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Structure of pion photoproduction amplitudes

V. Mathieu, J. Nys, C. Fernández-Ramírez, A. N. Hiller Blin, A. Jackura, A. Pilloni, A. P. Szczepaniak, and G. Fox (Joint Physics Analysis Center)
Phys. Rev. D 98, 014041 – Published 31 July 2018
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Abstract
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Article Text
  • INTRODUCTION
  • FORMALISM: SCALAR AMPLITUDES
  • FINITE ENERGY SUM RULES
  • THE LOW-ENERGY SIDE OF THE SUM RULES
  • COMBINED FIT OF THE FESR AND OBSERVABLES
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
    • References

    Abstract

    We derive and apply the finite energy sum rules to pion photoproduction. We evaluate the low-energy part of the sum rules using several state-of-the-art models. We show how the differences in the low-energy side of the sum rules might originate from different quantum number assignments of baryon resonances. We interpret the observed features in the low-energy side of the sum rules with the expectation from Regge theory. Finally, we present a model, in terms of a Regge-pole expansion, that matches the sum rules and the high-energy observables.

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    • Received 27 June 2018

    DOI:https://doi.org/10.1103/PhysRevD.98.014041

    Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

    Published by the American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Models & methods for nuclear reactionsPhotonuclear reactions
    Nuclear Physics

    Authors & Affiliations

    V. Mathieu1,*, J. Nys2, C. Fernández-Ramírez3, A. N. Hiller Blin4, A. Jackura5,6, A. Pilloni1, A. P. Szczepaniak5,6,1, and G. Fox7 (Joint Physics Analysis Center)

    • 1Theory Center, Thomas Jefferson National Accelerator Facility, 12000 Jefferson Avenue, Newport News, Virginia 23606, USA
    • 2Department of Physics and Astronomy, Ghent University, Ghent 9000, Belgium
    • 3Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Ciudad de México 04510, Mexico
    • 4Institut für Kernphysik & PRISMA Cluster of Excellence, Johannes Gutenberg Universität, D-55099 Mainz, Germany
    • 5Center for Exploration of Energy and Matter, Indiana University, Bloomington, Indiana 47403, USA
    • 6Physics Department, Indiana University, Bloomington, Indiana 47405, USA
    • 7School of Informatics and Computing, Indiana University, Bloomington, Indiana 47405, USA

    • *vmathieu@jlab.org

    Article Text

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    References

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    Issue

    Vol. 98, Iss. 1 — 1 July 2018

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    Images

    • Figure 1
      Figure 1

      The complex ν plane. The singularities (nucleon pole and the two cuts starting at the πN threshold) are in red. The integration contour is divided into two pieces as in Eq. (14), the contour surrounding the discontinuities and the circle CΛ of radius Λ.

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    • Figure 2
      Figure 2

      Low-energy region under investigation in this work in the ν−t plane. For a fixed value of t, the integration region in ν for the LHS of the FESR is indicated by the red solid line (the πN threshold) and the black dashed line (the cutoff Λ). The physical region of the process γN→πN is indicated by the gray shaded area, limited by z≡cosθ=±1.

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    • Figure 3
      Figure 3

      First moments of the RHS of the FESR Eq. (24) for A1,4(0,±) with SAID (red lines), MAID (blue lines), and ANL-O (green lines) models. The lowest spin particle on the corresponding Regge trajectory is indicated for convenience. The dashed (solid) lines correspond to the k=1 or k=2 (k=3 or k=4) moments and the cutoff is smax=4  GeV2.

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    • Figure 4
      Figure 4

      Chew-Frautschi plot for natural and unnatural parity mesons. The solid lines indicate the two Regge trajectories αN and αU in Eq. (27). The meson masses are taken from the Review of Particle Properties [52] except for the 2−− ρ2 and ω2 mesons taken from a quark model calculation [53].

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    • Figure 5
      Figure 5

      The imaginary part of the SAID (red lines), MAID (blue lines), and ANL-O (green lines) invariant amplitudes ν2A4(−) at t0=0  GeV2, t1=−0.3  GeV2, and t2=−0.6  GeV2. The vertical dashed line displays the beginning of the physical region.

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    • Figure 6
      Figure 6

      The imaginary part of the SAID (red lines), MAID (blue lines), and ANL-O (green lines) invariant amplitudes νA1(0,±) at t=0. The Δ(1232) resonance is responsible for peaks at 1.2 GeV in A1(±) and the nonvanishing S1(+)(t=0,k) integral. As expected from isospin symmetry Δ resonances do not contribute to Ai(0).

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    • Figure 7
      Figure 7

      First moments of the RHS of the FESR Eq. (24) for A2,3(0,+,−) with SAID (red lines), MAID (blue lines), and ANL-O (green lines) models. The lowest spin particle on the corresponding Regge trajectory is indicated for convenience. The dashed (solid) lines correspond to the moment k=1 or k=2 (k=3 or k=4) and the cutoff is smax=4  GeV2.

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    • Figure 8
      Figure 8

      The imaginary part of the SAID (red lines), MAID (blue lines), and ANL-O (green lines) invariant amplitudes ν2A3(+) at t0=0  GeV2, t1=−0.6  GeV2, and t2=−0.9  GeV2. The vertical dashed line displays the beginning of the physical region. The magnitude of the Born term is represented by the horizontal dot-dashed line (hidden by the x axis at t=t0).

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    • Figure 9
      Figure 9

      First moments of the RHS of the FESR Eq. (24) for A1,4(0,±) with SAID for three cutoffs: smax=(1.8  GeV)2 (blue lines), (2.0  GeV)2 (red lines), and (2.2  GeV)2 (green lines).

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    • Figure 10
      Figure 10

      First moments of the RHS of the FESR Eq. (24) for A2,3(0,±) with SAID for three cutoffs: smax=(1.8  GeV)2 (blue lines), (2.0  GeV)2 (red lines), and (2.2  GeV)2 (green lines).

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    • Figure 11
      Figure 11

      Lowest moments of the RHS of the FESR Eq. (24) for Ai(π0)=Ai(0)+Ai(+) with SAID, MAID, and JüBo (Lmax=5 is used) solutions for the process γp→π0p. The integral is truncated at smax=(2.0  GeV)2.

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    • Figure 12
      Figure 12

      The invariant amplitudes Ai with SAID, MAID, ANL-O, BnGa, and JüBo models for the process γp→π0p at t0=0 and t1=−0.8  GeV2.

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    • Figure 13
      Figure 13

      Moments of the t-channel invariant amplitudes F1(0,+) and F3(0,+), Eq. (28), with the SAID, MAID, and ANL-O models. The integral is truncated at smax=(2.0  GeV)2.

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    • Figure 14
      Figure 14

      Comparison between the observables computed with the parametrization of the amplitudes given by Eq. (28), Tables 3 and 4, and the data from [1, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74].

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    • Figure 15
      Figure 15

      Comparison between the high-energy side of the FESR (in red) computed with the parametrization of the amplitudes given by Eq. (28), Tables 3 and 4, and the low-energy side of the FESR (in blue) using the SAID model. The cutoff is smax=(2  GeV)2.

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