Role of the nonperturbative input in QCD resummed Drell-Yan QTQ_T-distributions

We analyze the role of the nonperturbative input in the Collins, Soper, and Sterman (CSS)'s $b$-space QCD resummation formalism for Drell-Yan transverse momentum ($Q_T$) distributions, and investigate the predictive power of the CSS formalism. We find that the predictive power of the CSS formalism has a strong dependence on the collision energy $\sqrt{S}$ in addition to its well-known $Q^2$ dependence, and the $\sqrt{S}$ dependence improves the predictive power at collider energies. We show that a reliable extrapolation from perturbatively resummed $b$-space distributions to the nonperturbative large $b$ region is necessary to ensure the correct $Q_T$ distributions. By adding power corrections to the renormalization group equations in the CSS formalism, we derive a new extrapolation formalism. We demonstrate that at collider energies, the CSS resummation formalism plus our extrapolation has an excellent predictive power for $W$ and $Z$ production at all transverse momenta $Q_T\le Q$. We also show that the $b$-space resummed $Q_T$ distributions provide a good description of Drell-Yan data at fixed target energies.Comment: Latex, 43 pages including 15 figures; typos were correcte

Differential Cross Section for Higgs Boson Production Including All-Orders Soft Gluon Resummation

The transverse momentum $Q_T$ distribution is computed for inclusive Higgs boson production at the energy of the CERN Large Hadron Collider. We focus on the dominant gluon-gluon subprocess in perturbative quantum chromodynamics and incorporate contributions from the quark-gluon and quark-antiquark channels. Using an impact-parameter $b$-space formalism, we include all-orders resummation of large logarithms associated with emission of soft gluons. Our resummed results merge smoothly at large $Q_T$ with the fixed-order expectations in perturbative quantum chromodynamics, as they should, with no need for a matching procedure. They show a high degree of stability with respect to variation of parameters associated with the non-perturbative input at low $Q_T$. We provide distributions $d\sigma/dy dQ_T$ for Higgs boson masses from $M_Z$ to 200 GeV. The average transverse momentum at zero rapidity $y$ grows approximately linearly with mass of the Higgs boson over the range $M_Z < m_h \simeq 0.18 m_h + 18$~GeV. We provide analogous results for $Z$ boson production, for which we compute $\simeq 25$ GeV. The harder transverse momentum distribution for the Higgs boson arises because there is more soft gluon radiation in Higgs boson production than in $Z$ production.Comment: 42 pages, latex, 26 figures. All figures replaced. Some changes in wording. Published in Phys. Rev. D67, 034026 (2003

Evolutionary trajectories in rugged fitness landscapes

We consider the evolutionary trajectories traced out by an infinite population undergoing mutation-selection dynamics in static, uncorrelated random fitness landscapes. Starting from the population that consists of a single genotype, the most populated genotype \textit{jumps} from a local fitness maximum to another and eventually reaches the global maximum. We use a strong selection limit, which reduces the dynamics beyond the first time step to the competition between independent mutant subpopulations, to study the dynamics of this model and of a simpler one-dimensional model which ignores the geometry of the sequence space. We find that the fit genotypes that appear along a trajectory are a subset of suitably defined fitness \textit{records}, and exploit several results from the record theory for non-identically distributed random variables. The genotypes that contribute to the trajectory are those records that are not \textit{bypassed} by superior records arising further away from the initial population. Several conjectures concerning the statistics of bypassing are extracted from numerical simulations. In particular, for the one-dimensional model, we propose a simple relation between the bypassing probability and the dynamic exponent which describes the scaling of the typical evolution time with genome size. The latter can be determined exactly in terms of the extremal properties of the fitness distribution.Comment: Figures in color; minor revisions in tex

Transverse Momentum Distributions for Heavy Quark Pairs

We study the transverse momentum distribution for a $pair$ of heavy quarks produced in hadron-hadron interactions. Predictions for the large transverse momentum region are based on exact order $\alpha_s^3$ QCD perturbation theory. For the small transverse momentum region, we use techniques for all orders resummation of leading logarithmic contributions associated with initial state soft gluon radiation. The combination provides the transverse momentum distribution of heavy quark pairs for all transverse momenta. Explicit results are presented for $b\bar b$ pair production at the Fermilab Tevatron collider and for $c\bar c$ pair production at fixed target energies.Comment: LaTeX (27 pages text, 8 figures not included, but available on request

New Fits for the Non-Perturbative Parameters in the CSS Resummation Formalism

We update the non-perturbative function of the Collins-Soper- Sterman resummation formalism in hadron collisions. Two functional forms in impact parameter space are considered, one with a pure Gaussian form with two parameters and the other with an additional linear term. The results for the two parameter fit are found to be g1=0.24+0.08-0.07 GeV^2, g2=0.34+0.07-0.08 GeV^2. The results for the three parameter fit are g1=0.15+004-0.03 GeV^2, g2=0.48+0.07-0.05 GeV^2, and g3=-0.58+0.26-0.20 GeV^-1. We discuss the potential for the full Tevatron Run I Z boson data for further testing of the universality of the non-perturbative function.Comment: 22 pages, 12 figures, LaTe

Statistical Mechanics of Elastica on Plane as a Model of Supercoiled DNA-Origin of the MKdV hierarchy-

In this article, I have investigated statistical mechanics of a non-stretched elastica in two dimensional space using path integral method. In the calculation, the MKdV hierarchy naturally appeared as the equations including the temperature fluctuation.I have classified the moduli of the closed elastica in heat bath and summed the Boltzmann weight with the thermalfluctuation over the moduli. Due to the bilinearity of the energy functional,I have obtained its exact partition function.By investigation of the system,I conjectured that an expectation value at a critical point of this system obeys the Painlev\'e equation of the first kind and its related equations extended by the KdV hierarchy.Furthermore I also commented onthe relation between the MKdV hierarchy and BRS transformationin this system.Comment: AMS-Tex Us

A narrative analysis of career transition themes and outcomes using chaos theory as a guiding metaphor

In a rapidly changing world of work little research exists on mid-career transitions. We investigated these using the open-systems approach of chaos theory as a guiding metaphor and conducted interviews with seven mid-career individuals chosen for their experience of a significant mid-career transition. Four common themes were identified through narrative analysis, where ‘false starts’ to a career were a common experience prior to finding a career ‘fit’. Career transitions, precipitated by a trigger state and/or event such as a period of disillusionment, were an important part of this ‘finding a fit’ process. Overall, career success outcomes were shaped by a combination of chaos elements: chance, unplanned events, and non-linearity of resultant outcomes. We discuss implications for future research and for practice

Baxterization, dynamical systems, and the symmetries of integrability

We resolve the `baxterization' problem with the help of the automorphism group of the Yang-Baxter (resp. star-triangle, tetrahedron, \dots) equations. This infinite group of symmetries is realized as a non-linear (birational) Coxeter group acting on matrices, and exists as such, {\em beyond the narrow context of strict integrability}. It yields among other things an unexpected elliptic parametrization of the non-integrable sixteen-vertex model. It provides us with a class of discrete dynamical systems, and we address some related problems, such as characterizing the complexity of iterations.Comment: 25 pages, Latex file (epsf style). WARNING: Postscript figures are BIG (600kB compressed, 4.3MB uncompressed). If necessary request hardcopy to [email protected] and give your postal mail addres

Semiclassical Mechanics of the Wigner 6j-Symbol

The semiclassical mechanics of the Wigner 6j-symbol is examined from the standpoint of WKB theory for multidimensional, integrable systems, to explore the geometrical issues surrounding the Ponzano-Regge formula. The relations among the methods of Roberts and others for deriving the Ponzano-Regge formula are discussed, and a new approach, based on the recoupling of four angular momenta, is presented. A generalization of the Yutsis-type of spin network is developed for this purpose. Special attention is devoted to symplectic reduction, the reduced phase space of the 6j-symbol (the 2-sphere of Kapovich and Millson), and the reduction of Poisson bracket expressions for semiclassical amplitudes. General principles for the semiclassical study of arbitrary spin networks are laid down; some of these were used in our recent derivation of the asymptotic formula for the Wigner 9j-symbol.Comment: 64 pages, 50 figure

Tevatron Run-1 Z Boson Data and Collins-Soper-Sterman Resummation Formalism

We examine the effect of the Z-boson transverse momentum distribution measured at the Run-1 of the Tevatron on the nonperturbative function of the Collins-Soper-Sterman (CSS) formalism, which resums large logarithmic terms from multiple soft gluon emission in hadron collisions. The inclusion of the Tevatron Run-1 Z-boson data strongly favors a Gaussian form of the CSS nonperturbative function, when combined with the other low energy Drell-Yan data in a global fit.Comment: Published version; minor modifications, three references added; 19 pages, 7 figure