factors of 2

[Elton Smith <elton@jlab.org>]

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