Section 2

Page 3

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 therefore assume infinite 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.

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”.

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.

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.

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.

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

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

• 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.

PAGE 4

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.

(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. Electrons, photons and neutral pions leave all their energy in ECAL, while charged pions and other neutral hadrons deposit all their energy in HCAL. Long-lived particle such as kaons, pions and $\Lambda$'s 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, $f_{ECAL}$ is set to $30\%$ and $f_{HCAL}$ to $70\%$ --- according to their expected decay products --- but this can be tuned by the user. Finally, muons, neutrinos and neutralinos, do not deposit anything in the calorimeters ($f_{ECAL}=f_{HCAL}=0$).

The resolution of the calorimeters is 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} where the sum runs over all particles that reach the given tower, and $\text{ln}\mathcal{N}(m,s)$ is the log-normal distribution with mean $m$ and variance $s$. 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

Par 1:

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

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.

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.

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.

PAGE 5

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.