Reparametrization Invariance Constraints on Inclusive Decay Spectra and Masses

Reparametrization invariance relations are determined for the inclusive decay spectra of heavy hadrons. They connect the leading order result to the lambda_1 term, and the lambda_2 and rho_2 terms, and imply that the lambda_1 and rho_2 terms in the total rate occur in the combinations 1+lambda_1/(2m_Q^2) and lambda_2-rho_2/m_Q. The relations are satisfied by the known results for the hadronic decay tensors for B -> X e nu, B -> X gamma and B -> X e+ e- decays. An interesting field-theory result, the connection between currents in full and effective theories and the change in currents under field redefinitions, is discussed. The hadron masses are given to order (Lambda_QCD)^3/m_Q^2 including radiative corrections, and provide an example illustrating the relation between renormalization and reparametrization invariance and mu-independence of 1/m_Q^3 corrections to physical quantities.Comment: 8 page

qq-Frequent hypercyclicity in spaces of operators

We provide conditions for a linear map of the form $C_{R,T}(S)=RST$ to be $q$-frequently hypercyclic on algebras of operators on separable Banach spaces. In particular, if $R$ is a bounded operator satisfying the $q$-Frequent Hypercyclicity Criterion, then the map $C_{R}(S)$=$RSR^*$ is shown to be $q$-frequently hypercyclic on the space $\mathcal{K}(H)$ of all compact operators and the real topological vector space $\mathcal{S}(H)$ of all self-adjoint operators on a separable Hilbert space $H$. Further we provide a condition for $C_{R,T}$ to be $q$-frequently hypercyclic on the Schatten von Neumann classes $S_p(H)$. We also characterize frequent hypercyclicity of $C_{M^*_\varphi,M_\psi}$ on the trace-class of the Hardy space, where the symbol $M_\varphi$ denotes the multiplication operator associated to $\varphi$.Comment: The previous version has been changed considerably with many corrections rectifie

Renormalization Group Scaling of the 1/m^2 HQET Lagrangian

The operator mixing matrix for the dimension six operators in the heavy quark effective theory Lagrangian is computed at one loop. The results are shown to be consistent with constraints from the equations of motion, and from reparametrization invariance.Comment: 8 pages, revte

The Nucleon-Nucleon Potential in the 1/N_c Expansion

The nucleon-nucleon potential is analysed using the 1/N_c expansion of QCD. The NN potential is shown to have an expansion in 1/N_c^2, and the strengths of the leading order central, spin-orbit, tensor, and quadratic spin-orbit forces (including isospin dependence) are determined. Comparison with a successful phenomenological potential (Nijmegen) shows that the large-N_c analysis explains many of the qualitative features observed in the nucleon-nucleon interaction. The 1/N_c expansion implies an effective Wigner supermultiplet symmetry for light nuclei. Results for baryons containing strange quarks are presented in an appendix.Comment: 17 pages, 3 figures, TeX, macros harvmac and eps

Deep inelastic scattering as x -> 1 using soft-collinear effective theory

Soft-collinear effective theory (SCET) is used to sum Sudakov double-logarithms in the x ->1 endpoint region for the deep inelastic scattering structure function. The calculations are done in both the target rest frame and the Breit frame. The separation of scales in the effective theory implies that the anomalous dimension of the SCET current is linear in ln mu, and the anomalous dimension for the Nth moment of the structure function is linear in ln N, to all orders in perturbation theory. The SCET formulation is shown to be free of Landau pole singularities. Some important differences between the deep inelastic structure function and the shape function in B decay are discussed.Comment: 19 pages, minor typos fixed, and a comment added on the longitudinal structure functio