Re: factors of 2

[Elton Smith <elton@jlab.org>]

HI Blake,

Great. You will probably want to correct the formulas in the analysis
note to avoid confusion.

Cheers, 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 Fri, 29 Feb 2008, Blake Leverington wrote:

> Hi Elton,
>
> I hope this answers everyone's questions about the time resolution and
> any factors of two. I have told you the formula I have been using
> incorrectly. The short note I've attached should clear this up.
>
> -Blake
>
> Elton Smith wrote:
> > 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
> >>>>>
> >>>>>
> >>>>>
> >>>>>
> >>>>>
> >>>
> >>>
> >
> >
> >
>