Determination of complete experiments using graphs

Authors

  • Yannick Wunderlich Helmholtz-Institut für Strahlen- und Kernphysik, University of Bonn
  • Philipp Kroenert
  • Farah Afzal
  • Annika Thiel

DOI:

https://doi.org/10.31349/SuplRevMexFis.3.0308065

Keywords:

Hadron spectroscopy, baryon espectroscopy, photonuclear reactions, amplitude-extraction problems, polarization observables, complete experiments, Moravcsik graphs

Abstract

This work presents ideas for the determination of complete experiments using graphs, which are based on a recently published, modified form of Moravcsik’s theorem. The lucid representation of complete experiments in terms of graphs, which is at the heart of the theorem, leads to a fully automated procedure that can determine complete experiments for in principle any reaction, i.e. for any number of amplitudes N . For larger N (i.e. N ≥ 4), the sets determined according to Moravcsik’s theorem turn out to be slightly overcomplete. A new type of directional graph has been proposed recently, which can decrease the length of the complete sets of observables in some of these cases. The presented results are relevant for reactions with larger numbers of spin-amplitudes, which are at the center of interest in forthcoming measurements, such as single-meson electroproduction (N = 6), two-meson photoproduction (N = 8) or vector-meson photoproduction (N = 12).

References

E. Klempt and J. M. Richard, Baryon spectroscopy, Rev. Mod. Phys. 82 (2010) 1095, https://doi.org/10.1103/RevModPhys.82.1095. [arXiv:0901.2055 [hep-ph]].

V. Crede and W. Roberts, Progress towards understanding baryon resonances, Rept. Prog. Phys. 76 (2013) 076301, https://doi.org/10.1088/0034-4885/76/7/076301. [arXiv:1302.7299 [nucl-ex]].

D. G. Ireland, E. Pasyuk and I. Strakovsky, Photoproduction Reactions and Non-Strange Baryon Spectroscopy, Prog. Part. Nucl. Phys. 111 (2020) 103752, https://doi.org/10.1016/j.ppnp.2019.103752. [arXiv:1906.04228 [nuclex]].

A. Thiel et al., Well-established nucleon resonances revisited by double-polarization measurements, Phys. Rev. Lett. 109 (2012) 102001, https://doi.org/10.1103/PhysRevLett.109.102001. https://doi.org/10.10.1103/PhysRevLett. 110.169102. https://doi.org/10.1103/PhysRevLett.110. 169101. [arXiv:1207.2686 [nucl-ex]].

M. Gottschall et al. [CBELSA/TAPS], First measurement of the helicity asymmetry for γp → pπ0 in the resonance region, Phys. Rev. Lett. 112 (2014) 012003, https://doi.org/10.1103/PhysRevLett.112.012003. [arXiv:1312.2187 [nucl-ex]].

J. Hartmann et al., The N(1520) 3/2- helicity amplitudes from an energy-independent multipole analysis based on new polarization data on photoproduction of neutral pions, Phys. Rev. Lett. 113 (2014) 062001, https://doi.org/10.1103/PhysRevLett.113.062001. [arXiv:1407.2163 [nucl-ex]].

F. Afzal et al. [CBELSA/TAPS], Observation of the pη0 Cusp in the New Precise Beam Asymmetry Σ Data for γp → pη, Phys. Rev. Lett. 125 (2020) 152002, https://doi.org/10.1103/PhysRevLett.125.152002. [arXiv:2009.06248 [nucl-ex]].

M. Dugger et al. [CLAS], Beam asymmetry Σ for π + and π 0 photoproduction on the proton for photon energies from 1.102 to 1.862 GeV, Phys. Rev. C 88 (2013) 065203, https://doi.org/10.1103/PhysRevC.88.065203. [arXiv:1308.4028 [nucl-ex]].

P. Collins et al. [CLAS], Photon beam asymmetry Σ for η and η 0 photoproduction from the proton, Phys. Lett. B 771 (2017) 213, https://doi.org/10.1016/j.physletb.2017.05.045. [arXiv:1703.00433 [nucl-ex]].

I. Senderovich et al. [CLAS], First measurement of the helicity asymmetry E in η photoproduction on the proton, Phys. Lett. B 755 (2016) 64, https://doi.org/10.1016/j.physletb.2016.01.044. [arXiv:1507.00325 [nucl-ex]].

S. Strauch et al. [CLAS], First Measurement of the Polarization Observable E in the ~p(~γ, π+)n Reaction up to 2.25 GeV, Phys. Lett. B 750 (2015) 53, https://doi.org/10.1016/j.physletb.2015.08.053. [arXiv:1503.05163 [nucl-ex]].

V. D. Burkert, N ∗ Experiments and what they tell us about Strong QCD Physics, EPJ Web Conf. 241 (2020) 01004, https://doi.org/10.1051/epjconf/202024101004. [arXiv:1912.11400 [nucl-ex]].

V. Burkert et al., The CLAS12 Spectrometer at Jefferson Laboratory, Nucl. Instrum. Meth. A 959 (2020) 163419, https://doi.org/10.1016/j.nima.2020.163419.

D. Hornidge et al. [A2 and CB-TAPS], Accurate Test of Chiral Dynamics in the Reaction, Phys. Rev. Lett. 111 (2013) 062004, https://doi.org/10.1103/PhysRevLett.111.062004. [arXiv:1211.5495 [nucl-ex]].

P. Adlarson et al. [A2], Measurement of π 0 photoproduction on the proton at MAMI C, Phys. Rev. C 92 (2015) 024617, https://doi.org/10.1103/PhysRevC.92.024617. [arXiv:1506.08849 [hep-ex]].

S. Gardner et al. [MAINZ-A2], Photon asymmetry measurements of −→γ p → π 0 p for Eγ = 320-650 MeV, Eur. Phys. J. A 52 (2016) 333, https://doi.org/10.1140/epja/i2016-16333-5. [arXiv:1606.07930 [nucl-ex]].

J. Annand et al. [A2 and MAMI], T and F asymmetries in π 0 photoproduction on the proton, Phys. Rev. C 93 (2016) 055209, https://doi.org/10.1103/PhysRevC.93.055209.

V. L. Kashevarov et al. [A2 Collaboration], Study of η and η 0 Photoproduction at MAMI, Phys. Rev. Lett. 118 (2017) 212001.

W. Briscoe et al. [A2], Cross section for γn → π 0n at the Mainz A2 experiment, Phys. Rev. C 100 (2019) 065205, https://doi.org/10.1103/PhysRevC.100.065205. [arXiv:1908.02730 [nucl-ex]].

H. Kohri et al. [LEPS], Differential cross section and photon beam asymmetry for the −→γ p → π + n reaction at forward π + angles at Eγ =1.5-2.95 GeV, Phys. Rev. C 97 (2018) 015205, https://doi.org/10.1103/PhysRevC.97.015205. [arXiv:1708.09574 [nucl-ex]].

H. Kohri [LEPS], Recent results of charged pion and kaon photoproduction on the proton at SPring-8/LEPS, EPJ Web Conf. 241 (2020) 01010, https://doi.org/10.1051/epjconf/202024101010.

H. Al Ghoul et al. [GlueX], Measurement of the beam asymmetry Σ for π 0 and η photoproduction on the proton at Eγ = 9 GeV, Phys. Rev. C 95 (2017) 042201, https://doi.org/10.1103/PhysRevC.95.042201. [arXiv:1701.08123 [nucl-ex]].

S. Adhikari et al. [GlueX], Beam Asymmetry Σ for the Photoproduction of η and η 0 Mesons at Eγ = 8.8GeV, Phys. Rev. C 100 (2019) 052201, https://doi.org/10.1103/PhysRevC.100.052201. [arXiv:1908.05563 [nucl-ex]].

S. Adhikari et al. [GlueX], The GLUEX beamline and detector, Nucl. Instrum. Meth. A 987 (2021) 164807, https://doi.org/10.1016/j.nima.2020.164807. [arXiv:2005.14272 [physics.ins-det]].

I. S. Barker, A. Donnachie and J. K. Storrow, Complete Experiments in Pseudoscalar Photoproduction, Nucl. Phys. B 95 (1975) 347, https://doi.org/10.1016/0550-3213(75)90049-8.

G. Keaton and R. Workman, Amplitude ambiguities in pseudoscalar meson photoproduction, Phys. Rev. C 53 (1996) 1434, https://doi.org/10.1103/PhysRevC.53.1434. [arXiv:nucl-th/9511040 [nucl-th]].

W. T. Chiang and F. Tabakin, Completeness rules for spin observables in pseudoscalar meson photoproduction, Phys. Rev. C 55 (1997) 2054, https://doi.org/10.1103/PhysRevC.55.2054. [nucl-th/9611053].

K. Nakayama, Explicit derivation of the completeness condition in pseudoscalar meson photoproduction, Phys. Rev. C 100 (2019) 035208, https://doi.org/10.1103/PhysRevC.100.035208. [arXiv:1809.00335 [nucl-th]].

Y. Wunderlich, P. Kroenert, F. Afzal and A. Thiel, Moravcsik’s theorem on complete sets of polarization observables reexamined, Phys. Rev. C 102 (2020) 034605, https://doi.org/10.1103/PhysRevC.102.034605. [arXiv:2004.14483 [nucl-th]].

Y. Wunderlich, New graphical criterion for the selection of complete sets of polarization observables and its application to single-meson photoproduction as well as electroproduction, Phys. Rev. C 104 (2021) 045203, https://doi.org/10.1103/PhysRevC.104.045203. [arXiv:2106.00486 [nuclth]].

G. Keaton and R. Workman, Ambiguities in the partial wave analysis of pseudoscalar meson photoproduction, Phys. Rev. C 54 (1996) 1437, https://doi.org/10.1103/PhysRevC.54.1437. [arXiv:nucl-th/9606052 [nucl-th]].

M. J. Moravcsik, Resolving the Discrete Ambiguities in Amplitude Determinations, J. Math. Phys. 26 (1985) 211. https://doi.org/10.1063/1.526787.

L. Tiator, R. L. Workman, Y. Wunderlich and H. Haberzettl, Amplitude reconstruction from complete electroproduction experiments and truncated partial-wave expansions, Phys. Rev. C 96 (2017) 025210 https://doi.org/10.1103/PhysRevC.96.025210. [arXiv:1702.08375 [nucl-th]].

W. Roberts and T. Oed, Polarization observables for twopion production off the nucleon, Phys. Rev. C 71 (2005) 055201 https://doi.org/10.1103/PhysRevC.71.055201. [nucl-th/0410012].

P. Kroenert, Y. Wunderlich, F. Afzal and A. Thiel, Minimal complete sets for two pseudoscalar meson photoproduction, Phys. Rev. C 103 (2021) 014607 https://doi.org/10.1103/PhysRevC.103.014607. [arXiv:2009.04356 [nuclth]].

P. Kroenert, “Minimal complete sets for two pseudoscalar meson photoproduction, contribution to HADRON 2021 (2021).

M. Pichowsky, C. Savkli and F. Tabakin, Polarization observables in vector meson photoproduction, Phys. Rev. C 53 (1996) 593, https://doi.org/10.1103/PhysRevC.53.593. [nucl-th/9509022].

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Published

2022-06-13

How to Cite

1.
Wunderlich Y, Kroenert P, Afzal F, Thiel A. Determination of complete experiments using graphs. Supl. Rev. Mex. Fis. [Internet]. 2022 Jun. 13 [cited 2022 Dec. 9];3(3):0308065 1-7. Available from: https://rmf.smf.mx/ojs/index.php/rmf-s/article/view/6059