Heavy-Quark Form Factors and Threshold Cross Section at O(\alpha_S^2)

During the last year, analytic expressions for the two-loop QCD corrections to the form factors for the vector, axial-vector, scalar and pseudo-scalar vertices involving a pair of heavy quarks, $Q \bar{Q}$, were calculated. The results are valid for arbitrary momentum transfer and mass of the heavy quarks. These form factors have a number of applications, including anomalous couplings, the $e^{+}e^{-} \to Q \bar Q$ cross section, and the forward-backward asymmetry of heavy quarks. Here the $Q {\bar Q}$ threshold cross section is presented with some new second order axial vector contributions.Comment: 5 pages. Presented at the International Europhysics Conference on High Energy Physics (HEP2005), July 21-27 2005, Lisboa, Portuga

Compasion of CVaR and markowitz approaches to formation of investment porfolios

The aim of research is formation of efficient frontiers of CVaR and Mean-Variance optimal portfolios. As a result, CVaR and Mean-Variance efficient frontiers were formed, graphs of dependencies risk vs yield, and yield vs CVaR were plotted

Two-Loop QCD Corrections to the Heavy Quark Form Factors: Axial Vector Contributions

We consider the Z Q Qbar vertex to second order in the QCD coupling for an on-shell massive quark-antiquark pair and for arbitrary momentum transfer of the Z boson. We present closed analytic expressions for the two parity-violating form factors of that vertex at the two-loop level in QCD, excluding the contributions from triangle diagrams. These form factors are expressed in terms of 1-dimensional harmonic polylogarithms of maximum weight 4.Comment: 57 pages, 5 figures. All the results in Section 6 of the paper are available in an electronic form in the file formulas.in

Decays of Scalar and Pseudoscalar Higgs Bosons into Fermions: Two-loop QCD Corrections to the Higgs-Quark-Antiquark Amplitude

As a first step in the aim of arriving at a differential description of neutral Higgs boson decays into heavy quarks, $h \to Q {\bar Q}X$, to second order in the QCD coupling $\alpha_S$, we have computed the $hQ{\bar Q}$ amplitude at the two-loop level in QCD for a general neutral Higgs boson which has both scalar and pseudoscalar couplings to quarks. This amplitude is given in terms of a scalar and a pseudoscalar vertex form factor, for which we present closed analytic expressions in terms of one-dimensional harmonic polylogarithms of maximum weight 4. The results hold for arbitrary four-momentum squared, $q^2$, of the Higgs boson and of the heavy quark mass, $m$. Moreover we derive the approximate expressions of these form factors near threshold and in the asymptotic regime $m^2/q^2 \ll 1$.Comment: 56 pages, 2 figure

Two-Loop QCD Corrections to the Heavy Quark Form Factors: Anomaly Contributions

We present closed analytic expressions for the order $\alpha_s^2$ triangle diagram contributions to the matrix elements of the singlet and non-singlet axial vector currents between the vacuum and a quark-antiquark state. We have calculated these vertex functions for arbitrary momentum transfer and for four different sets of internal and external quark masses. We show that both the singlet and non-singlet vertex functions satisfy the correct chiral Ward identities. Using the exact expressions for the finite axial vector form factors, we check the quality and the convergence of expansions at production threshold and for asymptotic energies.Comment: 24 pages, 6 figure

Two-Parton Contribution to the Heavy-Quark Forward-Backward Asymmetry in NNLO QCD

Forward-backward asymmetries, $A_{FB}^Q$, are important observables for the determination of the neutral-current couplings of heavy quarks in inclusive heavy quark production, $e^+ e^- \to \gamma^*, Z^* \to Q +X$. In view of the measurement perspectives on $A_{FB}^Q$ at a future linear collider, precise predictions of $A_{FB}^Q$ are required for massive quarks. We compute the contribution of the $Q \bar Q$ final state to $A_{FB}^Q$ to order \as^2 in the QCD coupling. We provide general formulae, and we show that this contribution to $A_{FB}^Q$ is infrared-finite. We evaluate these two-parton contributions for $b$ and $c$ quarks on and near the $Z$ resonance, and for $t$ quarks above threshold. Moreover, near the $t \bar t$ threshold we obtain, by expanding in the heavy-quark velocity $\beta$, an expression for $A_{FB}^{t \bar t}$ to order \as^2 and NNLL in $\beta$. This quantity is equal, to this order in $\beta$, to the complete forward-backward asymmetry $A_{FB}^t$.Comment: latex, 26 pages, 2 tables, 17 figure

Two-loop QCD Corrections to the Heavy Quark Form Factors: the Vector Contributions

We present closed analytic expressions of the electromagnetic vertex form factors for heavy quarks at the two-loop level in QCD for arbitrary momentum transfer. The calculation is carried out in dimensional regularization. The electric and magnetic form factors are expressed in terms of 1-dimensional harmonic polylogarithms of maximum weight 4.Comment: 79 pages, 3 figures. Version accepted by Nucl. Phys. B. All the results in Section 6 of the paper are available in an electronic form in the file formulas.in

Winter respiratory C losses provide explanatory power for net ecosystem productivity

Accurate predictions of net ecosystem productivity (NEPc) of forest ecosystems are essential for climate change decisions and requirements in the context of national forest growth and greenhouse gas inventories. However, drivers and underlying mechanisms determining NEPc (e.g., climate and nutrients) are not entirely understood yet, particularly when considering the influence of past periods. Here we explored the explanatory power of the compensation day (cDOY)defined as the day of year when winter net carbon losses are compensated by spring assimilationfor NEPc in 26 forests in Europe, North America, and Australia, using different NEPc integration methods. We found cDOY to be a particularly powerful predictor for NEPc of temperate evergreen needleleaf forests (R-2=0.58) and deciduous broadleaf forests (R-2=0.68). In general, the latest cDOY correlated with the lowest NEPc. The explanatory power of cDOY depended on the integration method for NEPc, forest type, and whether the site had a distinct winter net respiratory carbon loss or not. The integration methods starting in autumn led to better predictions of NEPc from cDOY then the classical calendar method starting 1 January. Limited explanatory power of cDOY for NEPc was found for warmer sites with no distinct winter respiratory loss period. Our findings highlight the importance of the influence of winter processes and the delayed responses of previous seasons' climatic conditions on current year's NEPc. Such carry-over effects may contain information from climatic conditions, carbon storage levels, and hydraulic traits of several years back in time.Peer reviewe

Atmospheric deposition, CO2, and change in the land carbon sink

Concentrations of atmospheric carbon dioxide (CO2) have continued to increase whereas atmospheric deposition of sulphur and nitrogen has declined in Europe and the USA during recent decades. Using time series of flux observations from 23 forests distributed throughout Europe and the USA, and generalised mixed models, we found that forest-level net ecosystem production and gross primary production have increased by 1% annually from 1995 to 2011. Statistical models indicated that increasing atmospheric CO2 was the most important factor driving the increasing strength of carbon sinks in these forests. We also found that the reduction of sulphur deposition in Europe and the USA lead to higher recovery in ecosystem respiration than in gross primary production, thus limiting the increase of carbon sequestration. By contrast, trends in climate and nitrogen deposition did not significantly contribute to changing carbon fluxes during the studied period. Our findings support the hypothesis of a general CO2-fertilization effect on vegetation growth and suggest that, so far unknown, sulphur deposition plays a significant role in the carbon balance of forests in industrialized regions. Our results show the need to include the effects of changing atmospheric composition, beyond CO2, to assess future dynamics of carbon-climate feedbacks not currently considered in earth system/climate modelling.Peer reviewe