Beta

Dear
I would like to thank the referee for reading the draft, carefully. Regarding the important comment of the referee we backed to the related papers in the QCD side. Two important papers are [13] and [14]. These papers were cited by [28] and [29]. We find that the temperature dependence of the thermal width of the quarkonium is presently not well determined. Also very different parameters have been used in the phenomenological studies. For example, in reference [13], using the NLO perturbative QCD calculation, one finds that the width increases as the quarkonium travels faster! While [14] shows that width vanishes in this regime of the velocities!
Also in [14], the effective field theory (EFT) have been used to study the width of quarkonium. As it was pointed out in this paper, “ If the bound state moves with respect to the medium, the EFT analysis becomes more complicated, because additional energy scales may appear”. Then they consider the case of “moderate velocities for which no further scales are induced”. To have more physical intuition they even push their results to ultra relativistic limit. Then we can compare our results from holography with QCD calculations at small velocity! This is the main reason to consider the higher derivative corrections at small velocities. An understanding of how the thermal width changes by these corrections may be essential for theoretical predictions in perturbative QCD.
We would like to mention some points about [28] and [29]. They use saddle point approximation to find the imaginary potential. The discussion on the thermal width can be found only in ref.[28] and there is not any plot about the thermal width in [29]. To more clarify these papers, We have plotted the thermal width from the approach of [29] and the result is shown in figure 1. This is an important figure where one can compare the results of the above papers. As it is clear from this plot at small velocity they do not have the same behavior. As a result, we decided to study higher derivative corrections and their effects on the thermal width.
Based on the comment by the referee, we revised the draft as follows: 1- Welcome to Authorea!
kazem
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