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Dissecting deuteron Compton scattering I: The observables with polarised initial states

  • Harald W. Grießhammer
Regular Article - Theoretical Physics
First Online:
Received:
Accepted:

Abstract

A complete set of linearly independent observables in Compton scattering with arbitrarily polarised real photons off an arbitrarily polarised spin-1 target is introduced, for the case that the final-state polarisations are not measured. Adopted from the one widely used, e.g., in deuteron photo-dissociation, it consists of 18 terms: the unpolarised cross section, the beam asymmetry, 4 target asymmetries and 12 asymmetries in which both beam and target are polarised. They are expressed by the helicity amplitudes and —where available— related to observables discussed by other authors. As application to deuteron Compton scattering, their dependence on the (isoscalar) scalar and spin dipole polarisabilities of the nucleon is explored in Chiral Effective Field Theory with dynamical Δ(1232) degrees of freedom at order e 2 δ 3. Some asymmetries are sensitive to only one or two dipole polarisabilities, making them particularly attractive for experimental studies. At a photon energy of 100 MeV, a set of 5 observables is identified from which one may be able to extract the spin polarisabilities of the nucleon. These are experimentally realistic but challenging and mostly involve tensor-polarised deuterons. Relative to Compton scattering from a nucleon, sensitivity to the “mixed” spin polarisabilities γ E1M2 and γ M1E2 is increased because of the interference with the D wave component of the deuteron and with its pion-exchange current. An interactive Mathematica 9.0 notebook with results for all observables at photon energies up to 120 MeV is available from hgrie@gwu.edu.

Keywords

Spin Polarisabilities Compton Scattering Helicity Amplitude Dipole Polarisabilities Deuteron Wave Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

  1. 1.
    H.W. Griesshammer, J.A. McGovern, D.R. Phillips, G. Feldman, Prog. Part. Nucl. Phys. 67, 841 (2012) arXiv:1203.6834 [nucl-th].ADSCrossRefGoogle Scholar
  2. 2.
    H. Paetz gen. Schieck, Nuclear Physics with Polarized Particles, in Lecture Notes in Physics, Vol. 842 (Springer, 2012).Google Scholar
  3. 3.
    D.G. Crabb, private communication.Google Scholar
  4. 4.
    W. Meyer, private communication.Google Scholar
  5. 5.
    D. Babusci, G. Giordano, A.I. L’vov, G. Matone, A.M. Nathan, Phys. Rev. C 58, 1013 (1998) arXiv:hep-ph/9803347.ADSCrossRefGoogle Scholar
  6. 6.
    J.W. Chen, X.d. Ji, Y.c. Li, Phys. Rev. C 71, 044321 (2005) arXiv:nucl-th/0408004.ADSCrossRefGoogle Scholar
  7. 7.
    J.-W. Chen, X.-d. Ji, Y.-c. Li, Phys. Lett. B 620, 33 (2005) arXiv:nucl-th/0408003.ADSCrossRefGoogle Scholar
  8. 8.
    D. Choudhury, D.R. Phillips, Phys. Rev. C 71, 044002 (2005) arXiv:nucl-th/0411001.ADSCrossRefGoogle Scholar
  9. 9.
    D. Choudhury, PhD Thesis Ohio University (2006).Google Scholar
  10. 10.
    H.W. Grießhammer, D. Shukla, Eur. Phys. J. A 46, 249 (2010) 48.ADSCrossRefGoogle Scholar
  11. 11.
    J.W. Chen, Nucl. Phys. A 653, 375 (1999) arXiv:nucl-th/9810021.ADSCrossRefGoogle Scholar
  12. 12.
    J. Karakowski, arXiv:nucl-th/9901011.
  13. 13.
    J.J. Karakowski, G.A. Miller, Phys. Rev. C 60, 014001 (1999) arXiv:nucl-th/9901018.ADSCrossRefGoogle Scholar
  14. 14.
    H. Arenhovel, M. Sanzone, Few-Body Syst. Suppl. 3, 1 (1991).CrossRefGoogle Scholar
  15. 15.
    H.W. Grießhammer, in preparation.Google Scholar
  16. 16.
    H.W. Grießhammer, T.R. Hemmert, Phys. Rev. C 65, 045207 (2002) arXiv:nucl-th/0110006.ADSCrossRefGoogle Scholar
  17. 17.
    R.P. Hildebrandt, H.W. Grießhammer, T.R. Hemmert, B. Pasquini, Eur. Phys. J. A 20, 293 (2004) arXiv:nucl-th/0307070.ADSCrossRefGoogle Scholar
  18. 18.
    B.R. Holstein, arXiv:hep-ph/0010129.
  19. 19.
    W. Detmold, B.C. Tiburzi, A. Walker-Loud, Phys. Rev. D 81, 054502 (2010) arXiv:1001.1131 [hep-lat].ADSCrossRefGoogle Scholar
  20. 20.
    M. Engelhardt, PoS LATTICE 2011, 153 (2011) arXiv:1111.3686 [hep-lat].Google Scholar
  21. 21.
    M. Lujan, A. Alexandru, F. Lee, PoS LATTICE 2011, 165 (2011) arXiv:1111.6288 [hep-lat].Google Scholar
  22. 22.
    A. Walker-Loud, C.E. Carlson, G.A. Miller, Phys. Rev. Lett. 108, 232301 (2012) arXiv:1203.0254 [nucl-th].ADSCrossRefGoogle Scholar
  23. 23.
    K. Pachucki, Phys. Rev. A 60, 3593 (1999).ADSCrossRefGoogle Scholar
  24. 24.
    C.E. Carlson, M. Vanderhaeghen, arXiv:1109.3779 [physics.atom-ph].
  25. 25.
    M.C. Birse, J.A. McGovern, Eur. Phys. J. A 48, 120 (2012) arXiv:1206.3030 [hep-ph].ADSCrossRefGoogle Scholar
  26. 26.
    G.A. Miller, Phys. Lett. B 718, 1078 (2013) arXiv:1209.4667 [nucl-th].ADSCrossRefGoogle Scholar
  27. 27.
    V. Bernard, N. Kaiser, U.G. Meißner, Phys. Rev. Lett. 67, 1515 (1991).ADSCrossRefGoogle Scholar
  28. 28.
    V. Bernard, N. Kaiser, U.G. Meißner, Int. J. Mod. Phys. E 4, 193 (1995) arXiv:hep-ph/9501384.ADSCrossRefGoogle Scholar
  29. 29.
    J.A. McGovern, D.R. Phillips, H.W. Grießhammer, Eur. Phys. J. A 49, 12 (2013) arXiv:1210.4104 [nucl-th].ADSCrossRefGoogle Scholar
  30. 30.
    M. Schumacher, Prog. Part. Nucl. Phys. 55, 567 (2005) arXiv:hep-ph/0501167.ADSCrossRefGoogle Scholar
  31. 31.
    H.W. Grießhammer, D.R. Phillips, J.A. McGovern, arXiv:1306.2200 [nucl-th].
  32. 32.
    M.E. Rose, Elementary Theory of Angular Momentum (Wiley, 1957).Google Scholar
  33. 33.
    A.R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, 1974).Google Scholar
  34. 34.
    Particle Data Group, Phys. Rev. D 86, 010001 (2012).CrossRefGoogle Scholar
  35. 35.
    R.P. Hildebrandt, H.W. Grießhammer, T.R. Hemmert, Eur. Phys. J. A 46, 111 (2010) arXiv:nucl-th/0512063.ADSCrossRefGoogle Scholar
  36. 36.
    R.P. Hildebrandt, Elastic Compton Scattering from the Nucleon and Deuteron, PhD Thesis Technische Universität München (2005) arXiv:nucl-th/0512064.
  37. 37.
    V. Pascalutsa, D.R. Phillips, Phys. Rev. C 67, 055202 (2003) arXiv:nucl-th/0212024.ADSCrossRefGoogle Scholar
  38. 38.
    H.W. Grießhammer, Proceedings Menu 2007, eConf section of the SLAC archive, arXiv:0710.2924.
  39. 39.
    H.W. Grießhammer, Prog. Part. Nucl. Phys. 55, 215 (2005) arXiv:nucl-th/0411080.ADSCrossRefGoogle Scholar
  40. 40.
    E.E. Jenkins, A.V. Manohar, Phys. Lett. B 255, 558 (1991).ADSCrossRefGoogle Scholar
  41. 41.
    E.E. Jenkins, A.V. Manohar, In Dobogokoe 1991, Proceedings, Effective field theories of the standard model 113 and Calif. Univ. San Diego - UCSD-PTH 91-30 (91/10, rec. Dec.) (201392) p. 26 (see conference index).Google Scholar
  42. 42.
    T.R. Hemmert, B.R. Holstein, J. Kambor, Phys. Lett. B 395, 89 (1997) arXiv:hep-ph/9606456.ADSCrossRefGoogle Scholar
  43. 43.
    T.R. Hemmert, B.R. Holstein, J. Kambor, J. Phys. G 24, 1831 (1998) arXiv:hep-ph/9712496.ADSCrossRefGoogle Scholar
  44. 44.
    S.R. Beane, M. Malheiro, D.R. Phillips, U. van Kolck, Nucl. Phys. A 656, 367 (1999) arXiv:nucl-th/9905023.ADSCrossRefGoogle Scholar
  45. 45.
    J.L. Friar, Ann. Phys. (NY) 95, 170 (1975).ADSCrossRefGoogle Scholar
  46. 46.
    J.L. Friar, Phys. Rev. C 16, 1504 (1977).ADSCrossRefGoogle Scholar
  47. 47.
    H. Arenhovel, Z. Phys. A 297, 129 (1980).ADSCrossRefGoogle Scholar
  48. 48.
    M. Weyrauch, H. Arenhovel, Nucl. Phys. A 408, 425 (1983).ADSCrossRefGoogle Scholar
  49. 49.
    E. Epelbaum, W. Gloeckle, U.-G. Meißner, Nucl. Phys. A 671, 295 (2000) arXiv:nucl-th/9910064.ADSCrossRefGoogle Scholar
  50. 50.
    R.B. Wiringa, V.G.J. Stoks, R. Schiavilla, Phys. Rev. C 51, 38 (1995).ADSCrossRefGoogle Scholar
  51. 51.
    R. Miskimen, Measuring the Spin-Polarizabilities of the Proton at , presentation at the INT workshop on Soft Photons and Light Nuclei, 17 June 2008, and private communication.Google Scholar
  52. 52.
    K. Aulenbacher, talk given at the Workshop to Explore Physics Opportunities with Intense, Polarized Electron Beams with Energy up to 300 MeV, MIT, 2013, in preparation.Google Scholar
  53. 53.
    L.C. Maximon, Phys. Rev. C 39, 347 (1989).ADSCrossRefGoogle Scholar
  54. 54.
    S.R. Beane, M. Malheiro, J.A. McGovern, D.R. Phillips, U. van Kolck, Nucl. Phys. A 747, 311 (2005) arXiv:nucl-th/0403088.ADSCrossRefGoogle Scholar
  55. 55.
    V.G. Stoks, R.A. Klomp, C.P. Terheggen, J.J. de Swart, Phys. Rev. C 49, 2950 (1994).ADSCrossRefGoogle Scholar
  56. 56.
    R.P. Hildebrandt, H.W. Grießhammer, T.R. Hemmert, D.R. Phillips, Nucl. Phys. A 748, 573 (2005) arXiv:nucl-th/0405077.ADSCrossRefGoogle Scholar
  57. 57.
    S.R. Beane, M. Malheiro, J.A. McGovern, D.R. Phillips, U. van Kolck, Phys. Lett. B 567, 200 (2003) arXiv:nucl-th/0209002.ADSCrossRefGoogle Scholar
  58. 58.
    D.L. Hornidge, B.J. Warkentin, R. Igarashi, J.C. Bergstrom, E.L. Hallin, N.R. Kolb, R.E. Pywell, D.M. Skopik et al., Phys. Rev. Lett. 84, 2334 (2000) arXiv:nucl-ex/9909015.ADSCrossRefGoogle Scholar
  59. 59.
    M.I. Levchuk, A.I. L’vov, Nucl. Phys. A 674, 449 (2000) arXiv:nucl-th/9909066.ADSCrossRefGoogle Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institut für Kernphysik (IKP-3), Institute for Advanced Simulation and Jülich Centre for Hadron PhysicsForschungszentrum JülichJülichGermany
  2. 2.Institute for Nuclear Studies, Department of PhysicsThe George Washington UniversityWashington DCUSA

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