Hi Michael,
Yes that is a good idea, but the event distribution from the
actual data will be more realistic, since we do NOT have ideal event
distributions. just look at the shape of the z-distribution I showed
at the meeting.
--Chris
TA-53/MPF-1/D111 P-23 MS H803
LANL, Los Alamos, NM 87545
505-665-9804(o) 665-4121(f) 662-0639(h)
On May 6, 2006, at 08:34:07, Michael Kohl wrote:
> 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: |
>>> |-------------------------------------|--------------------------|
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>>> +-------------------------------------+--------------------------+
>>
>
>
> +-------------------------------------+--------------------------+
> | 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. | |
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