Re: factors of 2

[Elton Smith <elton@jlab.org>]

Hi Blake,

Thanks for looking into this. But I think the equation for z should not
have the 1/2 for this new definition because of the energy terms:

DeltaT ={t_north*E_north - t_south*E_south}/Sum{E_north+E_south}

At least for the case where E_north - E_south, then
DeltaT = 1/2 (t_north - t_south)

z = veff * (Tleft - Tright)/2 = veff * DeltaT

Or am I still missing a factor?

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 started rerunning the timing resolution code this morning so hopefully
> it should be done tonight. I removed the 1/2 from the previous DeltaT so
> that DeltaT now is DeltaT ={t_north*E_north -
> t_south*E_south}/Sum{E_north+E_south}, without the factor of 1/2. I'll
> see how this affects the resolution but I suspect it will double it as z
> was previously assumed to be z = 0.5 *veff *DeltaT so that the z
> resolution should be double, from 0.7cm to 1.4cm at 1 GeV. I'll even
> redo the mean time resolution tomorrow as I've thought of new things to do.
>
> -Blake
>
>
>
>
> Elton Smith wrote:
> > 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
> >>>
> >>>
> >>>
> >>>
> >
> >
> >
>