NLO differential distributions of massive lepton-pair production in longitudinally polarized proton-proton collisions

We present the full next-to-leading order (NLO) corrected inclusive cross section $d^3\Delta \sigma/dQ^2/dy/dp_T$ for massive lepton pair production in longitudinally polarized proton-proton collisions $p + p\to l^+l^- + 'X'$. Here $'X'$ denotes any inclusive hadronic state and Q represents the invariant mass of the lepton pair which has transverse momentum p_T and rapidity y. All QCD partonic subprocesses have been included provided the lepton pair is created by a virtual photon, which is a valid approximation for $Q<50{\rm GeV}$. Like in unpolarized proton-proton scattering the dominant subprocess is given by $q(\bar q) + g \to \gamma^* + 'X'$ so that massive lepton pair production provides us with an excellent method to measure the spin density of the gluon. Our calculations are carried out using the method of n-dimensional regularization by making a special choice for the $\gamma_5$-matrix. Like in the case of many other prescriptions evanescent counter terms appear. They are determined by computing the NLO coefficient functions for $d\Delta\sigma/dQ^2$ and the polarized cross section for Higgs production using both n-dimensional regularization and a four dimensional regularization technique in which the $\gamma_5$-matrix is uniquely defined. Our calculations reveal that the non-singlet polarized coefficient function equals the unpolarized one up to a minus sign. We give predictions for double longitudinal spin asymmetry measurements at the RHIC.Comment: 56 pages, LaTeX, 20 postscript figures. We have changed the discussion of the various regularization schemes in the penultimate paragraph of section 1 and in the text between Eq. (2.17) and Eq. (2.18). Furthermore a more careful comparison between our results and those in refs. [13],[14] for the quark-anti-quark channel reveals that we have full agreement. Further some misprints like the ones occuring in Eq. (2.61) and table 1 in section 4 are correcte

Phase transitions in geometrothermodynamics

Using the formalism of geometrothermodynamics, we investigate the geometric properties of the equilibrium manifold for diverse thermodynamic systems. Starting from Legendre invariant metrics of the phase manifold, we derive thermodynamic metrics for the equilibrium manifold whose curvature becomes singular at those points where phase transitions of first and second order occur. We conclude that the thermodynamic curvature of the equilibrium manifold, as defined in geometrothermodynamics, can be used as a measure of thermodynamic interaction in diverse systems with two and three thermodynamic degrees of freedom

Nonconstant electronic density of states tunneling inversion for A15 superconductors: Nb3Sn

We re-examine the tunneling data on A15 superconductors by performing a generalized McMillan-Rowell tunneling inversion that incorporates a nonconstant electronic density of states obtained from band-structure calculations. For Nb3Sn, we find that the fit to the experimental data can be slightly improved by taking into account the sharp structure in the density of states, but it is likely that such an analysis alone is not enough to completely explain the superconducting tunneling characteristics of this material. Nevertheless, the extracted Eliashberg function displays a number of features expected to be present for the highest quality Nb3Sn samples.Comment: 11 pages, 11 figure

Geometrothermodynamics of black holes

The thermodynamics of black holes is reformulated within the context of the recently developed formalism of geometrothermodynamics. This reformulation is shown to be invariant with respect to Legendre transformations, and to allow several equivalent representations. Legendre invariance allows us to explain a series of contradictory results known in the literature from the use of Weinhold's and Ruppeiner's thermodynamic metrics for black holes. For the Reissner-Nordstr\"om black hole the geometry of the space of equilibrium states is curved, showing a non trivial thermodynamic interaction, and the curvature contains information about critical points and phase transitions. On the contrary, for the Kerr black hole the geometry is flat and does not explain its phase transition structure.Comment: Revised version, to be published in Gen.Rel.Grav.(Mashhoon's Festschrift

Poisson-Lie group of pseudodifferential symbols

We introduce a Lie bialgebra structure on the central extension of the Lie algebra of differential operators on the line and the circle (with scalar or matrix coefficients). This defines a Poisson--Lie structure on the dual group of pseudodifferential symbols of an arbitrary real (or complex) order. We show that the usual (second) Benney, KdV (or GL_n--Adler--Gelfand--Dickey) and KP Poisson structures are naturally realized as restrictions of this Poisson structure to submanifolds of this ``universal'' Poisson--Lie group. Moreover, the reduced (=SL_n) versions of these manifolds (W_n-algebras in physical terminology) can be viewed as subspaces of the quotient (or Poisson reduction) of this Poisson--Lie group by the dressing action of the group of functions. Finally, we define an infinite set of functions in involution on the Poisson--Lie group that give the standard families of Hamiltonians when restricted to the submanifolds mentioned above. The Poisson structure and Hamiltonians on the whole group interpolate between the Poisson structures and Hamiltonians of Benney, KP and KdV flows. We also discuss the geometrical meaning of W_\infty as a limit of Poisson algebras W_\epsilon as \epsilon goes to 0.Comment: 64 pages, no figure

Numerical convergence of the block-maxima approach to the Generalized Extreme Value distribution

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme Value Theory. We pursue these investigations by giving analytical expressions of Extreme Value distribution parameters for maps that have an absolutely continuous invariant measure. We compare these analytical results with numerical experiments in which we study the convergence to limiting distributions using the so called block-maxima approach, pointing out in which cases we obtain robust estimation of parameters. In regular maps for which mixing properties do not hold, we show that the fitting procedure to the classical Extreme Value Distribution fails, as expected. However, we obtain an empirical distribution that can be explained starting from a different observable function for which Nicolis et al. [2006] have found analytical results.Comment: 34 pages, 7 figures; Journal of Statistical Physics 201

Recoil and Threshold Corrections in Short-distance Cross Sections

We identify and resum corrections associated with the kinematic recoil of the hard scattering against soft-gluon emission in single-particle inclusive cross sections. The method avoids double counting and conserves the flow of partonic energy. It reproduces threshold resummation for high-p_T single-particle cross sections, when recoil is neglected, and Q_T-resummation at low Q_T, when higher-order threshold logarithms are suppressed. We exhibit explicit resummed cross sections, accurate to next-to-leading logarithm, for electroweak annihilation and prompt photon inclusive cross sections.Comment: minor modifications of the text, some references added. 51 pages, LaTeX, 6 figures as eps file

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

Energetic particle influence on the Earth's atmosphere

This manuscript gives an up-to-date and comprehensive overview of the effects of energetic particle precipitation (EPP) onto the whole atmosphere, from the lower thermosphere/mesosphere through the stratosphere and troposphere, to the surface. The paper summarizes the different sources and energies of particles, principally galactic cosmic rays (GCRs), solar energetic particles (SEPs) and energetic electron precipitation (EEP). All the proposed mechanisms by which EPP can affect the atmosphere are discussed, including chemical changes in the upper atmosphere and lower thermosphere, chemistry-dynamics feedbacks, the global electric circuit and cloud formation. The role of energetic particles in Earth’s atmosphere is a multi-disciplinary problem that requires expertise from a range of scientific backgrounds. To assist with this synergy, summary tables are provided, which are intended to evaluate the level of current knowledge of the effects of energetic particles on processes in the entire atmosphere