We consider the renormalization group equations (RGE) for the couplings of the standard model and its extensions. Using the hierarchy of the quark masses and of the Cabibbo-Kobayashi-Maskawa (CKM) matrix our argument is that a consistent approximation for the RGE should be based on the parameter $\lambda =|V_{\mathrm{us}}|\approx \mathrm{0.22.}$ We consider the RGE in the approximation where we neglect all the relative terms of the order $\sim {\lambda }^4$ and higher. Within this approximation we find the exact solution of the evolution equations of the quark Yukawa couplings and of the vacuum expectation value of the Higgs field. Then we derive the evolution of the observables: quark masses, CKM matrix, Jarlskog invariant, Wolfenstein parameters of the CKM matrix and the unitarity triangle. We show that the angles of the unitarity triangle remain constant. This property may restrict the possibility of new symmetries or textures at the grand unification scale.

We analyze some phenomenological implications of heterotic M theory with five-branes. Recent results for the effective four-dimensional action are used to perform a systematic analysis of the parameter space, finding the restrictions that result from requiring the volume of the Calabi-Yau manifold to remain positive. Then the different scales of the theory, namely the 11-dimensional Planck mass, the compactification scale, and the orbifold scale, are evaluated. The expressions for the soft supersymmetry-breaking terms are computed and discussed in detail for the whole parameter space. With this information we study the theoretical predictions for the supersymmetric contribution to the muon anomalous magnetic moment, using the recent experimental result as a constraint on the parameter space. We finally analyze the neutralino as a dark matter candidate in this construction. In particular, the neutralino-nucleon cross section is computed and compared with the sensitivities explored by present dark matter detectors.

T-odd correlations as physical observables in the $\overrightarrow{B}{K}^{*}{l}^{+}{l}^{-}$ decay are studied using the most general form of the effective Hamiltonian. It is observed that these quantities are very sensitive to the new physics. We estimate the potential of discovery of these quantities at future hadron colliders.

We calculate the neutralino relic density within the low-energy effective minimal supersymmetric extension of the standard model (effMSSM) taking into account slepton-neutralino, squark-neutralino and neutralino–chargino-neutralino coannihilation channels. By including squark (top squark and bottom squark) coannihilation channels we extend our comparative study to all allowed coannihilations and obtain the general result that all of them give sizable contributions to the reduction of the neutralino relic density. Because of these coannihilation processes some models (mostly with large neutralino masses) fall within the cosmologically interesting region for relic density, but other models drop out at this region. Nevertheless, the predictions for direct and indirect dark matter detection rates are not strongly affected by these coannihilation channels in the effMSSM.

In the minimal supersymmetric standard model the properties of the third generation sfermions are important from the viewpoint of discriminating the SUSY breaking models and in the determination of the Higgs boson mass. If gluinos are copiously produced at the CERN Large Hadron Collider, gluino decays into $t\overline{b}{\tilde{\chi }}_1^{-}$ through a top squark and sbottom can be studied using hadronic decays of the top quark. Using a W sideband method to estimate combinatorial backgrounds, the kinematical end point of the gluino decays can be measured. This implies that the fundamental parameters related to the third generation squarks might be reliably determined. The top-quark polarization dependence in the decay process may also be extracted by looking at the b jet distribution near the kinematical end point.

We discuss the salient features of the Zolotarev optimal rational approximation for the inverse square root function, in particular, for its applications in lattice QCD with the overlap Dirac quark. The theoretical error bound for the matrix-vector multiplication $H_w{(H}_w^2{)}^{-1/2}Y$ is derived. We check that the error bound is always satisfied amply, for any QCD gauge configurations we have tested. An empirical formula for the error bound is determined, together with its numerical values (by evaluating elliptic functions) listed in Table II as well as plotted in Fig. 3. Our results suggest that, with the Zolotarev approximation to ${(H}_w^2{)}^{-1/2},$ one can essentially preserve the exact chiral symmetry of the overlap Dirac operator to very high precision, for any gauge configuration on a finite lattice.

We discuss the semileptonic B decays of the form $\overrightarrow{B}J/\psi e\nu X$ as possible probes of intrinsic charm. We calculate the leading order perturbative contribution to the process $\overrightarrow{B}J/\psi e^{-}{\overline{\nu }}_{e}X$ and find it to be unobservably small, with a branching ratio $\sim {10}^{-10}.$ We propose a modified spectator model to estimate the intrinsic charm contribution and find that it can be significantly larger, with a branching ratio for $\overrightarrow{B}(c\overline{c}{)e}^{-}{\overline{\nu }}_{e}X$ as large as $5\times {10}^{-7}.$ We show that the process could be observed at these levels by the Collider Detector at Fermilab assuming a run II integrated luminosity of $15{\mathrm{fb}}^{-1},$ making this a useful reaction to probe the idea of intrinsic charm.

The masses of the negative parity $\mathrm{SU}\left(6\right)\mathrm{}$ 70-plet baryons are analyzed in the ${1/N}_c$ expansion to order ${1/N}_c$ and to first order in $\mathrm{SU}\left(3\right)\mathrm{}$ breaking. At this level of precision there are 20 predictions. Among them there are the well known Gell-Mann–Okubo and equal spacing relations, and four new relations involving $\mathrm{SU}\left(3\right)\mathrm{}$ breaking splittings in different $\mathrm{SU}\left(3\right)\mathrm{}$ multiplets. Although the breaking of $\mathrm{SU}\left(6\right)\mathrm{}$ symmetry occurs at zeroth order in ${1/N}_c,$ it turns out to be small. The dominant source of the breaking is the hyperfine interaction which is of the order of ${1/N}_c.$ The spin-orbit interaction, of zeroth order in ${1/N}_c,$ is entirely fixed by the splitting between the singlet states $\Lambda \mathrm{}\left(1405\right)\mathrm{}$ and $\Lambda \mathrm{}\left(1520\right),$ and the spin-orbit puzzle is solved by the presence of other zeroth order operators involving flavor exchange.

We investigate heavy quark photoproduction based on the ${\mathit{k}}_{\perp }$-factorization approach, focusing on the results from the saturation model. The deviations between the results using the unintegrated gluon distribution considering the saturation model and the derivative of the collinear gluon distribution are analyzed. Total cross sections and $p_T$ distributions are analyzed in detail, giving the deviations between the results of the color dipole approximation and the complete semihard approach.

We illustrate geometric scaling for the photon-proton cross section with a very simple saturation model. We describe the proton structure function $F_2$ at small x in a wide kinematical range with an elementary functional form and a small number of free parameters. We speculate that the symmetry between low and high $Q^2$ recently discovered in the data could be related to a well-known symmetry of the two-gluon-exchange dipole-dipole cross section.

Within a perturbative scalar QED model recently considered by Brodsky et al., we study how leading-twist Coulomb rescatterings affect the Drell-Yan cross section at small ${x=x}_{\mathrm{target}},$ and compare to the case of deep inelastic scattering at small $x_B.$ We show that in the range where the transverse momentum transferred to the target is large compared to its minimal value $\sim \mathcal{O}\mathrm{}\left(x\right),$ Coulomb rescatterings affect the DIS cross section but not the Drell-Yan production rate. This illustrates that the leading-twist parton distribution functions become nonuniversal when cross sections which are differential in target-related particles are considered.

The ${\nu }_{\mu }\to {\nu }_{\tau }$ oscillation hypothesis will be tested through ${\nu }_{\tau }$ production of $\tau$ in underground neutrino telescopes as well as long-baseline experiments. We provide the full QCD framework for the evaluation of tau neutrino deep inelastic charged current (CC) cross sections at leading twist, including next-to-leading-order (NLO) corrections, charm production, tau threshold, and target mass effects in the collinear approximation. We investigate the violation of the Albright-Jarlskog relations for the structure functions $F_{4,5}$ which occur only in heavy lepton $\left(\tau \right)$ scattering. Integrated CC cross sections for neutrino-nucleon interactions are evaluated naively over the full phase space and with the inclusion of DIS kinematic cuts. Uncertainties in our evaluation based on scale dependence, PDF errors and the interplay between kinematic and dynamical power corrections are discussed and/or quantified.

We propose a scheme of lepton mixing in which the unitary matrix that diagonalizes the neutrino mass matrix is bimaximal and the deviation from the bimaximal of the lepton mixing matrix is due to the unitary matrix that diagonalizes the charged-lepton mass matrix. This matrix is assumed to be hierarchical, like the quark mixing matrix. It is shown that in general it is possible to have a sizable value for $|U_{e3\mathrm{}}|$ together with an effective two-neutrino maximal mixing in solar neutrino experiments. If the effective mixing in solar neutrino experiments is less than maximal, as indicated by current data, $|U_{e3\mathrm{}}|$ is bounded from below. Furthermore, in general the violation of $\mathrm{CP}$ could be relatively large.

We perform global analysis of the solar neutrino data including the day and night spectra of events at SNO. In the context of two active neutrino mixing, the best fit of the data is provided by the large-mixing angle (LMA) Mikheyev-Smirnov-Wolfenstein solution with $\Delta m^2=6.15\mathrm{}\times {10}^{-5}{\mathrm{eV}}^2,{\tan }^2\theta =0.41,f_B=1.05,$ where $f_B$ is the boron neutrino flux in units of the corresponding flux in the standard solar model (SSM). At the $3\sigma$ level we find the following upper bounds: ${\tan }^2\theta <0.84\mathrm{}$ and $\Delta m^2<3.6\mathrm{}\times {10}^{-4}{\mathrm{eV}}^2.$ From a $1\sigma$ interval we expect the day-night asymmetries of the charged current and electron scattering events to be $A_{\mathrm{DN}}^{\mathrm{CC}}{=3.9\mathrm{}}_{-2.9}^{+3.6\mathrm{}}\%$ and $A_{\mathrm{DN}}^{\mathrm{ES}}{=2.1\mathrm{}}_{-1.4}^{+2.1\mathrm{}}\%.\mathrm{}$ The only other solution which appears at the $3\sigma$ level is the VAC solution with $\Delta m^2=4.5\mathrm{}\times {10}^{-10}{\mathrm{eV}}^2,$ ${\tan }^2\theta =2.1,$ and $f_B=\mathrm{0.75.}\mathrm{}$ The best fit point in the low probability, low mass region, with $\Delta m^2=0.93\mathrm{}\times {10}^{-7}{\mathrm{eV}}^2$ and ${\tan }^2\theta =0.64,$ is accepted at 99.95% $\left(3.5\mathrm{}\sigma \right)$ C.L. The least ${\chi }^2$ point from the small mixing angle solution region, with $\Delta m^2=4.6\mathrm{}\times {10}^{-6}{\mathrm{eV}}^2$ and ${\tan }^2\theta =5\mathrm{}\times {10}^{-4},$ could be accepted at the $5.5\sigma$ level only. In the three neutrino context the influence of ${\theta }_{13}$ is studied. We find that with an increase of ${\theta }_{13}$ the LMA best fit point shifts to a larger $\Delta m^2,$ the mixing angle is practically unchanged, and the quality of the fit becomes worse. The fits of LOW and SMA slightly improve. Predictions for the KamLAND experiment (total rates, spectrum distortion) have been calculated.

We study Wilson loops in $\mathcal{N}=4\mathrm{}$ super Yang-Mills (SYM) theory which are nonconstant in the scalar $\left({\mathrm{S}}^5\right)$ directions and open string solutions associated with them in the context of AdS conformal field theory correspondence. An interplay between Minkowskian and Euclidean pictures turns out to be nontrivial for time-dependent Wilson loops. We find that in the ${\mathrm{S}}^5$-rotating case there appears to be no direct open-string duals for the Minkowskian Wilson loops, and their expectation values should be obtained by analytic continuation from the Euclidean-space results. In the Euclidean case, we determine the dependence of the “quark-antiquark” potential on the rotation parameter $\nu ,$ both at weak coupling (i.e., in the 1-loop perturbative SYM theory) and at strong coupling (i.e., in the classical string theory in ${\mathrm{AdS}}_5\times {\mathrm{S}}^5).\mathrm{}$

We construct a particular class of quantum states for a massless, minimally coupled free scalar field which are of the form of a superposition of the vacuum and multimode two-particle states. These states can exhibit local negative energy densities. Furthermore, they can produce an arbitrarily large amount of negative energy in a given region of space at a fixed time. This class of states thus provides an explicit counterexample to the existence of a spatially averaged quantum inequality in four-dimensional spacetime.

A careful reduction of three-dimensional gravity to the Liouville description is performed, where all gauge fixing and on-shell conditions come from the definition of asymptotic de Sitter spaces. The roles of both past and future infinities are discussed and the conditions space-time evolution imposes on both Liouville fields are made explicit. Space-times which correspond to nonequivalent profiles of the Liouville field at ${\mathcal{I}}^{-}$ and ${\mathcal{I}}^{+}$ are shown to exist. The qualitative implications of this for any tentative dual theory are presented.

We systematically investigate the effect of short distance physics on the spectrum of temperature anisotropies in the cosmic microwave background produced during inflation. We present a general argument—assuming only low-energy locality—that the size of such effects is of order $H^2{/M}^2,$ where H is the Hubble parameter during inflation and M is the scale of the high-energy physics. We evaluate the strength of such effects in a number of specific string and M theory models. In weakly coupled field theory and string theory models, the effects are far too small to be observed. In phenomenologically attractive Hořava-Witten compactifications, the effects are much larger but still unobservable. In certain M theory models, for which the fundamental Planck scale is several orders of magnitude below the conventional scale of grand unification, the effects may be on the threshold of detectability. However, observations of both the scalar and tensor fluctuation contributions to the cosmic microwave background power spectrum—with a precision near the cosmic variance limit—are necessary in order to demonstrate unambiguously the existence of these signatures of high-energy physics. This is a formidable experimental challenge.

If $\tan \beta$ is large, down-type quark mass matrices and Yukawa couplings cannot be simultaneously diagonalized, and flavor violating couplings of the neutral Higgs bosons are induced at the one-loop level. These couplings lead to Higgs-mediated contributions to the decays $B_s\to {\mu }^{+}{\mu }^{-}$ and $B_d\to {\tau }^{+}{\tau }^{-},$ at a level that might be of interest for the current Fermilab Tevatron run, or possibly, at B factories. We evaluate the branching ratios for these decays within the framework of minimal gravity-, gauge- and anomaly-mediated supersymmetry breaking models, and also in $\mathrm{SU}\left(5\right)\mathrm{}$ supergravity models with nonuniversal gaugino mass parameters at the grand unified theory scale. We find that the contribution from gluino loops, which seems to have been left out in recent phenomenological analyses, is significant. We explore how the branching fraction varies in these models, emphasizing parameter regions consistent with other observations.

We study color superconductivity with $N_f=1,$ 2, and 3 massless flavors of quarks. We present a general formalism to derive and solve the gap equations for condensation in the even-parity channel. This formalism shows that the leading-order contribution to the gap equation is unique for all color superconductors studied here, and that differences arise solely at the subleading order. We discuss a simple method to compute subleading contributions from the integration over gluon momenta in the gap equation. Subleading contributions enter the prefactor of the color-superconducting gap parameter. In the case of color-flavor and color-spin locking we identify further corrections to this prefactor arising from the two-gap structure of the quasiparticle excitations. Computing the transition temperature $T_c,$ where the color-superconducting condensate melts, we find that these contributions lead to deviations from the BCS behavior $T_c\simeq 0.57{\phi }_0,$ where ${\phi }_0$ is the magnitude of the zero-temperature gap at the Fermi surface.