A DELPHES card for the CLIC detector
Emilia Leogrande Philipp Roloff Ulrike Schnoor Matthias Weber












§ DELPHES FOR FAST SIMULATION OF DETECTOR EFFECTS AT CLIC

The detector model for CLIC, CLICdet, has been defined and
described in <cit.> and its performance is discussed in detail in <cit.>.
Full simulation collision events can be obtained by running
the simulation and reconstruction chain on hadron-level Monte Carlo events generated e.g. with Whizard <cit.> and Pythia6 <cit.>.
Such a full detector simulation is performed for signal and background events for most of the studies carried out in the
framework of the CLICdp collaboration,
e.g. <cit.>.
 In order to optimise the design of the detector and to understand fully its impact on the proposed physics programme, the full detector simulation and event reconstruction framework is essential. However, for many studies including some of those of an exploratory nature or where the relative sensitivity to physics parameters is paramount, a faster simulation tool is extremely useful.



The fast simulation framework  <cit.> is a
modular system  which emulates the impact that the full detector simulation will  have on hadron-level simulation of collision events.  These include the  effects of detector geometry, detector
response and resolution as well as reconstruction performance of
physics objects.
It can be used to approximate those kinematic distributions for which the detector effects are well described by a parametrisation.
The simulation with requires much less CPU time
than a full detector simulation which models the interactions of particles with the material of the detector.
According to the specific detector, an input parameter card must
be provided.
This document describes the parameter card developed for the CLICdet
detector model.
It has been used for several studies carried out in the framework of the recent report on the CLIC potential for new physics <cit.>.

A generic layout of a general-purpose detector for particle collider experiments is
implemented in , of which some geometry parameters can be modified according
to the given detector model.
In addition, the performance of identification and reconstruction based on
certain objects and particle types can be defined in the detector
card.
The geometry and performance parameters inserted into the CLICdet card are described in Sec. <ref>.
The order in which detector effects are applied to generator level objects is described in Sec. <ref>.
Until recently, has been used predominantly for studies at hadron colliders, in
particular the LHC.
Jet clustering at colliders offers additional features which have been implemented into the framework in the context
of the development of the parameter card.
This is described in Sec. <ref>.
Sec. <ref> describes the validation of the card, comparing its results for important physics processes with full detector simulation. Additional validation plots can be found in Appendix <ref>.
The parameter card has been merged into the central repository
and can be accessed at <cit.>.
User instructions are given in Appendix <ref>.





§ PERFORMANCE PARAMETERS OF THE CLICDET DETECTOR



 §.§ The CLICdet detector



The current detector model for CLIC, CLICdet, is adapted to the high-energy collision environment at
CLIC and optimised for particle flow reconstruction.
The CLICdet concept was developed based on the lessons learned from
the previous detector models for CLIC: CLIC_ILD and CLIC_SiD <cit.>.




The CLICdet model comprises a low-mass silicon vertex and
tracking system with a central barrel and forward disks.
CLICdet is optimised for particle flow in particular by using highly
granular calorimetry based on
silicon-tungsten electromagnetic calorimeters and scintillator-steel
hadronic calorimeters.
A superconducting solenoid surrounding the calorimeters provides a
magnetic field of 4 T.
Beyond the solenoid, an iron yoke is interleaved with muon chambers.
In the forward region, close to the beam pipe, CLICdet contains
two specialised forward electromagnetic calorimeters to measure
luminosity and beam properties as well as to extend the acceptance.


The two previous models differ from CLICdet in the following main
aspects<cit.>:
The CLIC_SiD concept uses a 5 T magnetic field and a smaller radius
tracking system.
CLIC_ILD uses a TPC as tracking system.
In both cases, tungsten is used as absorber in the barrel of the hadronic calorimeter.
While the CLIC card is based on the CLICdet performance, some
of the validation studies for which no CLICdet simulation was available
are based on one of the previous detector concepts.



The right-handed coordinate system has its origin at the centre of the detector,
the z axis along the detector axis close to the beam direction, and the y axis pointing
upwards.
While most studies of  collisions employ the polar angle
θ coordinate, defined with respect to the positive z
axis, this note mainly uses the pseudorapidity as it is the standard for 
.
The pseudorapidity η is defined as η = -
ln[tan(θ/2)] and the distance Δ R in the
pseudorapidity-azimuth plane is defined as Δ R = √(Δη^2 + Δϕ^2).


Under the baseline staging scenario, CLIC is expected to deliver 1 ab^-1 of luminosity at √(s) = 380 GeV,
2.5 ab^-1 at √(s) = 1.5 TeV, and 5 ab^-1 at
√(s) = 3 TeV <cit.>.
The luminosity will be shared evenly between an electron beam
polarisation of P()=-80 % and +80 % at the first stage. At
the higher energy stages, 80 % (20 %) of the luminosity will be collected
with P()=-80 % (P()=+80 %).






 §.§ Performance parameters for the card

The performance of CLICdet has  been thoroughly evaluated using full detector simulation in <cit.>.
The detector geometry of CLICdet for the full simulation is implemented within
the framework <cit.> and simulated in
Geant4 <cit.>.
The reconstruction software is implemented in the Linear Collider
framework MARLIN <cit.>.
Track reconstruction is performed with the Conformal Tracking method <cit.>.
Based on the reconstructed tracks and calorimeter deposits, particle
flow clustering is performed using PandoraPFA
<cit.>.
Flavour tagging is applied using the LCFIPlus package <cit.>.


Three cards for the three energy stages of CLIC are provided in .
Performance parameters for the CLICdet cards are taken from studies for CLICdet described and referenced in the following.






  §.§.§ Track reconstruction performance

The tracking efficiency is based on studies of the conformal tracking algorithm in <cit.>.
Charged hadron efficiencies are based on the results for pions.
Efficiencies for muon tracks, electron tracks, and charged hadron
tracks are provided as a function of energy and pseudorapidity.
In addition, the momentum resolution from tracking is applied
according to a log-normal distribution with the resolution
given as Δ/ = a ⊕
b/(p sinθ) binned in pseudorapidity.
The parameters used in the CLICdet cards are derived from <cit.>.





  §.§.§ Calorimeter performance

takes into account the granularity of the calorimeter in terms of pseudorapidity and azimuthal angle.
Based on the geometry of the calorimeters  described in <cit.>, the Δη and Δϕ segmentations implemented in the CLICdet cards are listed in Table <ref>.





The energy resolution in the calorimeters is implemented in the
cards in terms of  absolute value,  Δ E = √( n^2 + s^2 E + c^2 E^2)
  with noise term n, stochastic term s, and constant term c.
In the CLICdet cards, separate resolution parameters are provided for the inner barrel, barrel, transition region and endcaps based on the results from <cit.>.
The resolution from neutral kaons is used for the HCAL, while the ECAL
resolution is determined from photons.



  §.§.§ Isolated leptons and photons

  Electron, photon, and muon candidates are selected from Particle
    Flow objects.
  Identification efficiencies are then applied to mimic the behavior
  found in full
  simulation <cit.>,
  which includes the effects of track reconstruction and particle flow analysis:
  for electrons with E>3 GeV, muons with E>2 GeV, and photons
  with E>2 GeV, the identification efficiencies are given as a function of energy and pseudo­rapidity <cit.>.

  
The isolation of an electron, muon or photon is determined according to the jet content
in a cone of Δ R =0.1 surrounding the object.
It is considered as isolated if the ratio of the transverse
momentum sum of the cone to the transverse momentum of the isolated object does not exceed 0.2.
These settings are adapted from isolation criteria used in various full-simulation studies with CLIC detector concepts, e.g. <cit.>.




  §.§.§ Heavy flavour tagging

Three working points for tagging of b jets with efficiencies of
50 %, 70 %, and 90 % are provided in the CLICdet cards.
 The corresponding mis-tagging efficiencies for light flavour and
 charm jets are
 extracted from the double spiral option of the vertex endcaps in <cit.> in bins of pseudorapidity and energy.

The c-tagging performance of CLICdet described
in <cit.> has not been implemented yet in the CLICdet cards.
 
 

  §.§.§ Tau lepton tagging

 The τ tagging efficiencies for the CLIC TauFinder algorithm have
 been studied in <cit.>.
 The CLICdet cards
 use efficiencies averaged for the three processes studied there,
 resulting in the efficiencies reported in
 Table <ref>.
 Jets are tagged as τ jets according to these efficiencies, using
 a mis-identification rate of 3 %.
 As the TauFinder uses a relatively simple, cut-based approach it is
 expected that its performance can be significantly improved with
 respect to these numbers by introducing a multivariate analysis.
 


 §.§ Effect of beam-induced backgrounds

The high bunch charge density at CLIC leads to strong radiation from the
incoming beams due to their interaction with the field of the other
beam.
This results in beam-induced background processes, e.g. .
To account for its effects, a jet energy smearing is applied.
It should be noted that the current implementation of the jet energy
smearing assumes massless jets.

In the reconstruction, timing information of the energy deposits in
the detector is used to reduce the impact
of the background. At the 380 GeV energy
stage, this allows almost complete mitigation of the effect <cit.>.
At the higher energy stages, some impact remains despite the timing cuts.
It is mimicked by applying an additional smearing of the jet energy.
The impact of background on the jet energy resolution depends on the
centre-of-mass energy, being  most
severe at √(s) = 3 TeV at CLIC. Therefore,  separate cards are supplied for
the three stages of CLIC, as given in Appendix <ref>.
For the energy stage at √(s)≈ 380 GeV, denoted as Stage
1, no jet energy
smearing is applied.
The jet energy is smeared according to the corresponding resolutions at Stages 2
(√(s)≈ 1.5 TeV) and 3 (√(s)≈ 3 TeV).






§ FAST SIMULATION AND RECONSTRUCTION



 §.§ Application chain

The various components (modules) are called in the CLICdet card in the following order:
Particles are propagated through the magnetic field of 4 T with the  module.
In the next step, charged hadrons, electrons, and muons are retained or rejected based on random numbers drawn according to the tracking efficiencies.
Their momenta are then smeared according to the corresponding momentum resolutions.
The tracking efficiencies as well as the momentum resolutions are
given as a function of pseudorapidity and transverse momentum, see Sec. <ref>.
Energy deposits in the electromagnetic and hadronic calorimeters are then generated from the given expected energy fractions, taking into account the granularity of the calorimeter towers and the resolutions described in Sec. <ref>.
A particle flow algorithm is applied to the tracks and calorimeter deposits using the  module.
Next, photon, charged hadron, electron, and muon reconstruction efficiencies and isolation efficiencies are applied according to Sec. <ref>.
To prepare for the jet clustering, isolated electrons, muons, and
photons are removed from the list of objects passed to the jet finder
using an  module.
Jet clustering with the VLC algorithm is applied to the remaining objects as described in Sec. <ref>.
In the CLICdet cards for the higher energy stages (Stages 2 and 3, √(s)>1 TeV), the effect of background is mimicked by applying a  module (see Sec. <ref>).
Finally, the ,  and  modules are run to first find the true flavour of the jet and then to apply tagging efficiencies as well as mis-tagging efficiencies for b-jets and hadronic τ candidates. Three working points for b tagging with tagging efficiencies of 50 %, 70 %, and 90 % are provided in bins of pseudorapidity and energy (Sec. <ref>). Tagging efficiencies for hadronic τs are provided in bins of transverse momentum (Sec. <ref>).





 §.§ Linear collider jet clustering

Due to the lower levels of background at lepton colliders,
rather large cone size parameters R can be used for jet clustering compared to typical values
at hadron colliders, leading to better
mass resolutions for hadronic resonances. 

 However, using larger R implies that the jets can have a substructure of smaller R jets. At analysis level, this is usually crucial information, e.g. for suppression of backgrounds with a  different jet multiplicity or in order to use the correct objects for invariant masses. 
 Therefore, jet clustering is often run in "exclusive mode" <cit.> as implemented in Fastjet <cit.>, with a fixed number of jets. This forces the algorithm to stop when a certain number of jets has been clustered, thus revealing the substructure information directly.
 

A suitable jet clustering algorithm for high-energy lepton collisions is the Valencia Linear Collider (VLC) algorithm <cit.>. It is a sequential recombination algorithm adapted to the linear collider environment.

The VLC algorithm as implemented in
FastJet-contribs <cit.>, the functionalities  for
exclusive jet clustering, and the related observables have been added
to the framework as part of this work.
In the CLICdet cards, the VLC is applied with β = γ = 1.0 and for all combinations of R = 0.5, 0.7, 1.0, 1.2,1.5 and exclusive number of jets N=2,3,4,5,6 in order to accommodate a range of jet multiplicities that might be useful for the analyses conducted with these cards.
A large value of R should be chosen  for the first centre-of-mass
stage of CLIC and slightly smaller R for higher centre-of-mass due
to higher levels of beam-induced background.





§ VALIDATION OF THE SIMULATION

The performance of the cards is validated for the three energy stages of CLIC separately by comparing various kinematic observables in important physics processes obtained with the corresponding CLICdet card with full simulation based on the CLIC_ILD, CLIC_SiD, and CLICdet models.

Studies in the CDR <cit.> use the CLIC_ILD and CLIC_SiD models.
Therefore, large event samples are available for these models and hence part of the validation uses CLIC_ILD or CLIC_SiD detector simulation.
The performance of these detector models is similar to that of
CLICdet for the relevant aspects.

The validation is based on the  processes summarised in
Table <ref>.
For each of the samples, the CLICdet card corresponding to the CLIC
energy stage has been used, i.e.  for Stage  the card named .






 §.§ Higgsstrahlung with hadronic Z decay at 350 GeV

The process →(→) (→incl.) is
evaluated at √(s)=350 GeV. This is an important process for the
CLIC physics programme as the model-independent measurement of Higgs
properties relies on it.
It allows  the performance of the CLICdet card to be validated for jets at
low energy and with low levels of beam-induced background.
For the validation, observables obtained by running with the
CLICdet card of the first stage are compared with full detector simulation for CLICdet, version CLIC_o3_v14.
In both cases, the same generator level events produced with
Whizard interfaced to Pythia6 for the parton shower
and hadronisation are used.
Jets from VLC with N = 4, R = 1 and β=γ=1 are used unless noted otherwise.



  Jet observables are shown in Fig. <ref>.
  Good agreement at the level of better than 5 % is found for
  central jets over most of the transverse momentum range above 10 GeV. Up to
  10 % disagreement is found in the forward region 1.5 <
  |η|<2.5. Larger disagreements exist only at low transverse momentum
  p_T<10 GeV and high transverse momentum p_T> 150 GeV.



  
  
Jet resolution threshold observables obtained from the exclusive clustering mode are shown in Fig. <ref>.
The variable y_23 (y_34) is the distance measure associated with
merging from 3 to 2 (4 to 3) jets <cit.>.
They are well-modelled apart from a slight
shift to higher values for .


  



  The Higgsstrahlung process is further analysed by choosing the
  configuration of two jets with an invariant mass closest to the mass
  of the Z boson, m_, among the possible combinations obtained by
  clustering the event with 2, 3, and 5 jets exclusively.
  Fig. <ref> shows the good agreement of the di-jet
  invariant mass for Z jets (left) and the recoil mass (right)
  between full simulation and .
   Systematic differences mostly below 10 % are seen in the low tail of the invariant
   mass distribution and in the slopes of the recoil mass.
Additional kinematic distributions can be found in Appendix <ref>.


  

 §.§ Semi-leptonic top-quark pairs associated with a Higgs boson at 1.4 TeV

  The process →  with semi-leptonic decay of the
   pair and Higgs decays to  at 1.4 TeV collision energy is simulated with the
  CLIC_SiD detector model <cit.>, including the beam-induced
  background from .
  Jet clustering is performed with the VLC algorithm with R = 1.0
  and N = 6.
  This process allows validation of the performance of leptons and jets,
  including the effect of beam-induced background.
  
  
  
  
  
  
  In the full simulation analysis, optimised isolation criteria are used
  which give good performance down to low momenta.
  A cut on the transverse momentum of electrons and muons requiring at
  least 20 GeV selects the region where the cone-based isolation with
  a transverse momentum ratio cut as implemented in is
  applicable.
  The performance of the CLICdet card for electrons is
  demonstrated in Fig. <ref>.  
  Good agreement can be seen in the transverse momentum of the electron,
  Fig. <ref> (left), with the distribution
  shifted to smaller values of transverse momentum.
  Fig. <ref> (right) shows the pseudorapidity
  distribution, which is well-modelled. 
 The performance of the fast simulation for muons and jets is
 presented in Appendix <ref>. 
   


 §.§ Di-boson production WW at 3 TeV

The performance of fast simulation for muons and jets is validated
using the process →ℓν at 3 TeV.
Jet clustering is performed with the VLC algorithm using R = 0.7 and
N = 2. Beam induced background is overlayed in the full
    simulation, and its effects are taken into account in the fast simulation.
Figure <ref> demonstrates the validation of the muon
simulation.
The transverse momentum  and
pseudorapidity are in agreement
between full and fast simulation.





  The performance of the simulation for jets at CLIC is
  presented in Fig <ref>.
The energy is shifted to lower values for .
The invariant mass of the two jets, associated with
the  boson, is reconstructed with a narrower width and shifted to
lower values in compared to the full simulation.
As the jet clusters all of the typically soft particles from the background distributed
within its entire area, the effect on the mass due to their angular
spread is larger than the effect on
the energy.
The description could be improved by smearing not only the energy but
also the mass.
Alternatively, one could overlay events.
However, highly granular timing information from the detector is crucial to suppress
contributions from .
The current implementation cannot estimate this suppression and its
impact on the reconstruction of the signal process
since no timing information is available in the simulation.

Additional kinematic distributions of jets can be found in Appendix <ref>.



  


 §.§ Di-muon mass resolution in Higgs decays to muon pairs at 350 GeV and 1.4 TeV


The di-muon mass resolution is validated in  H → decays at 350 GeV and 1.4 TeV.
The Higgs boson resonance peaks in the di-muon mass distributions for
the two energy stages are shown in Fig. <ref>. The corresponding mean and width obtained with a Gaussian fit are presented in Table <ref>.

The resulting  mean and width of the Gaussian di-muon peak are in good
agreement for (→) (→) events at 350 GeV and in
agreement within 30 % for  (→μμ) νν events at
1.4 TeV.
As shown in <cit.>, tracking
resolutions in the forward region are less well described by the assumed
parametrisation
than in the central region.
As the muons in -boson fusion (→) νν events are more forward in
the detector than those in (→) (→)
events,
this explains the larger discrepancy between and full
simulation for the di-muon mass in the -boson fusion (→μμ) νν process.






§ CONCLUSIONS

Three parameter cards for the detector model for CLIC, CLICdet, have been prepared for the framework.
They describe the CLICdet geometry and performance for the three energy stages of CLIC.
Performance parameters are based on full simulation studies of the detector response and reconstruction software.
The cards have been validated by comparing with full simulation for various processes.
At the first energy stage of CLIC with low levels of beam-induced background, the validation has found  good agreement in particular for single object observables. Also derived observables such as di-jet invariant masses are well described in the regions. At the higher energy stages, reasonable agreement has been found for transverse momentum, energy, and pseudorapidity distributions of leptons and jets. The absence of the beam-induced background in the fast simulation limits the ability to reproduce all observables fully accurately. A smearing of the jet energy has been applied to mimic the effects of background. This could be improved in the future by applying a smearing also to the jet mass.

As has so far been used mainly for studies at hadron colliders, some features of detectors at lepton colliders had not yet been implemented.
Exclusive jet clustering and the VLC algorithm have been added as part of this study.
In addition, implementations for c-tagging and for the very forward calorimeters as well as a refinement of the isolation criteria could be added in the future.
The possibility of overlaying beam-induced events would improve  the description of  detectors at linear colliders.
However, this would also require to add the simulation of time information to exploit the timing selection capabilities of the detector to suppress these background contributions.


Full simulation studies for future experiments remain indispensable for the evaluation of the detector performance.
Furthermore, they are necessary for analyses using observables that are sensitive to beam-induced backgrounds and rely on timing information, analyses based on tails of distributions that are not well-modelled by fast simulation,  as well as analyses using exotic signatures such as long-lived particles.

In conclusion, a good description of the detector concept for CLIC has been achieved in the fast simulation framework with the parameter cards discussed in this note.
These cards have been validated and have already been used for CLIC physics studies.
The implementation makes it possible to take advantage of the flexibility and accessibility of for studying many aspects of the CLIC physics potential.







§ ACKNOWLEDGEMENTS

We thank  Michele Selvaggi for helpful discussions.
This work benefited from services provided by the ILC Virtual Organisation, supported by the national resource providers of the EGI Federation. This research was done using resources provided by the Open Science Grid, which is supported by the National Science Foundation and the U.S. Department of Energy's Office of Science.



[title=References]  


§ INSTRUCTIONS FOR USING THE CLICDET CARDS

There are three cards for the three energy stages of CLIC. The user
chooses the one appropriate for the relevant energy stage as indicated in Table <ref>.
    
To understand the output of running the card, the b-tagging and the correct  choice of jet branches is described below.
    



 §.§ B-Tagging in the CLICdet DELPHES card

   B-tagging is implemented in the card with three working points
   (WP), which tag 50%, 70%, and 90% of all b-quark-initiated jets,
   respectively. The corresponding mis-tagging rates are implemented
   in the CLICdet card. uses a three-bit mask to store the b-tagging information in the following way, where
   
   
  * bit 0 is the tight WP with 50% b-tagging efficiency, 
  * bit 1 is
     the medium WP with 70% b-tagging efficiency,
  * bit 2 is the loose WP
     with 90% b-tagging efficiency.

This leads to the combinations indicated in Table <ref>.

   Loosely b-tagged jets are selected with ≥4; for
   medium b-tagged jets,  should be 2, 3, 6, or 7, and for the tight WP the  should be 1, 3, 5 or 7.



 §.§ Taking into account the effect of beam-induced background

 The levels of beam-induced events are higher at the high energy stages.
 To account for their effects,
 a jet energy smearing is applied in the two cards for Stage2 and Stage3.

 The branches with the jet energy smearing applied are then named  in the resulting root file.



§ SUPPLEMENTARY VALIDATION STUDIES



 §.§ Di-jet mass in Higgsstrahlung with hadronic Z decay at 350 GeV


Using exclusive jet clustering with N = 4, the Z jets are assigned
according to the combination closest to the mass of the Z boson.
The invariant mass of
  the two remaining jets after assigning the Z jets is shown in
  Fig. <ref>(right) as m_jj().





  

 §.§ Semi-leptonic top-quark pairs associated with a Higgs boson at 1.4 TeV



The fast simulation for muons is validated in
Fig. <ref>. Like for electrons
(Fig. <ref>),
the transverse momentum is described reasonably well, but
with an increase in contributions from at lower values.

 

     The jet performance  is demonstrated in Fig. <ref>. It
    includes the jet energy smearing mimicking the effects of background. The pseudorapidity distribution is
    well-modelled, while the spectrum for transverse
    momentum shows an increase of events with low as well as higher
    transverse momentum.
  



 §.§ Di-boson production WW at 3 TeV

The muon energy distribution is validated comparing  to full detector simulation with the CLIC_ILD model as
shown in Fig. <ref>.





 The  transverse momentum of the jets is 
  underestimated by the simulation, and it does not show all
  features of the CLIC_ILD detector geometry in the pseudorapidity,
  as shown in Fig. <ref>.


  


