Introduction to parton-shower event generators

This lecture discusses the physics implemented by Monte Carlo event generators for hadron colliders. It details the construction of parton showers and the matching of parton showers to fixed-order calculations at higher orders in perturbative QCD. It also discusses approaches to merge calculations for a varying number of jets, the interface to the underlying event and hadronization.Comment: 40 pages, 12 figures. Lectures presented at TASI 201

Soft-gluon resolution scale in QCD evolution equations

QCD evolution equations can be recast in terms of parton branching processes. We present a new numerical solution of the equations. We show that this parton-branching solution can be applied to analyze infrared contributions to evolution, order-by-order in the strong coupling $\alpha_s$, as a function of the soft-gluon resolution scale parameter. We examine the cases of transverse-momentum ordering and angular ordering. We illustrate that this approach can be used to treat distributions which depend both on longitudinal and on transverse momenta.Comment: Latex, 8 pages, 4 figure

A new nonlocal thermodynamical equilibrium radiative transfer method for cool stars

Context: The solution of the nonlocal thermodynamical equilibrium (non-LTE) radiative transfer equation usually relies on stationary iterative methods, which may falsely converge in some cases. Furthermore, these methods are often unable to handle large-scale systems, such as molecular spectra emerging from, for example, cool stellar atmospheres. Aims: Our objective is to develop a new method, which aims to circumvent these problems, using nonstationary numerical techniques and taking advantage of parallel computers. Methods: The technique we develop may be seen as a generalization of the coupled escape probability method. It solves the statistical equilibrium equations in all layers of a discretized model simultaneously. The numerical scheme adopted is based on the generalized minimum residual method. Result:. The code has already been applied to the special case of the water spectrum in a red supergiant stellar atmosphere. This demonstrates the fast convergence of this method, and opens the way to a wide variety of astrophysical problems.Comment: 13 pages, 9 figure

Improving predictions for collider observables by consistently combining fixed order calculations with resummed results in perturbation theory

With the constantly increasing precision of experimental data acquired at the current collider experiments Tevatron and LHC the theoretical uncertainty on the prediction of multiparticle final states has to decrease accordingly in order to have meaningful tests of the underlying theories such as the Standard Model. A pure leading order calculation, defined in the perturbative expansion of said theory in the interaction constant, represents the classical limit to such a quantum field theory and was already found to be insufficient at past collider experiments, e.g. LEP or Hera. Such a leading order calculation can be systematically improved in various limits. If the typical scales of a process are large and the respective coupling constants are small, the inclusion of fixed-order higher-order corrections then yields quickly converging predictions with much reduced uncertainties. In certain regions of the phase space, still well within the perturbative regime of the underlying theory, a clear hierarchy of the inherent scales, however, leads to large logarithms occurring at every order in perturbation theory. In many cases these logarithms are universal and can be resummed to all orders leading to precise predictions in these limits. Multiparticle final states now exhibit both small and large scales, necessitating a description using both resummed and fixed-order results. This thesis presents the consistent combination of two such resummation schemes with fixed-order results. The main objective therefor is to identify and properly treat terms that are present in both formulations in a process and observable independent manner. In the first part the resummation scheme introduced by Yennie, Frautschi and Suura (YFS), resumming large logarithms associated with the emission of soft photons in massive Qed, is combined with fixed-order next-to-leading matrix elements. The implementation of a universal algorithm is detailed and results are studied for various precision observables in e.g. Drell-Yan production or semileptonic B meson decays. The results obtained for radiative tau and muon decays are also compared to experimental data. In the second part the resummation scheme introduced by Dokshitzer, Gribov, Lipatov, Altarelli and Parisi (DGLAP), resumming large logarithms associated with the emission of collinear partons applicable to both Qcd and Qed, is combined with fixed-order next-to-leading matrix elements. While the focus rests on its application to Qcd corrections, this combination is discussed in detail and the implementation is presented. The resulting predictions are evaluated and compared to experimental data for a multitude of processes in four different collider environments. This formulation has been further extended to accommodate real emission corrections to beyond next-to-leading order radiation otherwise described only by the DGLAP resummation. Its results are also carefully evaluated and compared to a wide range of experimental data.:1. Introduction 1.1 Event generators 1.2 The event generator Sherpa 1.3 Outline of this thesis Part I YFS resummation & fixed order calculations 2 Yennie-Frautschi-Suura resummation 2.1 Resummation of virtual photon corrections 2.2 Resummation of real emission corrections 2.3 The Yennie-Frautschi-Suura form factor 3 A process independent implementation in Sherpa 3.1 The Algorithm 3.1.1 The master formula 3.1.2 Phase space transformation 3.1.3 Mapping of momenta 3.1.4 Event generation 3.2 Higher Order Corrections 3.2.1 Approximations for real emission matrix elements 3.2.2 Real emission corrections 3.2.3 Virtual emission corrections 4 The Z lineshape and radiative lepton decay corrections 4.1 The Z lineshape 4.1.1 Radiation pattern 4.1.2 Numerical stability 4.2 Radiative lepton decays 4.3 Summary and conclusions 5 Electroweak corrections to semileptonic B decays 5.1 Tree-level decay 5.2 Next-to-leading order corrections 5.2.1 Matching of different energy regimes 5.2.2 Short-distance next-to-leading order corrections 5.2.3 Long-distance next-to-leading order corrections 5.2.4 Structure dependent terms 5.2.5 Soft-resummation and inclusive exponentiation 5.3 Methods 5.3.1 BLOR 5.3.2 Sherpa/Photons 5.3.3 PHOTOS 5.4 Results 5.4.1 Next-to-leading order corrections to decay rates 5.4.2 Next-to-leading order corrections to differential rates 5.4.3 Influence of explicit short-distance terms 5.5 Summary and conclusions Part II DGLAP resummation & fixed order calculations 6 DGLAP resummation & approximate higher order corrections 6.1 Dokshitzer-Gribov-Lipatov-Altarelli-Parisi resummation 6.1.1 The naive parton model 6.1.2 QCD corrections to the parton model 6.1.3 Factorisation and the collinear counterterm 6.1.4 The DGLAP equations 6.2 Parton evolution 6.2.1 Approximate real emission cross sections 6.2.2 Parton evolution 6.2.3 Scale choices for the running coupling 6.3 Soft emission corrections 7 The reinterpretation and automisation of the POWHEG method 7.1 Decomposition of the real-emission cross sections 7.2 Construction of a parton shower 7.3 Matrix element corrections to parton showers 7.4 The reformulation of the POWHEG method 7.4.1 Approximate NLO cross sections 7.4.2 The POWHEG method and its accuracy 7.5 The single-singularity projectors 7.6 Theoretical ambiguities 7.7 MC@NLO 7.8 Realisation of the POWHEG method in the Sherpa Monte Carlo 7.8.1 Matrix elements and subtraction terms 7.8.2 The parton shower 7.8.3 Implementation & techniques 7.8.4 Automatic identification of Born zeros 7.9 Results for processes with trivial colour structures 7.9.1 Process listing 7.9.2 Tests of internal consistency 7.9.3 Comparison with tree-level matrix-element parton-shower merging 7.9.4 Comparison with experimental data 7.9.5 Comparison with existing POWHEG 7.10 Results for processes with non-trivial colour structures 7.10.1 Comparison with experimental data 7.11 Summary and conclusions 8 MENLOPS 8.1 Improving parton showers with higher-order matrix elements 8.1.1 The POWHEG approach 8.1.2 The ME+PS approach 8.2 Merging POWHEG and ME+PS - The MENLOPS 8.3 Results 8.3.1 Merging Systematics 8.3.2 ee -> jets 8.3.3 Deep-inelastic lepton-nucleon scattering 8.3.4 Drell-Yan lepton-pair production 8.3.5 W+jets Production 8.3.6 Higgs boson production 8.3.7 W-pair+jets production 8.4 Summary and conclusions Summary Appendix A Details on the YFS resummation implementation A.1 The YFS-Form-Factor A.1.1 Special cases A.2 A.2.1 Avarage photon multiplicity A.2.2 Photon energy A.2.3 Photon angles A.2.4 Photons from multipoles A.3 Massive dipole splitting functions A.3.1 Final State Emitter, Final State Spectator A.3.2 Final State Emitter, Initial State Spectator A.3.3 Initial State Emitter, Final State Spectator B Formfactors and higher order matrix elements for semileptonic B decays B.1 Form factor models of exclusive semileptonic B meson decays B.1.1 Form factors for B -> D l nu B.1.2 Form factors for B -> pi l nu B.1.3 Form factors for B -> D0* l nu B.2 NLO matrix elements B.2.1 Real emission matrix elements B.2.2 Virtual emission matrix elements B.3 Scalar Integrals B.3.1 General definitions B.3.2 Tadpole integrals B.3.3 Bubble integrals B.3.4 Triangle integrals C Explicit form of the leading order Altarelli-Parisi splitting functions C.1 Collinear limit of real emission matrix elements C.1.1 q -> gq splittings C.1.2 q -> qg splittings C.1.3 g -> qq splittings C.1.4 g -> gg splittings Bibliograph