ requires $m_h\lesssim 200\hspace{0.5em}\mathrm{GeV}.$ In supersymmetry, the presentation of the Higgs boson mass predictions can be significantly simplified, yet remain meaningful, by using a single supersymmetry breaking parameter ${\Delta }_S.$ We present Higgs boson mass limits in terms of ${\Delta }_S$ for the minimal supersymmetric model and the next-to-minimal supersymmetric model. We show that in next-to-minimal supersymmetry, the Higgs boson mass upper limit can be as large as $500\hspace{0.5em}\mathrm{GeV}$ even for moderate supersymmetry masses if the perturbative unification scale is low $\left(\Lambda \simeq 10\hspace{0.5em}\mathrm{TeV}\right).\mathrm{}$

Several extensions of the standard electroweak model allow new four-fermion interactions ${\overline{\nu }}_{\alpha }{\nu }_{\beta }\overline{f}f$ with a strength ${\epsilon }_{\alpha \beta }{G}_F,$ where $(\alpha ,\beta )$ are flavor indices. We reexamine their effects on flavor oscillations of massive (anti)neutrinos in supernovae, in order to achieve, in the region above the protoneutron star, an analytical treatment valid for generic values of the neutrino mixing angles $(\omega ,\phi ,\psi )=({\theta }_{12},{\theta }_{13},{\theta }_{23}).\mathrm{}$ Assuming that ${\epsilon }_{\alpha \beta }\ll 1,$ we find that the leading effects on the flavor transitions occurring at high (H) and low (L) density along the supernova matter profile can be simply embedded through the replacements $\overrightarrow{\phi }\phi +{\epsilon }_H$ and $\overrightarrow{\omega }\omega +{\epsilon }_L,$ respectively, where ${\epsilon }_H$ and ${\epsilon }_L$ are specific linear combinations of the ${\epsilon }_{\alpha \beta }’\mathrm{s}.$ Similar replacements hold for eventual oscillations in the Earth matter. From a phenomenological point of view, the most relevant consequence is a possible uncontrolled bias $(\overrightarrow{\phi }\phi +{\epsilon }_H)$ in the value of the mixing angle $\phi$ inferred by inversion of supernova neutrino data. Such a drawback, however, does not preclude the discrimination of the neutrino mass spectrum hierarchy (direct or inverse) through supernova neutrino oscillations.

We assess a mechanism which can transform neutrino-antineutrino asymmetries between flavors in the early universe, and confirm that such transformation is unavoidable in the near bimaximal framework emerging for the neutrino mixing matrix. We show that the process is a standard Mikheyev-Smirnov-Wolfenstein flavor transformation dictated by a synchronization of momentum states. We also show that flavor “equilibration” is a special feature of maximal mixing, and carefully examine new constraints placed on neutrino asymmetries. In particular, the big bang nucleosynthesis limit on electron neutrino degeneracy $|{\xi }_e|\lesssim 0.04$ does not apply directly to all flavors, yet confirmation of the large-mixing-angle solution to the solar neutrino problem will eliminate the possibility of degenerate big bang nucleosynthesis.

An injection of energy into the early Universe on a given characteristic length scale will result in turbulent motions of the primordial plasma. We calculate the stochastic background of gravitational radiation arising from a period of cosmological turbulence, using a simple model of isotropic Kolmogoroff turbulence produced in a cosmological phase transition. We also derive the gravitational radiation generated by magnetic fields arising from a dynamo operating during the period of turbulence. The resulting gravitational radiation background has a maximum amplitude comparable to the radiation background from the collision of bubbles in a first-order phase transition, but at a lower frequency, while the radiation from the induced magnetic fields is always subdominant to that from the turbulence itself. We briefly discuss the detectability of such a signal.

We give a higher even dimensional extension of vacuum colliding gravitational plane waves with the combinations of collinear and noncollinear polarized four-dimensional metrics. The singularity structure of space-time depends on the parameters of the solution.

An analysis is given as to why one cannot directly evaluate continuum moment equations, i.e., equations involving powers of the position variable times charge, current, or energy momentum operators, on the lattice. I examine two cases: a three point function evaluation of the nucleon magnetic moment and a four point function (charge overlap) evaluation of the pseudoscalar charge radius.

We study the conditions under which flavor violation arises in scalar-fermion interactions, as a result of the mixing phenomena between the standard model and exotic fermions. Phenomenological consequences are discussed within the specific context of a left-right model where these additional fermions have mirror properties under the new ${\mathrm{SU}\left(2\right)\mathrm{}}_R$ gauge group. Bounds on the parameters of the model are obtained from LFV processes; these results are then used to study the LFV Higgs decays $(\overrightarrow{H}\tau l_j,$ $l_j=e,\mu ),$ which reach branching ratios that could be detected at future colliders.

We estimate possible delayed $\beta$ decay signatures of the neutrino induced reactions on ${}^{16}\mathrm{O}$ in a two-step model: the primary neutrino $(\nu ,l)$ process, where l is the lepton in the final state, is described within the random phase approximation, while the subsequent decay of the excited nuclear state in the final channel is treated within the statistical model. We calculate partial reaction cross sections leading to $\beta$ unstable nuclei. We consider neutrino energies up to 500 MeV, relevant for atmospheric neutrino detection in Super-Kamiokande, and supernova neutrino spectra.

Most neutrino mass theories contain nonstandard interactions (NSI) of neutrinos which can be either nonuniversal (NU) or flavor changing (FC). We study the impact of such interactions on the determination of neutrino mixing parameters at a neutrino factory using the so-called “golden channels” ${\stackrel{\mathrm{(-)}}{\nu }}_e\to {\stackrel{\mathrm{(-)}}{\nu }}_{\mu }$ for the measurement of ${\theta }_{13}.$ We show that a certain combination of FC interactions in neutrino source and earth matter can give exactly the same signal as oscillations arising due to ${\theta }_{13}.$ This implies that information about ${\theta }_{13}$ can only be obtained if bounds on NSI are available. Taking into account the existing bounds on FC interactions, this leads to a drastic loss in sensitivity in ${\theta }_{13},$ at least two orders of magnitude. A near detector at a neutrino factory offers the possibility to obtain stringent bounds on some NSI parameters. Such a near site detector constitutes an essential ingredient of a neutrino factory and a necessary step towards the determination of ${\theta }_{13}$ and subsequent study of leptonic $\mathrm{CP}$ violation.

Solar neutrinos with nonzero magnetic moments will contribute to the electron scattering rates in the Super-Kamiokande experiment. The magnetic moment scattering events in Super-K can be accommodated in the standard vacuum oscillation or Mikheyev-Smirnov-Wolfenstein solutions by a change of the parameter space of mass square difference and mixing angle, but the shifted neutrino parameters obtained from Super-K will (for some values of neutrino magnetic moments) become incompatible with the fits from SNO, gallium, and chlorine experiments. We compute the upper bounds on the Dirac and Majorana magnetic moments of solar neutrinos by simultaneously fitting all the observed solar neutrino rates. The bounds of the magnetic moment matrix elements are of the order of ${10}^{-10}{\mu }_B.$

We construct boundary states representing D-strings in ${\mathrm{AdS}}_3$ space. These wrap-twisted conjugacy classes of SL(2, R) and the boundary states are therefore based on continuous representations only. We check Cardy’s condition and find a consistent open string spectrum. The open string spectrum on all the D-branes is the same.

We investigate Hilbert space in the Lorentz covariant approach to loop quantum gravity. We restrict ourselves to the space where all area operators are simultaneously diagonalizable, assuming that it exists. In this sector, quantum states are realized by a generalization of spin network states based on Lorentz Wilson lines projected on irreducible representations of an SO(3) subgroup. The problem of infinite dimensionality of the unitary Lorentz representations is absent due to this projection. Nevertheless, the projection preserves the Lorentz covariance of the Wilson lines so that the symmetry is not broken. Under certain conditions, the states can be thought of as functions on a homogeneous space. We define the inner product as an integral over this space. With respect to this inner product, the spin networks form an orthonormal basis in the investigated sector. We argue that it is the only relevant part of a larger state space arising in the approach. The problem of the noncommutativity of the Lorentz connection is solved by restriction to the simple representations. The resulting structure shows similarities with the spin foam approach.

We propose an alternative inflationary universe scenario in the context of Randall-Sundrum braneworld cosmology. In this new scenario the existence of extra dimension(s) plays an essential role. First, the brane universe is initially in the inflationary phase driven by the effective cosmological constant induced by a small mismatch between the vacuum energy in the five-dimensional bulk and the brane tension. This mismatch arises since the bulk is initially in a false vacuum. Then, false vacuum decay occurs, nucleating a true vacuum bubble with negative energy inside the bulk. The nucleated bubble expands in the bulk and consequently hits the brane, causing a hot big-bang brane universe of the Randall-Sundrum type. Here, the termination of the inflationary phase is due to the change of the bulk vacuum energy. The bubble kinetic energy heats up the universe. As a simple realization, we propose a model in which we assume an interaction between the brane and the bubble. We derive the constraints on the model parameters taking into account the following requirements: solving the flatness problem, no force which prohibits the bubble from colliding with the brane, a sufficiently high reheating temperature for the standard nucleosynthesis to work, and the recovery of Newton’s law up to 1 mm. We find that a fine-tuning is needed in order to satisfy the first and the second requirements simultaneously, although the other constraints are satisfied in a wide range of the model parameters.

We derive a general expression for the power spectra of scalar and tensor fluctuations generated during inflation given an arbitrary choice of boundary condition for the mode function at a short distance. We assume that the boundary condition is specified at a short-distance cutoff at a scale M which is independent of time. Using a particular prescription for the boundary condition at momentum $p\sim M,$ we find that the modulation to the power spectra of density and gravitational wave fluctuations is of order $\mathrm{}(H/M),$ where H is the Hubble parameter during inflation, and we argue that this behavior is generic, although by no means inevitable. With a fixed boundary condition, we find that the shape of the modulation to the power spectra is determined entirely by the deviation of the background spacetime from the de Sitter limit.

We propose a variation of spacetime noncommutative field theory to realize the stringy spacetime uncertainty relation without breaking any of the global symmetries of the homogeneous isotropic universe. We study the spectrum of metric perturbations in this model for a wide class of accelerating background cosmologies. Spacetime noncommutativity leads to a coupling between the fluctuation modes and the background cosmology which is nonlocal in time. For each mode, there is a critical time at which the spacetime uncertainty relation is saturated. This is the time when the mode is generated. These effects lead to a spectrum of fluctuations whose spectral index is different from what is obtained for commutative spacetime in the infrared region, but is unchanged in the ultraviolet region. In the special case of an exponentially expanding background, we find a scale-invariant spectrum. but with a different magnitude than in the context of commutative spacetime if the Hubble constant is above the string scale.