Journal of High Energy Physics

, 2017:129 | Cite as

Lattice operators for scattering of particles with spin

Open Access
Regular Article - Theoretical Physics

Abstract

We construct operators for simulating the scattering of two hadrons with spin on the lattice. Three methods are shown to give the consistent operators for P N , P V , V N and N N scattering, where P , V and N denote pseudoscalar, vector and nucleon. Explicit expressions for operators are given for all irreducible representations at lowest two relative momenta. Each hadron has a good helicity in the first method. The hadrons are in a certain partial wave L with total spin S in the second method. These enable the physics interpretations of the operators obtained from the general projection method. The correct transformation properties of the operators in all three methods are proven. The total momentum of two hadrons is restricted to zero since parity is a good quantum number in this case.

Keywords

Lattice QCD Lattice Quantum Field Theory 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    E. Berkowitz et al., Two-nucleon higher partial-wave scattering from lattice QCD, Phys. Lett. B 765 (2017) 285 [arXiv:1508.00886] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    M. Lüscher, Two particle states on a torus and their relation to the scattering matrix, Nucl. Phys. B 354 (1991) 531 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    R.A. Briceno, Two-particle multichannel systems in a finite volume with arbitrary spin, Phys. Rev. D 89 (2014) 074507 [arXiv:1401.3312] [INSPIRE].ADSGoogle Scholar
  4. [4]
    T. Luu and M.J. Savage, Extracting scattering phase-shifts in higher partial-waves from lattice QCD calculations, Phys. Rev. D 83 (2011) 114508 [arXiv:1101.3347] [INSPIRE].ADSGoogle Scholar
  5. [5]
    M. Göckeler et al., Scattering phases for meson and baryon resonances on general moving-frame lattices, Phys. Rev. D 86 (2012) 094513 [arXiv:1206.4141] [INSPIRE].ADSGoogle Scholar
  6. [6]
    V. Bernard, D. Hoja, U.-G. Meißner and A. Rusetsky, Matrix elements of unstable states, JHEP 09 (2012) 023 [arXiv:1205.4642] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    R.A. Briceño, Z. Davoudi and T.C. Luu, Two-nucleon systems in a finite volume: (I) quantization conditions, Phys. Rev. D 88 (2013) 034502 [arXiv:1305.4903] [INSPIRE].ADSGoogle Scholar
  8. [8]
    J.J. Dudek, R.G. Edwards, M.J. Peardon, D.G. Richards and C.E. Thomas, Toward the excited meson spectrum of dynamical QCD, Phys. Rev. D 82 (2010) 034508 [arXiv:1004.4930] [INSPIRE].ADSGoogle Scholar
  9. [9]
    S.J. Wallace, Partial-wave and helicity operators for the scattering of two hadrons in lattice QCD, Phys. Rev. D 92 (2015) 034520 [arXiv:1506.05492] [INSPIRE].ADSGoogle Scholar
  10. [10]
    C.E. Thomas, R.G. Edwards and J.J. Dudek, Helicity operators for mesons in flight on the lattice, Phys. Rev. D 85 (2012) 014507 [Erratum ibid. D 85 (2012) 039901] [arXiv:1107.1930] [INSPIRE].
  11. [11]
    J.J. Dudek, R.G. Edwards and C.E. Thomas, S and D-wave phase shifts in isospin-2 ππ scattering from lattice QCD, Phys. Rev. D 86 (2012) 034031 [arXiv:1203.6041] [INSPIRE].ADSGoogle Scholar
  12. [12]
    D.C. Moore and G.T. Fleming, Multiparticle states and the hadron spectrum on the lattice, Phys. Rev. D 74 (2006) 054504 [hep-lat/0607004] [INSPIRE].
  13. [13]
    M. Jacob and G.C. Wick, On the general theory of collisions for particles with spin, Annals Phys. 7 (1959) 404 [Annals Phys. 281 (2000) 774] [INSPIRE].
  14. [14]
    Particle Data Group collaboration, K.A. Olive et al., Review of particle physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
  15. [15]
    S. Weinberg, The quantum theory of fields I, Cambridge University Press, Cambridge U.K. (1995) [INSPIRE].CrossRefGoogle Scholar
  16. [16]
    V. Bernard, M. Lage, U.-G. Meißner and A. Rusetsky, Resonance properties from the finite-volume energy spectrum, JHEP 08 (2008) 024 [arXiv:0806.4495] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    D.J. Wilson, J.J. Dudek, R.G. Edwards and C.E. Thomas, Resonances in coupled πK, ηK scattering from lattice QCD, Phys. Rev. D 91 (2015) 054008 [arXiv:1411.2004] [INSPIRE].ADSGoogle Scholar
  18. [18]
    G. Moir, M. Peardon, S.M. Ryan, C.E. Thomas and D.J. Wilson, Coupled-channel Dπ, Dη and \( {D}_s\overline{K} \) scattering from lattice QCD, JHEP 10 (2016) 011 [arXiv:1607.07093] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    J. Elliot and P. Dawber, Symmetry in physics I, Oxford University Press, Oxford U.K. (1979).CrossRefGoogle Scholar
  20. [20]
    R.G. Edwards, J.J. Dudek, D.G. Richards and S.J. Wallace, Excited state baryon spectroscopy from lattice QCD, Phys. Rev. D 84 (2011) 074508 [arXiv:1104.5152] [INSPIRE].ADSGoogle Scholar
  21. [21]
    N. Isgur and M.B. Wise, Spectroscopy with heavy quark symmetry, Phys. Rev. Lett. 66 (1991) 1130 [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    D. Mohler, S. Prelovsek and R.M. Woloshyn, Dπ scattering and D meson resonances from lattice QCD, Phys. Rev. D 87 (2013) 034501 [arXiv:1208.4059] [INSPIRE].ADSGoogle Scholar
  23. [23]
    E. Wigner, Group theory, Academic Press, Cambridge U.S.A. (1959).MATHGoogle Scholar
  24. [24]
    Wolfram Research Inc., Mathematica version 10.4, Champaign U.S.A. (2016).Google Scholar
  25. [25]
    Lattice Hadron Physics (LHPC) collaboration, S. Basak et al., Clebsch-Gordan construction of lattice interpolating fields for excited baryons, Phys. Rev. D 72 (2005) 074501 [hep-lat/0508018] [INSPIRE].
  26. [26]
    C.B. Lang, L. Leskovec, M. Padmanath and S. Prelovsek, Pion-nucleon scattering in the Roper channel from lattice QCD, Phys. Rev. D in print [arXiv:1610.01422] [INSPIRE].
  27. [27]
    R.A. Briceño, Z. Davoudi, T. Luu and M.J. Savage, Two-nucleon systems in a finite volume. II. 3 S 1 - 3 D 1 coupled channels and the deuteron, Phys. Rev. D 88 (2013) 114507 [arXiv:1309.3556] [INSPIRE].
  28. [28]
    D. Varshalovich, Quantum theory of angular momentum, World Scientific, Singapore (1988) [INSPIRE].CrossRefGoogle Scholar

Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia
  2. 2.Jozef Stefan InstituteLjubljanaSlovenia
  3. 3.Theory Center, Jefferson LabNewport NewsU.S.A.
  4. 4.Institute of PhysicsUniversity of GrazGrazAustria

Personalised recommendations