[Clascomment] OPT-IN: Differential cross sections and spin density matrix elements for the reaction gamma p --> p omega

[Mike Williams]

Hi Marco,

To fully understand the bkgd method, one would have to read the JINST 
paper (which is in the "minor revision" stage now and should be published 
by the end of the summer...hopefully).  In Eq.(7), the 1st term (summing 
Q_i^2) is the 
statistical error and the second term (sum sigma_Q_i)^2 is the Q-factor 
uncertainties assuming 100% correlation (since they're added up, then 
squared...that's 100% correlated).

To understand the stat error, consider a simple example where all of the 
Q's are the same.  In that case, sum Q^2 = Q^2 N (where N is the number of 
events).  Thus, sigma = Q sqrt(N).  If Q=1 (all signal), the you'd get a 
stat error of sqrt(N) as expected.  For Q!=1, you need to remember that 
the stat error is on the total event sample (not the number of signal). 
Thus, e.g. Q=1/2, the stat error is 0.5 sqrt(N) for this simple example.

Cheers,

Mike

On Fri, 31 Jul 2009, Marco Ripani wrote:

> Hi,
> I don\'t understand formula (7) in the paper. Why do you add Q_i^2 to the yield uncertainty and in what sense does it represent 100 % correlation ? Sorry, I must be missing something here.
>
> Thanks
> Marco
>