Re: factors of 2

[Blake Leverington <leverinb@uregina.ca>]

Hi Elton,

I was just reviewing my notes, and it seems that if you assume that z = 
veff * delta_T / 2 then there should NOT be the factor of 0.5 in 
DeltaT.  DeltaT should equal delta_T for E_N = E_S. I should remove that 
factor of 1/2 in the note.

-Blake



Elton Smith wrote:
> Hi Blake,
>
> Yesterday we were going over the correspondence between the expected z
> position resolution and the time resolution. We have the following
> relation:
> z = veff * (Tleft - Tright)/2
> delta_z = veff * delta_T/2
> for delta_T = Tleft - Tright
>
> We have been assuming that the quoted delta_T (75 ps/sqrt(E) + 30) is
> given by the definition above. But the reference for the resolution is
> GlueX-doc-804 which you wrote. Refering to eqs 14, you use the following
> expression:
>
> DeltaT = 0.5*Sum{t_north*E_north - t_south*E_south}/Sum{E_north+E_south}
>
> At first, it looks like the definition for DeltaT = 0.5*delta_T, removing
> the 1/2 from the equation for z. However, on closer inspection, there are
> more questions. Taking the simple case where E_north=E_south (center of
> calorimeter), then
> DeltaT (E_north=E_south) = 0.25 * (t_north - t_south), so it looks like
> there is even an additional factor of 2.
>
> Can you help me sort this out?
>
> Thanks, Elton.
>
>
> Elton Smith
> Jefferson Lab MS 12H5
> 12000 Jefferson Ave
> Suite # 16
> Newport News, VA 23606
> elton@jlab.org
> (757) 269-7625
> (757) 269-6331 fax
>
>
>