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.

Exclusive vector meson production in pp collisions at the COMPASS experiment

Produktionsmechanismen für Teilchenproduktion im mittleren Energiebereich wurden in Proton-Proton Kollisionen innerhalb der COMPASS-Kollaboration mit Hilfe des COMPASS-Spektrometers am SPS Beschleuniger am CERN untersucht. Die verschiedenen Produktionsmechanismen werden mittels Produktion der Vektormesonen omega und phi studiert und können die diffraktive Anregung des Strahlteilchens mit anschliessendem Zerfall der Resonanz, zentrale Produktion und den damit verwandten “Shake-off” Mechanismus enthalten. Die für diese Arbeit verwendeten Daten wurden in den Jahren 2008 und 2009 mit 190 GeV/c-Protonen aufgenommen, die auf ein Flüssigwasserstofftarget trafen. Das Target war von einem Rückstoßprotonendetektor umgeben, der ein integraler Bestandteil des neuentwickelten Hadrontriggersystems ist. Für dieses System wurden außerdem einige neue Detektoren gebaut. Die Leistungsfähigkeit des Rückstoßprotonendetektors und des Triggersystems wird untersucht und Effizienzen extrahiert. Außerdem wird sowohl eine Methode zur Rekonstruktion von Rückstoßprotonen als auch eine Methode zur Kalibration des Rückstoßprotonendetektors entwickelt und beschrieben. Die Produktion von omega-Mesonen wurde in der Reaktion pp -> p omega p, omega -> pi+pi-pi0 und die Produktion von phi-Mesonen in der Reaktion pp -> p phi p, phi -> K+K- bei einem Impulsübertrag zwischen 0.1 (GeV/c)^2 und 1 (GeV/c)^2 gemessen. Das Produktionsverhältnis s(pp -> p phi p)/s(pp -> p omega p) wird als Funktion des longitudinalen Impulsanteils xF bestimmt und mit der Vorhersage durch die Zweigregel verglichen. Es ergibt sich eine signifikante Verletzung der Zweigregel, die abhängig von xF ist. Die Verletzung wird in Verbindung zu resonanten Strukturen im pomega-Massenspektrum diskutiert. Die xF-Abhängigkeit verschwindet, wenn man die Region niedriger pomega- und pphi-Masse entfernt, die solche resonanten Strukturen aufweist. Zusätzlich wird die Spinausrichtung bzw. das Spindichtematrixelement rho00 für omega- und phi-Mesonen untersucht. Die Spinausrichtung wird im Helizitätssystemrnanalysiert, welches für eine Abgrenzung von resonanten, diffraktiven Anregungen geeignet ist. Außerdem wird die Spinausrichtung in einem Referenzsystem mit Bezug auf die Richtung des Impulsübertrags untersucht, mit dessen Hilfe zentrale Prozesse wie zentrale Produktion oder “shake-off” abgegrenzt werden. Auch hier wird eine Abhängigkeit von xF und der invarianten Masse des pomega-Systems beobachtet. Diese Abhängigkeit kann wieder auf die resonanten Strukturen in der Produktion von omega-Mesonen zurückgeführt werden. Die Ergebnisse werden abschließend im Hinblick auf die verschiedenen Produktionsmechanismen diskutiert.

Single meson production in proton diffraction at 190 GeV/c at COMPASS

The quark model successfully describes all ground state bary-ons as members of $SU(N)$ flavour multiplets. For excited baryon states the situation is totally different. There are much less states found in the experiment than predicted in most theoretical calculations. This fact has been known for a long time as the 'missing resonance problem'. In addition, many states found in experiments are only poorly measured up to now. Therefore, further experimental efforts are needed to clarify the situation.rnrnAt mbox{COMPASS}, reactions of a $190uskgigaeVperclight$ hadron beam impinging on a liquid hydrogen target are investigated.rnThe hadron beam contains different species of particles ($pi$, $K$, $p$). To distinguish these particles, two Cherenkov detectors are used. In this thesis, a new method for the identification of particles from the detector information is developed. This method is based on statistical approaches and allows a better kaon identification efficiency with a similar purity compared to the method, which was used before.rnrnThe reaction $pprightarrow ppX$ with $X=(pi^0,~eta,~omega,~phi)$ is used to study different production mechanisms. A previous analysis of $omega$ and $phi$ mesons is extended to pseudoscalar mesons. As the resonance contributions in $peta$ are smaller than in $ppi^0$ a different behaviour of these two final states is expected as a function of kinematic variables. The investigation of these differences allows to study different production mechanisms and to estimate the size of the resonant contribution in the different channels.rnrnIn addition, the channel $pprightarrow ppX$ allows to study baryon resonances in the $pX$ system.rnIn the mbox{COMPASS} energy regime, the reaction is dominated by Pomeron exchange. As a Pomeron carries vacuum quantum numbers, no isospin is transferred between the target proton and the beam proton. Therefore, the $pX$ final state has isospin $textstylefrac{1}{2}$ and all baryon resonances in this channel are $N^ast$ baryons. This offers the opportunity to do spectroscopy without taking $Delta$ resonances into account. rnrnTo disentangle the contributions of different resonances a partial wave analysis (PWA) is used. Different resonances have different spin and parity $J^parity$, which results in different angular distributions of the decay particles. These angular distributions can be calculated from models and then be fitted to the data. From the fit the contributions of the single resonances as well as resonance parameters -- namely the mass and the width -- can be extracted. In this thesis, two different approaches for a partial wave analysis of the reaction $pprightarrow pppi^0$ are developed and tested.