Bunch Fitting: Relative Scaler Asymmetries


In the following below, I will be focusing on comparisons of the ZDC to the VPDX scaler bit combination. I noticed that if I compare ZDCE  to VPDE or ZDCW to VPDW, the fit parameters vary substantially from fill-to-fill, correlated to the spin pattern. I have thus chosen to look at VPDX as the "minimum bias" scaler subsystem to look for asymmetries in the ZDC, although there are several more possibilities to be looked at.

Furthermore, I will be focusing on asymmetry numbers

  • 1 -- yellow single spin
  • 2 -- blue single spin
  • 3 -- double spin
  • 4 -- like sign
  • 8 -- unlike sign

Everything below is for Run 13 pp510 Longitudinal

-----[ri vs. bXing]--------------------------------------------------------

The two plots below show, for a single run, the ratio ri vs. bXing number; the upper plot is for ri=ZDCE/VPDX and the lower plot is for ri=ZDCW/VPDX.
The error bars are the σ uncertainties of ri. This ratio seems to decrease coming out of each abort gap, and has an unexplained 3-by-3 modulation (shows up with different phases in different runs);
It seems to be more evident in the ZDCE/VPDX than in ZDCW/VPDX, although I haven't looked at that many runs yet. Without accidentals/multiples corrections, the slopes of these fall-offs are steeper.

EDIT (09.11.14): there was a bug where these plots have the bXing no. shifted back by 2 bXings; it's fixed now and the bug did not impact the fit results. The updated plots are shown below:

-----[Sum of H-factor over bXings]--------------------------------------------------------

Looking at the H-factor vs. the bXing number for each run gives a sense of the spin patterns. Summing the H-factors over the bXings gives a sense of how many of each type
of spin state were collided during a run. For example, for the double spin asymmetry, the H-factor is the product of the blue beam and yellow beam helicities. This is so that H=+1
if the helicities are the same and H=-1 if the helicities are opposite. If for a run (fill), the spin pattern was such that we had the same number of like spin states as unlike spin states, then
summing the H-factor over bXing number would yield zero for that run or fill. This never seems to be the case, since for an ideal run (no empty / bad bXings), we usually have 24 bXings
with one type of spin state, and 26 bXings for each of the other three (24+26+26+26 = 102 total bXings; 2 abort gaps are 9 bXings each).

The plots below show the sum of H-factors over bXings vs. run index for the 5 asymmetries under consideration here; most of the fill boundaries are clearly shown in these plots, which
will also be evident in the asymmetry fit parameter plots shown below.

EDIT (09.11.14): There was a bug in the code where the bXings marked as "bad" ("kicked") from the relative luminosity were not being carried over to the bunch fitting code; this
is fixed now and the new 'Sum over H' plots are shown below. It doesn't look like the bug impacted the fit results, but I've updated all the plots below to reflect the change.

-----[Example Sigma Functions]--------------------------------------------------------

For asymmetry 3, the four sigma functions are shown below. Other asymmetry numbers show similar sigma function behaviour.

-----[Constant Fit Parameters]--------------------------------------------------------

The chi^2 minimising constant fit parameter vs. run index is shown below for asymmetry number 3 for the ZDCE/VPDX and ZDCW/VPDX; other asymmetry numbers show almost
exaclty the same fit result; the error bars are propagated statistical uncertainties.

The error on the fits are NOT zero as the plots indicate, they are 3.3e-7.

-----[Asymmetry Fit Parameters]--------------------------------------------------------

Finally, I show the asymmetries resulting from the bunch fitting. Again, error bars are the propagated statistical uncertainties, and the red fit lines are constant fits. I show each asymmetry in a pair of plots: 
one for the ZDCE/VPDX ratio and the other for the ZDCW/VPDX ratio.