## SciPost Submission Page

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

### by N. V. Shevchenko

#### - Published as SciPost Phys. Proc. 3, 041 (2020)

### Submission summary

As Contributors: | Nina Shevchenko |

Arxiv Link: | https://arxiv.org/abs/1910.09826v2 |

Date accepted: | 2019-12-20 |

Date submitted: | 2019-12-16 |

Submitted by: | Shevchenko, Nina |

Submitted to: | SciPost Physics Proceedings |

Proceedings issue: | 24th European Few Body Conference (University of Surrey, U.K.) |

Discipline: | Physics |

Subject area: | Quantum Physics |

Approach: | Theoretical |

### Abstract

The paper is devoted to the $\bar{K}NNN$ system, consisting of an antikaon and three nucleons. Four-body Faddeev-type AGS equations are being solved in order to find possible quasi-bound state in the system.

Published as SciPost Phys. Proc. 3, 041 (2020)

### Author comments upon resubmission

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.

### List of changes

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