One-Loop Helicity Amplitudes for ttbar Production at Hadron Colliders

We present compact analytic expressions for all one-loop helicity amplitudes contributing to ttbar production at hadron colliders. Using recently developed generalised unitarity methods and a traditional Feynman based approach we produce a fast and flexible implementation.Comment: 29 pages, 5 figures, v2 typos corrected (journal version

Multi-loop Integrand Reduction with Computational Algebraic Geometry

We discuss recent progress in multi-loop integrand reduction methods. Motivated by the possibility of an automated construction of multi-loop amplitudes via generalized unitarity cuts we describe a procedure to obtain a general parameterisation of any multi-loop integrand in a renormalizable gauge theory. The method relies on computational algebraic geometry techniques such as Gr\"obner bases and primary decomposition of ideals. We present some results for two and three loop amplitudes obtained with the help of the Macaulay2 computer algebra system and the Mathematica package BasisDet.Comment: Contribution to the 15th International Workshop on advanced computing and analysis techniques (ACAT 2013), 16-21 May, Beijing, China. 8 pages, 2 figure

Multi-loop integrand reduction techniques

We review recent progress in D-dimensional integrand reduction algorithms for two loop amplitudes and give examples of their application to non-planar maximal cuts of the five-point all-plus helicity amplitude in QCD.Comment: 8 pages, Contribution to the proceedings of Loops and Legs in Quantum Field Theory, 27 April - 2 May 2014, Weimar, German

The Spectrum Characteristic of Hydrogen Bonds

It has been observed that in certain substances containing hydroxyl hydrogen the relatively narrow and intense absorption bands which ordinarily are characteristic of the O-H group appear to be absent. Since in these cases it appears very probable that the hydroxyl hydrogen is involved in the formation of the type of linkage known as the "hydrogen bond" it has been suggested that the absence of bands may be taken as a criterion for the presence of such bond (1). On the other hand the O-H fundamental band appears strongly in a number of substances containing hydroxyl groups in which the hydrogens are supposed to be engaged in linkages which Bernal and Megal prefer, in this case, to call "hydroxyl bonds" (2). These substances include ice and a number of minerals examined by Coblentz (3). These observations have left the situation somewhat unclear since they leave the question open as to whether the O-H absorption in the cases first mentioned has merely shifted to some new region where it has not been observed, or whether it has really disappeared. If the latter were true there would appear to be a considerable difference between the hydrogen linkages in the two cases

QCD corrections to the hadronic production of a heavy quark pair and a W-boson including decay correlations

We perform an analytic calculation of the one-loop amplitude for the W-boson mediated process 0 \to d u-bar Q Q-bar l-bar l, retaining the mass for the quark Q. The momentum of each of the massive quarks is expressed as the sum of two massless momenta and the corresponding heavy quark spinor is expressed as a sum of two massless spinors. Using a special choice for the heavy quark spinors we obtain analytic expressions for the one-loop amplitudes which are amenable to fast numerical evaluation. The full next-to-leading order (NLO) calculation of hadron+hadron \to W(\to e nu) b b-bar with massive b-quarks is included in the program MCFM. A comparison is performed with previous published work.Comment: 45 pages, 17 figure

Computation of multi-leg amplitudes with NJet

In these proceedings we report our progress in the development of the publicly available C++ library NJet for accurate calculations of high-multiplicity one-loop amplitudes. As a phenomenological application we present the first complete next-to-leading order (NLO) calculation of five jet cross section at hadron colliders.Comment: 8 pages, 5 figures, Contribution to the proceedings of "ACAT 2013" conference, Beijing, China, May 201

On-shelļ methods for perturbative QCD

We present new on-shell techniques for the calculation of colour ordered helicity amplitudes in QCD. We review the methods of on-shell recursion and the MHV rules before applying them to tree-level processes within the Standard Model. The MHV rules are applied to QCD corrections to Higgs amplitudes in the heavy top quark limit at tree- level, generating simple n֊point expressions for specific helicity configurations as well as developing more generally applicable recursion relations. We then generalise the on-shell recursion relations for massless QCD to include massive propagating particles and apply them to amplitudes with massive scalar particles, vector bosons and fermions. We then apply on-shell methods to compute the cut-constructible parts of 1-loop Higgs plus multi-gluon amplitudes fixing the remaining rational terms through Feynman diagrams. In all cases we find that the on-shell methods generate simpler analytic expressions than the traditional off-shell methods

Comparing efficient computation methods for massless QCD tree amplitudes: Closed Analytic Formulae versus Berends-Giele Recursion

Recent advances in our understanding of tree-level QCD amplitudes in the massless limit exploiting an effective (maximal) supersymmetry have led to the complete analytic construction of tree-amplitudes with up to four external quark-anti-quark pairs. In this work we compare the numerical efficiency of evaluating these closed analytic formulae to a numerically efficient implementation of the Berends-Giele recursion. We compare calculation times for tree-amplitudes with parton numbers ranging from 4 to 25 with no, one, two and three external quark lines. We find that the exact results are generally faster in the case of MHV and NMHV amplitudes. Starting with the NNMHV amplitudes the Berends-Giele recursion becomes more efficient. In addition to the runtime we also compared the numerical accuracy. The analytic formulae are on average more accurate than the off-shell recursion relations though both are well suited for complicated phenomenological applications. In both cases we observe a reduction in the average accuracy when phase space configurations close to singular regions are evaluated. We believe that the above findings provide valuable information to select the right method for phenomenological applications.Comment: 22 pages, 9 figures, Mathematica package GGT.m and example notebook is included in submissio

The O–H Band in the Vapors of Some Organic Acids and of Tertiary Amyl Alcohol in the Region λ9700

Absorption bands corresponding to the third harmonic of the O–H vibration have been observed in the vapors of formic, acetic, propionic and trichloracetic acids, with centers at about 10202.8, 10242, 10235 and 10250 cm^(‐1), respectively. Formic acid alone gave a band with resolvable fine structure, but this has unusual features and may be described as a hybrid. The simultaneous presence of characteristics similar to those of both "perpendicular" and "parallel" type bands of symmetrical molecules is due to the fact that the change in electric moment produced by the O–H vibration has components along two of the principal axes of the molecule. Rotational constants for the formic acid molecule have been evaluated and the moments of inertia were found to be 85.2, 74.4 and 10.81×10^(‐40) g cm^2. The structures of the organic acid molecules are discussed and a comparison is made with nitric acid. In tert‐amyl alcohol a band with single broad maximum at about 10414 cm^(‐1) was found