# Three-by-three pattern in Scaler Counts Ratios

During the initial studies of scaler asymmetries using bunch-fitting algorithm, we noticed that there was a "pattern of threes" in the ratio of scaler counts from one detector to another plotted vs. bXing number. It was usually "three high" followed by "three low" and so on. Here is an example, for CDF-corrected ZDCE / VPDX ratio for a single run:

In order to characterize this 3-by-3 modulation, I have done the following study. This figure is a visual aid to the description; it is a sample plot of a scaler counts ratio vs. bXing number, for 18 bXings:

The wavelength of this pattern is 6 bXings, so we study this effect for phases 0-5 bXings. Denote the phase as "P".

Each bXing will fall into 1 of 20 bins of 6 consecutive bXings, denoted by the integer bin number B, defined as:

Within each bin of 6 bXings, we expect there to be three bXings which will have a high ratio and three bXings which will have a low ratio.
We therefore call the three bXings with a higher bXing number the "Right" bXings (blue color) and the other three which have a lower bXing number the "Left" bXings (red color). Explicitly, a given bX is:

For each set of 6 bXings, we also compute the average ratio.

Then, for every bXing, we divide the ratio by the average within it's set of 6 bXings and fill either the distribution of "Left" bXings (red color distributions) or "Right" bXings (blue color distributions). The sum of the two distributions is shown in black.

The data are presented in 8-panel figures, where each panel is for a single spin pattern. Each vertically-aligned pair of panels is a single spin pattern where the upper panel is the blue beam <--> yellow beam reversal of the lower panel.

The bXing phase P is written in the title along with the pattern number. There is one image of 8 plots for each phase P=0-6.
... it seems that the value of P does not substantially alter the distribtuions (perhaps there's a coding bug?) I've therefore only shown the phases for the rate-safe corrected ratio; all other plots just have P=0

The data set is Run 13 pp510 Longitudinal.

CONCLUSIONS:
--> The conclusion is that this effect is not dependent on spin pattern. When looking through these plots, note that the first and fourth columns are one spin pattern class while the second and third are another class (the classes
are SSSSOOOO and OOOOSSSS).
--> rate-safe corrected pattern 32 has a bimodal structure, but so do the red and blue distributions.
--> CDF ZDCE/VPDX has a number of bimodal distributions, but ZDCW/VPDX does not
--> "self-consistency" VPDE/VPDX and VPDW/VPDX much narrower than ZDCE/ZDCX and ZDCW/ZDCX; for the VPD, W/X is narrower than E/X; for the ZDC, E/X is narrower than W/X
==================================================================================================
:::: Rate-Safe Corrected Ratio
==================================================================================================

----------------------[Rate-Safe Corrected ZDC/VPD]-------------------------------

==================================================================================================
:::: CDF Corrected ZDC bits to VPDX
==================================================================================================

----------------------[CDF Corrected ZDCX/VPDX]-------------------------------

----------------------[CDF Corrected ZDCE/VPDX]-------------------------------

----------------------[CDF Corrected ZDCW/VPDX]-------------------------------

==================================================================================================
:::: CDF Corrected VPD bits to ZDCX
==================================================================================================

----------------------[CDF Corrected VPDE/ZDCX]-------------------------------

----------------------[CDF Corrected VPDW/ZDCX]-------------------------------

==================================================================================================
:::: CDF Corrected VPD E/W bits to VPDX
==================================================================================================

----------------------[CDF Corrected VPDE/VPDX]-------------------------------

----------------------[CDF Corrected VPDW/VPDX]-------------------------------

==================================================================================================
:::: CDF Corrected ZDC E/W bits to ZDCX
==================================================================================================

----------------------[CDF Corrected ZDCE/ZDCX]-------------------------------

----------------------[CDF Corrected ZDCW/ZDCX]-------------------------------

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