Estimation of Nucleon D-Term in QCD

Round 1

Reviewer 1 Report

In this manuscript the light-cone sum rules (LCSR) are used at leading order

to obtain a "preliminary upper estimation" for the nucleon gravitational 

form factor D(t) which is sometimes also referred to as the D-term form

factor. The manuscript contains several unclear points which should be

addressed.

1. The term "upper estimation" is not clear. Does the author mean that 

his result is an estimate for the upper limit for D(t)? Does this mean 

that D(t)_{correct result in LCSR} \le D(t)_{estimated here}? If yes, 

which terms have been neglected? How does the author know which sign 

the neglected terms have? It is important to explain this point.

2. In the lines 54-56 the author "argues" that in order to extend the 

preceding calculations performed for electromagnetic form factors to the 

case of gravitational form factors he has to weight the electromagnetic 

form factors with the certain tensor structure. 

It is not clear what this means. What is the basis for this "argument"? 

Is this an assumption by the author? Is this a model? Or, did the author 

derive the exact expressions for the gravitational form factors in the 

LCSR approach (and found that these expressions correspond to the 

electromagnetic form factors up to a "certain tensor structure")?

3. The author writes in the line 76 that his "thorough numerical analysis 

shows that the unknown $\tilde{T}^{+-}_{1[\bar\psi_-\psi_-]}$ contribution 

can be estimated" by the expression in Eq.(17).

It would be important to provide some more detail: why is Eq.(17) a good

approximation? How big are the neglected terms? Is there a small parameter 

which justifies such an approximation?

4. Line 77: Why is it justified to neglect the C-term from the F-combination?

5. The author speaks of "analytical continuation of the obtained fitting 

functions to the region of small t" in line 83. The "term analytical

continuation" cannot be used in this context. This is an "extrapolation" 

to the region of small t. Such an extrapolation introduces an uncontrolled 

uncertainty and model-dependence in the study. This should be remarked.

6. In the manuscript the author mentions the chiral quark-soliton 5 times 

(line 11, 27, 86, 87, 107) and the Skyrme model 4 times (line 27, 86, 88, 108). 

The author quotes the review [2] as a reference for these works which is not

accurate. Instead the author should refer to the original references:

  K.Goeke et al, Phys. Rev. D 75 (2007) 094021

  doi:10.1103/PhysRevD.75.094021

  [hep-ph/0702030].

  K.Goeke et al, Phys. Rev. C 75 (2007) 055207

  doi:10.1103/PhysRevC.75.055207

  [hep-ph/0702031].

  C.Cebulla at al, Nucl.Phys.A 794 (2007) 87

  doi:10.1016/j.nuclphysa.2007.08.004

  [hep-ph/0703025].

Author Response

see attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

In this paper the author considers the light-cone sum rules to obtain the gravitational form factor D(t) which is very important in order to understand the mechanical properties of nucleon such as pressure inside the nucleon. The results are of interest for further work in this field, and I would suggest publishing the paper in Particles provided the following minor question is addressed:

1. Fig. 1 represent the fitting of the nucleon gravitational form factor D(t) at low -t region. Is it possible to get the flavor contributions to the nucleon form factor D(t)? 

Author Response

see attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The function R(t) in Fig.1 is difficult to see. Recommend to adjust the scale on the y-axis such that the function can be seen clearly. Otherwise the author has improved the manuscripts in many respects.

Author Response

I thank the Referee for his remark. As you can find, the present version includes the rescaled fig.1.

With best regards,

Igor V. Anikin 

Reviewer 2 Report

I recommend the manuscript for publication in Particles in its present form. 

Author Response

I thank the Referee for his positive consideration of the paper.

With best regards,

Igor V. Anikin