;; This buffer is for notes you don't want to save, and for Lisp evaluation.
;; If you want to create a file, visit that file with C-x C-f,
;; then enter the text in that file's own buffer.


Hi Dick

For the last line of the calculation, I have
a problem with taking <Pmu> (from the lever arm)
as the multiplier. This goes to the heart of
why we have a systematic uncertainty due to
the psPACT. I'll try and explain my concern.

Let's assume:

i)  in zone 1 a fraction m stop in the metal,
    and (1-m) stop in the gas
ii) no fast depolarisation in the gas
    (and pmu0=1 for both metal and gas)
iiv) lambda_metal = 1
     lambda_gas   = 30

That means
   Pmu(t)_true = m * exp( - lambda_metal * t)
                 + (1-m) * exp( - lambda_gas * t)

When we measure Pmu(t), we enforce a single
exponential. Our single lambda value is
partially compensating for the gas stops.
Our mistake should then be calculated using
the lever arm method, substituting
Pmu(t)_true and Pmu(t)_measured for Pmu(t).
The correction depends on m, but it's not
as bad as (1-m)*<Pmu> = (1-m)*7.7%.

Let's use s68, which has systematic
 <Pmu> * 2.7% * 7.0% (i.e. in zone 1, has m = 0.9981)

Made a toy that fits 

 m       (1-m)*<Pmu>  measured   real mistake
         [x 1e-4]     lambda     [x 1e-4]
 1.0     0            1.0000     0
 0.9999  0.08         1.0025     0.08
 0.999   0.8          1.025      0.8
 0.998   1.5          1.050      1.7
 0.995   3.9          1.124      4.1
 0.99    7.7          1.248      8.3


Fast depolarisation is easier.