AN paper Q & A
Flemming Videbaek :
A few persons/groups have made suggestions to this sentence. Now it's changed to be:
"The Roman Pot stations are located on either side of the STAR interaction point (IP) at 55.5 m and 58.5 m with horizontal and vertical insertions of detectors respectively."
Andrzej Sandacz:
> A) line 172
> typo: double "in" before "Fig. 1"
Done !
> B) line 211 and Eqs (7), (8), (9)
> L^{eff}, and also L^{eff}_x, L^{eff}_y are not defined explicitely.
> One can try to infer which elements of the transport matrix may correspond to L^{eff} by guessing that they must be the largest
> values, but still distiction between L^{eff}_x and L^{eff}_y is not straightforward.
> selected example with values of the transport matrix elements for a particular store. I understand the aim of the change:
> to give idea about values of TM elements. But for an average reader these precise values probably are only of moderate
> interest. Thus I would propose to go back to the previous version, i.e. general Eq. (7) with symbols, which is more transparent.
Now, we have the transport matrix in both symbols and in real nos. and so L^{eff}_x and L^{eff}_y are clearly defined.
>C) lines 243-244
>It should then look like "[...] of this particular store, and then averaged over the stores."
Done !
> D) Table I
> First double-line with "<" and ">" does not look nice
> Each pair of numbers separated by "-"
> E.g. "0.003-0.005 0.005- 0.01 etc"
Done !
> E) line 298
> missing "In" before "table II"
Hal for the Argonne group :
> ** line 124 - "... which the non-flip ..." -> "... which a non-flip ..."
Done !
> ** l.135 - "... from the BNL AGS ..."
Done !
> ** l.143,4 - you may wish to consider a slight change in wording to "... two helicity conserving (phi_1 and phi_3),
> two double helicity-flip (phi_2 and phi_4), and one single helicity flip (phi_5) amplitude - see Ref[3] for definitions."
Done !
> ** l.150 - please change to "Each of the amplitudes consist of ..."
Done ( => Each of the amplitudes consists of ...") !
> ** l.156 - the formula for phi_5^had(s,t) is split on two lines. Please consider modifying the LaTeX to insure it all fits on a single line,
> or perhaps use an equation environment for it.
Done !
> ** l.163,4 - probably for consistency, change to "...constant, gamma = 0.5772 is Euler's constant, and ..."
Done !
> ** l.166, 190, 193 - we think the LaTeX symbol \approx may be more appropriate in these cases and others in the paper
> than the symbol \sim. Please consider changing.
Done (the one on p. 190 changed to "about" as Stephen suggested and also changed on pages 219, 241, 242, 262, 263 and 272) !
> ** l.168 - maybe change "downstream" -> "away from"??
A few persons/groups have made suggestions to this sentence. Now it's changed to be:
"The Roman Pot stations are located on either side of the STAR interaction point (IP) at 55.5 m and 58.5 m with horizontal and vertical insertions of detectors respectively."
> ** l.172 - "... position at the interaction ..." Also remove one "in" later in the line - "in in" -> "in"
Done !
> ** l.212,3 - add non-breaking space between "West" and "(W)" so the "(W)" doesn't end up alone on the following page.
Done !
> ** l.214 - "... in small corrections of less ..."
Done !
> ** l.215 - "... from our data; see ..."
Done !
> ** l.220 - perhaps "This figure" -> "Figure 2"
Done !
> ** l.225 - "... with p = 100.22 GeV/c the beam momentum." or something like this to explain why p is not 100.00.
Actually, even the total energy is not 100.00 GeV. All of these come from the fact that G-gamma has been set to be 191.5 between 191 and 192 (to avoid integers which might result in resonance). We've changed it to be "p = 100.2 GeV/c" as have the fraction error in the order about 1e-4.
> ** Eq. 11 - this equation assumes perfectly transversely polarized beams. We believe it is possible that due to
> non-ideal beam orbits and magnetic fields or magnet alignments, the beams may have a small longitudinal
> component at the STAR IR even when the rotators are off. This could lead to a (A_LS = A_SL)sin(phi) term in the
> equation. It will (probably) also be negligible in your analysis as you describe ~ line 241. Please consider whether
> you wish to add such a term in the equation and a couple words in the text about it. Alternately, you might
> mention that higher order correction terms are ignored in the equation.
We now mention "higher order correction terms are ignored" under Equation 11, as you suggest.
> ** l.250 - "Obtained" -> "The derived" or "The values of epsilon' obtained"
Done ("The derived") !
> ** l.253,4 - perhaps combine this single sentence paragraph with the preceding paragraph??
It's appropriate to leave this short paragraph as it is because the content in this paragraph
(64 bunches for different spin patterns) is relevant to previous 4/5 paragraphs, not just the preceding paragraph.
> ** l.255 - "errors" -> "uncertainties"?? "...of t, the background ..."
Done !
> ** l.256 - "The two main ..." "...uncertainty in the t reconstruction ..."
Done !
> ** l.272 - perhaps quote the actual values instead of "~55" and "~10"??
The "collinearity" in reality is slightly different from run to run, not just one single value.
> ** l.275 - "is unpolarized, the asymmetry ..."
Done !
> ** l.281 - probably better to use non-breaking spaces so there is no break in the equation for <P_B - P_Y>.
Done !
> ** l.283 - do we understand correctly that there may be a false asymmetry that is proportional to the beam polarization, and it has not been ruled out by your tests?
There we try to explain in detail that the false asymmetry is ~ 0.
> ** l.298 - "In Table II we show ..." "In line one of the table ..." or "In the first line of the table ..."
Done !
> ** Fig.4 caption - "... show statistical uncertainties."
Done !
> ** Fig.5 caption - circle -> ellipse in two places.
> We are also not sure whether the ends of the crosses shouldn't lie on the edges of the one sigma ellipses.
Done ! And the ends of the crosses DO lie on the edges of the one sigma ellipse if one looks carefully or uses a ruler to guide one's eyes. ( This is like one of those optical illusion. )
> ** Fig.6 - The text and error bar run into each other for (d).
> Fig.6 caption - is the vertical dashed line the average of experimental values or just zero or ...??
> Please include in the caption.
We've added "The vertical dashed line indicates where Im($r_5$)=0." at the end of the Fig. 6 caption.
> ** l.299,300 - this sentence is a bit confusing. You use "variable" for both deltaB and Re r_5, we believe. Maybe
> something like "The remaining lines show changes of Re r_5 and Im r_5 when the parameter was varied by +/- 1 sigma
> during the fit procedure." We are not sure this is even what is meant. Sorry.
Actually, you've understood perfectly. We've made the changes as you've suggested.
> ** l.303-305 - suggest slight rewording "The total systematic error, including the effects related to lines 2-7 of Table II, is obtained by
> adding the covariance error matrices. The final result on r_5 is shown in Fig. 5, with contributions from both statistical and systematic
>uncertainties."
Done !
> ** l.308,9 - "... more emphasized in estimating ..." we are confused by this and aren't sure what the authors are trying to say.
It just says the AN peak is more sensitive to Im(r5) and thus attracts more attention. This explains why we
look at the Im(r5)'s in Fig. 6.
> ** l.310 - "...Fig. 6, together ..." "theoretical models based on various ..." or "theoretical models related to various ..."
Done ( changed to ", together with predictions of theoretical model based on various ..." ) !
> ** Finally, there seems to be a mixture of "tenses" in the text. For example, in line 217 the analysis is described in present tense "angles
> are reconstructed", "requirement is imposed", while in l. 222 the past tense occurs "events were used". Please have someone who is
> really good at grammar (not us!!) check through the tenses.
The action of doing "data selection" section was meant to be written in 'past tense'. Thank you for spotting those two "present tense" cases and we have corrected them (to "past tense"). Another one on line "p. 193" has also been corrected.
Panjab University :
> Page 6 line no. 222
> After the selection chi**2 < 9, please explain.
Most cuts are at 3 sigma-level and so this so-called chi**2 at 3-sigma is 3**2 = 9.
> Page 7 FIG. 3
> Is it possible to display the distribution of forbidden asymmetry for the five t ranges in
> FIG. 3(a)-(e) instead of showing for the whole range of t in FIG.3f?
>In FIG. 3(a) the error bars are large for two points around phi 80. Similar trend is seen in FIG. 3(e).
>It is not seen for the negative phi values. Any reason.
We feel that the figures are already too busy and it's not good to add more. The larger error b\
ars are because of low statistics and they're related to how close the respective vertical roma\
n pots were moved to the center of the beampipe. During the run, we tried to move the pots as c\
lose to the beampipe as possible without having too much background.
> Page 8 Table 1
> First bin (0.003< -t <0.005), the statistics is less(20%) as compared to other bin. Its width is
> 0.002 as compared to 0.005 and 0.15 for other bins. I think fit in FIG. 4 should be made removing this point.
The point with the smallest -t range is probably the most interesting point in this measurement and it contributes a lot in determining the shape.
Janusz from the Cracow group :
> General:
> Explain fully the coordinate system shown in Fig. 1
In the caption of Fig. 1, I now add "Positive y is pointing towards the sky and positive x is pointing to the center of the RHIC ring."
> Check the use of error vs. uncertainty
Hal from the Argonne group has made similar comments and we adopted his corrections for the usage of error vs uncertainty. It's also a common theme of argument among physicists of different schools.
> Section 2
> 142. two identical particles - -> two protons
Done !
> 144. At very high energy sqrt(s) - -> At high centre of mass energy, sqrt(s),
Now, we define "center of mass energy" for sqrt(s) in "Introduction" (the 1st time that it appears, line 127) and here, we just say "At very high sqrt(s)".
> 154-155. The contribution of the two spin-flip amplitudes, …., to the asymmetry AN is small as indicated by both experimental estimates [] and th. pred.[18]
OK. We have changed it to :
"The contribution of the two double spin-flip hadronic amplitudes, …., to the asymmetry AN is small, as indicated by both th. pred.[18] and experimental estimates [19,20]".
> 158. Remove word due
"due" removed added "process" at the end. Changed to "...contribution to the elastic scattering process."
> 160. Make comma after formula (5) and continue with: where tc …
If we do this, there would be two "where". We keep it as it is.
> Section 3
> 168. on each side - -> on West and East side
A few persons/groups have made suggestions to this sentence. Now it's changed to be:
"The Roman Pot stations are located on either side of the STAR interaction point (IP) at 55.5 m and 58.5 m with horizontal and vertical insertions of detectors respectively."
> 171. their angles .. IPs - -> their scattering angles at the IP
Done !
> 178. Replace: the sensitive with this
Done !
> 190. Give also value of the distance of 10 mm in units of the beam width at RPs.
It's about 10-12 sigma's but it's probably difficult to be exact.
>Section 4
>199. replace: adjacent with such since same orientation planes are not adjacent
Done !
> 214. small correction less than 4 $\mu$rad, the full - -> small, less than 4 $\mu$rad, correction, the full
We've adopted Hal's suggestion : "small corrections of less than 4 $\mu$rad" .
> 218-221. are not very clear, especially the use of “similar’ or “typical”
> replace: are taken from the fits similar to those in Fig. 2 - -> are taken from the fits to data performed for each run. An example is presented in Figs. 2(a) and 2(b).
We've changed to "are taken from the fits to data performed for each data segment. An example is shown in Fig.~2."
> 222. After the selection… - -> The requirement of … left about 21 million events for asymmetry measurement
Done !
> 224. 4-momentum transfer t assigned - -> four-momentum transfer, t, was assigned
Done !
>Section 5
>235. asymmetry $\epsilon(\phi)$ - -> asymmetry, $\epsilon_N(\phi)$,
Done !
> 242. leading to a constraint .. neglected- -> constraining \delta(\phi) to ~0.002 which can be safely neglected.
Done !
> 243. polarization sum of - -> the sum of polarizations of both beams for
Done !
> 245. according to Eq. (12) - -> of formula given by Eq. (12)
Done ( "of the formula given by Eq. (12)" ) !
> 250. Omit: (“forbidden asymmetry” later on) .. Fig. 3(f) - -> asymmetry which may be used for estimation of the detector induced asymmetries (see below) is
> shown in Fig. 3(f) for the whole t-range.
It's felt that the present form is clearer.
>256. The major systematic errors … originate from - -> The major systematic uncertainties of the present measurement are due to …
Done ( changed to "The major systematic uncertainties of the experiment are due to ...") !
> 257. the position of the t = 0 trajectory … - -> the position of the t = 0 elastically scattered proton trajectory or the beam position
"t = 0 trajectory" is an ideal trajectory with no scattering.
> 258. in the focusing quadrupoles … RPs. - -> in the Q1-Q3 focusing quadrupoles.
Done !
> 268-269. The simulation included … optics - -> Simulation of the elastically scattered proton transport through the RHIC magnetic
> lattice and the apertures was performed and the detector acceptance was calculated.
The present form seems cleaner and the acceptance is mentioned in the following sentence.
> 270. the West, while for the East - -> the West side, while for the East side
Done !
> 274-275. Assuming the background is unpolarized - -> Assuming that the background is the beam polarization independent …
"unpolarized" is probably easier to understand.
> 277. Remove: The polarizations … [27]. Move this reference to the next sentence so: Polarizations and total errors - -> Polarizations
> and their uncertainties … for the four stores were … [27].
Done !
> 280. 4 - -> four
Done !
> 283-284. Replace these lines with: The false – detector induced – asymmetry, $\epsilon_F$, which is independent of the beam polarization
> can be expressed in terms of …
> 285. remove whole line 285
The present form seems clearer.
> 287. This result in a false asymmetry - -> This gives …
Done !
> Section 6
> 293. along with two curves of predictions - -> together with predictions
Done !
> 297-298. contours for 1 \sigma confidence level -> 1$\sigma$ confidence level contours
Done !
>298-302. Table II shows the fitted values of Re r5 and Im r5 together with statistical and total systematic uncertainties. Also, the contributions
> to the systematic uncertainty are given in this table. They are due to: systematic uncertainty on Leff , alignment ……. .They were obtained by
> changing the value of the considered parameter by $\pm$1 standard deviation.
A few people have commented/suggested, we've changed to:
"In Table II, we show the central value of the fit and uncertainties on Re$\:r_5$ and Im$\:r_5$ due to various effects. In the first line of the table,
the statistical error to the fit with the central value of the parameters is shown. The remaining lines show changes of Re$\:r_5$ and Im$\:r_5$,
when the parameter was varied by $\pm$1$\:\sigma$ during the fit procedure. ......"
> 302. One can see … - -> The dominant source of the systematic uncertainty is due to the beam polarization uncertainty.
Done !
> 304. make a new paragraph starting with: The final result on … . The error bars represent the systematic and statistical uncertainties added in quadrature.
We've made a new paragraph.
> 308-309 Remove sentence: Since the maximum... since it is not needed
This sentence explains why we look at Im(r5), but not Re(r5).
> Figures and Tables:
> Fig 2: .. The curves represent the fit of the Gaussian signal and a linear background
Changed to "The overlaid curves represent the fits with a Gaussian signal and a linear background."
> Fig 3: … shown in Tab. I. (f) Asymmetry $\epsilon^\prime$ proportional to the difference of polarizations of the beams, $P_B -P_Y$,
> for the whole measured t-range.
Changed to "Table 1 ... measured t range."
> Fig. 4: The measured single spin asymmetry, $A_N$, as a function of the four-momentum transfer, t. … . The solid and dashed lines represent
> results of calculations with fitted $r_5$ and $r_5 = 0 $ values, respectively.
Added the word "measured".
> Table 1.
> Nbr - -> No
Done !
> Present the main result with bold face font
It's difficult to say which nos. are more important in this table. ( And we have changed 1st two lines into one line as Andrzej has suggested. )
> Table II. …. Measurement induced uncertainties (1) – statistical, …. (4). Uncertainties associated with the fit: (5) – the total cross-section …
Changed to "Table II: ..... (1): Statistical Uncertainties. (2)-(4): Systematic uncertainties associated with this measurement.
(5)-(7): Systematic uncertainties associated with ...."
Steven Heppelmann for Penn State U. :
>If I look for an issue it would be the rather large chi-square value on Figure 3b (32.68 for 17 DOF). This is fairly unlikely
>(1-2%) and might suggest that the errors bars on the 17 points should actually be about sqrt[2] larger than the ones
>plotted. In fact, most of the points of Figure 3 have chi2/dof >1 which as a group is somewhat unlikely too.
>Because the statistical error from the fits are only about 1/2 of the error on polarization, I don't think the story would
>change much but I just wanted to comment and ask if some words in the text should be added to indicate that this has
>been considered in the systematic error analysis.
If we look at the variation of point-to-point, it's bigger than statistical variations. That means there
are some point-to-point systematic uncertainties. These variations are likely from the variations of
geometry of t=0 and the uncertainties are factored in systematic uncertainty of delta_t(alignment).
If we add systematic errors to the points before the fits, we'll certainly get better/more realistic chi-sqs.
The other point is that the function we are fitting with is not "perfect".
If we add high order/off-set terms, such as phi0 which we've decided to drop, chi-squares get better.
We have chi2/dof = 11.1/16, 25.8/16, 12.6/16, 23.2/16, and 14.2/16 for the 5-bins (when phi0 is included).
The errors look small partly because we use the same “large scale” for all the plots because
we want to accommodate the with the largest AN scale, ie. 3(a), in which the chi2/dof = 11.32/17 < 1.
For the other 3 fits, chi2/dof~1.18, 1.54 and 1.32 which seem to be reasonable experimental fitting results.
And of course, we've used the method/formula to calculate the error on each bin.
Shan Dong University :
> 1)In line 214,215, "full transport matrix was used", does this mean Eq(8),Eq(9) and L_{x,y}^{eff} are not used for
> the calculation of angles? If so, how to understand the uncertainties of L^{eff} in line 257,263,274 and in table II?
> Or they are only used in estimating the uncertainties?
L^{eff} (for x or y) are just two of the elements (the two > 20 m) in the transport matrix
and so when the transport matrix was used, they were indeed used. These were the two dominating terms in the transport matrix and the other elements are very small
compared to L^{eff}. Conceptually, it's often easier to just consider these two terms
when you try to understand various things in the analysis. So, equations (8) and (9) are
just approximations to help people understand/grasp the main idea and the transport
matrix has been used in the analysis. And indeed, the uncertainties L^{eff} are
essentially the uncertainties of the transport.
> 2) Line 223, ""angles $theta$ and azimuthal angle $phi$..." , suggest to change to
> "angle $theta$ and azimuthal angle $phi$..."
Done !
> 3) Line 241: "preliminary results of this experiment [20] show that..."
> Are these results not part of this analysis or not further checked using the
> final data sample? It is a bit surprising to cite preliminary results of ourselves
> for the same analysis, as we are the same collaboration or group.
The double-spin asymmetries A_NN/A_SS indeed belong to another set of analysis. Unlike the single-spin asymmetry (A_N) in this paper, there is NO square-root formula for extracting A_NN/A_SS. The square-root formula helps cancel out a lot of luminositybunch variance etc. We therefore need reliable normalization (bunch intensities etc.) for the A_NN/A_SS analysis which is an ongoing effort. We'd like to publish the A_N and r5 results first.
> 4) In line 305, "Re r_5 =0.00167 +/- 0.0063 in line 306 Im r_5=0.00722+/-0.057",
> The rounding of the digits should be consistent and make real sense as in other places
> in the paper.
What we've done is to show 3 significant figures for the measurements and 2-significant figures
for the errors. A "typical" (but not always) rule for displaying experimental uncertainties is to show
1-significant figure less since the uncertainty is an estimate and cannot be more precise than the best
estimate of the measured value. For some errors are too small compared to the dominant one (polarization),
so we've also restricted the significance to 4 decimal points which is ~O(1%) of relative accuracy.
> 5)in line 312, got somewhat confused with the words "...due to...". Suggest to remove "due".
Done !
Stephen Bültmann :
> line 171 : only -> almost exclusively
Done !
> line 172 : insensitive -> nearly insensitive
Done !
> line 190 : "was ~ 10 um" --- may use "about"
Done !
> line 204 : "vertical pots" -> "vertical RPs"
Done !
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