[Frost] Correction

[dugger at jlab.org]

Priya,

Thanks. I now have a better understanding of slide 6. It looks like I was
way off in my understanding :(

Question: Did you mean to write that you fit to
[( av_target_pol(period 4) - av_target_pol(period 2) ) *T*sin(alpha)  ]/
[2 + ( av_target_pol(period 4) + av_target_pol(period 2)) ) *T *
sin(alpha) ]

?

Also, it seems to me that if the polarizations are correct, you would not
necessarily have the extracted value of T equal to zero. As long as the
polarizations of period 2 and period 4 are not the same, you should be
able to obtain a non-zero T. However, the closer the values of the two
polarizations are to one another, the larger your error bars would be for
such a determination of T (that is why it is good to have the values of
the polarization to be large and of opposite sign).

Note:

If you fit to

par0*sin(alpha)/[2 + par1*sin(alpha)],

where par0 and par1 are the fit parameters, you could then form

par0/par1 = [av_target_pol(period 4) - av_target_pol(period
2)]/[av_target_pol(period 4) + av_target_pol(period 2)]

and this is also equal to

(x - 1)/(x + 1), where x = av_target_pol(period 4)/av_target_pol(period 2)

You could then extract x and and compare your result of x with the values
of the target polarizations from the tables. This would allow a clean
statement about the accuracy of the table values of polarization between
periods 2 and 4.

Heck, you could fit to
(par0 - par1)*sin(alpha)/[2 + (par0 + par1)*sin(alpha)]

and, in this case,
par0/par1 = x .

There are probably a whole bunch of ways to try and extract the ratio of
polarization.

Take care,
Michael


> Hi,
>
> My apologies for the late reply. I had to meet some deadlines today and
> hence the delay. Mike, what I showed on slide 6 was basically a plot to
> check whether the sign of the polarization assigned to period #4 in the
> g9b
> run table was correct or not. Since the asymmetry T obtained by using
> periods 1 and 2 matched with the asymmetry T obtained from the g9b- linear
> dataset (PARA + PERP datasets), I assumed for the time-being that periods
> 1
> and 2 are good. Of course, I have to check the observable T obtained from
> g9b-lin PARA+PERP datasets by using the AMO datasets. Based on the
> assumption that the periods 1 and 2 are good, here is what I did to check
> whether period 4 was good or not -
>
> According to the table, period 4 should have a negatively polarized target
> and period 2 should also have a negatively polarized target. To check the
> sign of the target polarization in period 4, I thought that if period 4
> has
> a positive target polarization instead, then the asymmetry formed in the
> lab phi distribution of period 4 and period 2 per kinematic bin should not
> be flat. In this case I will get a non-zero value for the observable T. On
> the other hand, if the sign of the target in period 4 is correct, then the
> angular distribution will be flat and T = 0. So, I formed the asymmetry -
>
> (N(period 4) - flux_ratio *N(period 2)) /(N(period 4) + flux_ratio *
> N(period 2)), fitted it with the equation -
>
> [( av_target_pol(period 4) + av_target_pol(period 2) ) *T*sin(alpha)  ]/ [
>    2 + ( av_target_pol(period 4) - av_target_pol(period 2) ) *T *
> sin(alpha) ] ,
>
> and extracted T. Here alpha is the angle between the reaction plane and
> the
> target pol.
>
> I did this for each cos(theta_omega)c.m. bin. The plot on slide # 6 is a
> plot of this extracted T vs. cos(theta_omega)c.m. It doesn't look like the
> T that I saw when I used periods 1 and 2 (showed on slide # 3) which means
> that the sign of the target polarization in period 4 is correct, but since
> the T has an offset from zero in all cos theta bins, it means there is
> some
> other problem when I am using the period 4. As it was pointed out at the
> FROST meeting, it could be any kind of normalization issue. I will use
> period 5 now to extract T and compare my results with the other periods.
> This will give us a better idea of what's going on.
>
> Best regards,
> Priya
>
> On 5 February 2015 at 13:44, Michael Dugger <dugger at jlab.org> wrote:
>
>>
>> Hi,
>>
>> I was having a difficult time understanding Priya's plot on slide 6 of
>> her
>> presentation and, it turns out, my comments regarding the plot were
>> incorrect.
>>
>> This is how I now understand the plot (Priya, please correct me if I am
>> wrong about this):
>>
>> There is some parameter Priya obtains from fitting (I will call this
>> parA)
>> that represents target_polarization*T. This parA is determined for set 2
>> and 4. (Let me call parA from set 2 parA2, and parA from set 4 as
>> parA4.)
>>
>> To obtain the points on the plot an asymmetry is formed:
>>
>> asymmetry = (parA4/mtp4 - parA2/mtp2)/(parA4/mtp4 + parA2/mtp2) ,
>>
>> where mtp2 (mtp4) is the measured target polarization for run set 2 (4).
>>
>> This should be equal to
>>
>> asymmetry = (ttp4/mtp4 - ttp2/mtp42/(ttp4/mtp4 + ttp2/mtp2) ,
>>
>> where ttp2 (ttp4) is the true target polarization for run set 2 (4).
>>
>> If we assume that ttp2 = mtp2 (i.e. set 2 has correctly measured
>> polarization) and allow ttp2/mtp2 = x, then
>>
>> asymmetry = (x-1)/(x+1)
>>
>> Now, since the plot on slide six shows asymmetry ~ 0.1 then
>>
>> 0.1 = (x-1)/(x+1) ->
>> 0.1x + 0.1 = x-1 ->
>> 1.1 = 0.9x ->
>> x = 1.1/0.9 = 1.2
>>
>> This would mean that the measured polarization for set 4 (with the
>> assumption that set 2 has a correctly measured polarization) is off by
>> 20%
>> .
>>
>> In short: In the meeting, I was wrong about what the plot represented,
>> and
>> if I am now correct in my interpretation, then Priya's plot does show a
>> clear relationship for the polarization between the two runs sets, and
>> that the polarization between set 2 and 4 could be wrong by about 20%.
>>
>> Sorry about the long email. I just wanted to clear up any confusion I
>> might have caused.
>>
>> Take care,
>> Michael
>>
>>
>> _______________________________________________
>> Frost mailing list
>> Frost at jlab.org
>> https://mailman.jlab.org/mailman/listinfo/frost
>>
>
>
>
> --
> Regards,
>
> Priyashree Roy
> Graduate student
> Florida State University
> Tallahassee, U.S.
>