[d2n-analysis-talk] Beta distribution

[Brad Sawatzky]

On Sat, 27 Mar 2010, David Flay wrote:

> I've been tweaking the S1 average times for each paddle, and it turns
> out that that shoulder on beta seems to be highly correlated to the
> 4th and 5th paddles (3rd and 4th indices if we start from 0).
> Attached are the some characteristic plots.
> 
> I think beta has improved, but I'm not sure how much more I can do to
> get the shoulder to fully go away.  If you look at my previous plots
> of beta, you'll see <now> that the higher end of beta decays much
> smoother (in fact, it almost perfectly matches an exponential decay).

The behavior of the 'LHRS beta' plot isn't very illustrative.  The tail
is driven by the calibration error around x=0.25.  The tail is small
because only that small region of the focal plane is miscalibrated.

> There are still some blips in beta vs. track-x, however.

It's these blips in the 'Beta vs. X' and 'S1 vs x' plots that contain
all the information.  The logic is this:
  Assumptions:
    - The LHRS focal plane in this kinematic is dominated by electrons.
    - The distribution of those electrons in x, y is reasonably uniform.
    - The distance between S1 and S2m is constant (or at least does not
      change radically from paddle to paddle).
  Conclusions:
    - The time it takes for an electron to travel between the two
      scintillator planes is essentially constant.  (The electron is
      traveling at 'c' and the distance between the planes is fixed.)
    - Therefore any observed variation in (t_S2m - t_S1) across the
      focal plane is either
        A) an artifact of the electronics, or
        B) a bug in the analysis code.

(A) is corrected by appropriately fixing the various calibration
constants.  If those are all correct, then there must be a bug in the
code: ie. (B).

(B) is more disturbing than (A).  I think the problem is in (A).


There are a number of things that puzzle me about these plots:
 a) The x-range populated in the Beta vs. x plot is quite different
    (smaller) than the x-range populated by the s1 and s2m plots.  Why?
 b) S1 is supposed to have 6 paddles, yet there are far more than 6
    discrete regions showing different structure in the S1 plot.
 c) Judging by the extent of the offset regions in the S1 vs. X plot, I
    can convince myself that there are at least 14 discrete "blocks"
    plotted, if I count the little blips at the far edges then I get 16.
 d) S2m carries the timing for the trigger L1A (which is the common stop
    for S1).
 e) Therefore, the variation seen is S1 vs. X is really paddle-to-paddle
    variation in the _S2m_ paddle offsets.

That (e) is where you should focus your attention.

-- Brad

-- 
Brad Sawatzky, PhD <brads at jlab.org>  -<>-  Jefferson Lab / Hall C / C111
Ph: 757-269-5947  -<>-  Fax: 757-269-5235  -<>- Pager: brads-page at jlab.org
The most exciting phrase to hear in science, the one that heralds new
  discoveries, is not "Eureka!" but "That's funny..."   -- Isaac Asimov