Unveiling the pole structure of S-matrix using deep learning

Authors

  • Denny Lane Sombillo NIP, University of the Philippines and RCNP, Osaka University
  • Y. Ikeda Department of Physics, Kyushu University
  • T. Sato Osaka University
  • A. Hosaka University of the Philippines Diliman

DOI:

https://doi.org/10.31349/SuplRevMexFis.3.0308067

Keywords:

πN scattering

Abstract

Particle scattering is a powerful tool to unveil the nature of various subatomic phenomena. The key quantity is the scattering amplitude whose analytic structure carries the information of the quantum states. In this work, we demonstrate our first step attempt to extract the pole configuration of inelastic scatterings using the deep learning method. Among various problems, motivated by the recent new hadron phenomena, we develop a curriculum learning method of deep neural network to analyze coupled channel scattering problems. We show how effectively the method works to extract the pole configuration associated with resonances in the πN scattering.

References

S. L. Olsen, T. Skwarnicki, and D. Zieminska, Nonstan- dard heavy mesons and baryons: Experimental evidence, Rev. Mod. Phys. 90, 015003 (2018), arXiv:1708.04012 [hep-ph].

R. Aaij et al. (LHCb Collaboration), Observation of a narrow pentaquark state, Pc(4312)+, and of two-peak structure of the Pc (4450)+ , Phys. Rev. Lett. 122, 222001 (2019), arXiv:1904.03947 [hep-ex].

R. Aaij et al. (LHCb Collaboration), Observation of structure in the J/ψ -pair mass spectrum, Sci. Bull. 65, 1983 (2020), arXiv:2006.16957 [hep-ex].

X.-K. Dong, V. Baru, F.-K. Guo, C. Hanhart, and

A. Nefediev, Coupled-Channel Interpretation of the LHCb Double- J/ψ Spectrum and Hints of a New State Near the J/ψJ/ψ Threshold, Phys. Rev. Lett. 126, 132001 (2021), arXiv:2009.07795 [hep-ph].

E. Wang, W.-H. Liang, and E. Oset, Analysis of the e+e− → J/ψDD ̄ reaction close to the threshold con- cerning claims of a χc0 (2P ) state, Eur. Phys. J. A 57, 38 (2021), arXiv:1902.06461 [hep-ph].

J. Haidenbauer and U. G. Meißner, On the structure in the ΛN cross section at the ΣN threshold, (2021), arXiv:2105.00836 [nucl-th].

S. Capstick and W. Roberts, Quark models of baryon masses and decays, Prog. Part. Nucl. Phys. 45, S241 (2000), arXiv:nucl-th/0008028.

R. L. Jaffe, Ordinary and extraordinary hadrons, AIP Conf. Proc. 964, 1 (2007), arXiv:hep-ph/0701038.

A. Ali, J. S. Lange, and S. Stone, Exotics: Heavy Pen- taquarks and Tetraquarks, Prog. Part. Nucl. Phys. 97, 123 (2017), arXiv:1706.00610 [hep-ph].

Y.-R. Liu, H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, Pentaquark and Tetraquark states, Prog. Part. Nucl. Phys. 107, 237 (2019), arXiv:1903.11976 [hep-ph].

X.-K. Dong, F.-K. Guo, and B.-S. Zou, Explaining the Many Threshold Structures in the Heavy-Quark Hadron Spectrum, Phys. Rev. Lett. 126, 152001 (2021), arXiv:2011.14517 [hep-ph].

F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, Q. Zhao, and B.-S. Zou, Hadronic molecules, Rev. Mod. Phys. 90, 015004 (2018), arXiv:1705.00141 [hep-ph].

Y. Yamaguchi, A. Hosaka, S. Takeuchi, and M. Takizawa, Heavy hadronic molecules with pion exchange and quark core couplings: a guide for practitioners, J. Phys. G 47, 053001 (2020), arXiv:1908.08790 [hep-ph].

T. Hyodo, Structure and compositeness of hadron res- onances, Int. J. Mod. Phys. A 28, 1330045 (2013), arXiv:1310.1176 [hep-ph].

M. Bayar, F. Aceti, F.-K. Guo, and E. Oset, A Discussion on Triangle Singularities in the Λb → J/ψK−p Reaction, Phys. Rev. D 94, 074039 (2016), arXiv:1609.04133 [hep- ph].

F.-K. Guo, X.-H. Liu, and S. Sakai, Threshold cusps and triangle singularities in hadronic reactions, Prog. Part. Nucl. Phys. 112, 103757 (2020), arXiv:1912.07030 [hep- ph].

S. X. Nakamura, Triangle singularity appearing as an X(3872)-like peak in B → (J/ψπ+π−)Kπ, Phys. Rev. D 102, 074004 (2020), arXiv:1912.11830 [hep-ph].

W. R. Frazer and A. W. Hendry, S-Matrix Poles Close to Threshold, Phys. Rev. 134, B1307 (1964).

B. C. Pearce and B. F. Gibson, Observable effects of poles and shadow poles in coupled-channel systems, Phys. Rev. C 40, 902 (1989).

A. M. Badalyan, L. P. Kok, M. I. Polikarpov, and Y. A. Simonov, Resonances in coupled channels in nuclear and particle physics, Phys. Rep. 82, 31 (1982).

C. Hanhart, J. R. Pelaez, and G. Rios, Remarks on pole trajectories for resonances, Phys. Lett. B 739, 375 (2014), arXiv:1407.7452 [hep-ph].

D. Morgan and M. Pennington, f0 (S ∗ ): molecule or quark state?, Phys. Lett. B 258, 444 (1991).

D. Morgan, Pole counting and resonance classification, Nucl. Phys. A 543, 632 (1992).

V. Baru, J. Haidenbauer, C. Hanhart, Y. Kalashnikova, and A. E. Kudryavtsev, Evidence that the a(0)(980) and f(0)(980) are not elementary particles, Phys. Lett. B 586, 53 (2004), arXiv:hep-ph/0308129.

S. Weinberg, Evidence that the deuteron is not an ele- mentary particle, Phys. Rev. 137, B672 (1965).

G. Carleo, I. Cirac, K. Cranmer, L. Daudet, M. Schuld, N. Tishby, L. Vogt-Maranto, and L. Zdeborova ́, Machine learning and the physical sciences, Rev. Mod. Phys. 91, 045002 (2019), arXiv:1903.10563 [physics.comp-ph].

D. L. B. Sombillo, Y. Ikeda, T. Sato, and A. Hosaka, Classifying the pole of an amplitude using a deep neural network, Phys. Rev. D 102, 016024 (2020), arXiv:2003.10770 [hep-ph]. http://gwdac.phys.gwu.edu/analysis/pin_analysis. html.

R. L. Workman, R. A. Arndt, W. J. Briscoe, M. W. Paris, and I. I. Strakovsky, Parameterization dependence of T matrix poles and eigenphases from a fit to πN elastic scattering data, Phys. Rev. C 86, 035202 (2012), arXiv:1204.2277 [hep-ph].

R. A. Arndt, W. J. Briscoe, I. I. Strakovsky, and R. L. Workman, Extended partial-wave analysis of πN scat- tering data, Phys. Rev. C 74, 045205 (2006), arXiv:nucl- th/0605082.

H. Kamano, S. X. Nakamura, T. S. H. Lee, and T. Sato, Nucleon resonances within a dynamical coupled-channels model of πN and γN reactions, Phys. Rev. C 88, 035209 (2013), arXiv:1305.4351 [nucl-th].

N. Kaiser, P. B. Siegel, and W. Weise, Chiral dynamics and the S11 (1535) nucleon resonance, Phys. Lett. B 362, 23 (1995), arXiv:nucl-th/9507036.

R. G. Newton, Structure of the Many-Channel S-matrix, J. Math. Phys. 2, 188 (1961).

K. J. L. Couteur and R. E. Peierls, The structure of a non-relativistic S-matrix, Proc. R. Soc. Lon. A. 256, 115 (1960).

D. L. B. Sombillo, Y. Ikeda, T. Sato, and A. Hosaka, Model independent analysis of coupled-channel scatter- ing: A deep learning approach, Phys. Rev. D 104, 036001 (2021), arXiv:2105.04898 [hep-ph].

J. L. Elman, Learning and development in neural net- works: the importance of starting small, Cognition 48, 71 (1993).

Y. Bengio, J. Louradour, R. Collobert, and J. Weston, Curriculum learning, in Proceedings of the 26th Annual International Conference on Machine Learning , ICML ’09 (Association for Computing Machinery, New York, NY, USA, 2009) p. 41–48.

A. Graves, M. G. Bellemare, J. Menick, R. Munos, and K. Kavukcuoglu, Automated curriculum learning for neu- ral networks, in Proceedings of the 34th International Conference on Machine Learning, Proceedings of Ma- chine Learning Research, Vol. 70 (PMLR, International Convention Centre, Sydney, Australia, 2017) pp. 1311– 1320.

G. Hacohen and D. Weinshall, On The Power of Cur- riculum Learning in Training Deep Networks, (2019), arXiv:1904.03626 [cs.LG].

Downloads

Published

2022-05-20

How to Cite

1.
Sombillo DL, Ikeda Y, Sato T, Hosaka A. Unveiling the pole structure of S-matrix using deep learning. Supl. Rev. Mex. Fis. [Internet]. 2022 May 20 [cited 2024 Apr. 26];3(3):0308067 1-6. Available from: https://rmf.smf.mx/ojs/index.php/rmf-s/article/view/6133