Monte Carlo Event Generators

In the framework of the analysis presented here, theMC event generators PYTHIA 6.4 [33-35], HERWIG 6.5.10 [36-38], and MC NLO 3.4 [39, 40] are used to compute efficiencies, kinematic distributions, and for comparisons with the experimental results. All programs were run with their default parameter settings, except when mentioned otherwise. 

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In this chapter the theoretical concepts relevant to describe the physics of heavy quarks at the LHC are introduced. The main ideas of Quantum Chromodynamics are reviewed, before their appUcation to high-energy hadron-hadron collisions is discussed. This includes the factorization ansatz, the evolution of the parton distribution functions, the partonic processes important for beauty quark production and the phenomenological treatment of heavy quark fragmentation. A further section is dedicated to the description of the decay of -hadrons via the weak interaction. The Monte Carlo event generators which are used in this analysis to generate full hadronic events within the QCD framework are presented in the last section. 

The momentum imbalance of the partons participating in the hard interaction is reflected in the rapidity distribution of the outgoing particles. The tfansverse momentum of the outgoing partons in the center-of-mass frame of the colUding partons is denoted by pr and is of particular interest for the Monte Carlo event generators (see Sect. 3.6). 

The Boltzmann constant is represented by kB. It is more difficult to use Monte Carlo methods to investigate dynamic events as there is no intrinsic concept of time but an ensemble average over the generated states of the system should give the same equilibrium thermodynamic properties as the MD methods. A good review of both MD and the Monte Carlo methods can be found in the book by Frenkel and Smit [40]. 

Example 24 Consider as an example the set of 19 Monte Carlo generated, normally distributed values with a mean = 2.25 and a standard deviation = 1.43 used in Section 1.8.1 Table 1.24 is constructed in six steps. The experimental (observed) frequencies are compared with the theoretical (expected) number. The critical x -value for p = 0.05 and/ = 4 is 9.49, thus no difference in distribution function is detected. Note that the first and last classes extend to infinity it might even be advisable to eliminate these poorly defined classes by merging them with the neighboring ones is found as 1.6648 in this case the critical x is 5.991. Columns zi, Zr, ACP, expected events, and x are provided in program HISTO, option (Display) ... 

Performing estimation and risk analysis in the presence of uncertainty requires a method that reproduces the random nature of certain events (such as failures in the context of reliability theory). A Monte-Carlo simulation addresses this issue by running a model many times and picking values from a predefined probability distribution at each run (Mun 2006). This process allows the generation of output distributions for the variables of interest, from which several statistical measures (such as mean, variance, skewness) can be computed and analyzed. 

Simulation Approach to incorporate market forces into a decision model. A typical simulation model is Monte Carlo simulation, which employs randomly generated events to drive the model and assess outcomes. 

Within the Central Electricity Generating Board (CEGB), the "double contingency" principle is adopted in considering criticality in the CAGR fuel routes. Thus, at least two Independent low-probability events must occur before criticality can be reached. For clearances based on calculations a criterion is adopted that if one such event takes place, the cMculated Keff plus an appropriate allowance for uncertainties should be <0.95. This uncertainty allowance includes a systematic component and a random component, statistics plus data, etc., taken at the three standard deviation levels. Two computer codes are employed, the lattice code WIMS (Ref. 1) for survey work and the Monte Carlo cbcle MONK (Ref. 2) for... 

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