2012/12/06 by A. Švarc, Alfred Svarc, Svarc, Alfred +7 · 1 citation
Biochemistry, Genetics and Molecular Biology · Chemistry · Mathematics · Physics and Astronomy · #Advanced NMR Techniques and Applications #Algorithm #Applied mathematics #Complex plane #Eigenvalues and eigenvectors #Electron Spin Resonance Studies #FOS: Physical sciences #Formalism (music) #High Energy Physics - Phenomenology (hep-ph) #Laurent series #Mathematical analysis #Mathematics #Nuclear Experiment (nucl-ex) #Nuclear Theory (nucl-th) #Physics #Physics of Superconductivity and Magnetism #Power series #Pure mathematics #Quantum mechanics #Series (stratigraphy) #Series expansion #Singular value #hep-ph #nucl-ex #nucl-th
paper · pdf · doi:10.48550/arxiv.1212.1295
published in arXiv (Cornell University) (Cornell University) · 9 pages, 2 figures, 2 tables
openalex publication_date 2012/12/06 · arxiv created 2012/12/20 · arxiv updated 2012/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a new approach to quantifying pole parameters of single-channel processes based on Laurent expansion of partial wave T-matrices. Instead of guessing the analytical form of non-singular part of Laurent expansion as it is usually done, we represent it by the convergent series of Pietarinen functions. As the analytic structure of non-singular term is usually very well known (physical cuts with branhcpoints at inelastic thresholds, and unphysical cuts in the negative energy plane), we show that we need one Pietarinen series per cut, and the number of terms in each Pietarinen series is automatically determined by the quality of the fit. The method is tested on a toy model constructed from two known poles, various background terms, and two physical cuts, and shown to be robust and confident up to three Pietarinen series. We also apply this method to Zagreb CMB amplitudes for the N(1535) 1/2- resonance, and confirm the full success of the method on realistic data. This formalism can also be used for fitting experimental data, and the procedure is very similar as when Breit-Wigner functions are used, but with one modification: Laurent expansion with Pietarinen series is replacing the standard Breit-Wigner T-matrix form.