Towards a Preliminary A_LL

Links for the 2006 Neutral Pion A_LL analysis

The numbered links below are in 'chronological' type order (i.e. more or less the order in which they should be looked at.) The 'dotted' links below the line are a side-effect in Drupal that lists all daughter pages in alphebetical order. They are the exact same as the numbered links and probably should just be ignored.

1. Run List QA

2. Polarization Files

3. Relative Luminosity Files

4. Cuts etc.

5. Pt Dependent Mass

6. Invariant Mass Distribution

7. Yield Extraction

8. A_LL and Statistical Errors

9. Systematic Errors

10. Sanity Checks

11. DIS Presentation

A_LL

The measurement of A_LL for inclusive neutral pion production is seen below along with statistical error bars and a systematic error band. This asymmetry was calculated using a class developed by Adam Kocoloski (see here for .cpp file and here for .h file.) Errors bars are statistical only and propagated by ROOT. The gray band below the points represents the systematic uncertainties as outlined here. The relative luminosities are calculated on a run by run basis from Tai's raw scalar counts. Each BBC timebin is treated seperately. The theory curves are GRSV predictions from 2005. These will change slightly for 2006.

Bin A_LL (x10^-2)

1 0.80 +/- 1.15

2 0.58 +/- 1.36

3 2.03 +/- 1.89

4 -0.84 +/- 3.06

Cuts and Parameters

Here I will detail the some general information about my analysis; topics that aren't substantial enough to warrant their own page but need to be documented. I will try to be as thorough as I can.

Data

Run 6 PP Long 2 Only.

Run Range: 7131043 - 7156040

Fill Range: 7847 - 7957

Days: 131 - 156 (May 11 - June 5, 2006)

HTTP L2gamma triggered data (IDs 5, 137611)

Run List

Trees using StSkimPionMaker (found in StRoot/StSpinPool/) and Murad's spin analysis chain macro

Trees located in /star/institutions/mit/ahoffman/Pi0Analysis/Murads_Production_1_08/

Cluster Finding Conditions

Detector Seed Add

BEMC 0.4 GeV 0.05 GeV

SMDe/p 0.4 GeV 0.005 GeV

Pion Finding Cuts

Event passes online and software trigger for L2gamma

Energy asymmetry (Zgg) <= 0.8

Charged track veto (no photon can have a charged track pointing to its tower)

BBC timebins 6,7,8,9 (in lieu of a z vertex cut)

At least one good SMD strip exists in each plane

-0.95 <= eta <= .95

Z vertex found

Pt Bins for A_LL

All reconstructed pion candidates are separated by Pt into four bins:

5.20 - 6.75

6.75 - 8.25

8.25 - 10.5

10.5 - 16.0

Simulation

Full pythia (5 to 45 GeV/c in partonic Pt, weighted)

Single pion, photon, and eta simulations (2 - 25 GeV/c in particle Pt, unweighted)

EMC simulator settings:

15% Tower Spread

25% SMD Spread

SMD Max ADC: 700

SMD Max ADC spread: 70

(see this link for explanation of SMD Max ADC parameters)

Four representative timestamps used:

20060516, 062000 (40%)

20060525, 190000 (25%)

20060530, 113500 (25%)

20060603, 130500 (10%)

Full pythia trees located in /star/institutions/mit/ahoffman/Pi0Analysis/MC_Production_2_08/

Single particle trees located in /star/institutions/mit/ahoffman/Pi0Analysis/single_particle_simulations/

DIS 2008 Presentation

Below you will find a link to a draft my DIS 2008 presentation.

Energy Subtracted A_LL Calculation

For my single particle Monte Carlo studies, I argued (here) that I needed to add a small amount of energy to each reconstructed photon to better match the data. This small addition of energy brings the simulation mass distributions into better alignment with the mass distributions in the data. I did not, however, subtract this small bit of energy from reconstructed (data) pions. This affects A_LL in that pion counts will migrate to lower Pt bins and some will also exit the low end of the mass windown (or enter the high end.) So I calculated A_LL after subtracting out the 'extra' energy from each photon. The plot below shows the original A_LL measurement in black and the new measurement in red.

The values from both histograms are as follows:

Bin black (orig) red (new)

1 .0080 .0095

2 .0058 .0092

3 .0203 .0196

4 -.0084 -.0069

So things do not change too much. I'm not sure which way to go with this one. My gut tells me to leave the data alone (don't correct it) and assign a systematic to account for our lack of knowledge of the 'true' energy of the photons. The error would be the difference between the two plots, that is:

Bin Sys. Error (x10^-3)

1 1.5

2 3.4

3 0.7

4 1.5

Integral Delta G Study

Using Werner's code I calculated A_LL for pi0 production over my eta range for 15 different integral values of Delta G. Below I plot the measured A_LL points and all of those curves.

I then calculated chi^2 for each of the curves. Below is the chi^2 vs. integral delta g.

The red line shoes minimum chi^2 + 1. For my points, GRSV-Std exhibits the lowest chi^2, but GRSV-Min is close. My data indicates a small positive integral value of delta g in the measured x range.

Invariant Mass Distribution

The two-photon invariant mass distribution can be roughly broken up into four pieces, seen below^*.

Fig. 1

The black histogram is the invariant mass of all pion candidates (photon pairs) with pt in the given range. I simulate each of the four pieces in a slightly different way. My goal is to understand each individual piece of the puzzle and then to add all of them together to recreate the mass distribution. This will ensure that I properly understand the backgrounds and other systematic errors associated with each piece. To understand how I simulate each piece, click on the links below.

1. Pion Peak

2. Eta Peak

3. Low Mass Background

4. Combinatoric Background.

Once all of the four pieces are properly simulated they are combined to best fit the data. The individual shapes of are not changed but the overall amplitude of each piece is varied until the chisquared for the fit is minimized. Below are plots for the individual bins. Each plot contains four subplots that show, clockwise from upper left, the four individual peices properly normalized but not added; the four pieces added together and compared to data (in black); the ratio of data/simulatio histogramed for the bin; and a data simulation comparison with error bars on both plots.

Bin 1: 5.2 - 6.75 GeV/c

Bin 2: 6.75 - 8.25 GeV/c

Bin 3: 8.25 - 10.5

Bin 4: 10.5 - 16.0

Below there is a table containing the normalization factors for each of the pieces for each of the bins as well as the total integrated counts from each of the four pieces (rounded to the nearest whole count.)

Table 1: Normalization factors and total counts

bin	low norm.	low integral	pion norm.	pion integral	eta norm.	eta integral	mixed norm.	mixed integral
1	121.3	9727	146.4	75103	20.91	5290	0.723	44580
2	77.34	4467	77.81	51783	20.86	6175	0.658	34471
3	40.13	3899	29.41	23687	12.93	6581	1.02	18630
4	5.373	1464	5.225	8532	2.693	3054	0.521	6276

Table 2 below contains, for each source of background, the total number of counts in the mass window and the background fraction [background/(signal+background)].

Table 2: Background counts and Background Fraction

Bin	Low Counts	Low B.F (%)	Eta Counts	Eta B.F (%)	Mixed Counts	Mixed B.F (%)
1	2899	3.60	1212	1.50	4708	5.84
2	2205	3.96	917	1.65	3318	5.96
3	2661	9.29	633	2.21	1507	5.26
4	858	8.56	170	1.70	591	5.89

_{* Note: An astute observer might notice that the histogram in the top figure, for hPtBin2, does not exactly match the hPtBin2 histogram from the middle of the page (Bin 2.) The histogram from the middle of the page (Bin 2) is the correct one. Fig. 1 includes eta from [-1,1] and thus there are more total counts; it is shown only for modeling purposes.}

Combinatoric Background

The last piece of the invariant mass distribution is the combinatoric background. This is the result of combining two non-daughter photons into a pion candidate. Since each photon in an event is mixed with each other photon in an attempt to find true pions, we will find many of these combinatoric candidates. Below is a slide from a recent presentation describing the source of this background and how it is modeled.

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As it says above we take photons from different events, rotate them so as to line up the jet axes from the two events, and then combine them to pion candidates. We can then run the regular pion finder over the events and plot out the mass distribution from these candidates. The result can be seen below.

These distributions will be later combined with the other pieces and normalized to the data. For those who are interested in the errors on these plots please see below.

Eta Peak

I treat the eta peak in a similar way as the pion peak. I throw single etas, flat in Pt from 2 - 25, and reconstruct the two-photon invariant mass distribution for the results. The thrown etas are weighed according to the PHENIX cross-section as outlined here. The mass distributions for the four pt bins can be seen below. (I apologize for the poor labeling, the x-axis is Mass [GeV/c^2] and the y-axis is counts.) Don't worry about the scale (y-axis.) That is a consequence of the weighting. The absolute scale will later be set by normalizing to the data.

These plots will later be combined with other simulations and normalized to the data. The shape will not change. For those interested in the errors, that can be seen below.

Low Mass Background

The low mass background is the result of single photons being artifically split by the detector (specifically the SMD.) The SMD fails in it's clustering algorithm and one photon is reconstructed as two, which, by definition, comprises a pion candidate. These will show up with smaller invariant masses than true pions. Below is a slide from a recent presentation that explaines this in more detail and with pictures.

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We can reproduce this background by looking at singly thrown photons and trying to find those that are artificially split by the clustering algorithm. Indeed when we do this, we find that a small fraction (sub 1%) do indeed get split. We can then plot the invariant mass of these pion candidats. The results can be seen below. (x-axis is mass in GeV/c^2.)

These mass distributions will later be combined with other pieces and normalized to the data. For those interested in the errors on these histograms please see below.

Pion Peak

To study the pion peak section of the invariant mass distribution I looked at single pion simulations. The pions were thrown with pt from 2 - 25 GeV/c flat and were reconstructed using the cuts and parameters described in the cuts, etc. page. The mass of each reconstructed pion is corrected by adding a small amount of energy to each photon (as outlined here.) After this correction the peak of the reconstructed mass distribution is aligned with the peak of the data. The mass distributions from the four bins can be seen below.

Later, these peaks will be normalized, along with the other pieces, to the data. However, the shape will not change.

If you are interested in seeing the errors on the above plots, I reproduce those below.

Polarization

I am using the final polarization numbers from run 6, released by A. Bazilevsky to the spin group on December 4, 2007. The files can be found below.

Pt Dependent Mass

The two-photon invariant mass is given (in the lab frame) by

M = Sqrt(2E₁E₂(1 - Cos(theta)))

where E₁ and E₂ are the energies of the two photons and theta is the angle between those photons. For every real photon we should measure ~135 MeV, the rest mass of the pi0. Of course, the detectors have finite resolution and there is some uncertainty in our measurement of each of the three quantities above, so we should end up measuring some spread around 135 MeV.

But it is not that simple. We do not see a simple spread around the true pion mass. Instead, we see some pt dependence in the mean reconstructed mass.

The above left plot shows the two-photon invariant mass distribution separated into 1 GeV bins. The pion peak region (between ~.1 and .2 GeV) has been fit with a gaussian. The mean of each of those gaussians has been plotted in the above right as a function of Pt. Obviously the mean mass is increasing with Pt. This effect is not particularly well understood. It's possible that the higher the Pt of the pion, the closer together the two photons will be in the detector and the more likely it is that some of the energy from one photon will get shifted to the other photon in reconstruction. This artificially increases the opening angle and thus artificially increases the invariant mass. Which is essentially to say that this is a detector effect and should be reproducible in simulation. Indeed...

The above plot overlays (in red) the exact same measurement made with full-pythia monte carlo. The same behavior is exhibited in the simulation. Linear fits to the data and MC yield very similar results...

-- M = 0.1134 + 0.0034*Pt (data)

-- M = 0.1159 + 0.0032*Pt (simulation)

If we repeat this study using single-particle simulations, however, we find some thing slightly different.

-- M = 0.1045 + 0.0033*Pt

So even in single-particle simulation we still see the characteristic rise in mean reconstructed mass. (This is consistent with the detector-effect explanation, which would be present in single-particle simulation.) However, the offset (intercept) of the linear fit is different. These reconstructed pions are 'missing' ~11 MeV. This is probably the effect of jet background, where other 'stuff' in a jet get mixed in with the two decay photons and slightly boost their energies, leading to an overall increase in measured mass.

The upshot of this study is that we need to correct any single-particle simulations by adding a slight amount of extra energy to each photon.

Relative Luminosity

For my relative luminosity calculations I use Tai's relative luminosity file that was released on June 14th, 2007.

Luminosity File

I read this using the StTamuRelLum class, which, given a run number and BBC timebin, reads in the raw scalar values for each spinbit. Each event is assigned raw scalar counts for each spinbit and every event from the same run with the same timebin should have the same scalar counts assigned. When it comes time to calculate my asymmetry, the relative luminosity is calculated from these scalar counts.

Run List

Below you will find the runlist I used for all of the studies leading up to a preliminary result. For a more detailed look at how I arrived at this runlist please see my run QA page.

Golden Run List

Sanity Checks

Below there are links to various 'sanity' type checks that I have performed to make sure that certain quantities behave as they should

Mass Windows

The nominal mass window was chosen 'by eye' to maximize the number of pion candidates extracted while minimizing the backgrounds (see yield extraction page.) I wanted to check to see how this choice of mass window would affect the measurement of A_^LL. To this end, A_LL was calculated for two other mass windows, one narrower than the nominal window (.12 - .2 GeV) and one wider than the nominal window (.01 - .3 Gev). The results are plotted below where the nominal window points are in black, the narrow window points are in blue and the wide window points are in red. There is no evidence to indicate anything more than statistical fluctuations. No systematic error is assigned for this effect.

Revised Eta Systematic

After some discussion in the spin pwg meeting and on the spin list, it appears I have been vastly overestimating my eta systematic as I was not properly weighing my thrown single etas. I reanalyzed my single eta MC sample using weights and I found that the background contribution from etas underneath my pion peak is negligible. Thus I will not assign a systematic error eta background. The details of the analysis are as follows. First I needed to assign weights to the single etas in my simulation. I calculated these weights based on the published cross section of PP -> eta + X by the PHENIX collaboration (nucl-ex 06110066.) These points are plotted below. Of course, the PHENIX cross section on reaches to Pt = 11 GeV/c and my measurement reaches to 16 GeV/c. So I need to extrapolate from the PHENIX points out to higher points in Pt. To do this I fit the PHENIX data to a function of the form Y = A*(1 + (Pt)/(Po))^-n. The function, with the parameters A = 19.38, P0 = 1.832 and n = 10.63, well describes the available data.

I then caluclate the (properly weighted) two-photon invariant mass distribution and calculate the number of etas underneath the pion peak. The eta mass distributions are normalized to the data along with the other simulations. As expected, this background fraction falls to ~zero. More specifically, there was less than ten counts in the signal reigon for all four Pt bins. Even considering a large background asymmetry (~20%) this becomes a negligable addition to the total systematic error. The plots below show the normalized eta mass peaks (in blue) along with the data (in black.) As you can see, the blue peaks do not reach into the signal reigion.

Unfortunately, the statistics are not as good, as I have weighted-out many of the counts. I think that the stats are good enough to show that Etas do not contribute to the background at any significant level. For the final result I think I would want to spend more time studying both single particle etas and etas from full pythia.

I should also note that for this study, I did not have to 'correct' the mass of these etas by adding a slight amount of energy to each photon. At first I did do this correction and found that the mass peaks wound up not lining up with the data, When I removed the correction, I found the peaks to better represent the data.

In summary: I will no longer be assigning a systematic from eta contamination, as the background fraction is of order 0.01% and any effect the would have on the asymmetry would be negligible.

Single Spin Asymmetries

The plots below show the single spin asymmetries (SSA) for the blue and yellow beams, as a function of run index. These histograms are then fit with flat lines. The SSA's are consistent with zero.

Systematics

We need to worry about a number of systematic effects that may change our measurement of A_LL. These effects can be broadly separated into two groups: backgrounds and non backgrounds. The table below summarizes these systematic errors. A detailed explanation of each effect can be found by clicking on the name of the effect in the table.

Systematic Effect	value {binwise} (x10^-3)
Low Mass Background	{1.0; 1.1; 3.8; 1.0}
Combinatoric Background	{1.0; 0.86; 1.6; .03}
Photon energy Uncertainty	{1.5; 3.4; 0.7; 1.5}
Non Longitudinal Components^*	0.94
Relative Luminosity^*	0.03
Total^**	{2.3; 3.8; 4.3; 2.0}

* These numbers were taken from the Jet Group

** Quadrature sum of all systematic errors

Alternate Calculation of Eta Systematic

At the moment I am calculating the systematic error on A_LL from the presence of Etas in the signal reigon using theoretical predictions to estimate A_LL^eta. The study below is an attempt to see how things would change if I instead calculated this systematic from the measured A_LL^eta. Perhaps, also, this would be a good place to flesh out some of my original motivation for using theory predictions.

First order of buisness is getting A_LL^eta. Since this was done in a quick and dirty fashion, I have simply taken all of my pion candidates from my pion analysis and moved my mass window from the nominal pion cuts to a new window for etas. For the first three bins this window is .45 GeV/c² < mass < .65 GeV/c² and for the fourth bin this is .5 GeV/c² < mass < .7 GeV/c². Here is a plot of A_LL^eta, I apologize for the poor labeling.

I guess my first reason for not wanting to use this method is that, unlike the other forms of background, the Etas A_LL ought to be Pt dependent. So I would need to calculate the systematic on a bin-by-bin basis, and now I start to get confused because the errors on these points are so large. Should I use the nominal values? Nominal values plus one sigma? I'm not sure.

For this study I made the decison to use A_LL^true as the values, where A_LL^true is calculated from the above A_LL using the following formula:

A_LL^M = (A_LL^T + C*A_LL^Bkgd)/(1 + C)

Remembering that a large portion the counts in the Eta mass window are from the combinatoric background. I then calculate the background fraction or comtamination factor for this background (sorry I don't have a good plot for this) and get the following values

Bin Bkg fraction

1 77.2%

2 60.9%

3 44.6%

4 32.6%

Plugging and chugging, I get the following values for A_LL^true:

Bin A_LL^T

1 .0298

2 .0289

3 -.0081

4 .175

Using these values of ALL to calculate the systematic on A_LL^pion I get the following values:

Bin Delta_A_LL^pion (x10^-3)

1 .33

2 .38

3 .63

4 3.1

Carl was right that these values would not be too significant compared to the quad. sum of the other systematics, except for final bin which becomes the dominant systematic. In the end, I would not be opposed to using these values for my systematic *if* the people think that they tell a more consistent story or are easier to justify/explain than using the theory curves. (i.e. if they represent a more accurate description of the systematic.)

Combinatoric Systematic

For the combinatoric background systematic we first estimate the background contribution (or contamination factor) to the signal reigon. That is we integrate our simulated background to discern the precentage of the signal yield that is due to background counts. The plots below show, for each of the four bins, the background fraction underneath the singal peak. The background (simulation) is in green and the signal (data) is in black and the background that falls in the signal reigon is filled-in with green.

The background fractions for the bins are

Bin 1: 6.1%

Bin 2: 6.1%

Bin 3: 5.7%

Bin 4: 6.2%

Then I consider how much this background fraction could affect my measured asymmetry. So I need to meausre the asymmetry in the high-mass reigon. I do this, taking the mass window to be 1.2 to 2.0 GeV/c². I do not expect this asymmetry to be Pt-dependant, so I fit the asymmetry with a flat line and take this to be the asymmetry of the background, regardless of Pt. The plot below shows this asymmetry and fit.

Finally, I calculate the systematic error Delta_A_LL = A_LL^True - A_LL^Measured where:

A_LL^M = (A_LL^T + C*A_LL^Bkgd)/(1 + C)

And C is the background fraction. This yields in the end as a systematic error (x10^-3):

Bin 1: 1.0

Bin 2: 0.9

Bin 3: 1.6

Bin 4: 0.03

Eta Systematic

For the eta background systematic we first estimate the background contribution (or contamination factor) to the signal reigon. That is we integrate our simulated background to discern the precentage of the signal yield that is due to background counts. The plots below show, for each of the four bins, the background fraction underneath the singal peak. The background (simulation) is in blue and the signal (data) is in black and the background that falls in the signal reigon is filled-in with. Below that is the same four plots but blown up to show the contamination.

Here we blow up these plots

The background fractions for the bins are

Bin 1: 1.50%

Bin 2: 1.65%

Bin 3: 2.21%

Bin 4: 1.70%

Then I consider how much this background fraction could affect my measured asymmetry. So I need to measure the asymmetry in the etas. So instead of measuring the asymmetry in the etas I will use a theoretic prediction for A_LL. From GRSV standard and GRSV min I approximate that the size of A_LL in my Pt range to be between 2 - 4%.

I stole this plot from C. Aidala's presentation at DNP in Fall 2007. Since GRSV-Max is ruled out by the 2006 jet result I restrict myself only to min, standard and zero. For a conservative estimate on the systematic, I should pick, for each Pt bin, the theory curve that maximizes the distance between the measured and theoretical asymmetries. Unfortunately, at this time I do not have predictions for Pt above 8, so I must extrapolate from this plot to higher bins. For the first two bins this maximum distance would correspond to GRSV standard (A_LL^bg ~ 0.02). For the third bin, this would correspond to GRSV = 0 (A_LL^bg ~ 0.). For the fourth bin (which has a negative measured asymmetry) I extrapolate GRSV standard to ~4% and use this as my background A_LL.

Systematic (x10^-3)

Bin 1: 0.18

Bin 2: 0.23

Bin 3: 0.43

Bin 4: 0.82

Low Mass Systematic

For the low mass background systematic we first estimate the background contribution (or contamination factor) to the signal reigon. That is we integrate our simulated background to discern the precentage of the signal yield that is due to background counts. The plots below show, for each of the four bins, the background fraction underneath the singal peak. The background (simulation) is in red and the signal (data) is in black and the background that falls in the signal reigon is filled-in with red.

The background fractions for the bins are

Bin 1: 3.5%

Bin 2: 4.2%

Bin 3: 9.3%

Bin 4: 8.3%

Then I consider how much this background fraction could affect my measured asymmetry. So I need to meausre the asymmetry in the low-mass reigon. I do this, taking the mass window to be 0 to 0.7 GeV/c². I do not expect this asymmetry to be Pt-dependant, so I fit the asymmetry with a flat line and take this to be the asymmetry of the background, regardless of Pt. The plot below shows this asymmetry and fit.

Finally, I calculate the systematic error Delta_A_LL = A_LL^True - A_LL^Measured where:

A_LL^M = (A_LL^T + C*A_LL^Bkgd)/(1 + C)

And C is the background fraction. This yields in the end as a systematic error (x10^-3):

Bin 1: 1.0

Bin 2: 1.1

Bin 3: 3.7

Bin 4: 1.1

Yield Extraction

After all the pion candidates have been found and all the cuts applied, we need to extract the number of pions in each bin (in each spin state for A_LL.) To do this we simply count the number of pion candidates in a nominal mass window. I chose the mass window to try to maximize the signal region and cut out as much background as possible. For the first three Pt bins, this window is from .08 - .25 GeV/c² and in the last bin the window is from .1 - .3 GeV/c². The window for the last Pt bin is shifted mostly to cut out more of the low mass background and to capture more pions with higher than average reconstructed mass. The windows can be seen below for bins 2 and 4.

These Pt bins are broken down by spin state, and the individual yields are reported below.

Spin Sorted Yields
Bin	uu	du	ud	dd	Total
1	20209	20088	19961	20231	80489
2	14088	14057	13645	13825	55615
3	7224	7080	7107	7204	28615
4	2505	2470	2552	2491	10018