Beyond Heavy Top Limit In Higgs Boson Production At LHC

QCD corrections to inclusive Higgs boson production at the LHC are evaluated at next-to-next-to leading order. By performing asymptotic expansion of the cross section near the limit of infinitely heavy top quark we obtained a few first top mass-suppressed terms. The corrections to the hadronic cross sections are found to be small compared to the scale uncertainty, thus justifying the use of heavy top quark approximation in many published results.Comment: Talk at Moriond QCD 2010 conference, La Thuile, March 13-20 201

Finite top quark mass effects in NNLO Higgs boson production at LHC

We present next-to-next-to-leading order corrections to the inclusive production of the Higgs bosons at the CERN Large Hadron Collider (LHC) including finite top quark mass effects. Expanding our analytic results for the partonic cross section around the soft limit we find agreement with a very recent publication by Harlander and Ozeren \cite{Harlander:2009mq}.Comment: 15 page

Production of scalar and pseudo-scalar Higgs bosons to next-to-next-to-leading order at hadron colliders

We consider the production of intermediate-mass CP-even and CP-odd Higgs bosons in proton-proton and proton-anti-proton collisions. We extend the recently published results for the complete next-to-next-to-leading order calculation for a scalar Higgs boson to the pseudo-scalar case and present details of the calculation that might be useful for similar future investigations. The result is based on an expansion in the limit of a heavy top quark mass and a subsequent matching to the expression obtained in the limit of infinite energy. For a Higgs boson mass of 120 GeV the deviation from the infinite-top quark mass result is small. For 300 GeV, however, the next-to-next-to-leading order corrections for a scalar Higgs boson exceed the effective-theory result by about 9% which increases to 22% in the pseudo-scalar case. Thus in this mass range the effect on the total cross section amounts to about 2% and 6%, respectively, which may be relevant in future precision studies.Comment: 29 page

O (alpha 4 s) loop-by-loop contributions to heavy quark pair production in hadronic collisions

The present state of the theoretical predictions for the hadronic heavy hadron production is not quite satisfactory. The full next-to-leading order (NLO) ${cal O} (alpha_s^3)$ corrections to the hadroproduction of heavy quarks have raised the leading order (LO) ${cal O} (alpha_s^2)$ estimates but the NLO predictions are still slightly below the experimental numbers. Moreover, the theoretical NLO predictions suffer from the usual large uncertainty resulting from the freedom in the choice of renormalization and factorization scales of perturbative QCD.In this light there are hopes that a next-to-next-to-leading order (NNLO) ${cal O} (alpha_s^4)$ calculation will bring theoretical predictions even closer to the experimental data. Also, the dependence on the factorization and renormalization scales of the physical process is expected to be greatly reduced at NNLO. This would reduce the theoretical uncertainty and therefore make the comparison between theory and experiment much more significant. In this thesis I have concentrated on that part of NNLO corrections for hadronic heavy quark production where one-loop integrals contribute in the form of a loop-by-loop product. In the first part of the thesis I use dimensional regularization to calculate the ${cal O}(ep^2)$ expansion of scalar one-loop one-, two-, three- and four-point integrals. The Laurent series of the scalar integrals is needed as an input for the calculation of the one-loop matrix elements for the loop-by-loop contributions. Since each factor of the loop-by-loop product has negative powers of the dimensional regularization parameter $ep$ up to ${cal O}(ep^{-2})$, the Laurent series of the scalar integrals has to be calculated up to ${cal O}(ep^2)$. The negative powers of $ep$ are a consequence of ultraviolet and infrared/collinear (or mass ) divergences. Among the scalar integrals the four-point integrals are the most complicated. The ${cal O}(ep^2)$ expansion of the three- and four-point integrals contains in general classical polylogarithms up to ${rm Li}_4$ and $L$-functions related to multiple polylogarithms of maximal weight and depth four. All results for the scalar integrals are also available in electronic form. In the second part of the thesis I discuss the properties of the classical polylogarithms. I present the algorithms which allow one to reduce the number of the polylogarithms in an expression. I derive identities for the $L$-functions which have been intensively used in order to reduce the length of the final results for the scalar integrals. I also discuss the properties of multiple polylogarithms. I derive identities to express the $L$-functions in terms of multiple polylogarithms. In the third part I investigate the numerical efficiency of the results for the scalar integrals. The dependence of the evaluation time on the relative error is discussed. In the forth part of the thesis I present the larger part of the ${ cal O}(ep^2)$ results on one-loop matrix elements in heavy flavor hadroproduction containing the full spin information. The ${cal O}(ep^2)$ terms arise as a combination of the ${cal O}(ep^2)$ results for the scalar integrals, the spin algebra and the Passarino-Veltman decomposition. The one-loop matrix elements will be needed as input in the determination of the loop-by-loop part of NNLO for the hadronic heavy flavor production.Der heutige Zustand der theoretischen Vorhersagen für die hadronische Produktion schwerer Hadronen ist nicht zufriedenstellend. Die vollständigen ``next-to-leading order'' (NLO) ${cal O} (alpha_s^3)$ Korrekturen zur hadronischen Produktion schwerer Quarks haben die Beiträge der führenden Ordnung (``leading order'' - LO) ${cal O} (alpha_s^2)$ etwas vergrössert, aber die NLO Vorhersagen sind immer noch etwas unterhalb der experimentellen Werte. Darüberhinaus sind die theoretischen NLO Vorhersagen ungenau, weil die Unsicherheit aus der Freiheit in der Wahl der Renormierungs- und der Faktorisierungsskalen der störungstheoretischen QCD relativ gross ist. Man hofft, dass eine ``next-next-to-leading order'' (NNLO) ${cal O} (alpha_s^4)$ Rechnung die theoretischen Vorhersagen den experimentellen Daten besser beschreibt. Auserdem erwartet man, dass die Abhängigkeit von den Faktorisierungs- und Renormierungsskalen des physikalischen Prozesses bei NNLO strark reduziert wird. Dies würde die theoretische Unsicherheit reduzieren, und dafür den Vergleich zwischen Theorie und Experiment wesentlich signifikanter machen. In dieser Arbeit habe ich mich auf den Teil der NNLO Rechnungen für hadronische Produktion schwerer Quarks konzentriert, bei der Einschleifenintegrale in der Form eines Produktes zweier Schleifen beitragen. Im ersten Teil der Arbeit benutze ich die dimensionale Regularisierung, um die Ordnung ${cal O} (alpha_s^2)$ Entwicklung der skalaren Einschleifen Ein-, Zwei-, Drei- und Vierpunktintegrale zu berechnen. Die Laurent-Reihe der skalaren Integrale wird als Input für die Berechnung der Einschleifen-Matrixelemente für die Beiträge der Schleifenprodukte benötigt. Weil jeder Faktor dieser Schleifenprodukte negative Potenzen des dimensionalen Regularisierungsparametres $ep$ bis zu ${cal O} (ep^{-2})$ besitzt, muss die Laurent-Reihe für die skalaren Integrale bis zu ${cal O} (ep^2 )$ berechnet werden. Die negativen Potenzen von $ep$ sind eine Konsequenz von Ultraviolett- und Infrarot-/ kollinearen (oder Massen-) Divergenzen. Unter den skalaren Integralen sind die Vierpunktintegrale die kompliziertesten. Die ${cal O} (ep^2 )$ Entwicklung der Drei- und Vierpunktintegrale enthält im allgemeinen klassische Polylogarithmen bis $Li_{4}$, und $L$- Funktionen, die mit multiplen Polylogarithmen von maximal Gewicht und Tiefe vier zusammenhängen. Alle Ergebnisse für die skalaren Integrale sind in elektronischer Form verfügbar. Im zweiten Teil dieser Arbeit diskutiere ich die Eigenschaften der klassischen Polylogarithmen. Ich präsentiere Algorithmen, welche es erlauben, die Anzahl der Polylogarithmen in einem algebraischen Ausdrück zu reduzieren.Ich leite Identitäten f"ur die $L$-Funktionen ab, die häufig in der Arbeit verwendet wurden, um die Länge der Endergebnisse für die skalaren Integrale zu reduzieren. Dar"uberhinaus diskutiere ich die Eigenschaften der multiplen Polylogarithmen. Ich leite Identitäten her, um die $L$-Funktionen durch multiple Polylogarithmen auszudrücken. In dritten Teil untersuche ich die numerische Effizienz der Ergebnisse für die skalaren Integrale. Die Abhängigkeit der Rechenzeit vom relativen Fehler wird diskutiert. Im vierten Teil dieser Arbeit präsentiere ich den grösseren Teil der ${cal O} (ep^2)$ Ergebnisse für Einschleifen-Matrixelemente zur hadronischen Produktion schwerer Quarks einschliesslich der vollständigen Spininformation. Die ${cal O} (ep^2)$ Terme treten als Kombination der ${cal O} (ep^2)$ Ergebnisse für die skalaren Integrale, der Spinalgebra und der Passarino-Veltman Zerlegung auf. Die Einschleifen-Matrixelemente werden als Input in der Bestimmung des Schleifenproduktanteils von NNLO für die hadronische Produktion schwerer Quarks benötigt

Health-status outcomes with invasive or conservative care in coronary disease

BACKGROUND In the ISCHEMIA trial, an invasive strategy with angiographic assessment and revascularization did not reduce clinical events among patients with stable ischemic heart disease and moderate or severe ischemia. A secondary objective of the trial was to assess angina-related health status among these patients. METHODS We assessed angina-related symptoms, function, and quality of life with the Seattle Angina Questionnaire (SAQ) at randomization, at months 1.5, 3, and 6, and every 6 months thereafter in participants who had been randomly assigned to an invasive treatment strategy (2295 participants) or a conservative strategy (2322). Mixed-effects cumulative probability models within a Bayesian framework were used to estimate differences between the treatment groups. The primary outcome of this health-status analysis was the SAQ summary score (scores range from 0 to 100, with higher scores indicating better health status). All analyses were performed in the overall population and according to baseline angina frequency. RESULTS At baseline, 35% of patients reported having no angina in the previous month. SAQ summary scores increased in both treatment groups, with increases at 3, 12, and 36 months that were 4.1 points (95% credible interval, 3.2 to 5.0), 4.2 points (95% credible interval, 3.3 to 5.1), and 2.9 points (95% credible interval, 2.2 to 3.7) higher with the invasive strategy than with the conservative strategy. Differences were larger among participants who had more frequent angina at baseline (8.5 vs. 0.1 points at 3 months and 5.3 vs. 1.2 points at 36 months among participants with daily or weekly angina as compared with no angina). CONCLUSIONS In the overall trial population with moderate or severe ischemia, which included 35% of participants without angina at baseline, patients randomly assigned to the invasive strategy had greater improvement in angina-related health status than those assigned to the conservative strategy. The modest mean differences favoring the invasive strategy in the overall group reflected minimal differences among asymptomatic patients and larger differences among patients who had had angina at baseline

Initial invasive or conservative strategy for stable coronary disease

BACKGROUND Among patients with stable coronary disease and moderate or severe ischemia, whether clinical outcomes are better in those who receive an invasive intervention plus medical therapy than in those who receive medical therapy alone is uncertain. METHODS We randomly assigned 5179 patients with moderate or severe ischemia to an initial invasive strategy (angiography and revascularization when feasible) and medical therapy or to an initial conservative strategy of medical therapy alone and angiography if medical therapy failed. The primary outcome was a composite of death from cardiovascular causes, myocardial infarction, or hospitalization for unstable angina, heart failure, or resuscitated cardiac arrest. A key secondary outcome was death from cardiovascular causes or myocardial infarction. RESULTS Over a median of 3.2 years, 318 primary outcome events occurred in the invasive-strategy group and 352 occurred in the conservative-strategy group. At 6 months, the cumulative event rate was 5.3% in the invasive-strategy group and 3.4% in the conservative-strategy group (difference, 1.9 percentage points; 95% confidence interval [CI], 0.8 to 3.0); at 5 years, the cumulative event rate was 16.4% and 18.2%, respectively (difference, 121.8 percentage points; 95% CI, 124.7 to 1.0). Results were similar with respect to the key secondary outcome. The incidence of the primary outcome was sensitive to the definition of myocardial infarction; a secondary analysis yielded more procedural myocardial infarctions of uncertain clinical importance. There were 145 deaths in the invasive-strategy group and 144 deaths in the conservative-strategy group (hazard ratio, 1.05; 95% CI, 0.83 to 1.32). CONCLUSIONS Among patients with stable coronary disease and moderate or severe ischemia, we did not find evidence that an initial invasive strategy, as compared with an initial conservative strategy, reduced the risk of ischemic cardiovascular events or death from any cause over a median of 3.2 years. The trial findings were sensitive to the definition of myocardial infarction that was used