Hi Chris,
On Sat, 6 May 2006, Christopher Crawford wrote:
> Hi Michael,
>
> Thanks for elucidating the discussion at the BLAST meeting; that was the
> point I was trying to make. Of course in practice, your formula is
> implemented by the simpler one:
>
> < theta_s > \equiv \sum_i (w_i * theta_s(z_i)) / \sum_i (w_i) where
> 'i' runs over the event sample, and the weight of each event 'w_i' can be
> taken as unity.
>
> It would also be helpful to provide 'th_nominal' for each of the fieldmaps
> as a reference. So if I understand, the main point is that we need to
> compare different extractions / measurements in terms of 'th_nominal' to
> avoid dependence of the event distribution.
>
> One final thing, I don't think the event distribution does not make much
> difference, since I got pretty much the same result for each Q^2 bin, left
> and right sector, but if you look at the z-distributions for each, they are
> wildly different. There are even gaping holes in some.
>
That is why I suggested to calculate the <dth>_yield also for the MC
event sample. We know where te target is, and we know (by MC) how nature
would distribute events. On the other hand the measurement of z by
tracking may be questionable as you point out. In MC, one could even use
the "tossed" z-distribution instead of the "reconstructed" one.
Regards,
Michael
>
> On May 5, 2006, at 22:52:46, Michael Kohl wrote:
>
>> Hi,
>>
>> -On the discussion of "average" vs "nominal" spin angle:
>> In Doug's routine, the spin profile parametrized as a 9th order
>> polynomial is evaluated relative to a "nominal" spin angle (which
>> happens to be theta(z=0)).
>> Doug's profile:
>> th(z) = th_nominal + \sum_i a_i z^i, i=1..9
>> = th_nominal + dth(z)
>> The yield-weighted average spin angle (over the allowed length of the
>> target) of Doug's profile is thus
>> <th>_yield = 1/40 * \int_{-20}^{20}[dz \rho(z) th(z)]
>> = th_nominal + <dth>_yield,
>> where \rho(z) is the target density distribution along z (normalized
>> to 1), and <dth>_yield is the yield-weighted average of the
>> polynomial terms.
>> While theta_nominal is a quantity of the detector that does not
>> depend on the reaction channel, the quantities \rho(z), <th>_yield
>> and <dth>_yield are dependent on the particular considered reaction,
>> or even on the sector.
>>
>> The average angle <th>_yield can be determined from both ed elastic
>> and ep elastic asymmetry analysis; as such, this number is not yet
>> useful for any other reaction unless it is converted into the
>> "nominal" angle. In order to do this for the given reaction,
>> <dth>_yield = 1/40*\sum_i{\int_{-20}^{20}[dz \rho(z) a_i z^i]}, i=1..9
>> needs to be determined which is a simple number.
>> This said, comparing the spin angles from ed elastic and ep elastic
>> must only be done for the resulting theta_nominal, but not for the
>> yield-averaged numbers!
>>
>> Chris has evaluated <th>_yield and <dth>_yield for ep elastic:
>> ep elastic(47): <th>_yield = 45.8 +- ??? degrees
>> <dth>_yield = -0.8
>> -> theta_nominal = 46.6
>> ed elastic(32): <th>_yield = 31.4
>> <dth>_yield = ???
>>
>> There is deuterium data for both 47 (2005) and 32 (2004) degree
>> settings. Only the latter is available so far with the latest
>> recrunch, the former is being crunched right now.
>>
>> For each of the 32 and 47 degree settings, the same theta_nominal
>> ought to be used by every analysis. The resulting <th>_yield for each
>> reaction channel is dependent on the specific yield distribution
>> \rho(z) which may be different in each channel. It may even depend on
>> the sector. In order to calculate the average angle in any reaction
>> channel from a given "universal" map, it needs to be averaged
>> over the specific yield (=evaluating <dth>_yield). Eugene has done
>> this for 32-deg=2004 d(e,e'n): <dth>_yield = <th>_yield - theta_nominal
>> en quasielastic(32): <dth>_yield (left sector) = -2.27 deg
>> <dth>_yield (right sector) = -2.42 deg
>>
>> The resulting average <th>_yield is a number which can be quoted in a
>> paper for the considered reaction, but it is of no further use if the
>> extraction of observables relies on the same common spin angle map.
>>
>> Nevertheless it is a good idea to compare the various <dth>_yield of
>> the various reaction channels (e,e'), d(e,e'p), (e,e'pi+), ...
>> Comparing ep elastic with en quasielastic, there seems to be some
>> significant difference, -0.8 deg vs -2.4 deg.
>> One should do the same exercise for MC-generated (cross-section
>> weighted) target distributions rho(z) for each channel, in order to
>> exclude that there are any surprises. Keep in mind that the
>> Q2bin-by-Q2bin target distributions in ep elastic from reconstructed
>> data looked rather funny, and they are prone to systematics in the
>> reconstruction. In MC, the tossed and accepted z distribution can be
>> used directly, without the reconstruction uncertainty.
>>
>>
>> Regards,
>>
>> Michael
>>
>>
>>
>>
>> +-------------------------------------+--------------------------+
>> | Office: | Home: |
>> |-------------------------------------|--------------------------|
>> | Dr. Michael Kohl | Michael Kohl |
>> | Laboratory for Nuclear Science | 5 Ibbetson Street |
>> | MIT-Bates Linear Accelerator Center | Somerville, MA 02143 |
>> | Middleton, MA 01949 | U.S.A. |
>> | U.S.A. | |
>> | - - - - - - - - - - - - | - - - - - - - - -|
>> | Email: kohlm@mit.edu | K.Michael.Kohl@gmx.de |
>> | Work: +1-617-253-9207 | Home: +1-617-629-3147 |
>> | Fax: +1-617-253-9599 | Mobile: +1-978-580-4190 |
>> | http://blast.lns.mit.edu | |
>> +-------------------------------------+--------------------------+
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>
+-------------------------------------+--------------------------+
| Office: | Home: |
|-------------------------------------|--------------------------|
| Dr. Michael Kohl | Michael Kohl |
| Laboratory for Nuclear Science | 5 Ibbetson Street |
| MIT-Bates Linear Accelerator Center | Somerville, MA 02143 |
| Middleton, MA 01949 | U.S.A. |
| U.S.A. | |
| - - - - - - - - - - - - | - - - - - - - - -|
| Email: kohlm@mit.edu | K.Michael.Kohl@gmx.de |
| Work: +1-617-253-9207 | Home: +1-617-629-3147 |
| Fax: +1-617-253-9599 | Mobile: +1-978-580-4190 |
| http://blast.lns.mit.edu | |
+-------------------------------------+--------------------------+
This archive was generated by hypermail 2.1.2 : Mon Feb 24 2014 - 14:07:33 EST