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.
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References
E. Berkowitz et al., Two-nucleon higher partial-wave scattering from lattice QCD, Phys. Lett. B 765 (2017) 285 [arXiv:1508.00886] [INSPIRE].
M. Lüscher, Two particle states on a torus and their relation to the scattering matrix, Nucl. Phys. B 354 (1991) 531 [INSPIRE].
R.A. Briceno, Two-particle multichannel systems in a finite volume with arbitrary spin, Phys. Rev. D 89 (2014) 074507 [arXiv:1401.3312] [INSPIRE].
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].
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].
V. Bernard, D. Hoja, U.-G. Meißner and A. Rusetsky, Matrix elements of unstable states, JHEP 09 (2012) 023 [arXiv:1205.4642] [INSPIRE].
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].
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].
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].
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].
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].
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].
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].
Particle Data Group collaboration, K.A. Olive et al., Review of particle physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
S. Weinberg, The quantum theory of fields I, Cambridge University Press, Cambridge U.K. (1995) [INSPIRE].
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].
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].
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].
J. Elliot and P. Dawber, Symmetry in physics I, Oxford University Press, Oxford U.K. (1979).
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].
N. Isgur and M.B. Wise, Spectroscopy with heavy quark symmetry, Phys. Rev. Lett. 66 (1991) 1130 [INSPIRE].
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].
E. Wigner, Group theory, Academic Press, Cambridge U.S.A. (1959).
Wolfram Research Inc., Mathematica version 10.4, Champaign U.S.A. (2016).
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].
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].
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].
D. Varshalovich, Quantum theory of angular momentum, World Scientific, Singapore (1988) [INSPIRE].
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ArXiv ePrint: 1607.06738
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Prelovsek, S., Skerbis, U. & Lang, C.B. Lattice operators for scattering of particles with spin. J. High Energ. Phys. 2017, 129 (2017). https://doi.org/10.1007/JHEP01(2017)129
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DOI: https://doi.org/10.1007/JHEP01(2017)129