Re: factors of 2

[Elton Smith <elton@jlab.org>]

HI Blake,

There is still another factor of two. If you simply remove the 1/2 in
the note for E_N=E_S, then DeltaT = 1/2 delta_T and one also needs to
remove the 1/2 in the equation for z.

Now, removing the 1/2 in the note is fine as long as that is what you
actually did to obtain the sigma. And this should be checked. Otherwise,
the measured width is either higher or lower relative the actual value of
delta_T which is what we believe we are measuring. So can you check what
was actually calculated to obtain the width?

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

On Tue, 12 Feb 2008, Blake Leverington wrote:

> 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
> >
> >
> >
>