Coulomb-Nuclear Interference in Polarized pA Scattering

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper deals with an interesting and potentially important topic. It is rather technical and therefore suited for readers that have some expertise on the topic, whereas a wider readership would gain by some more explanation/discussion, in particular of a conceptual kind. However, since these spin-related issues connect to other unsolved spin puzzles, I suggest that the paper is published in the present form after a careful polishing with corrections and reformulations (errors/typos/unclear are e.g. on lines 12, 26-27, 63, 65, 88).

Comments on the Quality of English Language

Acceptable after considering comment above.

Author Response

AUTHORS:
We thank the referee for the improving comments and found mistakes/typos. We extended explanations in Introduction.

Reviewer 2 Report

Comments and Suggestions for Authors

First the authors give explicit expressions for the hadronic amplitude abstracted from the Regge formalism. Then they make a serious effort to include the Coulomb amplitude and phase in two different ways. This is a difficult topic where phenomenology plays an important role. In this respect the authors  propose new methods which will be useful to others coming  into this field of research. On these matters any inside or motivation from QCD would have been important.

Furthermore, the authors extended the article to include scattering on nuclei which is new and useful.

The article studies pNucleus collisions and in particular the interference between spin-flip and no-spin-flip amplitudes. Their idea includes photon exchanges before and/or after the hadronic interaction which interaction is taken from Regge theory. The result of this first attempt is the generation of a new phase which leads to an explanation of Rick data. Imrpovements may come in the future. 

Abstract:

We made the first attempt to understand the observed unusual t-dependence of single spin asymmetry observed in the HJET experiment at RHIC.  Contrary to the usual division of the interaction amplitudes into pure electromagnetic and strong interaction terms with a Coulomb phase, we combine the strong interaction with the Coulomb-Nuclear graph.  In this treatment we consider the short-range hadronic interaction as a correction to the long-range electromagnetic term, i.e. treat it as absorptive corrections. The corrections significantly modify the Coulomb-nuclear interference, which is a source of the single-spin azimuthal asymmetry at very small angles.

The second sentence in the abstract has " hadrons is is presented" with the word  " is  " repeated.  It does not make sense.  Instead of this: On the contrary to the usual division of the interaction amplitudes to pure electromagnetic and strong interaction terms with Coulomb corrections (Coulomb phase), we combine Usually the interaction of hadrons is is presented as long-range Coulomb interaction and short-range strong interaction with Coulomb corrections.

I suggest: On the contrary to the usual division of the interaction amplitudes to pure electromagnetic and strong interaction terms with Coulomb corrections (Coulomb phase), we combine  the  interaction of hadrons to be  presented as long-range Coulomb interaction plus short-range strong interaction with Coulomb corrections.

Keywords: single spin asymmetry, Coulomb nuclear interference, Pomeron spin.

Similar improvements are needed throughout the article.   1) 1st paragraph of section 2 should read: "..........where for   for small-angle elastic scattering t ≡ −q 2 ≈ −q T2 they are comparable". 2)after Eq (11) :  " For pp elastic scattering....." 3)Before Eq (16) : "The Nuclear electromagnetic formfactors in Eqs (14-23) have the form...." 4. 2nd paragraph of  Section 3:   "Alternatively, one can combine (C) and (CN)...."

 

 

Author Response

REFEREE:
First the authors give explicit expressions for the hadronic amplitude abstracted from the Regge formalism. Then they make a serious effort to include the Coulomb amplitude and phase in two different ways. This is a difficult topic where phenomenology plays an important role. In this respect the authors  propose new methods which will be useful to others coming  into this field of research. On these matters any inside or motivation from QCD would have been important.
AUTHORS:
Glauber approximations is a rather general approach describing hadron-nucleus amplitude. However Gribov's inelastic corrections are model dependent. We employ the QCD motivated color-dipole representation and provide a references 7, 8, 19 (old numbering) with detailed description of this method.

We thank the referee for noticing several typos, and proposing improvements in the text. We adopted all of them in teh revised manuscript.

 

Reviewer 3 Report

Comments and Suggestions for Authors

The authors of the article "Coulomb-Nuclear Interference in Polarized pA Scattering " propose a method for describing the asymmetry in the process of small-angle elastic pA scattering with a single spin flip. For this purpose, they use equations connecting the derivatives of the scattering cross sections by the 4-momentum transfer squared with real and imaginary parts of the scattering amplitudes with and without spin flip. On the basis of the known approximate expressions characterizing the asymmetry of small-angle elastic pp-scattering, the unification of the electromagnetic contribution to the amplitude of pA scattering with an absorptive correction to it arising from strong interactions makes it possible to calculate the amplitudes of elastic proton scattering on atomic nuclei in the framework of the Born, Glauber, and eikonal approximations.

This was done for carbon, gold, aluminum, and ruthenium. The dependence of the azimuthal asymmetry of elastic pA scattering on the 4-momentum transfer squared has been found for them and these results have been compared with the available experimental data. The graphics on which they are compared do not indicate a high degree of accuracy of the proposed theoretical description of the very nontrivial behavior of the system observed experimentally. However, its most characteristic features (in particular, the presence of two maximums in both the theoretical and experimental curves) are the same.

This can be considered as a success in understanding the mechanisms of occurrence of azimuthal asymmetry in polarized elastic hadron scattering.The obtained results can be used to develop new approaches in the field of physics of fundamental interactions. I think, the article "Coulomb-Nuclear Interference in Polarized pA Scattering " by Boris Kopeliovich, Michal Krelina and Irina Potashnikova deserves to be published in the journal "Universe".

 

Author Response

We thank the referee for careful reading and appreciation of our results.

Reviewer 4 Report

Comments and Suggestions for Authors

In this paper, the authors calculate the single-spin asymmetry in polarized proton-nucleus elastic scattering in the CNI region and obtain interesting results compared with data. 

Here are my remarks after reading the paper:

1. In the abstract, the authors state that: "here we consider short-range hadronic interaction as a correction to the long-range electromagnetic term, i.e. treat it as absorptive corrections". This statement is quite general, and in general, it is not true. As the authors are well aware of, in quantum chromodynamics (QCD), the theory describing the strong force, there is no straightforward way to treat the short-range hadronic interaction as a correction to the long-range electromagnetic term. These forces are treated as distinct and mutually nonperturbative phenomena. Fortunately, the authors' intentions become clearer along the paper. Therefore, I suggest that the authors be more precise in the description of their framework in the introduction, since their formulation is misleading.

2. Concerning the abstract, there are some confusing sentences from line 10 to 14, which must be rewritten.

3. The introduction could benefit from a general description of the importance of the problem chosen. While the introduction is very clear from technical point of view, the relevance of the pA scattering, unpolarized and polarized, is missing. This could put off some readers. 

4. The reasoning behind the formulas (24) to (27) and (28) to (31) should be explained and commented.

5. There are several minor English language mistakes in the lines: 38, 40, 46, 59, 60 (an extra ')' ), 65, 88. Also, the recurrent use of comma or dot before formulas should be corrected.

6. In formula (11), the upper index 'pA' is missing.

The results obtained seem correct. However, some explanations of the formalism used to obtain these results should be given, as stated above (4.).

I believe that, after addressing these issues, the paper can be published.

 

 

 

 

 

 

 

Comments on the Quality of English Language

The English is serviceable but minor corrections are in order.

Author Response

We are thankful to the referee for improving comments and pointing at mistakes and typos. Following the referee report, we corrected abstract, extended introduction, explained or added proper references to clarify (24)-(27) and (28)-(31). Made more corrections requested by the referee.