Two loop integrals and QCD scattering

We present the techniques for the calculation of one- and two-loop integrals contributing to the virtual corrections to 2→2 scattering of massless particles. First, tensor integrals are related to scalar integrals with extra powers of propagators and higher dimension using the Schwinger representation. Integration By Parts and Lorentz Invariance recurrence relations reduce the number of independent scalar integrals to a set of master integrals for which their expansion in є = 2 — D/2 is calculated using a combination of Feynman parameters, the Negative Dimension Integration Method, the Differential Equations Method, and Mellin-Barnes integral representations. The two-loop matrix-elements for light-quark scattering are calculated in Conventional Dimensional Regularisation by direct evaluation of the Feynman diagrams. The ultraviolet divergences are removed by renormalising with the MS scheme. Finally, the infrared singular behavior is shown to be in agreement with the one anticipated by the application of Catani's formalism for the infrared divergences of generic QCD two-loop amplitudes

Mixed QCD-electroweak corrections to Higgs boson production in gluon fusion

We compute the 3-loop O(\alpha \alpha_s) correction to the Higgs boson production cross section arising from light quarks using an effective theory approach. Our calculation probes the factorization of QCD and electroweak perturbative corrections to this process. We combine our results with the best current estimates for contributions from top and bottom quarks to derive an updated theoretical prediction for the Higgs boson production cross section in gluon fusion. With the use of the MSTW 2008 parton distribution functions that include the newest experimental data, our study results in cross sections approximately 4-6% lower for intermediate Higgs boson masses than those used in recent Tevatron analyses that imposed a 95% confidence level exclusion limit of a Standard Model Higgs boson with M_H=170 GeV.Comment: 16 pgs., 5 figs. References and discussion added. Numerical results updated to use recent MSTW 2008 PDFs, which decrease the predicted Tevatron cross sectio

The gluon-fusion uncertainty in Higgs coupling extractions

We point out that the QCD corrections to the gluon-fusion Higgs boson production cross section at the LHC are very similar to the corrections to the Higgs decay rate into two gluons. Consequently, the ratio of these two quantities has a theoretical uncertainty smaller than the uncertainty in the cross section alone by a factor of two. We note that since this ratio is the theoretical input to analyses of Higgs coupling extractions at the LHC, the reduced uncertainty should be used; in previous studies, the full cross section uncertainty was employed.Comment: 4 pages, 3 figure

Higgs boson production at hadron colliders: differential cross sections through next-to-next-to-leading order

We present a calculation of the fully differential cross section for Higgs boson production in the gluon fusion channel through next-to-next-to-leading order in perturbative QCD. We apply the method introduced in \cite{Anastasiou:2003gr} to compute double real emission corrections. Our calculation permits arbitrary cuts on the final state in the reaction $hh \to H + X$. It can be easily extended to include decays of the Higgs boson into observable final states. In this Letter, we discuss the most important features of the calculation, and present some examples of physical applications that illustrate the range of observables that can be studied using our result. We compute the NNLO rapidity distribution of the Higgs boson, and also calculate the NNLO rapidity distribution with a veto on jet activity.Comment: 4 pgs, 2 figs; references adde

One-loop QCD contributions to differential cross-sections for Higgs production at N3^3LO

We present one-loop contributions to the fully differential Higgs boson gluon-fusion cross-section for Higgs production via gluon fusion. Our results constitute a necessary ingredient of a complete N$^3$LO determination of the cross-section. We perform our computation using a subtraction method for the treatment of soft and collinear singularities. We identify the infrared divergent parts in terms of universal splitting and eikonal functions, and demonstrate how phase-space integrations yield poles (up to $1/\epsilon^6$ ) in the dimensional regulator $\epsilon=(4-d)/2$. We compute the coefficients of the $\epsilon$ expansion, including the finite part numerically. As a demonstration of our numerical implementation, we present the corrections at N$^3$LO due to one-loop amplitudes in the rapidity and transverse momentum of the Higgs boson.Comment: 25 pages, 2 figure

Removing infrared divergences from two-loop integrals

Feynman amplitudes at higher orders in perturbation theory generically have complex singular structures. Notwithstanding the emergence of many powerful new methods, the presence of infrared divergences poses significant challenges for their evaluation. In this article, we develop a systematic method for the removal of the infrared singularities, by adding appropriate counterterms that approximate and cancel divergent limits point-by-point at the level of the integrand. We provide a proof of concept for our method by applying it to master-integrals that are found in scattering amplitudes for representative two-to-two scattering processes of massless particles. We demonstrate that, after the introduction of counterterms, the remainder is finite in four dimensions. In addition, we find in these cases that the complete singular dependence of the integrals can be obtained simply by analytically integrating the counterterms. Finally, we observe that our subtraction method can be also useful in order to extract in a simple way the asymptotic behavior of Feynman amplitudes in the limit of small mass parameters.Comment: 53 pages, 13 figure

Dilepton rapidity distribution in the Drell-Yan process at NNLO in QCD

We compute the rapidity distribution of the virtual photon produced in the Drell-Yan process through next-to-next-to-leading order in perturbative QCD. We introduce a powerful new method for calculating differential distributions in hard scattering processes. This method is based upon a generalization of the optical theorem; it allows the integration-by-parts technology developed for multi-loop diagrams to be applied to non-inclusive phase-space integrals, and permits a high degree of automation. We apply our results to the analysis of fixed target experiments.Comment: 5 pages, revte

Light Quark Mediated Higgs Boson Threshold Production in the Next-to-Leading Logarithmic Approximation

We study the amplitude of the Higgs boson production in gluon fusion mediated by a light quark loop and evaluate the logarithmically enhanced radiative corrections to the next-to-leading logarithmic approximation which sums up the terms of the form $\alpha_s^n\ln^{2n-1}(m_H/m_q)$ to all orders in the strong coupling constant. This result is used for the calculation of the process cross section near the production threshold and gives a quantitative estimate of the three and four-loop bottom quark contribution to the Higgs boson production at the Large Hadron Collider.Comment: 25 pages, 6 figure

The one-loop gluon amplitude for heavy-quark production at NNLO

We compute the one-loop QCD amplitude for the process gg-->Q\bar{Q} in dimensional regularization through order \epsilon^2 in the dimensional regulator and for arbitrary quark mass values. This result is an ingredient of the NNLO cross-section for heavy quark production at hadron colliders. The calculation is performed in conventional dimensional regularization, using well known reduction techniques as well as a method based on recent ideas for the functional form of one-loop integrands in four dimensions.Comment: 27 pages, 3 figure