The original official paper review site is :

http://drupal.star.bnl.gov/STAR/subsys/pp2pp/ANpaper-review.

 

The PLB's version of the paper (that the reviewers have read) is PLB-D-12-01054.pdf .  Our responses are in "blue". 
 

Revised version is  AN-review.pdf.

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Dear Dr. Weerts,

Thank you for your email of Sept. 25, 2012 which included the comments from two reviewers.  We thank the reviewers for their careful reading of the manuscript and their thoughtful comments.  In the enclosed response, we have addressed all of the reviewers’ comments and questions point-by-point.  We have also revised the manuscript following the reviewers’ comments and suggestions.

Yours sincerely,

Kin Yip (Dr.)
( for the STAR Collaboration )

 

 

Reviewer #1 :

This letter addresses one of long standing issues in hadron scattering at low t, namely the existence of a hadronic spin-flip amplitude. The results presented in this work show that hadronic single-spin amplitudes are vanishingly small at this s, making of A_N a calculable observable.

This work is definitely worth publishing in this journal (after some of the criticisms given below are addressed).

Comments and suggestion

Abstract, line 5
… with the absence of a hadronic … -> … with a vanishing hadronic …

Done.

Page 5, around line 10
The selection procedure is not very clear in the text; if two clusters are found in the same Si plane, the event is rejected or not? If I understood correctly, only events with multiple matched clusters are rejected? What is the fraction of multiple clusters per Si plane? And the fraction of events with more than one cluster per Si plane that are accepted? Wouldn’t be simpler to reject all events with more than one cluster per Si plane, thus reducing further the background?

There are two cases: a) More than one cluster in one plane and no cluster in another plane measuring the same coordinate. Those events are rejected and they were less than 0.2% of the elastic data sample; b) Events with multiple clusters in at least one plane and at least one cluster in another plane measuring the same coordinate. If those events were rejected the elastic data sample would be reduced by 12.7%. The reason we retained events in that class is that there are instrumental effects which can cause extra hits in a Si plane: delta rays, very infrequent pedestal fluctuations. So rejecting an event where one out of eight planes has such a problem would not be right. We also have an additional collinearity cut (comparing the two proton candidates at opposite sides of the IP) before an elastic event is accepted to further reduce the background. 

The fraction of events per Si plane with 2 or more clusters is about 2%.

We have checked the signal background ratio using collinearity distributions like those in Fig. 2 of our paper manuscript for this category of events (with multiple clusters in one plane) and they appeared to be the same as the other candidate events.  This has further convinced ourselves that these have the same characteristics as the rest of the events.  As we have mentioned in the paper, from the collinearity distribution we have observed that the background is < 0.5% which gives rise to delta(A_N)/A_N of < 1%.

 

Page 4, top
Somewhere it should be mentioned that these calculations are performed using 1 photon exchange electromagnetic amplitudes. In reality QED cannot predict these amplitudes since they relay on measured form factors, etc.

We change "with the electromagnetic amplitudes phi^{em}_i described by QED"  to   "with the electromagnetic one-photon exchange amplitudesphi^{em}_i described by QED using the measured  anomalous magnetic moment of the proton".

Page 5
For somebody not familiar with STAR, what are West and East? Also Yellow and Blue should be defined better. Which beam turns clockwise?

West and East are with respect to the Interaction Point (IP).  Next to the word "West" (between two transport matrices), we now say "West side of the IP (WHI,WHO)".  And on page 6 below the 2^nd transport matrix, we add "with respect to the IP" after "East~(E) and West~(W) arms".  Looking down (in -y direction), the Blue beam circulates clockwise and the Yellow beam circulates counterclockwise.  We have now explained this in the caption of Fig. 1.
 

Page 6, 3rd paragraph
phi is measured w.r.t. which direction?

We've now added "(measured counterclockwise from the positive x-axis)" after "azimuthal angle phi".
 

Page 6, Equation 11
In principle, this expression could also contain a term proportional to sin(phi) leading to an up-down asymmetry, which is violating time reversal, and that could be used to further investigate systematic effects. Was this up-down asymmetry studied?

This up-down asymmetry is forbidden by parity conservation.   Doing a fit by function like
                                          A_N * cos(phi) + A_S * sin(phi)
is equivalent to fitting
                                          A_N' * cos(phi - phi_0)

 

which we've done.  This phi_0 (A_S) has a natural explanation of proton spin tilted from vertical axis. 

We used this (pi-phi0) formula to be consistent with our previously published [PLB A_N here] result and because that formula is insensitive to small phi0 values. We also note that those effects would contribute to the false asymmetry which is epsilon_F= -0.0004+-0.0010 as described on the bottom of page 8.

Nevertheless we have performed the cross checks, as commented now on page 9 above the Table I. See our response to your question on page 7, regarding "There are additional systematical checks that one can perform in addition to Equation 13".  As in response to that question and as mentioned in the text [page 9] we used other analyses as a cross check. In those analyses it was found that phi0 was ~<8 deg thus allowing a correction of no more than 1 percent to A_N, which is smaller than the major contribution to our systematic error to beam polarization.

Page 6, 8 lines from bottom
… higher order correction terms … -> … higher order terms …

Done.

Page 6, last line
square root formula -> some authors prefer to call it “geometrical mean”

We have changed " so-called ``square root formula'' [25] "  to " geometric mean [25] "  
        and                   "In the square root formula" to "When using geometric means in the asymmetry formula".

 

Page 7, Equation 12
Define N.

We add "N is the number of events detected in the respective spin and respective phi states".
 

Page 7, line 7
A_NN and A_SS are small, but what is the error on A_NN and A_SS? Are they compatible with zero? If so, then say A_NN and A_SS are very small, compatible with zero.

Done.  We added "(and compatible with zero)".
 

Page 7, epsilon^prime
It would be interesting to see epsilon^prime as a function of t (same binning as epsilon) and not just for the whole t range.

We've of course plotted these and looked at them ourselves.  They are all small and apart from some fluctuations (due to less statistics), including them in the paper there was no additional information to gain and we therefore decided not to show alongside with the 5 epsilon plots becasue of the space constraint.
 

Page 7
There are additional systematical checks that one can perform in addition to Equation 13.
For instance one could extract A_N for the two beams separately and then compare the results. One could also obtain an unpolarized beam by assigning wrong spin orientation to different proton bunches and extract A_N. Were such or similar studies performed? If so they should be added to the discussion.

Yes, we have done the cross checks mentioned.  We added the following in the paragraph just above Table I (page 9):

"We have also done the cross checks to extract A_N using beam polarization of the two beams.  The resulting A_N values were found to be compatible with those in Table I within their statistical uncertainties."


Page 8, Table 1
I would add sys errors (other than from beam polarization) in the table as an additional line even though they are small compared to other errors.

We now show the systematic error of A_N and we explain in the caption of this Table that the systematic error is due to beam polarization.  As we described in the text,  detector/beam related systematic uncertainties on A_N mostly cancel out.  The only non-negligibly significant systematic error on AN determination is the uncertainty of the polarization of the beam.

Page 9, Figure 4
Should include also sys errors in the plot, for instance as a separate horizontal band.

Most systematic errors are correlated/scale errors, so displaying horizontal errors on the curve could be misleading.  We chose to present those errors in Table I.

What are the chi^2 values for the two fits? What is the likelihood that the data are described by the r_5=0 hypothesis?
The points are displayed at the average value of t, <t>, for each bin. Talking of statistical error bars for t to me doesn’t make much sense. Remove 3rd sentence.

We've added the chi^2 values of the two fits in Fig. 4.  The probability (p-value) that the data are described by r_5=0 is 0.57.  The horizontal statistical error includes contribution from the beam divergence: [delta_t/t for single t measurement]/sqrt(N).

 

Page 9, Figure 5
It is not clear to me what one should learn from comparing the two confidence ellipses. It is fine to show the stat and sys errors separately, but I would show only the confidence ellipse obtained with full errors.

We chose to show the correlation of uncertainties contributed by statistically and systematically separately.  We believe they are useful to demonstrate how systematic and statistical uncertainties contribute to the correlation of the fit parameters.

 

Page 10, Table 2
delta b -> delta B

Done.

 

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Reviewer #2 :

The paper reports precision measurements of the transverse single spin asymmetry in elastic pp collisions in diffractive region at high center of mass energy, a continuation of previous measurements at BNL such as the one by S. Bultmann et al. PLB (2006). The measured ratio r5 which is the ratio of the single spin flip to non-flip amplitudes was found to be consistent with zero indicating the absence of hadronic spin flip amplitudes which was also expected from previous measurements such as the one by Okada et al. and by the fact that r5 does not seem to vary with energy. These kind of measurements were initially motivated by the need for absolute polarimeters to determine the beam polarization at RHIC. Not much theoretical progress has been seen for the last two decades indicating that most models do not need hadronic spin-flip amplitude to describe the analyzing power A_N and therefore I do not recommend the present results for publication as a letter. Below are few comments and questions that might be useful to the authors to improve further the paper.

 

We think that our result is of considerable interest because it is the only precision measurement at high energies, where the scattering amplitude is dominated by Pomeron exchange. Extrapolation from lower energy measurements is helpful but not sifficient. Physics Letters B has a tradition of publishing results when the precision has been improved, in this case our measurement improves considerably the result of the pp2pp experiment, S. Bultmann et al. PLB (2006).  The value of this work is that it clearly constrains the size of the r5, which is very small.

Given the uniqueness of polarized colliding beams at RHIC the motivation for this experiment was to answer the experimental question about the existence of the hadronic spin flip as posed by Lapidus [1], and as expressed in the original proposal of the pp2pp experiment.

 

1.  B. Z. Kopeliovich and L. I. Lapidus Yad. Fiz. 19 (1974) 218 [Sov. J. Nucl. Phys. 19 (1974) 114]

Editing

Abstract:

1. at this ?s ---> define it  " .. at this center of mass energy, we ...."

Done.  We now define it at the 1st line of the abstract (and remove "the center of mass energy"  from originally the 2^nd line of the 3^rd paragraph in page 3).

I. Introduction

1. When summarizing the models, it is important to have a brief and clear description. The impact picture model description should be clarified further.

We change "impact picture model based on rotating matter picture for..." for a clearer description to  "impact picture model assuming that the spin-flip contribution is sensitive to the impact parameter distribution of matter in..."

2. Explain after reference [7] how AN in the CNI region is a sensitive probe to the hadronic spin-flip amplitude by linking AN to r5.

Since we define r_5 in Section II, we add after reference [8] (which used to be reference [7])  :  ", which will be discussed in more details in Section II".

II. Hadronic spin-flip amplitude in elastic collisions

1. "Thus the relative amplitude r5 is the measure of single spin flip contribution to elastic scattering" --->  "Thus r5 is the ratio of the single spin flip amplitude (phi5) to non-flip amplitudes  (phi1 and phi3)"

We've changed it to "Thus r5 is the measure of the ratio of the hadronic single spin flip amplitude (phi5) to hadronic single non-flip amplitudes  (phi1 and phi3)"

III. Detection of elastic proton-proton collisions at RHIC

1. The name of the Roman pots should be changed in Fig.1. It should be RP instead of WH, WV, ...

We feel that it is important to show the names of the Roman Pots as they describe their location. 

We've added the following sentence in this Section after the 1st appearance of Fig. 1 :
"There are eight Roman Pots, four on each side of the IP.  Four approach beam horizontally WHI, WHO (EHI, EHO) and four approach beam vertically WVU, WVD (EVU, EVD) as shown in Fig. 1."

Also, next to the word "West" ( between the two transport matrices ), we now have "West side of the IP (WHI,WHO)" instead.

2. Fig 1 caption should be modified to better describe the figure. For example mentioning that the detectors are located in different RHIC rings. There are also fade green vertical lines very close to the interaction point or STAR detector but no labels on them.

We added: "The detectors are placed on the outgoing beams." in the caption and we have cleaned up the figure to get rid of some shadows in the original figure.

V. Single spin asymmetries

1. ?' = -0.0007 (minus is missing)

Done.

2. It would be better if Tab.1 also include other systematics.

We now show the systematic error of A_N, A_N(syst).  And we made it clear in the caption of this Table that the systematic uncertainty on A_N is from polarization uncertainties.

VI. Results and Conclusions

1. "The measured values of AN ... together with predictions based.."  ----> "The measured values of AN ....together with parameterizations based.."

Done.

2. Tab 2 line 7, replace "b" by "B" to be consistent with the text.

Done.


Questions

1. From the reported measurements, can an upper limit be set for the contributions of the hadronic spin-flip amplitudes to SSA?

Since the real and imaginary parts of r5 are all correlated, we cannot just use r5 +/- delta(r5) as the limits.  All the errors are shown in Table II.  We are showing in Table I the errors on delta(A_N) due to statistical and systematic errors.  We have estimated the contribution of the hadronic spin-flip amplitude to SSA using r5.


2. All the models cited in the paper are at least 22 years old and no new models have been developed or published since the last RHIC measurement in 2006. Is there any obvious reason? The original motivation was the need for an absolute polarimeter to determine the beam polarization at RHIC.

It is true that the models are based on the original work by  Buttimore et. al [3]. That work was improved being motivated by a desire to see if a caclulation could be developed to be appleid for absolute polarimetry measurements at RHIC. The most recent calcutation, which takes into account up to date measurements, was published in 2008  [T.L Trueman Phys. Rev. D77, 054005 (2008)], which we added as ref. 4. It needs to be pointed out that absolute polarimtery at RHIC is done using a polarized Hydrogen jet target, which is experimentally the right thing to do, as it removes a theoretical uncertainty of the calculation A_N. As the history of this particular field shows more measurements help constrain theoretical models, where ther is no "absolute" calculation.

3. In the introduction, the authors claimed that the reported measurements offer an opportunity to reveal important information on the nature of the pomeron. The reader would expect to find more discussion about this in the last section "Results and conclusions".
 

We do conclude that the spin flip due to the interference of the Pomeron and Coulomb amplitudes is very small.  

4. The scintillators of which RPs are used for the event trigger

All scintillators of the RPs are used for event triggering and we require coincidence of scintillator hits at both sides of the IP to trigger for elastic events. The elastic coincidences are constructed based on collinearity using (EHI-WHO, EHO-WHI, WVU-EVD, WVD-EVU) combinations of scintillator hits in Roman Pots.


5. If only one cluster in the pair of planes was found, its coordinate was saved for further analysis. What does it means? Do you use it at the end or not?

Yes, it is used.  When there was only one cluster, it indicates that there was an inefficiency in the other plane for that particular event. 

We now change "its coordinate was saved for further analysis" to "we use its coordinate in the analysis".

6. How the width of the distributions in Fig.2 are affected by the beam emittance and the vertex position along z especially if the beam comes with a non-zero angle at the interaction point and how do they affect the transport matrix?

 

The width is primarily due to the beam emittance angular divergence, as confirmed by an independent vernier scan. Beam emmitence is not the major contribution to the resolution in t and its effect is quoted in Table1.  

 

The z-vertex position contribution is very close to zero because of very small a_11 (one of the non-diagonal transport matrix element). The effect is a correction to the major component of the transport matrix L_eff by the amount (a11*z-vertex or a31*z_vertex), for example, where a11 and a31 are the elements of the transport matrix as described in the text. The vertex in STAR is centered at z=0 as determined using the reconstructed STAR TPC's tracks. The z vertex size (sigma_z) is about 50 cm, which yields 0.4 percent correction in terms of the sigma_theta, hence and its contribution can be negelcted as it is much smalller than beam angular divergence.

The crossing angle correction, and other effects due to the beam offset at the Roma Pot location were corrected for in our alignment procedure using data as they result in the common offset of the beam or t=0 trajectory with respect to which the (x,y) positions need to be measured in order to determine the scattering angle.

 
7. What is the uncertainty of the vertex position?

 

The vertex uncertainty (sigma_x or sigma_y) is about 1 mm, as estimated using correlations between the measured track angles and positions overlapping region of the Horizontal and Vertical RPs  and independently by the vernier scans. Because of a11 and a31 terms being small due to the parallel to point focusing their contribution to the angular resolution is small as well, of the order of 16 microradians in the worst case of a31=0.2, to be compared with the 40 microradians contribution due the beam divergence.

 

8. What is the origin of the background (inelastic interactions?) and how does it vary with the momentum transfer t or the x-y coordinate?

The main origin of background comes from beam halo.  Relatively speaking, the largest backgrounds are located at the center of the roman pot closest to the center of the beam / beam pipe and we reject events in these small regions as we mentioned in the last sentence of Section IV.

 

9. What are the detectors efficiencies?

Each detector (plane) is >99% efficient.  We'd like to point out that since we're measuring asymmetries, we don't need to use detector efficiencies in our calculations.

10. How does the fit result change with 5 deg bins in phi? What are the uncertainties of the azimuthal angle?

We've tried the 5-deg phi-bins and the results of the AN fits are statistically consistent with the fits using 10-deg phi-bins. The 10-degree binning used in the analysis is to balance a good resolution in phi and statistical significance in each bin.

The uncertainties to the average azimuthal angle (from RP geometry, Leff in the transport matrix etc.) are very small ~0.002 rad which gives negligible contribution to AN.

 

11. It would be useful to compare the data in Fig.4 with the latest calculations for example the one by C. Bourrely at el. PRD76 (2007) 053002 and it should also be added to the references.

The model quoted above is a CNI curve with sigma_tot, rho and B from their model of elastic scattering. Since the values of \sigma_tot, \rho and B differ very little from COMPETE model predictions we used to calculate CNI curve (r5=0) that prediction lies on top of the curve CNI curve we are showing and we now add this reference in addition to the reference of COMPETE.

12. Fig. 6 shows that data and theory for Im(r5) seems independent of energy. Can you comment on that and its implication on the phase shift between spin-flip and non-flip parts of the pomeron amplitude?

It's described in the figure caption that the models 1,2,3 are energy independent and the model 4 is energy-dependent.  Ours is an experimental paper, hence we are interpreting our result in terms of r5, which is what was done in other experimental papers as well. We certainly think that our result will be used by our theoretical colleagues to extract other variables of interest.

13. Discussion is missing on the physics implication of the measurements and what assumptions will be discarded by models prediction non zero Im(r5).

We do interpret the results in terms of r5, which is common in the experimental papers, see our answer to question 12. We believe that the above question is best answered by our theoretical colleagues and we shall certainly follow up with them on this and question 12.