This document describes the novel techniques used to simulate the common Snowmass 2013 Energy Frontier Standard Model backgrounds for future hadron colliders. The purpose of many Energy Frontier studies is to explore the reach of high luminosity data
sets at a variety of high energy colliders. The generation of high statistics samples which accurately model large integrated luminosities for multiple center-of-mass energies and pile-up environments is not possible using an unweighted event generation strategy -- an approach which relies on event weighting was necessary. Even with these improvements in efficiency, extensive computing resources were required. This document describes the specific approach to event generation using Madgraph5 to produce parton-level processes, followed by parton showering and hadronization with Pythia6, and pile-up and detector simulation with Delphes3. The majority of Standard Model processes for pp interactions at $sqrt(s)$ = 14, 33, and 100 TeV with 0, 50, and 140 additional pile-up interactions are publicly available.
In this work we present the implementation of generators for W and Z bosons in association with two jets interfaced to parton showers using the POWHEG BOX. We incorporate matrix elements from the parton-level Monte Carlo program MCFM in the POWHEG BO
X, allowing for a considerable improvement in speed compared to previous implementations. We address certain problems that arise when processes that are singular at the Born level are implemented in a shower framework using either a generation cut or a Born suppression factor to yield weighted events. In such a case, events with very large weights can be generated after the shower through a number of mechanisms. Events with very small transverse momentum at the Born level can develop large transverse momentum either after the hardest emission, after the shower, or after the inclusion of multi-parton interactions. We present a solution to this problem that can be easily implemented in the POWHEG BOX. We also show that a full solution to this problem can only be achieved if the generator maintains physical validity also when the transverse momentum of the emitted partons becomes unresolved. One such scheme is the recently-proposed MiNLO method for the choice of scale and the exponentiation of Sudakov form factors in NLO computations. We present a validation study of our generators, by comparing their output to available LHC data.
We perform an analytic calculation of the one-loop amplitude for the W-boson mediated process 0 to d u-bar Q Q-bar l-bar l, retaining the mass for the quark Q. The momentum of each of the massive quarks is expressed as the sum of two massless momenta
and the corresponding heavy quark spinor is expressed as a sum of two massless spinors. Using a special choice for the heavy quark spinors we obtain analytic expressions for the one-loop amplitudes which are amenable to fast numerical evaluation. The full next-to-leading order (NLO) calculation of hadron+hadron to W(to e nu) b b-bar with massive b-quarks is included in the program MCFM. A comparison is performed with previous published work.
By integrating a series provided by Knopp, a series representation of the Euler-Mascheroni constant arises. The infinite sum representation of {gamma} is determined through Fourier series (sawtooth wave).
