Sensitivity of multipoles to phase variations in pion photo- and electro-production analyses
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Regular Article - Experimental Physics
Sensitivity of multipoles to phase variations in pion photo- and electro-production analyses L. Markou1,a , E. Stiliaris2,b , C. N. Papanicolas1,c 1 2
The Cyprus Institute, K. Kavafi 20, 2121 Nicosia, Cyprus National and Kapodistrian University of Athens, 15771 Athens, Greece
Received: 2 July 2020 / Accepted: 13 October 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020 Communicated by Nicolas Alamanos
Abstract We use the Athens Model Independent Analysis Scheme (AMIAS) to examine the validity of using the Fermi– Watson theorem in the multipole analyses of pion photoproduction and electroproduction data. A standard practice in this field is to fix the multipoles’ phases from π N scattering data, making use of the Fermi–Watson theorem. However, these phases are known with limited accuracy and the effect of this uncertainty on the obtained multipole extraction has not been fully explored yet. Using AMIAS we constrain the phases within their experimentally determined uncertainty. We first analyze sets of photoproduction pseudodata of increasing statistical precision and subsequently we apply the methodology for a re-analysis of the Bates/Mainz electroproduction data. It is found that the uncertainty induced by the π N phases uncertainty to the extracted solutions would be significant only in the analysis of data with much higher precision than the current available experimental data.
1 Introduction Pion photoproduction and pion-nucleon scattering are related by unitarity through a common S matrix [1] and the Fermi– Watson (FW) theorem [2] requires the (γ , π ) and (π, π ) channels to have the same phase below the two-pion threshold. Multipole analyses below this threshold are subject to this theoretical constraint which requires all multipoles with different character but the same quantum numbers I, l, J to have the same phase, ±nπ , which is identical to the corresponding π N scattering phase shift. The pion photoproduction multipole phases and the scattering phase shifts are related through [2]: a e-mail:
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I I Al± = |Al± |ei(δ I l J +nπ )
(1)
where δ I l J is the pion-nucleon scattering phase shift, I is the isospin quantum number, l the angular momentum, J the total angular momentum and “±” is used to distinguish whether J and the spin are parallel or anti-parallel. AlI = {ElI , MlI , L lI } denotes the electric, magnetic or longitudinal nature of the multipole. As π N scattering phase shifts are easier to measure and therefore known with higher precision their utilization in leptonic channels is widely used. This theoretical constraint provides a very powerful tool for multipole analyses in photoproduction and electroproduction. Multipoles are complex functions of the center mass energy W and by applying the FW theorem the number of unknown parameters is halved since only the moduli of the I | need t
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