Matching next-to-leading-order QCD calculations with shower Monte Carlo Simulations: single vector boson and higgs boson productions in powheg

In the past years, next-to-leading order (NLO) QCD computations have become standard tools for phenomenological studies at lepton and hadron colliders. On the experimental side, instead, general purpose Shower Monte Carlo (SMC) programs have become the main tools used in the analysis. These programs perform a resummation of all order leading logarithmic contributions in soft and collinear approximation. The whole process is thus represented as a parton shower, in which subsequent emissions are strongly ordered. Being fully exclusive, it is easy to interface them with phenomenological hadronization models, enabling the comparison with experimental data. However, they do not enforce NLO accuracy. In view of increasing precision required to disentangle signals from backgrounds, at present and future colliders, it has become clear that SMC programs should be improved, when possible, with NLO results. In this way a large amount of the acquired knowledge on QCD corrections would be made directly available to the experimentalists, in a flexible form that they could easily use for simulations. The problem of merging NLO calculations with parton shower simulations is basically that of avoiding overcounting, since the SMC programs already implement approximate NLO corrections. Several proposals have appeared in the literature during past years to overcome this problem. However, the first general solution to the overcounting was the MC@NLO proposal. The basic idea of MC@NLO is that of avoiding the overcounting by subtracting from the exact NLO cross section its approximation, as implemented in the SMC program to which the NLO computation is then matched. Such approximated cross section is computed analytically, and is SMC dependent. On the other hand, the MC subtraction terms are process-independent, and thus, for a given SMC, can be computed once and for all. In the current version of the MC@NLO code, the MC subtraction terms have been computed for the HERWIG SMC. In turns out, however, that in general, the exact NLO cross section minus the MC subtraction terms does not need to be positive. Therefore MC@NLO can generate events with negative weights. For the processes implemented so far, negative-weighted events may reach about 10--15% of the total. More recently, a method, named POWHEG (Positive Weight Hardest Emission Generator), was proposed that overcomes the problem of negative weighted events, and that is not SMC specific. In the POWHEG method the hardest radiation is generated first, with a technique that yields only positive-weighted events using the exact NLO matrix elements. The POWHEG output can then be interfaced to any SMC program that is either pt-ordered, or allows the implementation of a pt veto. The POWHEG method has been successfully tested in several production processes, both at leptonic and hadronic colliders. Among these we list: $ZZ$, $Q\bar{Q}$ hadroproduction, $ q\bar{q}$ and top pairs production and decay from $e^+e^-$ annihilation, Drell-Yan vector boson production, $W'$ production, Higgs boson production via gluon fusion, Higgs boson production associated with a vector boson (Higgs-strahlung) and single top, both in the $s$- and $t$-channel production mechanism. Detailed comparisons have been carried out between the POWHEG and MCatNLO results, and reasonable agreement has been found, which nicely confirms the validity of both approaches. In the present work we give a detailed description of the POWHEG method and an overview of two specific applications: single vector boson and Higgs boson production via gluon fusion. We first present the features of a general subtraction scheme. Then, we illustrate in detail two such schemes, which we adopted in calculations appearing in this thesis: the Catani and Seymour (CS) and the Frixione, Kunszt and Signer (FKS) one. Next we concentrate on the application of the POWHEG method to the process of single vector boson production, where, in the POWHEG framework, the Catani-Seymour subtraction approach was employed for the first time. We also introduced a generalization of the method in order to deal with vanishing Born cross sections, as in the case of $W^\pm$ production. Matrix elements were evaluated from scratch using helicity amplitude methods, including finite width effects, $Z/\gamma$ interference and angular correlations of decay products. Our program has been interfaced both with HERWIG and with PYTHIA, two of the most popular Shower Monte Carlo used in simulations. Results were found in remarkable agreement both with Tevatron data and with the MC@NLO program. We also discuss results at the LHC collider. Higgs boson production via gluon fusion process is then presented, with applications to both Tevatron and LHC colliders. Gluon fusion is the predominant Higgs boson production channel over a wide range of masses. Matrix elements were evaluated analytically and regularized according to the FKS subtraction formalism. In this case, results show agreement with MC@NLO distributions up to next-to-next-to-leading order (NNLO) contributions. However, we fully understand the origin of these discrepancies and show that the POWHEG framework allows enough flexibility to get rid of them, if it is needed. Our results were also checked against NNLO and $q_T$ resummed available calculations, giving expected results.