<html><head><meta http-equiv="Content-Type" content="text/html charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class="">Dear Michael,<div class=""><br class=""></div><div class="">Your explanation and simple Q-factor example from last week were very helpful to clarify the discussion. I, too, agree that you can not reconstruct background-free azimuthal distributions from Q-factors if the Q-factors are not functions of that azimuthal angle. Ignoring that gives, as you show, the diluted results for the extracted polarization observable if you analyze the angular dependence of sums of Q-factors.</div><div class=""><br class=""></div><div class="">As discussed during the last FROST meeting, our double-pion analysis relies on Q-factors where the azimuthal angle <b class="">is ignored</b> in the determination of the Q-factors. Our Q-factors are ratios of the unpolarized signal to the unpolarized total yield. I have put together a simplified example, following your case, which shows that one gets the correct results when such Q-factors are properly used in the moments method and that one gets diluted results (as in your example) if incorrect weights are used.</div><div class=""><br class=""></div><div class=""><a href="https://www.jlab.org/Hall-B/secure/g9/g9_strauch/mtg/FROST_meeting_2016_08_18.pdf" class="">https://www.jlab.org/Hall-B/secure/g9/g9_strauch/mtg/FROST_meeting_2016_08_18.pdf</a></div><div class=""><br class=""></div><div class="">We can discuss this some more during tomorrow’s meeting.</div><div class=""><br class=""></div><div class="">All the best,</div><div class="">Steffen</div><div class=""><br class=""></div><div class=""><br class=""></div><div style=""><blockquote type="cite" class=""><div class="">On Aug 12, 2016, at 11:04 AM, Michael Dugger <<a href="mailto:dugger@jlab.org" class="">dugger@jlab.org</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><br class="">Derek,<br class=""><br class="">Thanks for the comments. In the FROST meeting we have been discussing the manner that Q-factors are constructed. In particular, we have been talking about what would happen if the azimuthal information was neglected when constructing the distance to nearest neighbors for Q-factor determination and how such an omission would effect the beam asymmetry.<br class=""><br class="">I'm new to the Q-factor stuff and I'm just trying to learn how the Q-factors are properly constructed.<br class=""><br class="">Take care,<br class="">Michael<br class=""><br class="">On Fri, 12 Aug 2016, Derek Glazier wrote:<br class=""><br class=""><blockquote type="cite" class="">Hi Michael<br class=""> Apologies if I have missed the point of the discussion. I think the behaviour observed in your nice analysis is what would be expected.<br class=""> The Q-factor explicitly requires inclusion of all variables that will be used in further analysis, so in your case certainly phi must be included in the nearest neighbours search. For other reactions also involving fits to decay angles for example, these decay angles must also be included in the nearest neighbour search.<br class=""> If this is not done then it is probably not actually the Q-factor method that is being applied but just a single probabilistic weight function for all events. So if the signal and background ratio change as a function of the variable you are interested in, clearly the single probabilistic weight function will not apply at all values of the variable. Instead the Q-factor is equivalent to making many probabilistic weight functions for events in very small bins of phi so the signal/background is approximately constant for that bin. This also has the implication that if the range of your phi bin for N nearest neighbours is large (e.g. if you have low statistics, or many variables) Q-factor will not work so well.<br class=""> Sorry if this adds to any confusion, but in short I agree with your analysis.<br class="">Cheers<br class="">Derek<br class=""><br class="">On 11/08/16 23:38, Michael Dugger wrote:<br class=""><blockquote type="cite" class="">Hi,<br class="">During our discussion today, regarding the<br class="">Q-factor dependence on azimuthal angle, it<br class="">became clear that I needed to have a better<br class="">explanation. I have created an example that<br class="">I hope illustrates the point I was trying<br class="">to make.<br class="">A simple Q-factor example can be found at<br class=""><a href="https://userweb.jlab.org/~dugger/omega/omega6.pdf" class="">https://userweb.jlab.org/~dugger/omega/omega6.pdf</a><br class="">Note: The 2nd slide is just a repeat of what<br class="">I had shown previously. The new information starts<br class="">on slide 3.<br class="">In addition, I have attached the plot<br class="">(allCos.png) that Barry requested (moment method<br class="">for integrated polar angle).<br class="">Take care,<br class="">Michael<br class="">_______________________________________________<br class="">Frost mailing list<br class="">Frost@jlab.org<br class="">https://mailman.jlab.org/mailman/listinfo/frost<br class=""></blockquote><br class=""><br class=""></blockquote>_______________________________________________<br class="">Frost mailing list<br class=""><a href="mailto:Frost@jlab.org" class="">Frost@jlab.org</a><br class="">https://mailman.jlab.org/mailman/listinfo/frost<br class=""></div></blockquote></div><br class=""></body></html>