[Frost] Efficiency issues and offset

Thu Feb 26 14:27:04 EST 2015

Dear Mike,

Just a brief comment on your binning study: I don’t think there are systematic uncertainties related to the binning; at least not as large.  Your fit function on page 3 of your 2/26/2015 report is:

f(phi) = A[1 + B sin(phi)]

Your data, however, are in each bin the integrals of the underlying distribution over the bin width, Delta phi.  If you integrate the function f(phi) over a finite bin width, say from phi1 to phi2, with phi = (phi1 + phi2) / 2, and Delta phi = phi2 - phi1, you get:

data(phi) Delta phi = A [ 1 + B sin(phi) * sin(Delta phi/2) / (Delta phi/2) ] Delta phi.

In the second term, what your fit actually determines, is not B, but B * sin(Delta phi/2) / (Delta phi/2).  If you correct your fit result by that factor you get the correct value for B.  The correction factors for your numbers of bins 6, 12, 18, and 36 are 0.955, 0.989, 0.995, and 0.999, respectively; quite compatible to the values you got for your uncorrected B.

All the best,
Steffen

On Feb 26, 2015, at 1:33 PM, Michael Dugger <dugger at jlab.org> wrote:

> 
> Hi,
> 
> During the meeting I said that the azimuthal distributions for pi+ N when 
> using 36 bins looked great. I should have said that I think they look 
> good. So, I'm downgrading from "great" to "good".
> 
> One thing to note: In my plots I am using the trigger corrections that I 
> presented on 26th of June 2014:
> 
> https://userweb.jlab.org/~dugger/frost/trigCorr.pdf
> 
> with more details (from 10th July 2014 presentation) here:
> 
> https://userweb.jlab.org/~dugger/frost/trigCorr2.pdf
> 
> To Give a better idea as to how the data looks for all cosTheta bins
> I randomly picked two energies to put on the web of the azimuthal 
> distribution (did not have time to link all them right now). Links to 
> plots are at the bottom of this email.
> 
> When I run the numbers for all energies and angles I get an offset 
> 63.7+/-0.1 and am within 1.5 degrees of what Ross has (62.2+/-0.3). The 
> advantage Ross has when performing the study is that he looks at both F 
> and T (I just look at T).
> 
> Take care,
> Michael
> 
> ------------------
> 
> For W = 1475 MeV
> 
> cosTheta = -0.95 
> http://www.public.asu.edu/~dugger/frost/pipN1475_neg0.95.gif
> 
> cosTheta = -0.85 
> http://www.public.asu.edu/~dugger/frost/pipN1475_neg0.85.gif
> 
> cosTheta = -0.75 
> http://www.public.asu.edu/~dugger/frost/pipN1475_neg0.75.gif
> 
> cosTheta = -0.65 
> http://www.public.asu.edu/~dugger/frost/pipN1475_neg0.65.gif
> 
> cosTheta = -0.55 
> http://www.public.asu.edu/~dugger/frost/pipN1475_neg0.55.gif
> 
> cosTheta = -0.45 
> http://www.public.asu.edu/~dugger/frost/pipN1475_neg0.45.gif
> 
> cosTheta = -0.35 
> http://www.public.asu.edu/~dugger/frost/pipN1475_neg0.35.gif
> 
> cosTheta = -0.25 
> http://www.public.asu.edu/~dugger/frost/pipN1475_neg0.25.gif
> 
> cosTheta = -0.15 
> http://www.public.asu.edu/~dugger/frost/pipN1475_neg0.15.gif
> 
> cosTheta = -0.05 
> http://www.public.asu.edu/~dugger/frost/pipN1475_neg0.05.gif
> 
> cosTheta = 0.05 
> http://www.public.asu.edu/~dugger/frost/pipN1475_pos0.05.gif
> 
> cosTheta = 0.15 
> http://www.public.asu.edu/~dugger/frost/pipN1475_pos0.15.gif
> 
> cosTheta = 0.25 
> http://www.public.asu.edu/~dugger/frost/pipN1475_pos0.25.gif
> 
> cosTheta = 0.35 
> http://www.public.asu.edu/~dugger/frost/pipN1475_pos0.35.gif
> 
> cosTheta = 0.45 
> http://www.public.asu.edu/~dugger/frost/pipN1475_pos0.45.gif
> 
> cosTheta = 0.55 
> http://www.public.asu.edu/~dugger/frost/pipN1475_pos0.55.gif
> 
> cosTheta = 0.65 
> http://www.public.asu.edu/~dugger/frost/pipN1475_pos0.65.gif
> 
> cosTheta = 0.75 
> http://www.public.asu.edu/~dugger/frost/pipN1475_pos0.75.gif
> 
> cosTheta = 0.85 
> http://www.public.asu.edu/~dugger/frost/pipN1475_pos0.85.gif
> 
> cosTheta = 0.95 
> http://www.public.asu.edu/~dugger/frost/pipN1475_pos0.95.gif
> 
> ------------------
> 
> For W = 1625 MeV
> 
> cosTheta = -0.95 
> http://www.public.asu.edu/~dugger/frost/pipN1625_neg0.95.gif
> 
> cosTheta = -0.85 
> http://www.public.asu.edu/~dugger/frost/pipN1625_neg0.85.gif
> 
> cosTheta = -0.75 
> http://www.public.asu.edu/~dugger/frost/pipN1625_neg0.75.gif
> 
> cosTheta = -0.65 
> http://www.public.asu.edu/~dugger/frost/pipN1625_neg0.65.gif
> 
> cosTheta = -0.55 
> http://www.public.asu.edu/~dugger/frost/pipN1625_neg0.55.gif
> 
> cosTheta = -0.45 
> http://www.public.asu.edu/~dugger/frost/pipN1625_neg0.45.gif
> 
> cosTheta = -0.35 
> http://www.public.asu.edu/~dugger/frost/pipN1625_neg0.35.gif
> 
> cosTheta = -0.25 
> http://www.public.asu.edu/~dugger/frost/pipN1625_neg0.25.gif
> 
> cosTheta = -0.15 
> http://www.public.asu.edu/~dugger/frost/pipN1625_neg0.15.gif
> 
> cosTheta = -0.05 
> http://www.public.asu.edu/~dugger/frost/pipN1625_neg0.05.gif
> 
> cosTheta = 0.05 
> http://www.public.asu.edu/~dugger/frost/pipN1625_pos0.05.gif
> 
> cosTheta = 0.15 
> http://www.public.asu.edu/~dugger/frost/pipN1625_pos0.15.gif
> 
> cosTheta = 0.25 
> http://www.public.asu.edu/~dugger/frost/pipN1625_pos0.25.gif
> 
> cosTheta = 0.35 
> http://www.public.asu.edu/~dugger/frost/pipN1625_pos0.35.gif
> 
> cosTheta = 0.45 
> http://www.public.asu.edu/~dugger/frost/pipN1625_pos0.45.gif
> 
> cosTheta = 0.55 
> http://www.public.asu.edu/~dugger/frost/pipN1625_pos0.55.gif
> 
> cosTheta = 0.65 
> http://www.public.asu.edu/~dugger/frost/pipN1625_pos0.65.gif
> 
> cosTheta = 0.75 
> http://www.public.asu.edu/~dugger/frost/pipN1625_pos0.75.gif
> 
> cosTheta = 0.85 
> http://www.public.asu.edu/~dugger/frost/pipN1625_pos0.85.gif
> 
> cosTheta = 0.95 
> http://www.public.asu.edu/~dugger/frost/pipN1625_pos0.95.gif
> 
> 
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