Backgrounds for Fast Simulation Collider Studies at GeV
Various proposals for a new collider operating below 1 TeV are now under consideration by the worlwide High Energy Physics community. Among these are the International Linear Collider and the Circular Electron Positron Collider. We describe high statistics Standard Model background simulation samples generated with MG5_aMC@NLO for collider studies at GeV. Fast detector simulation is performed with Delphes and DSiD, the detector card for the SiD detector. The samples are compared with other simulation samples generated with Whizard.
With the discovery of the Standard Model (SM) Higgs boson at the Large Hadron Collider (LHC) [1, 2], the case for a new collider for precision Higgs measurements is strong [3, 4, 5]. The clean environment, where the initial state is well known and can be used to enhance final state measurements, contrasts with the more challenging environment at the LHC. The case is made even stronger by the potential for top quark measurements, which until now have only been made at hadron colliders. Possible new physics below 1 TeV makes the collider case even stronger.
Two proposals, with somewhat complementary energy regimes, have been made for an collider sited in Asia. The International Linear Collider (ILC) baseline design  calls for a linear machine with GeV sited in Japan. The Circular Electron Positron Collider (CEPC) baseline design  calls for a circular machine with GeV sited in China.
Full simulation studies with comprehensive collider backgrounds have been made for SM Higgs boson, top quark and new physics scenarios. But the background samples are in many cases statistically limited by the computing demands of full detector simulation, motivating fast detector simulation. The Delphes fast detector simulator [8, 9, 10, 11], which has been used extensively for LHC studies, is a generic detector simulation suitable for use in studies which uses tcl text files to describe a particular detector’s performance.
In this study we use MG5_aMC@NLO 2.3.3  to generate and processes for and GeV. At each separate backgrounds are produced for two beam polarization configurations, and . At GeV additional backgrounds are produced with unpolarized beams. For the polarized beam samples, the integrated luminosities are approximately five times the projected target luminosities of the current ILC run scenarios. For the unpolarized beam samples at GeV, the integrated luminosity is five times a GigaZ production, while for GeV the integrated luminosity matches the statistics of the polarized beam samples. For validation, the polarized MG5_aMC@NLO samples are compared with the samples generated with Whizard  for the ILC Detailed Baseline Design (DBD) study .
Fast detector simulation is performed on both the MG5_aMC@NLO samples and DBD Whizard samples using Delphes and the DSiD detector card . DSiD is modeled on the full simulation performance of the SiD detector as described in  and is available on HepForge  at dsid.hepforge.org. SiD was designed as a detector for the ILC, but it has also recently been proposed as a detector for CEPC .
|[GeV]||G-20 ()/()||H-20 ()/()||I-20 ()/()|
2 Operating Scenarios
The run program for an collider must be optimized for the set of measurements which various center-of-mass energies, beam polarizations, and integrated luminosities can provide. This can only be done when the physics landscape below 1 TeV is illuminated by the LHC, but assuming that mostly SM particles will be produced at lower energies and any possible BSM particles will be produced at higher energies, a first optimization can be made.
Precision boson studies motivate running at the pole. Precision SM Higgs boson measurements motivate running scenarios for GeV, near the maximum cross section for production, while precision top quark measurements motivate running scenarios for GeV, just above threshold for . In both cases background from can be greatly reduced by colliding righthanded electrons with lefthanded positrons () since -channel production only occurs in interactions of lefthanded electrons with righthanded positrons (). At higher center-of-mass energies like GeV, BSM physics motivates a more democratic luminosity sharing between beam polarizations. For many BSM scenario signals background from is not problematic, and the precision measurement of the chiral structure of new couplings argues for equal luminosity sharing of beam polarization configurations.
The physics goals for the CEPC, precision Higgs and boson studies, motivate lower energies ( GeV). For the ILC, precision top quark and new physics studies motivate higher energies. The report issued by the ILC Parameters Joint Working Group  identifies three operating scenarios based on these and other considerations: G-20, H-20 and I-20. All three scenarios envision a 20 year lifetime of the collider with one luminosity upgrade.
G-20, motivated more by new physics than SM measurements, envisions most datataking at higher . H-20 and I-20 envision considerably more dataking at lower than G-20. In the H-20 scenario most lower energy datataking occurs at GeV, enhancing the precision of SM Higgs measurements, while in I-20 most low energy datataking occurs at GeV. In G-20 the beam polarization configuration is democratic, while in H-20 and I-20 the configuration is preferred over by a ratio 3:1. For the ILC at GeV, 10% of luminosity is reserved in all three scenarios for and beam configurations, while 20% is reserved for these configurations at GeV.
The proposed luminosity sharing (in ab) between beam configurations and for the three scenarios is shown in Table 1. In Table 1 and hereafter, is denoted while is denoted 111This notation differs from , where the handedness precedes the handedness, ie and vice versa.. Throughout this note, the ILC nominal 80% electron and 30% positron polarization is assumed.
3 Standard Model Processes
SM backgrounds and their cross section at colliders have been discussed in [19, 20] and elsewhere. SM background processes for any collider can be classified by center of mass energy, beam polarization and initial and final states.
Inital states include and , where the in an initial state originates from bremstrahlung. The final states are categorized by the number of fermions (1, 2, 3, 4, etc.) after boson decay. See Table 2 for SM background typology and Figure 1 for the SM background process cross section as a function of for unpolarized beams.
The SM background simulation for the CEPC run scenario have been described in detail , where event generation is performed with Whizard with detailed ISR and bremstrahlung simulated with GuineaPig . For the ILC run scenarios, SM background simulation has been described in detail in . For full simulation benchmark studies for DBD study, SM background samples with integrated luminosities of 250fb were generated for each , , GeV with Whizard 1.40 using Pythia6  for showering and hadronization and saved in StdHEP format . The samples were generated with 100% lefthanded or righthanded electrons and positrons, from which new mixed samples were made assuming 30% positron beam polarization and 80% electron beam polarization.
All SM background processes are included in the DBD samples. Beam conditions and backgrounds specific to ILC design parameters and bunch structure were generated with GuineaPig and passed to Whizard, including detailed beamstrahlung and bremstrahlung processes with the resulting beam energy distribution. In addition to the processes in Table 2, the DBD samples also include pileup from bunch-bunch interactions: to hadronic mini-jets and other low hadrons, as well as low beam-induced pairs. Both the CEPC and ILC DBD samples include interference effects. Whizard includes all diagrams producing the same final states through distinct intermediate particles and therefore includes the interference between these diagrams. For example, some final states can be produced either by or intermediate states. When specifying the fermion final states Whizard includes their interference. In order to avoid divergent cross sections, kinematic cuts are imposed on the DBD Whizard samples during generation. The invariant mass of a pair of colored particles is required to be at least 10 GeV, while for a pair of colorless particles it is required to be at least 4 GeV. The minimum for q massless t-channel process is required to be 4 GeV.
Events in the DBD samples are weighted. Since some processes have prohibitively large cross sections, these events have large weights in order to reach the target integrated luminosity. Some signal processes of interest are weighted with small weights in order to provide a high statistics sample for study. Mean event weights of order are due mostly to processes with weight 12.5, processes with weight 125 and the process with weight 12,500. See Table 3 for the DBD samples used to compare with the backgrounds described in this note.222For more details and the DBD Whizard StdHEP files and logfiles see https://confluence.slac.stanford.edu/ display/ilc/Standard+Model+Data+Samples.
4 Generation and Simulation
The background samples in this study were generated with MG5_aMC@NLO 2.3.3  with showering and hadronization by Pythia6 libraries implemented in the pythia-pgs package. While MG5_aMC@NLO can calculate higher order corrections, only leading order samples were generated. Polarized samples for and GeV are generated with electron polarization fixed to 80% and positron polarization fixed to 30%. Additional samples at GeV are generated with unpolarized beams. For a summary of the background MG5_aMC@NLO samples see Tables 6,5,7,8.
Rather than specifiying multiple fermion final states, as was done for the DBD samples, intermediate top pair, diboson and triboson states are specified in MG5_aMC@NLO, which are then decayed with Pythia6 to all-fermion final states. Interference effects between the same fermion final states with distinct intermediate states is therefore not included, though MG5_aMC@NLO is capable of doing this. Fermion pair, diboson and triboson () states from initial states are generated with MG5_aMC@NLO, specifiying beam type 0 (no PDF) for both electron and positron. Inelastic Compton scattering processes () with final states are generated by specifiying beam type 0 for the electron or positron (no PDF) and beam type 3 (photon PDF from electron beam) for the photon. In the latter case MG5_aMC@NLO uses the effective photon approximation to simulate the Weizsacker-Williams photons generated by bremstrahlung. Finally, the () processes are simulated by specifiying beam type 3 for both electron and positron, using the effective photon approximation for both photons.
|[GeV]||Pol.||Process||[pb] CEPC||[pb] MG5|
|[GeV]||Pol.||Process||[pb] ILC||[pb] MG5|
For each generated process with polarized beams, we generate a number of events whose equivalent luminosity is approximately five times the most optimistic operating scenario of scenarios G-20, H-20 and I-20, namely 10ab for each beam polarization at GeV, 6.75ab for polarization at and 2.25ab for polarization at . For each process with unpolarized beams at GeV the luminosity is chosen to match the statistics of the polarized beam samples, and at GeV the luminosity is chosen to be five times a GigaZ production, or ab.
In order to ensure that the process cross section converges, the event particles enter the effective detector radius, and to speed production, in some samples kinematic cuts have been applied to generator particles. In , and processes, a photon requirement GeV is imposed. In the and samples requirements GeV and GeV are imposed. Finally, in the and samples a requirement GeV and keV, respectively, are imposed.
We perform fast detector simulation with both the MG5_aMC@NLO samples and the DBD samples using Delphes3 and the DSiD detector card. The DSiD detector card is modeled on the full simulation performance of the SiD detector. The detector object efficiencies, fake rates and resolutions specified in the DSiD detector card can be reproduced in complex event environments as demonstrated in the validation documentation .
5 Background Analysis
We emphasize that in this study both the DBD and MG5 samples are submitted to fast detector simulation with Delphes using the same DSiD card. Any difference between their distributions in the Delphes files cannot therefore be due to detector effects. The differences in generation between the DBD and CEPC samples and the MG5/DSiD samples described here, already discussed above, are here made explicit:
beamstrahlung is not included in the MG5/DSiD samples; the beam energy distribution is idealized
interference in distinct fermion final states between different intermediate bosonic states is included in the DBD and CEPC samples but is not in the MG5/DSiD samples
some MG5/DSiD samples include generator cuts on event particle to control divergent cross sections and ensure the particles enter the detector, while the DBD and CEPC samples include cuts on fermion pair invariant mass
all MG5/DSiD sample events are unweighted () so the samples should be scaled by cross section to the desired luminosity, while the DBD samples are weighted () to achieve a target luminosity
Any background analysis which uses these samples should account for differences and assign any necessary uncertainties.
For illustration, we perform the following background studies. For each we perform an analysis of the Delphes files with Root 5.34, exploiting multicore capability with Proof. At GeV we reconstruct the SM Higgs in using the recoil technique with . The selection requires two oppositely charged, acollinear () muons with GeV, GeV and invariant mass GeV. See Figure 3 for the GeV reconstructed mass distributions.
For GeV we reconstruct top pair events with in which one decays leptonically and the other decays hadronically. The signal selection requires exactly one lepton with GeV, missing transverse energy GeV, at least four jets with GeV exactly two of which must be -tagged. The hadronic is reconstructed from the two leading untagged jets while the leptonic is reconstructed from the lepton and the missing energy. To reconstruct the top quarks, each -jet is assigned to the reconstructed which maximizes the since the top quarks are produced near threshold. For the GeV sample we reconstruct top pair events exactly as for GeV except that -jets are assigned to the which minimizes . See Figure 3 for the GeV reconstructed mass distributions, where in both cases the distributions are normalized to the DBD cross sections in Table 4.
Systematic and statistical uncertainties on the yields can be evaluated as follows. Reduction in cross section due to beam energy loss can be estimated from Table 4 to be 10% and 25%, respectively, for the Higgs recoil and top pair analyses. Moreover, the recoil mass is smeared by the beam energy distribution if radiative losses are not recovered. Interference between intermediate states affects both the Higgs recoil (intermediate and states with final state) and top pair analyses (intermediate and states with states). For the Higgs recoil analysis, the cross sections for polarization () are calculated by MG5_aMC@NLO to b 8.4fb for , 453.9fb for and 462.4fb for including interference. The relative uncertainty is therefore below 1%, the reported generator uncertainty. For the top pair analysis the effect is negligible compared to the uncertainty introduced by beam energy distribution. Since background from and events with GeV, as well as events with GeV, avoid the generator level requirements at GeV, some background is neglected. Because events at GeV are generated without kinematic constraints, any omitted top pair background is negligible. The statistical uncertainty on the yields are computed straightforwardly and scale as . Comparing with a DBD sample with integrated luminosity ab and event weight , the improvement in statistical uncertainty is approximately . For events with large weights , the improvement factor is approximately .
We have described the production of fast simulation background samples for new physics studies at a future collider like the ILC or CEPC. Events are generated for a variety of run scenarios with approximately five times the integrated luminosity envisaged by the most optimistic run scenario for each . The events are generated with MG5_aMC@NLO with detector simulation performed by Delphes using the DSiD detector card. Finally, the samples are compared to the ILC background samples made for the DBD study and CEPC background samples.
Systematic uncertainties associated with the MG5_aMC@NLO samples have been estimated. These samples lack a detailed simulation of initial state radiation and beamstrahlung. The background from radiative return events is absent, and both pileup from bunch-bunch interactions and a realistic beam energy distribution are absent. Nevertheless, these shortcomings can be ameliorated. Moreover, the MG5/DSiD samples compare favorably to the DBD and CEPC in statistical uncertainty due to the large integrated luminosities and unweighted events in the MG5/DSiD samples.
The author thanks Jan Strube and Tomohiko Tanabe for feedback on an early draft of this paper, the Alder Institute for High Energy Physics for financial support, and the HKUST Institute for Advanced Study Program on High Energy Physics 2017 for travel support.
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