Cuba—a library for multidimensional numerical integration

Hahn, Thomas

doi:10.1016/j.cpc.2005.01.010

Cited by 896 publications

(804 citation statements)

References 10 publications

(12 reference statements)

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“…iHixs evaluates the contribution to the cross-section in NNLO QCD and includes important electroweak effects. A detailed description of the theoretical contributions [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] which are incorporated and accounted for in iHixs can be found in the corresponding publication [5].…”

Section: Introductionmentioning

confidence: 99%

Inclusive Higgs boson cross-section for the LHC at 8 TeV

Anastasiou

Buehler

Herzog

et al. 2012

J. High Energ. Phys.

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We present the inclusive Higgs boson cross-section at the LHC with collision energy of 8 TeV. Our predictions are obtained using our publicly available program iHixs which incorporates NNLO QCD corrections and electroweak corrections. We review the convergence of the QCD perturbative expansion at this new energy and examine the impact of finite Higgs width effects. We also study the impact of different parton distribution functions on the cross-section. We present tables with the cross-section values and estimates for their uncertainty due to uncalculated higher orders in the perturbative expansion and parton densities.

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Section: Introductionmentioning

confidence: 99%

Inclusive Higgs boson cross-section for the LHC at 8 TeV

Anastasiou

Buehler

Herzog

et al. 2012

J. High Energ. Phys.

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“…We calculated them (for q 2 = −1) using FIESTA with the Cuba [16] Vegas integrator and 1 500 000 sampling points for integration. Our results alongside with the corresponding analytical expressions (transformed to the numerical form) from [13] Here for each MI we provide our numerical result for coefficients of ε-expansion in comparison (in parentheses) with the known from [13] analiycal results (if any).…”

Section: Numerical Results For Four-loop Massless Propagatorsmentioning

confidence: 99%

Applications of FIESTA

Tentyukov¹,

Smirnov²

2011

Proceedings of 13th International Workshop on Advanced Computing and Analysis Techniques in Physics Research — PoS(ACAT2010)

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Sector decomposition in its practical aspect is a constructive method used to evaluate Feynman integrals numerically. We present a new program performing the sector decomposition and integrating the expression afterwards. The program can be also used in order to expand Feynman integrals automatically in limits of momenta and masses with the use of sector decompositions and Mellin-Barnes representations. The program is parallelizable on modern multicore computers and even on multiple computers. Also we demonstrate some new numerical results for four-loop massless propagator master integrals.

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“…The value I of (7) does not depend on ρ, but the corresponding variance of (8) does, so we may minimise the variance (8) by varying the function ρ subject to the constraint that it is correctly normalised N(ρ) ≡ dx ρ(x) = 1. Performing the required functional differentiation with the Lagrange multiplier λ…”

Section: Importance Samplingmentioning

confidence: 99%

Monte Carlo integration with subtraction

Arthur

Kennedy

2013

Computer Physics Communications

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This paper investigates a class of algorithms for numerical integration of a function in d dimensions over a compact domain by Monte Carlo methods. We construct a histogram approximation to the function using a partition of the integration domain into a set of bins specified by some parameters. We then consider two adaptations; the first is to subtract the histogram approximation, whose integral we may easily evaluate explicitly, from the function and integrate the difference using Monte Carlo; the second is to modify the bin parameters in order to make the variance of the Monte Carlo estimate of the integral the same for all bins. This allows us to use Student's t-test as a trigger for rebinning, which we claim is more stable than the χ 2 test that is commonly used for this purpose. We provide a program that we have used to study the algorithm for the case where the histogram is represented as a product of onedimensional histograms. We discuss the assumptions and approximations made, as well as giving a pedagogical discussion of the myriad ways in which the results of any such Monte Carlo integration program can be misleading.

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Cuba—a library for multidimensional numerical integration

Cited by 896 publications

References 10 publications

Inclusive Higgs boson cross-section for the LHC at 8 TeV

Inclusive Higgs boson cross-section for the LHC at 8 TeV

Applications of FIESTA

Monte Carlo integration with subtraction

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