Four-Body Faddeev-Type Calculation of the $\bar{K}NNN$ System: Preliminary Results

I am thankful to the referee for his/her report, but I cannot agree with all his/her remarks. The first claim is that I present preliminary results. But I would like to remind that this paper is a contribution to conference proceedings. As far as I know, it is quite normal to present preliminary results at conferences and publish them in the corresponding conference proceedings. When I "gain full confidence", I will publish a paper in an impact journal.

Below there are my replies to "few more minor comments": - In the introduction the author writes more accurate calculations are needed'', but no argument is given. Does she suspects there is an error in the reported results? does she has a better input? \I cite 3 other papers: one was performed using many-body G-matrix method for the three-body system, which is not well-grounded. In addition, AY potential, which was used there, does not describe antiK N experimental data. Another is a variational calculation, which evaluated only real part of the quasi-bound state using only real part of the (necessarily) complex antiK N potential, while the width of the state was somehow estimated after. The last one is a Faddeev-type AGS calculation, which should be the most accurate one. But the authors used two my antiK N potentials and obtained strongly different corresponding 4-body binding energies. Which I - keeping my experience with my own three-body Faddeev-type calculations using these potentials - cannot understand. That's why I am sure, that more accurate Faddeev-type calculation is necessary. This explanation is too long and detailed for the introduction of a conference paper, due to this I did not include it into the text of the paper.

• separabelize'' is not a word. Same for its derivatives. \The sentences containing "separabelize" and its derivatives were reformulated.

• The second term in Eq. (15) is just a delta function. \It is a delta function only at the fixed energy z=E_B, as is written above Eq.(14). Energy z in Eqs.(14,15) is arbitrary.

• The argument why the EDPA is accurate enough and under what condition should be presented. This is clearly not a general truth. \Yes, it is not a general truth, that's why the sentence about accuracy of the EDPA is started by "According to the authors, ..." (the authors of the method, of cause, - I do not write about myself in such a way in the paper). The argument is probably their results obtained using the EDPA and compared with the exact ones.

• Rephrase At the begin we''. \Done: "We started by writing down the system Eq.(\ref{4AGSsepVT}) for $18$ channels $\sigma_{\alpha}$ with $\alpha =$ $NN$ or $\bar{K}N$, considering three nucleons as nonindentical particles:"

• Eq. (17), the channels are not defined. \The channels are written in an explicit form in Eq.(17). Does the referee insist on a special notation for every of them?

• What about 3-body interactions? \"No three-body potentials were used since the four-body Faddeev-type equations are too complicated in their original form with "normal" pair potentials already." was added to the end of 3.1

• Sec. 3.1 three our separable'' --> three separable''. \No: the potentials are ours since I had constructed them.

• There. A ref. to the potentials is missing. \Thank you, added.

• The fitted AV18 NN interaction - in what energy range does the fitted interaction reproduce the data? \"... at low energies up to $500$ MeV ..." was added into the sentence starting from "It reproduces Argonne v18"

• End of 3.2 ASG--> AGS \Corrected

• If Sec. 4 is included in the manuscript comparison with other published works must be included and discussed. \Here the referee contradicts himself/herself: how can I include comparisons with other results if I should (according to the referee) remove Section 4 completely - with all my preliminary results?.. On the other hand, comparison of preliminary results with others is of no use.

The sentences containing "separabelize" and its derivatives were reformulated.

The sentence started "At the begin we" was rewritten:
"We started by writing down the system Eq.(\ref{4AGSsepVT}) for $18$ channels
$\sigma_{\alpha}$ with $\alpha =$ $NN$ or $\bar{K}N$, considering three nucleons
as nonindentical particles:"

"No three-body potentials were used since the four-body Faddeev-type equations
are too complicated in their original form with "normal" pair potentials already."
was added to the end of 3.1

References to the antiK N potentials were added to the 3rd sentence of 3.1.

"... at low energies up to $500$ MeV ..." was added into the sentence starting
from "It reproduces Argonne v18"

End of 3.2: ASG--> AGS was corrected