Semi-numerical evaluation of one-loop corrections

We present a semi-numerical method to compute one-loop corrections to multi-leg processes. We apply the method to the study of Higgs plus four parton and six gluon amplitudes.We present a semi-numerical method to compute one-loop corrections to multi-leg processes. We apply the method to the study of Higgs plus four parton and six gluon amplitudes

Tensorial Reconstruction at the Integrand Level

We present a new approach to the reduction of one-loop amplitudes obtained by reconstructing the tensorial expression of the scattering amplitudes. The reconstruction is performed at the integrand level by means of a sampling in the integration momentum. There are several interesting applications of this novel method within existing techniques for the reduction of one-loop multi-leg amplitudes: to deal with numerically unstable points, such as in the vicinity of a vanishing Gram determinant; to allow for a sampling of the numerator function based on real values of the integration momentum; to optimize the numerical reduction in the case of long expressions for the numerator functions.Comment: 20 pages, 2 figure

Automation of one-loop QCD corrections

We present the complete automation of the computation of one-loop QCD corrections, including UV renormalization, to an arbitrary scattering process in the Standard Model. This is achieved by embedding the OPP integrand reduction technique, as implemented in CutTools, into the MadGraph framework. By interfacing the tool so constructed, which we dub MadLoop, with MadFKS, the fully automatic computation of any infrared-safe observable at the next-to-leading order in QCD is attained. We demonstrate the flexibility and the reach of our method by calculating the production rates for a variety of processes at the 7 TeV LHC.Comment: 64 pages, 12 figures. Corrected the value of m_Z in table 1. In table 2, corrected the values of cross sections in a.4 and a.5 (previously computed with mu=mtop/2 rather than mu=mtop/4). In table 2, corrected the values of NLO cross sections in b.3, b.6, c.3, and e.7 (the symmetry factor for a few virtual channels was incorrect). In sect. A.4.3, the labeling of the four-momenta was incorrec

On the Numerical Evaluation of Loop Integrals With Mellin-Barnes Representations

An improved method is presented for the numerical evaluation of multi-loop integrals in dimensional regularization. The technique is based on Mellin-Barnes representations, which have been used earlier to develop algorithms for the extraction of ultraviolet and infrared divergencies. The coefficients of these singularities and the non-singular part can be integrated numerically. However, the numerical integration often does not converge for diagrams with massive propagators and physical branch cuts. In this work, several steps are proposed which substantially improve the behavior of the numerical integrals. The efficacy of the method is demonstrated by calculating several two-loop examples, some of which have not been known before.Comment: 13 pp. LaTe

Conducting rigorous research with subgroups of at-risk youth: lessons learned from a teen pregnancy prevention project in Alaska

In 2010, Alaska Department of Health and Social Services (DHSS) received federal funding to test an evidence-based teen pregnancy prevention program. The grant required a major modification to an existing program and a randomized control trial (RCT) to test its effectiveness. As the major modifications, Alaska used peer educators instead of adults to deliver the program to youth aged 1419 instead of the original curriculum intended age range of 1214. Cultural and approach adaptations were included as well. After 4 years of implementation and data collection, the sample was too small to provide statistically significant results. The lack of findings gave no information about the modification, nor any explanation of how the curriculum was received, or reasons for the small sample. This paper reports on a case study follow-up to the RCT to better understand outcome and implementation results. For this study, researchers reviewed project documents and interviewed peer educators, state and local staff, and evaluators. Three themes emerged from the data: (a) the professional growth of peer educators and development of peer education, (b) difficulties resulting from curriculum content, especially for subpopulations of sexually active youth, youth identified as lesbian, gay, bisexual, transgender, queer, intersex and/or asexual, pregnant, and parenting youth and (c) the appropriateness of an RCT with subpopulations of at-risk youth. Three recommendations emerged from the case study. First, including as many stakeholders as possible in the program and evaluation design phases is essential, and must be supported by appropriate funding streams and training. Second, there must be recognition of the multiple small subpopulations found in Alaska when adapting programs designed for a larger and more homogeneous population. Third, RCTs may not be appropriate for all population subgroups.Ye

Feynman rules for the rational part of the Electroweak 1-loop amplitudes

We present the complete set of Feynman rules producing the rational terms of kind R_2 needed to perform any 1-loop calculation in the Electroweak Standard Model. Our results are given both in the 't Hooft-Veltman and in the Four Dimensional Helicity regularization schemes. We also verified, by using both the 't Hooft-Feynman gauge and the Background Field Method, a huge set of Ward identities -up to 4-points- for the complete rational part of the Electroweak amplitudes. This provides a stringent check of our results and, as a by-product, an explicit test of the gauge invariance of the Four Dimensional Helicity regularization scheme in the complete Standard Model at 1-loop. The formulae presented in this paper provide the last missing piece for completely automatizing, in the framework of the OPP method, the 1-loop calculations in the SU(3) X SU(2) X U(1) Standard Model.Comment: Many thanks to Huasheng Shao for having recomputed, independently of us, all of the ${\rm R_2}$ effective vertices. Thanks to his help and by comparing with an independent computation we performed in a general $R_\xi$ gauge, we could fix, in the present version, the following formulae: the vertex $A l \bar l$ in Eq. (3.6), the vertex $Z \phi^+ \phi^-$ in Eq. (3.8), Eqs (3.16), (3.17) and (3.18

Towards W b bbar + j at NLO with an automatized approach to one-loop computations

We present results for the O(alpha_s) virtual corrections to q g -> W b bbar q' obtained with a new automatized approach to the evaluation of one-loop amplitudes in terms of Feynman diagrams. Together with the O(alpha_s) corrections to q q' -> W b bbar g, which can be obtained from our results by crossing symmetry, this represents the bulk of the next-to-leading order virtual QCD corrections to W b bbar + j and W b + j hadronic production, calculated in a fixed-flavor scheme with four light flavors. Furthermore, these corrections represent a well defined and independent subset of the 1-loop amplitudes needed for the NNLO calculation of W b bbar. Our approach was tested against several existing results for NLO amplitudes including selected O(alpha_s) one-loop corrections to W + 3 j hadronic production. We discuss the efficiency of our method both with respect to evaluation time and numerical stability.Comment: 14 pages, 3 figure

Multivariate discrimination and the Higgs + W/Z search

A systematic method for optimizing multivariate discriminants is developed and applied to the important example of a light Higgs boson search at the Tevatron and the LHC. The Significance Improvement Characteristic (SIC), defined as the signal efficiency of a cut or multivariate discriminant divided by the square root of the background efficiency, is shown to be an extremely powerful visualization tool. SIC curves demonstrate numerical instabilities in the multivariate discriminants, show convergence as the number of variables is increased, and display the sensitivity to the optimal cut values. For our application, we concentrate on Higgs boson production in association with a W or Z boson with H -> bb and compare to the irreducible standard model background, Z/W + bb. We explore thousands of experimentally motivated, physically motivated, and unmotivated single variable discriminants. Along with the standard kinematic variables, a number of new ones, such as twist, are described which should have applicability to many processes. We find that some single variables, such as the pull angle, are weak discriminants, but when combined with others they provide important marginal improvement. We also find that multiple Higgs boson-candidate mass measures, such as from mild and aggressively trimmed jets, when combined may provide additional discriminating power. Comparing the significance improvement from our variables to those used in recent CDF and DZero searches, we find that a 10-20% improvement in significance against Z/W + bb is possible. Our analysis also suggests that the H + W/Z channel with H -> bb is also viable at the LHC, without requiring a hard cut on the W/Z transverse momentum.Comment: 41 pages, 5 tables, 29 figure

Polynomials, Riemann surfaces, and reconstructing missing-energy events

We consider the problem of reconstructing energies, momenta, and masses in collider events with missing energy, along with the complications introduced by combinatorial ambiguities and measurement errors. Typically, one reconstructs more than one value and we show how the wrong values may be correlated with the right ones. The problem has a natural formulation in terms of the theory of Riemann surfaces. We discuss examples including top quark decays in the Standard Model (relevant for top quark mass measurements and tests of spin correlation), cascade decays in models of new physics containing dark matter candidates, decays of third-generation leptoquarks in composite models of electroweak symmetry breaking, and Higgs boson decay into two tau leptons.Comment: 28 pages, 6 figures; version accepted for publication, with discussion of Higgs to tau tau deca

Efficiency improvements for the numerical computation of NLO corrections

In this paper we discuss techniques, which lead to a significant improvement of the efficiency of the Monte Carlo integration, when one-loop QCD amplitudes are calculated numerically with the help of the subtraction method and contour deformation. The techniques discussed are: holomorphic and non-holomorphic division into sub-channels, optimisation of the integration contour, improvement of the ultraviolet subtraction terms, importance sampling and antithetic variates in loop momentum space, recurrence relations.Comment: 34 pages, version to be publishe