First steps towards the reconstruction of the squark flavour structure

We would like to thank the Referee for reviewing our manuscript and providing us with the useful comments, which we hereby address:

1) In the introduction of our manuscript, we state that recently it has been shown that current experimental limits (leading to the null result mentioned by the Referee) do not apply as they are to the case of non-negligible flavour mixing, see our Ref. [37]. In the maximal mixing case, squarks would even escape detection in current analyses. However, in Ref. [37], a complementary analysis is proposed which will cover the case of generation mixing in the squark sector. This strategy is based on the search for the mixed final state containing a top quark and a charm-flavoured jet plus missing energy stemming from the two associated neutralinos appearing in the squark decays. We therefore assume that such channels can be accessed at the LHC with sufficient luminosity, as discussed in Ref. [37]. 
The mixed “charm-top” channel may be used to obtain the observable $R_{c/t}$, together with the standard “top-top” channel. Note that $R_{c/t}$ is the observable having the largest impact on our study. However, we admit that we did not recast the analysis in order to check the expected accuracy of $R_{c/t}$. Such an analysis, involving mainly experimental knowledge, is beyond the scope of the present manuscript. 

The experimental uncertainties fixed in our likelihood-based analysis can be adapted to the actual observation of a squark-like state, and the associated decays. Concerning the multivariate analysis, the analysis proposed in our manuscript does not exploit the associated uncertainties. This will be rather technical to address and rely again on experimental knowledge associated to the actual observation, such that this point is beyond the scope of our paper.


2) The results of the MLP analysis are presented as histograms, in which a MLP value is computed for each point of the sample. If the MLP is rather efficient, the two distributions associated to the categories to be separated peak at the extremities (0 and 1). 

As an example, looking at Fig. 6, if a set of observables is leading to an MLP response of 1, the parameter point is very likely to belong to the “red” category, i.e. be a charm-like state, the ratio “red”/”blue” being very large. 

We can determine the efficiency of the classifier with respect to a certain misidentification rate. This is done by fixing a cut on the MLP value, defined such that the ratio of the “blue” area over the “red” area above the cut corresponds to the misidentification rate associated to the “red” category. The efficiency for the “red” category is then obtained as the ratio of the “red” area above the cut and the total “red” area. The same can of course be carried out for the “blue” category.

To give an example, in terms of physical interpretation, the “charm MFV” category given in Table 3: the “probability” to count an actual “charm MFV” parameter point into this category is 95%, assuming that 10% of the other parameter points (not belonging to this category) are classified as “charm MFV” (misidentification). 

Consequently, decreasing the misidentification rate (by changing the cut) will lead to a decrease of the efficiency.


3) The Referee is right that the matrices N, U, and V are not properly defined in our manuscript. We will add their definition to the manuscript.


We will be happy to modify and resubmit our manuscript according to the above points, in particular the motivation of our study and a clearer explanation of the MLP results.

We would like to thank the Referee for reviewing our manuscript and providing us with the useful comments, which we hereby address:

1) We agree with the Referee that a more complete analysis will be in order, including experimental details and uncertainties. However, in our opinion, this is to be done in the case of an actual observation at the LHC or future collider, which would make the whole study necessary and well adapted to the observation. We did not assume any specific mass values nor other observables in our scan of the parameter space. We thus show the feasibility of the proposed study in a generic way. For a concrete case, i.e. in case of an actual observation, this study has to be adapted on the actual observation and its associated uncertainties. 

Concerning the Referee’s comment on the observable $R_{c/t}$, we agree that it may be experimentally challenging. However, as discussed in Ref. [37], the mixed “top-charm” final state can be reached via a dedicated search strategy. We base our study on the assumption that this strategy is employed, such that the corresponding part of parameter space, featuring sizeable generation mixing, is covered. This mixed “top-charm” channel may be used to obtain the observable $R_{c/t}$, together with the standard “top-top” channel.

2) We will be happy to improve the presented Figures, in particular providing axis ticks and labels (if missing) together with a measure of the shown probability densities.

We will be happy to modify our manuscript according to the above points, and provide a revised version.

We would like to thank the Referee for the evaluation of our manuscript and for her/his interest in our work.

Regarding the questions concerning the uncertainties:

“I have one question to the authors to be addressed prior to publication: How would a change in the experimental uncertainties, assumed to be 25% for all observables entering the analysis, affect the results of the applied methods?”

During our analysis, we had investigated the question of the impact of the uncertainties mentioned by the Referee by varying the value of $\sigma_i$ for a given reference point.

As expected, increasing the uncertainties $\sigma_i$ leads to an increase in the uncertainty $\sigma(x_{\tilde{t}})$ obtained from the Gaussian fit.

However, special care has to be taken when reducing the value of $\sigma_i$. First, the quality of the Monte Carlo sampling plays a crucial role. Indeed, if the parameter space is not populated well enough, the Gaussian fit “breaks down”, i.e. it cannot yield a meaningful result. In addition, if one considers the more general setup, e.g. without fixing the gaugino parameters, degeneracies between the observables and the top-content $x_{\tilde{t}}$ appear, as can be seen in Fig. 3 of our manuscript. This may lead to additional complications concerning the uncertainties.

This is why, in this first attempt of reconstructing the top content $x_{\tilde{t}}$, we do not perform a dedicated analysis of the impact of the uncertainties $\sigma_i$. In the present work, we focus on showing that it is possible to obtain information on the flavour content (in particular $x_{\tilde{t}}$) rather than presenting a complete analysis including the uncertainties.

However, this question will need to be addressed properly in the case of an actual observation of a squark-like state. In this situation, the analysis proposed here will become crucial, and information about the underlying uncertainties will be known.

As a last comment, let us emphasize that the observables should have different uncertainties $\sigma_i$.

“Are the uncertainties in the ratios $R_{c/t}$ and $R_{b/t}$ the limiting factor in discriminiating between different flavour contents, as one might naively assume?”

The Referee is right by assuming that the uncertainties on $R_{c/t}$ and $R_{b/t}$ would be the most limiting factors in the analysis. In particular, $R_{c/t}$ is the most constraining observable, since it shows a strong correlation with the parameter $x_{\tilde{t}}$, as can be seen in Fig. 3 of our manuscript.

We will be happy to update our manuscript with the above comments, should it be judged necessary by the Referee or the Editor.