Climate variability and climate change vulnerability and adaptation. Workshop summary

Representatives from fifteen countries met in Prague, Czech Republic, on September 11-15, 1995, to share results from the analysis of vulnerability and adaptation to global climate change. The workshop focused on the issues of global climate change and its impacts on various sectors of a national economy. The U.N. Framework Convention on Climate Change (FCCC), which has been signed by more than 150 governments worldwide, calls on signatory parties to develop and communicate measures they are implementing to respond to global climate change. An analysis of a country`s vulnerability to changes in the climate helps it identify suitable adaptation measures. These analyses are designed to determine the extent of the impacts of global climate change on sensitive sectors such as agricultural crops, forests, grasslands and livestock, water resources, and coastal areas. Once it is determined how vulnerable a country may be to climate change, it is possible to identify adaptation measures for ameliorating some or all of the effects.The objectives of the vulnerability and adaptation workshop were to: The objectives of the vulnerability and adaptation workshop were to: Provide an opportunity for countries to describe their study results; Encourage countries to learn from the experience of the more complete assessments and adjust their studies accordingly; Identify issues and analyses that require further investigation; and Summarize results and experiences for governmental and intergovernmental organizations

Amplitudes and Spinor-Helicity in Six Dimensions

The spinor-helicity formalism has become an invaluable tool for understanding the S-matrix of massless particles in four dimensions. In this paper we construct a spinor-helicity formalism in six dimensions, and apply it to derive compact expressions for the three, four and five point tree amplitudes of Yang-Mills theory. Using the KLT relations, it is a straightforward process to obtain amplitudes in linearized gravity from these Yang-Mills amplitudes; we demonstrate this by writing down the gravitational three and four point amplitudes. Because there is no conserved helicity in six dimensions, these amplitudes describe the scattering of all possible polarization states (as well as Kaluza-Klein excitations) in four dimensions upon dimensional reduction. We also briefly discuss a convenient formulation of the BCFW recursion relations in higher dimensions.Comment: 26 pages, 2 figures. Minor improvements of the discussio

Coulomb Phase Gluon Scattering at Strong Coupling

We calculate corrections to gluon scattering amplitudes in a Coulomb phase using gauge/string duality. The Coulomb phase considered is a maximal rank breaking of $SU(n_1+n_2)\to SU(n_1)\times SU(n_2) \times U(1)$. This problem therefore has 3 scales involved: 1) the scale of the massive fields $M_W$ arising from the spontaneous breaking of the gauge group; 2) The scale of the scattering, characterized by the Mandelstam variables $s,t,u$; 3) The IR regulator $m_{IR}$. We find corrections in the hard scattering limit $|s|,|t|,|u|\gg m_{IR}^2 \gg M_W^2$, and also find below threshold corrections with $M_W^2 \gg |s|,|t|,|u|$. We find that the corrections in the second case are finite, and so are IR regulator independent.Comment: 17+17 pages, 3 figure

Two-Loop g -> gg Splitting Amplitudes in QCD

Splitting amplitudes are universal functions governing the collinear behavior of scattering amplitudes for massless particles. We compute the two-loop g -> gg splitting amplitudes in QCD, N=1, and N=4 super-Yang-Mills theories, which describe the limits of two-loop n-point amplitudes where two gluon momenta become parallel. They also represent an ingredient in a direct x-space computation of DGLAP evolution kernels at next-to-next-to-leading order. To obtain the splitting amplitudes, we use the unitarity sewing method. In contrast to the usual light-cone gauge treatment, our calculation does not rely on the principal-value or Mandelstam-Leibbrandt prescriptions, even though the loop integrals contain some of the denominators typically encountered in light-cone gauge. We reduce the integrals to a set of 13 master integrals using integration-by-parts and Lorentz invariance identities. The master integrals are computed with the aid of differential equations in the splitting momentum fraction z. The epsilon-poles of the splitting amplitudes are consistent with a formula due to Catani for the infrared singularities of two-loop scattering amplitudes. This consistency essentially provides an inductive proof of Catani's formula, as well as an ansatz for previously-unknown 1/epsilon pole terms having non-trivial color structure. Finite terms in the splitting amplitudes determine the collinear behavior of finite remainders in this formula.Comment: 100 pages, 33 figures. Added remarks about leading-transcendentality argument of hep-th/0404092, and additional explanation of cut-reconstruction uniquenes

Black Hole Entropy Associated with Supersymmetric Sigma Model

By means of an identity that equates elliptic genus partition function of a supersymmetric sigma model on the $N$-fold symmetric product $S^N X$ of $X$ ($S^N X=X^N/S_N$, $S_N$ is the symmetric group of $N$ elements) to the partition function of a second quantized string theory, we derive the asymptotic expansion of the partition function as well as the asymptotic for the degeneracy of spectrum in string theory. The asymptotic expansion for the state counting reproduces the logarithmic correction to the black hole entropy.Comment: 11 pages, no figures, version to appear in the Phys. Rev. D (2003

Unweighted event generation in hadronic WZ production at order(alpha_S)

We present an algorithm for unweighted event generation in the partonic process pp -> WZ (j) with leptonic decays at next-to-leading order in alpha_S. Monte Carlo programs for processes such as this frequently generate events with negative weights in certain regions of phase space. For simulations of experimental data one would like to have unweighted events only. We demonstrate how the phase space from the matrix elements can be combined to achieve unweighted event generation using a second stage Monte Carlo integration over a volume of real emissions (jets). Observable quantities are kept fixed in the laboratory frame throughout the integration. The algorithm is applicable to a broader class of processes and is CPU intensive.Comment: 9 pages, 4 figure

Direct Extraction Of One Loop Rational Terms

We present a method for the direct extraction of rational contributions to one-loop scattering amplitudes, missed by standard four-dimensional unitarity techniques. We use generalised unitarity in D=4-2\e dimensions to write the loop amplitudes in terms of products of massive tree amplitudes. We find that the rational terms in 4-2\e dimensions can be determined from quadruple, triple and double cuts without the need for independent pentagon contributions using a massive integral basis. The additional mass-dependent integral coefficients may then be extracted from the large mass limit which can be performed analytically or numerically. We check the method by computing the rational parts of all gluon helicity amplitudes with up to six external legs. We also present a simple application to amplitudes with external massless fermions.Comment: 35 pages, 6 figures. Major revisions: new analytic results for gluon amplitudes and new section on treatment of massless fermions. References added and typos corrected. Accepted for publication in JHE

Complete Order alpha_s^3 Results for e^+ e^- to (gamma,Z) to Four Jets

We present the next-to-leading order (O(alpha_s^3)) perturbative QCD predictions for e^+e^- annihilation into four jets. A previous calculation omitted the O(alpha_s^3) terms suppressed by one or more powers of 1/N_c^2, where N_c is the number of colors, and the `light-by-glue scattering' contributions. We find that all such terms are uniformly small, constituting less than 10% of the correction. For the Durham clustering algorithm, the leading and next-to-leading logarithms in the limit of small jet resolution parameter y_{cut} can be resummed. We match the resummed results to our fixed-order calculation in order to improve the small y_{cut} prediction.Comment: Latex2e, 17 pages with 5 encapsulated figures. Note added regarding subsequent related work. To appear in Phys. Rev.

Scattering amplitudes with massive fermions using BCFW recursion

We study the QCD scattering amplitudes for \bar{q}q \to gg and \bar{q}q \to ggg where q is a massive fermion. Using a particular choice of massive fermion spinor we are able to derive very compact expressions for the partial spin amplitudes for the 2 \to 2 process. We then investigate the corresponding 2 \to 3 amplitudes using the BCFW recursion technique. For the helicity conserving partial amplitudes we again derive very compact expressions, but were unable to treat the helicity-flip amplitudes recursively, except for the case where all the gluon helicities are the same. We therefore evaluate the remaining partial amplitudes using standard Feynman diagram techniques.Comment: 21 page