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Dear all,
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<div class="">I am sharing here Andrew’s follow-up message with the mailing list as this is very useful information.
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<div class="">Thank you Andrew!</div>
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<div class="">—Michael</div>
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<div>Dr. Michael Kohl</div>
<div>Interim Chair</div>
<div>Joint Professor and Staff Research Scientist</div>
<div>Physics Department, Hampton University, Hampton, VA 23668, USA</div>
<div>Jefferson Lab, 12000 Jefferson Avenue, Newport News, VA 23606, USA</div>
<div>Phone: +1-757-727-5153 (HU office)</div>
<div><a href="mailto:kohlm@jlab.org" class="">Email: kohlm@jlab.org</a></div>
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<div class="">Begin forwarded message:</div>
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<span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif; color:rgba(0, 0, 0, 1.0);" class=""><b class="">From:
</b></span><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif;" class="">Andrew Puckett <<a href="mailto:puckett@jlab.org" class="">puckett@jlab.org</a>><br class="">
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<span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif; color:rgba(0, 0, 0, 1.0);" class=""><b class="">Subject:
</b></span><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif;" class=""><b class="">FOM "weighted" vs "unweighted" examples from GEp-III/GEp-2gamma</b><br class="">
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<span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif; color:rgba(0, 0, 0, 1.0);" class=""><b class="">Date:
</b></span><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif;" class="">December 4, 2025 at 1:32:25 PM EST<br class="">
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<span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif; color:rgba(0, 0, 0, 1.0);" class=""><b class="">To:
</b></span><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif;" class="">Michael Kohl <<a href="mailto:kohlm@jlab.org" class="">kohlm@jlab.org</a>><br class="">
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Following up today’s meeting discussion: </div>
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<a href="https://inspirehep.net/literature/1613323" data-outlook-id="c5579c98-93d0-41fa-a45a-a7b392c3a4b0" class="">https://inspirehep.net/literature/1613323</a></div>
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Focus on Figs. 9,10, Table V, Fig. 12, and Table XI. The main variables on which the asymmetry depends are the polar scattering angle in the FPP and the spin precession variation within the acceptance. </div>
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We should focus on the 2.5 GeV^2 and 8.5 GeV^2 kinematics, since these have precession angles close to 90 deg (270 deg) respectively, so the effect of spin precession on the acceptance-averaged azimuthal asymmetry is minimal. </div>
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The acceptance-averaged focal-plane asymmetries are shown in Tab. V, with all events passing all the selection criteria. </div>
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The ratio c/s is a proxy for PT/PL which is a proxy for GE/GM. If I take the weighted average of FPP1 and FPP2 asymmetries in Tab. V for, e.g., the high-epsilon, 2.5 GeV^2, and then form the ratio, the implied relative statistical uncertainty in the FF ratio
is about 1.03%. </div>
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On the other hand, if I go to Table XI, the fractional uncertainty in the final FF ratio from the unbinned ML extraction is 0.85%. </div>
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So the effect of weighting events by analyzing power (parametrization and distribution shown in Fig. 14 and Tab. VII) and spin transport matrix elements event-by-event (see e.g. Fig. 12) for this kinematics is about a 17% reduction of the error bar. </div>
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The reduction for 5.2 GeV^2 is obviously much bigger. </div>
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In SBS the spin precession angle (for protons anyway) is roughly constant within the acceptance (not sure about neutron precession). So the main effect will be the Ay variation within the acceptance. If the Ay distribution is constant, then there would be effectively
no difference in FOM between an unbinned ML extraction and extracting the acceptance-average azimuthal asymmetry a la Tab. V and Figs. 9,10. </div>
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Cheers,</div>
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Andrew</div>
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<span style="font-family: Century, serif; font-size: 12pt;" class="">Andrew Puckett<br class="">
Professor, Physics Department<br class="">
University of Connecticut<br class="">
196 Auditorium Road, Unit 3046<br class="">
Storrs, CT 06269-3046<br class="">
Office phone: (860) 486-7137<br class="">
</span><span style="font-family: Century, serif; font-size: 12pt; color: rgb(5, 99, 193);" class=""><u class=""><a href="https://puckett.physics.uconn.edu/" title="https://puckett.physics.uconn.edu" data-outlook-id="fae261f7-80fd-4510-8e38-c1fb267125b9" style="margin-top: 0px; margin-bottom: 0px;" class="">https://puckett.physics.uconn.edu</a></u></span><span style="font-family: Century, serif; font-size: 12pt;" class=""><br class="">
</span><span style="font-family: Century, serif; font-size: 12pt; color: rgb(5, 99, 193);" class=""><u class=""><a href="mailto:andrew.puckett@uconn.edu" data-outlook-id="64346a39-e5d9-4e9c-ac65-ff7e19916539" style="margin-top: 0px; margin-bottom: 0px;" class="">puckett@jlab.org</a></u></span></div>
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