Section 2

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Section 2.2

Par 2:

L3: ”in the transverse direction” is at best redundant, but has actual very little meaning here. Transverse to what ?Suggest to drop ”in the transverse direction” with no loss of information.

addressed

L4: It is bad to assume the same granularity for ECAL and HCAL, as it is in general not the case in HEP detectors, for very good physics reasons (in the sense that (i) electromagnetic showers are much more compact than hadron showers, and (ii) it has important consequences for the performance of the particle-flow reconstruction.). The assumption might actually be the origin of the some of the disagreements seen in the particle-flow performance later in the article. The ”computational reasons” are not spelt out, but it is difficult to understand why computing limitations would force anyone to make such an unrealistic assumption.

Showers are not produced in Delphes as the particle momenta are simply smeared according to the relevant calorimeter resolution. The discreteness of the calorimeter has simply an impact on the (eta,phi) resolution of the final observables. As it is, the pessimistic spatial resolution assumed in ECAL only affects photons, since for electrons we have the track information and we assume infinite (eta,phi) resolution. If there was a consistent difference in the performances due the this calorimeter simplification, it would first appear in the calorimeter resolutions, which seems to be correctly reproduced. The "computational reasons" are that with the current state of the implementation, the combinatorics are reduced, and this has an impact on the the jet clustering procedure, especially in the presence of pile-up.

Par 3:

L3: ”Neutral pions” do not leave their energy in ECAL, as they decay promptly to two photons (i.e., they are not ”long-lived particles reaching the calorimeters”. Suggest to drop ”and neutral pions”.

addressed.

L3-7: ”while charged pions and other neutral hadrons deposit all their energy in HCAL. Long-lived particle such as kaons, pions and Lambdas are considered stable by most event generators. In Delphes, such particles are assumed to deposit a fixed fraction of their energy both in ECAL and HCAL. By default, fECAL is set to 30% and fHCAL to 70% according to their expected decay products ... etc.” There are several problems with the logic of the above:

• The two sentences contradict themselves : do charged pions deposit all their energy in HCAL, or in both ECAL and HCAL?

• In the second sentence, one should be more specific and write e.g. charged pions instead of pions (pi0s are not long lived).

• Are ”such particles” stable in Delphes? If yes why is there a discussion about their decay products? Are fECAL and fHCAL fixed, or do they depend on the decay products (if any)? How exactly do fECAL and fHCAL depend on the decay products? What does ”according to their decay products” mean ? What are the decay products of charged pions in DELPHES ?

All in all, the whole paragraph needs substantial work, and the DELPHES implementation might need serious revision if what is currently described is indeed implemented.

The whole paragraph has been re-written for better clarity. The "according to their decay products" expression was referring only to lambda and k-shorts, whose decay products are considered, as an approximation, on average 30% electromagnetically interacting, and 70% strongly interacting. On the other hand charged pions deposit 100% in HCAL if it has not been decayed by the event generator. These are set by default in the configuration file, but they can, as explained >>> in the text, be changed.

Eq 2.1 : It is not clear whether the same resolution is used for ECAL and HCAL. It is not clear either whether the ECAL resolution is different for photons and for those hadrons that leave 30% of their energy in the ECAL. It would be very useful for the reader’s understanding to have a table of the values of S, N and C used to reproduce the CMS and ATLAS performance. Are these values compatible with the actual CMS and ATLAS resolution, or do they have to be tuned to reproduce the performance ? Along the same line, the calorimeter granularities and the tracker resolutions used for the two detectors would need to be spelt out and compared to the actual values.

For producing the plots we use the nominal resolutions from CMS and ATLAS. The resolution is different for ECAL and HCAL (the text has been changed to make this clear). We are not in favour of quoting the CMS and ATLAS resolutions, since, at this level, we want to stay general and not give the impression that Delphes is limited to these two experiments. We emphasize that Delphes can be used with completely different parameters, corresponding to any generic (symmetric) detector

Eq 2.2. : Several problems here too.

• It is not clear whether the shower energy is or is not distributed over

several towers. Neither Eq 2.2 nor the text seems to mention that. I seem to understand that the energy of each particle is concentrated in a single tower from the algorithm described later on, but the casual reader will certainly miss this subtlety.

addressed: the sentence: "The energy of each particle is concentrated in

one single tower." has been added.

• sigma(ECAL) and sigma(HCAL) are undefined, even though the casual reader may go as far as guessing that they are defined by equation 2.1 (?)

addressed: "The parameters $sigma_{ECAL}$ and $sigma_{HCAL}$ are respectively the ECAL and HCAL resolutions, defined in equation~(\ref{eq:calores})"

• What is the physics motivation for doing a log-normal instead of a Gaussian smearing?

The lognomal distribution resembles to a gaussian when mean > 6*sigma, that is for most values at high energy, but has the advantage a low energy to be always positive. This ensures to to avoid the positive bias in the effective mean and s.d >>> induced by having a truncated gaussian.

• To define a log-normal distribution, one usually gives the mean and sigma of the logarithm of the distribution, which is normal. Here, are the authors talking about the mean and variance of the log-normal distribution? I guess so, but it would be good to clarify.

We are talking about the mean and the variance of the lognormal, which have pretty complicated expression in terms of the mean and variance of the normal variable, which, as the referee correctly remarked, are the ones that are usually given. >>>However, it is clear from the text that m, and s are the mean and variance of the log-normal distribution and not the mean and variance of the normal distribution.

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L2/3: It is difficult to understand why one would want to ”avoid having to deal with discrete tower positions”. ”Discrete tower positions” are actually happening in CMS and ATLAS, and are being dealt with without difficulties. The authors may want to be more explicit about their motives here.

To reduce computing time the size of cells is actually bigger than CMS or ATLAS. As a result spikes can appear in angular distributions, if proper binning is not chosen. Therefore we apply this smearing for purely cosmetical reasons, and has indeed no impact whatsoever on the physics objects angular resolution.

(michele suggested section 2.2)

After propagating in the magnetic field, long-lived particles reach the calorimeters. The electromagnetic calorimeter, ECAL, is responsible for measuring the energy of electrons and photons, while the hadronic calorimeter, HCAL, measures the energy of strongly interacting particles.

In \DELPHES, the calorimeters have a finite segmentation in pseudo-rapidity and azimuthal angle ($\eta$,$\phi$). The size of the elementary cells can be defined in the configuration file. For simplicity the segmentation is uniform and for computational reasons we assume the same granularity for ECAL and HCAL. The coordinate of the resulting calorimeter object, the tower, is computed as the geometrical center of the cell.

Long-lived particles reaching the calorimeters deposit a fixed fraction of their energy in the corresponding ECAL ($f_{ECAL}$) and HCAL ($f_{HCAL}$) cells. Since ECAL and HCAL are perfectly overlaid, each particle reaches one ECAL and one HCAL cell. By default in \DELPHES electrons and photons leave all their energy in ECAL ($f_{ECAL}=1$), hadrons deposit all their energy in HCAL ($f_{HCAL}=1$), with the exception of kaons and $\Lambda$ that share their energy deposit between ECAL and HCAL ($f_{ECAL}=0.3$ and $f_{ECAL}=0.7$), while muons, neutrinos and neutralinos, do not deposit anything in the calorimeters. In practice, the user has the freedom to change the default setup, and define for each long-lived particle more accurate values for $f_{ECAL}$ and $f_{HCAL}.

The resolutions of ECAL and HCAL are independently parametrised as a function of the particle energy and the pseudo-rapidity: \begin{equation} \left(\frac{\sigma}{E}\right)^{2 = \left(\frac{S(\eta)}{\sqrt{E}}\right)}2

+ \left(\frac{N(\eta)}{E}\right)^{2 + C(\eta)}2\

\label{eq:calores} \end{equation} where $S$, $N$ and $C$ are respectively the \textit{stochastic}, \textit{noise} and \textit{constant} terms. The electromagnetic and hadronic energy deposits are independently smeared by a log-normal distribution with variance $\sigma$. The final tower energy is then computed as: \begin{equation} E_{Tower} = \sum_{particles}\text{ln}\mathcal{N}\left(f_{ECAL} \cdot E,\sigma_{ECAL}(E,\eta)\right) +\text{ln}\mathcal{N}\left(f_{HCAL} \cdot E,\sigma_{HCAL}(E,\eta)\right) . \label{eq:etow} \end{equation} The energy of each particle is concentrated in one single tower and the sum runs over all particles that reach the given tower. $\text{ln}\mathcal{N}(m,s)$ is the log-normal distribution with mean $m$ and variance $s$. The parameters $sigma_{ECAL}$ and $sigma_{HCAL}$ are respectively the ECAL and HCAL resolutions, defined in equation~(\ref{eq:calores}). A calorimeter tower is also characterized by its position in the ($\eta$,$\phi$) plane, given by the geometrical center of the corresponding cell. In order to avoid having to deal with discrete tower positions, an additional uniform smearing of the position over the cell range is performed.

Calorimeter towers are, along with tracks, crucial ingredients for reconstructing isolated electrons and photons, as well as high-level objects such as jets and missing transverse energy.

Section 2.3

(michele general comment) As said in the comments in the introduction, it was decided to call the algorithm energy-flow in Delphes. We believe it is more appropriate for Delphes, since such algorithm is aimed at optimizing the performances of jets and missing energy. Particle identification is perfect by construction in Delphes, since it is based on MC truth. Also, following the referee's suggestions, the energy-flow algorithm has been sensibly re-visited, as well as the section 2.3 of the paper.

Par 1:

L2: ”reconstructing the event” ! ”reconstructing all the individual par- ticles in the event”.

see comment at the beginning of Section 2.3

Par 2:

L5: Drop ”if particle-flow is switched on” are it is obvious in the context of Section 2.3 ”Particle Flow Reconstruction”. (Two occurrences.)

addressed

L5: ”We assume it is always convenient to estimate charged particle mo- menta via the the tracker.” This is a wrong assumption. As the transverse momentum or the pseudo-rapidity increases, the transverse momentum reso- lution becomes worse than the calorimeter resolution. This assumption may be the reason of the disagreement between DELPHES and CMS in Fig.5 (left), where the jet pT resolution is significantly pessimistic at high pT. This caveat must be mentioned in the text, either here, or when discussing Fig. 5, or (better) in both places. The same comment applies to the last sentence of PAGE 4 and the first sentence of PAGE 5.

Figure 5 has been updated, and the discrepancy at high energy is not present anymore. It is already mentionned that this assumption is true in reality only up to some energy threshold, but we adopt it however for any energy. After the new energy-flow implementation, we have noticed that the agreement is now good at high energy (Fig. 5).

Par 3.

There seems to be here again an overall misunderstanding of what a particle-flow algorithm is for. The authors seem to believe that it is aimed at reconstructing jets and missing energy. The particle-flow algorithm aims at reconstructing all individual particles in the event with an optimal resolution by making use of the identification capabilities of a detector. It can therefore provide a list a photon, charged leptons, and charged/neutral hadrons, that can be later used to define all sorts of physics objects - not limited to jets and missing energy.

See previous answer about our decision to talk about "PF-like emulation". We don't want to perform a real reconstruction, and therefore a real particle-id algorithm, but to emulate its effects. The gains from PF are larger on jets and MET than on other high-level objects, and therefore the need for an emulation of PF effects is stronger for jets and MET.

(michele: agree with this!)

First bullet: ”Hits” are not defined, and it is difficult to understand the concept of a ”hit that originate from a particle”. The expression ”at least one among fECAL and fHCAL is non-zero” carries little meaning. The footnote content is not related whatsoever to the information in this bullet.

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The two bullets here contain quite involved a logic, which is difficult to follow even by experts. The suggestion is to work the text out and come with a clearer version.

First bullet :

L6: Add ”and he corresponding hits are dropped.” after ”such tracks get stored as particle-flow tracks”.

L8/9: The energy smearing was already addressed earlier in the text. Why repeating it here ?

L9/10: Do I understand properly that when a charged pion and a pho- ton leave energy in the same tower, the PF algorithm is assumed to be smart enough to find the photon, irrespectively of the ECAL granularity and the photon energy ? That’s overly optimistic, and it does not allow the DELPHES user to make studies about the relevance of a better calorimeter granularity, for example. On the other hand, the assumption that, when an electron and a neutron point to the same HCAL tower, the e ID is smart enough to detect it, is almost correct for most detector designs.

Second bullet:

L6/10 : ”The resolution will be exactly the same. It is therefore useless ... the full calorimeter tower.” This logic is incorrectly representing that of a sound particle flow algorithm. While it is true that the resolution (and actually the value) of the energy would be (not ”will be”) the same, replac- ing a charged hadron + a neutral hadron by the sole calorimetric energy deposit has several drawbacks for data analysis. First, it artificially reduces the reconstructed charged multiplicity - which may be precious, e.g., when determining the charged isolation of a particle. Second, it reduces the ability of pile-up mitigation (mentioned in the next paragraph), by losing the ori- gin vertex information. Third, it worsens the angular resolution of the jets, that become limited by the tower granularity. Fourth, it does not follow the particle-flow philosophy that aims at reconstructing all particles in an event.

Also, the logic of the two bullets misses an important point : when the calorimetric energy is compatible (within a small number of st. deviations) with the track momentum, no neutral hadrons is created even if there is one; and when the calorimetric energy is in excess of the track momentum, a neutral hadron is always created, even if there is none. The current imple- mentation DELPHES misses both aspects, which tends to explain the too good resolution of jet pT at low pT.

Last par, last line : It is not true that the emulation of the PF algorithm reproduces the performance of, e.g., CMS, even for jets. (See related com- ments later.) Again, it would be interesting for the reader to understand the resolution parameters used in DELPHES to get to this performance.

(michele suggested section 2.3)

\subsection{Energy-flow Reconstruction}\label{sec:pfrec}

The philosophy of the energy-flow approach is to maximally make use of the information provided by the various sub-detectors for reconstructing the event. This modus operandi has been adopted by several experimental collaborations (see for example~\cite{bib:eflow,bib:pflow}) but intrinsically depends on the specificity of the experimental device. In \DELPHES, we opted for a simplified approach based on the tracking system and the calorimeters for implementing the energy-flow event reconstruction.

If the momentum resolution of the tracking system is higher than the energy resolution of calorimeters, it can be convenient to use the tracking information within the tracker acceptance for estimating the charged particles momenta. In real experiments, the tracker resolution will be better than the calorimeter resolution only up to some energy threshold. In \DELPHES, we assume it is always convenient to estimate charged particle momenta via the the tracker.

The particle-flow algorithm produces two collections of 4-vectors --- particle-flow tracks and particle-flow towers --- that will serve later as input for reconstructing jets and missing transverse energy with a higher resolution. For each calorimeter cell, the algorithm counts: \begin{itemize} \item $N_{calo}$, the total number of hits that originate from all long-lived standard model particles propagating within the calorimeter acceptance, provided that at least one among $f_{ECAL}$ and $f_{HCAL}$ is non-zero.~\footnote{Muons, neutrinos and neutralinos do not deposit any energy in the calorimeters.} Each time the calorimeter cell is reached by such a particle, $N_{calo}$ is incremented by 1. Similarly we define $N_{calo-HCAL}$ ($N_{calo-ECAL}$) which gets incremented if a particle with $f_{HCAL}>0$ ($f_{ECAL}>0$) reaches the calorimeter cell.

\item $N_{trk}$, the number of hits that originate from a reconstructed track. Due to tracking inefficiencies, some charged particles will not be reconstructed as tracks, but will produce a hit in a calorimeter cell. By construction $N_{trk} \leq N_{calo}$. We also define $N_{trk-HCAL}$ ($N_{trk-ECAL}$) which is incremented if a charged particle reconstructed as a track with $f_{HCAL}>0$ ($f_{ECAL}>0$) reaches the calorimeter cell.

\end{itemize}

The following two scenarios may occur, $N_{calo}=N_{trk}$ and $N_{calo}>N_{trk}$. The first case is trivial and corresponds to a scenario where the calorimeter cell has been hit only by charged particles that have produced a track. If the particle-flow algorithm is switched on, each track associated to this particular cell will result in a particle-flow track. In this case no particle-flow tower is produced. Here we choose to simply make use of the superior energy and momentum resolution of the tracking system for estimating the charged particles 4-momenta.

The second case occurs when either one or more neutral particles did produce a hit in the calorimeter cell, or when at least one charged particle did not result in a reconstructed track. The most trivial occurrence is when $N_{trk}=0$, which means that only neutrals and mis-reconstructed charged particles have produced a hit. In this case the particle-flow algorithm will trivially produce a single particle-flow tower. If $N_{trk}>0$ there are two possibilities that need to be treated separately: \begin{itemize} \item if the calorimeter cell is hit only by particles that deposit their total energy either in ECAL or in HCAL it is convenient to consider the two calorimeter sub-components independently. This translates into the condition $N_{calo-ECAL}+N_{calo-HCAL} = N_{calo}$. Moreover, if at least one of the calorimeter sub-components is hit exclusively by particles associated with a reconstructed track, that is, $N_{calo-ECAL}=N_{trk-ECAL}$ (or $N_{calo-HCAL}=N_{trk-HCAL}$), then such tracks get stored as particle-flow tracks. All remaining HCAL (or ECAL) hits will result in a single particle-flow tower. The energy of the particle-flow tower is obtained by smearing according to the HCAL (ECAL) resolution alone. These cases correspond for instance to a calorimeter cell being hit by an electron and a neutron (or by a charged pion and a photon). \item if the previous conditions are not satisfied, only one particle-flow tower (and no particle flow-tracks) is produced. This 4-vector has the energy of the full tower, obtained by applying the procedure explained in equation~(\ref{eq:etow}). This case occurs frequently when one sub-detector (HCAL or ECAL) is hit both by a neutral and a charged particle. In this case, the neutral energy would have to be indirectly calculated by subtracting the charged energy from the total calorimeter energy. The resolution on the total energy taken directly from the calorimeter, or calculated by adding the charged and neutral component, will be exactly the same. It is therefore useless to consider separately these two components in this case. Therefore we simply take as final particle-flow object the full calorimeter tower.

\end{itemize}

The output of the particle-flow algorithm consists in two collections of objects. The particle-flow tracks contain charged particles estimated with a good resolution. The particle-flow towers contain in general a combination of charged and neutral particles, and are characterized by a lower resolution. As will be shown in sections~\ref{sec:jets} and~\ref{sec:pus}, besides producing high-resolution inputs for jets and missing transverse energy, the particle-flow approach can be pretty useful for addressing pile-up subtraction. While very simple when compared to what is actually required in real experiments, the algorithm described above is shown to reproduce well the performance achieved at LHC later in section~\ref{sec:validation}.