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Anatomy of relativistic pion loop corrections to the electromagnetic nucleon coupling

Chueng-Ryong Ji, W. Melnitchouk, and A. W. Thomas
Phys. Rev. D 88, 076005 – Published 9 October 2013
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  • INTRODUCTION
  • PION-NUCLEON INTERACTION
  • VERTEX CORRECTIONS
  • PARTON DISTRIBUTIONS AND MOMENTS
  • CONCLUSION
  • ACKNOWLEDGEMENTS
  • APPENDICES
    • References

    Abstract

    We present a relativistic formulation of pion loop corrections to the coupling of photons with nucleons on the light front. Vertex and wave function renormalization constants are computed to lowest order in the pion field, including their nonanalytic behavior in the chiral limit, and studied numerically as a function of the ultraviolet cutoff. Particular care is taken to explicitly verify gauge invariance and Ward-Takahashi identity constraints to all orders in the mπ expansion. The results are used to compute the chiral corrections to matrix elements of local operators, related to moments of deep-inelastic structure functions. Finally, comparison of results for pseudovector and pseudoscalar coupling allows the resolution of a longstanding puzzle in the computation of pion cloud corrections to structure function moments.

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    • Received 26 June 2013

    DOI:https://doi.org/10.1103/PhysRevD.88.076005

    © 2013 American Physical Society

    Authors & Affiliations

    Chueng-Ryong Ji1, W. Melnitchouk2, and A. W. Thomas3

    • 1Department of Physics, North Carolina State University, Raleigh, North Carolina 27692, USA
    • 2Jefferson Lab, 12000 Jefferson Avenue, Newport News, Virginia 23606, USA
    • 3CSSM and CoEPP, School of Chemistry and Physics, University of Adelaide, Adelaide SA 5005, Australia

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    Issue

    Vol. 88, Iss. 7 — 1 October 2013

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    Images

    • Figure 1
      Figure 1
      Pion loop corrections to the photon–nucleon coupling in the PV pion-nucleon theory: (a) photon coupling to the bare nucleon, (b) wave function renormalization, (c) rainbow diagram with coupling to the nucleon, (d) rainbow diagram with coupling to the pion, (e) Kroll-Ruderman diagrams, (f) pion tadpole diagram with coupling to the pion-nucleon vertex, (g) pion bubble diagram with coupling to the pion.Reuse & Permissions
    • Figure 2
      Figure 2
      Contributions to the vertex renormalization Z1N from terms in Eq. (10) proportional to 1/DπDN2 (dashed line), 1/DπDN (dot-dashed line), 1/Dπ (dotted line), and the sum (solid line), as a function of the k⊥ momentum cutoff Λ.Reuse & Permissions
    • Figure 3
      Figure 3
      Contributions to the vertex renormalization Z1π from terms in Eq. (18) proportional to 1/DπDN (dot-dashed line), 1/Dπ (dotted line), and the sum (solid line), as a function of the k⊥ momentum cutoff Λ.Reuse & Permissions
    • Figure 4
      Figure 4
      Contributions to the vertex renormalization Z1KR from terms in Eq. (23) proportional to 1/DπDN (dot-dashed line), 1/Dπ (dotted line), and the sum (solid line), as a function of the k⊥ momentum cutoff Λ.Reuse & Permissions
    • Figure 5
      Figure 5
      Contributions to the vertex renormalization Z1 from the photon–nucleon coupling Z1N (solid line), photon–pion coupling Z1π (dashed line), and Kroll-Ruderman terms Z1KR (dot-dashed line), as a function of the k⊥ momentum cutoff Λ. Note that the sum of the pion tadpole and bubble contributions to Z1 vanishes.Reuse & Permissions
    • Figure 6
      Figure 6
      Nucleon tadpole (solid line) and pion bubble (dashed line) contributions to the vertex renormalization as a function of the k⊥ momentum cutoff Λ.Reuse & Permissions
    • Figure 7
      Figure 7
      Coupling of an electromagnetic current to a proton (with momentum p) dressed by a pion (with momentum k): (a), (b) wave function renormalization diagrams, (c) rainbow diagram with coupling to the proton, (d) rainbow diagram with coupling to the π+, (e), (f) Kroll-Ruderman diagrams, (g) tadpole diagram with coupling to the ππpp vertex, (h) bubble diagram with coupling to the pion. The current brings in a momentum q.Reuse & Permissions
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