A High-Statistics Lattice Calculation of λ1\lambda_1 and λ2\lambda_2 in the BB meson

We present a high-statistics lattice calculation of the kinetic energy $-\lambda_1/2 m_b$ of the heavy quark inside the $B$-meson and of the chromo-magnetic term $\lambda_2$, related to the $B^*$--$B$ mass splitting, performed in the HQET. Our results have been obtained from a numerical simulation based on 600 gauge field configurations generated at $\beta=6.0$, on a lattice volume $24^3 \times 40$ and using, for the meson correlators, the results obtained with the SW-Clover $O(a)$ improved lattice action for the light quarks. For the kinetic energy we found $-\lambda_1=\langle B \vert \bar h (i\vec{D})^{2} h \vert B \rangle /(2 M_B )=-(0.09 \pm 0.14)$~GeV$^2$, which is interesting for phenomenological applications. We also find $\lambda_2= 0.07 \pm 0.01$ GeV$^2$, corresponding to $M^2_{B^*}-M^2_B= 4 \lambda_2= 0.280 \pm 0.060$ GeV$^2$, which is about one half of the experimental value. The origin of the discrepancy with the experimental number needs to be clarified.Comment: 26 pages, latex, 5 figure

Renormalization of the Lattice HQET Isgur-Wise Function

We compute the perturbative renormalization factors required to match to the continuum Isgur-Wise function, calculated using lattice Heavy Quark Effective Theory. The velocity, mass, wavefunction and current renormalizations are calculated for both the forward difference and backward difference actions for a variety of velocities. Subtleties are clarified regarding tadpole improvement, regulating divergences, and variations of techniques used in these renormalizations.Comment: 28 pages, 0 figures, LaTeX. Final version accepted for publication in Phys. Rev. D. (Minor changes.

Spectator Effects in Inclusive Decays of Beauty Hadrons

We present a model-independent study of spectator effects, which are responsible for the lifetime differences between beauty hadrons. These effects can be parametrized in terms of hadronic matrix elements of four four-quark operators. For $B$ mesons, the coefficients of the non-factorizable operators turn out to be much larger than those of the factorizable ones, limiting considerably the usefulness of the vacuum insertion approximation. Non-factorizable contributions to the lifetime ratio $\tau(B^-)/\tau(B_d)$ could naturally be of order 10--20%, and not even the sign of these contributions can be predicted at present. In the case of the $\Lambda_b$ baryon, heavy-quark symmetry is used to reduce the number of independent matrix elements from four to two. In order to explain the large deviation from unity in the experimental result for $\tau(\Lambda_b)/\tau(B_d)$, it is necessary that these baryon matrix elements be much larger than those estimated in quark models. We have also reexamined the theoretical predictions for the semileptonic branching ratio of $B$ mesons and charm counting, finding that, given the present theoretical and experimental uncertainties, there is no significant discrepancy with experiment.Comment: 32 pages, 5 postscript figures included, revised version to appear in Nuclear Physics

Phenomenological constraints on SUSY SU(5) GUTs with non-universal gaugino masses

We study phenomenological aspects of supersymmetric SU(5) grand unified theories with non-universal gaugino masses. For large tan beta, we investigate constraints from the requirement of successful electroweak symmetry breaking, the positivity of stau mass squared and the b to s gamma decay rate. In the allowed region, the nature of the lightest supersymmetric particle is determined. Examples of mass spectra are given. We also calculate loop corrections to the bottom mass due to superpartners.Comment: 10 pages, 2 figures (8 eps files), uses REVTeX. Replaced to match the version to be published in PRD: minor corrections and addition

Exclusive Decays of Beauty Hadrons

The principal difficulty in deducing weak interaction properties from experimental measurements of $B$-decays lies in controlling the strong interaction effects. In this talk I review the status of theoretical calculations of the amplitudes for exclusive leptonic and semileptonic decays, in the latter case with special emphasis on the extraction of the $V_{cb}$ and $V_{ub}$ matrix elements.Comment: Invited lecture presented at the workshop "Beauty '96", Rome, June 17-21 1996. 19 pages, latex, axodraw.sty, 7 figure

Plastic Flow in Two-Dimensional Solids

A time-dependent Ginzburg-Landau model of plastic deformation in two-dimensional solids is presented. The fundamental dynamic variables are the displacement field \bi u and the lattice velocity {\bi v}=\p {\bi u}/\p t. Damping is assumed to arise from the shear viscosity in the momentum equation. The elastic energy density is a periodic function of the shear and tetragonal strains, which enables formation of slips at large strains. In this work we neglect defects such as vacancies, interstitials, or grain boundaries. The simplest slip consists of two edge dislocations with opposite Burgers vectors. The formation energy of a slip is minimized if its orientation is parallel or perpendicular to the flow in simple shear deformation and if it makes angles of $\pm \pi/4$ with respect to the stretched direction in uniaxial stretching. High-density dislocations produced in plastic flow do not disappear even if the flow is stopped. Thus large applied strains give rise to metastable, structurally disordered states. We divide the elastic energy into an elastic part due to affine deformation and a defect part. The latter represents degree of disorder and is nearly constant in plastic flow under cyclic straining.Comment: 16pages, Figures can be obtained at http://stat.scphys.kyoto-u.ac.jp/index-e.htm

A Phenomenological Analysis of Heavy Hadron Lifetimes

A phenomenological analysis of lifetimes of bottom and charmed hadrons within the framework of the heavy quark expansion is performed. The baryon matrix element is evaluated using the bag model and the nonrelativistic quark model. We find that bottom-baryon lifetimes follow the pattern $\tau(\Omega_b)\simeq\tau(\Xi_b^-)>\tau(\Lambda_b)\simeq\tau(\Xi_b^0)$. However, neither the lifetime ratio $\tau(\Lambda_b)/\tau( B_d)$ nor the absolute decay rates of the $\Lambda_b$ baryon and $B$ mesons can be explained. One way of solving both difficulties is to allow the presence of linear $1/m_Q$ corrections by scaling the inclusive nonleptonic width with the fifth power of the hadron mass $m_{H_Q}$ rather than the heavy quark mass $m_Q$. The hierarchy of bottom baryon lifetimes is dramatically modified to $\tau(\Lambda_b)>\tau(\Xi_b^-)>\tau(\Xi_b^0)>\tau( \Omega_b)$: The longest-lived $\Omega_b$ among bottom baryons in the OPE prescription now becomes shortest-lived. The replacement of $m_Q$ by $m_{H_Q}$ in nonleptonic widths is natural and justified in the PQCD-based factorization approach formulated in terms of hadron-level kinematics. For inclusive charmed baryon decays, we argue that since the heavy quark expansion does not converge, local duality cannot be tested in this case. We show that while the ansatz of substituting the heavy quark mass by the hadron mass provides a much better description of the charmed-baryon lifetime {\it ratios}, it appears unnatural and unpredictive for describing the {\it absolute} inclusive decay rates of charmed baryons, contrary to the bottom case.Comment: 35 pages, to appear in Phys. Rev. The CDF result on the lifetime ratio of Lambda_b and B_d is discusse

Rare Charm Decays in the Standard Model and Beyond

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 $c\to u\ell^+\ell^-$ 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 $D\to\pi\ell^+\ell^-$ and $D\to\rho\ell^+\ell^-$ are sensitive to non-universal 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.Comment: 45 pages, typos fixed, discussions adde

Gaugino Mass Nonuniversality and Dark Matter in SUGRA, Strings and D Brane Models

The effects of nonuniversality of gaugino masses on dark matter are examined within supersymmetric grand unification, and in string and D brane models with R parity invariance. In SU(5) unified models nonuniversality in the gaugino sector can be generated via the gauge kinetic energy function which may depend on the 24, 75 and 200 dimensional Higgs representations. We also consider string models which allow for nonuniversality of gaugino masses and D brane models where nonuniversality arises from embeddings of the Standard Model gauge group on five branes and nine branes. It is found that with gaugino mass nonuniversality the range of the LSP mass can be extended much beyond the range allowed in the universal SUGRA case, up to about 600 GeV even without coannihilation effects in some regions of the parameter space. The effects of coannihilation are not considered and inclusion of these effects may further increase the allowed neutralino mass range. Similarly with the inclusion of gaugino mass nonuniversality, the neutralino-proton ($\chi -p$) cross-section can increase by as much as a factor of 10 in some of regions of the parameter space. An analysis of the uncertainties in the quark density content of the nucleon is given and their effects on $\chi -p$ cross-section are discussed. The predictions of our analysis including nonuniversality is compared with the current limits from dark matter detectors and implications for future dark matter searches are discussed.Comment: Revised version, 23 pages, Latex, and 7 figure

First lattice calculation of the B-meson binding and kinetic energies

We present the first lattice calculation of the B-meson binding energy and of the kinetic energy -lambda(1)/2m(Q) of the heavy-quark inside the pseudoscalar B-meson. This calculation has required the non-perturbative subtraction of the power divergences present in matrix elements of the Lagrangian operator and of the kinetic energy operator , The non-perturbative renormalisation of the relevant operators has been implemented by imposing suitable renormalisation conditions on quark matrix elements, in the Landau gauge. Our numerical results have been obtained from several independent numerical simulations at beta = 6.0 and 6.2, and using, for the meson correlators, the results obtained by the APE group at the same values of beta. Our best estimate, obtained by combining results at different values of beta, is = 190(-30)(+50) MeV. For the running mass, we obtain () = 4.17 +/- 0.06 GeV, in reasonable agreement with previous determinations. From a subset of 36 configurations, we were only able to establish a loose upper bound on the 6-quark kinetic energy in a B-meson, lambda(1) = [B\\B]/(2M(B)) < 1 GeV2. This shows that a much larger statistical sample is needed to determine this important parameter