Abstract
We present the first determination of ρπ scattering, incorporating dynamically-coupled partial-waves, using lattice QCD, a first-principles numerical approach to QCD. Considering the case of isospin-2 ρπ, we calculate partial-wave amplitudes with J ≤ 3 and determine the degree of dynamical mixing between the coupled S and D-wave channels with JP = 1+. The analysis makes use of the relationship between scattering amplitudes and the discrete spectrum of states in the finite volume lattice. Constraints on the scattering amplitudes are provided by over one hundred energy levels computed on two lattice volumes at various overall momenta and in several irreducible representations of the relevant symmetry groups. The spectra follow from variational analyses of matrices of correlations functions computed with large bases of meson-meson operators. Calculations are performed with degenerate light and strange quarks tuned to the physical strange quark mass so that mπ ∼ 700 MeV, ensuring that the ρ is stable against strong decay. This work demonstrates the successful application of techniques, opening the door to calculations of scattering processes that incorporate the effects of dynamically-coupled partial-waves, including those involving resonances or bound states.
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References
FOCUS collaboration, J.M. Link et al., Study of the D 0 → π − π + π − π + decay, Phys. Rev. D 75 (2007) 052003 [hep-ex/0701001] [INSPIRE].
M. Lüscher, Volume dependence of the energy spectrum in massive quantum field theories. 1. Stable particle states, Commun. Math. Phys. 104 (1986) 177 [INSPIRE].
M. Lüscher, Volume dependence of the energy spectrum in massive quantum field theories. 2. Scattering states, Commun. Math. Phys. 105 (1986) 153 [INSPIRE].
P.F. Bedaque, Aharonov-Bohm effect and nucleon nucleon phase shifts on the lattice, Phys. Lett. B 593 (2004) 82 [nucl-th/0402051] [INSPIRE].
V. Bernard, M. Lage, U.G. Meissner and A. Rusetsky, Scalar mesons in a finite volume, JHEP 01 (2011) 019 [arXiv:1010.6018] [INSPIRE].
R.A. Briceño, Two-particle multichannel systems in a finite volume with arbitrary spin, Phys. Rev. D 89 (2014) 074507 [arXiv:1401.3312] [INSPIRE].
R.A. Briceño and Z. Davoudi, Moving multichannel systems in a finite volume with application to proton-proton fusion, Phys. Rev. D 88 (2013) 094507 [arXiv:1204.1110] [INSPIRE].
R.A. Briceño, Z. Davoudi, T.C. Luu and M.J. Savage, Two-baryon systems with twisted boundary conditions, Phys. Rev. D 89 (2014) 074509 [arXiv:1311.7686] [INSPIRE].
N.H. Christ, C. Kim and T. Yamazaki, Finite volume corrections to the two-particle decay of states with non-zero momentum, Phys. Rev. D 72 (2005) 114506 [hep-lat/0507009] [INSPIRE].
X. Feng, X. Li and C. Liu, Two particle states in an asymmetric box and the elastic scattering phases, Phys. Rev. D 70 (2004) 014505 [hep-lat/0404001] [INSPIRE].
Z. Fu, Rummukainen-Gottlieb’s formula on two-particle system with different mass, Phys. Rev. D 85 (2012) 014506 [arXiv:1110.0319] [INSPIRE].
P. Guo, J. Dudek, R. Edwards and A.P. Szczepaniak, Coupled-channel scattering on a torus, Phys. Rev. D 88 (2013) 014501 [arXiv:1211.0929] [INSPIRE].
M.T. Hansen and S.R. Sharpe, Multiple-channel generalization of Lellouch-Lüscher formula, Phys. Rev. D 86 (2012) 016007 [arXiv:1204.0826] [INSPIRE].
C.h. Kim, C.T. Sachrajda and S.R. Sharpe, Finite-volume effects for two-hadron states in moving frames, Nucl. Phys. B 727 (2005) 218 [hep-lat/0507006] [INSPIRE].
M. Lage, U.-G. Meissner and A. Rusetsky, A method to measure the antikaon-nucleon scattering length in lattice QCD, Phys. Lett. B 681 (2009) 439 [arXiv:0905.0069] [INSPIRE].
L. Leskovec and S. Prelovsek, Scattering phase shifts for two particles of different mass and non-zero total momentum in lattice QCD, Phys. Rev. D 85 (2012) 114507 [arXiv:1202.2145] [INSPIRE].
N. Li and C. Liu, Generalized Lüscher formula in multichannel baryon-meson scattering, Phys. Rev. D 87 (2013) 014502 [arXiv:1209.2201] [INSPIRE].
S. He, X. Feng and C. Liu, Two particle states and the S-matrix elements in multi-channel scattering, JHEP 07 (2005) 011 [hep-lat/0504019] [INSPIRE].
K. Rummukainen and S.A. Gottlieb, Resonance scattering phase shifts on a nonrest frame lattice, Nucl. Phys. B 450 (1995) 397 [hep-lat/9503028] [INSPIRE].
R.A. Briceño, J.J. Dudek and R.D. Young, Scattering processes and resonances from lattice QCD, Rev. Mod. Phys. 90 (2018) 025001 [arXiv:1706.06223] [INSPIRE].
C.B. Lang, L. Leskovec, D. Mohler and S. Prelovsek, Axial resonances a 1 (1260), b 1 (1235) and their decays from the lattice, JHEP 04 (2014) 162 [arXiv:1401.2088] [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].
K. Orginos et al., Two nucleon systems at m π ∼ 450 MeV from lattice QCD, Phys. Rev. D 92 (2015) 114512 [arXiv:1508.07583] [INSPIRE].
R.A. Briceño and Z. Davoudi, Three-particle scattering amplitudes from a finite volume formalism, Phys. Rev. D 87 (2013) 094507 [arXiv:1212.3398] [INSPIRE].
M.T. Hansen and S.R. Sharpe, Relativistic, model-independent, three-particle quantization condition, Phys. Rev. D 90 (2014) 116003 [arXiv:1408.5933] [INSPIRE].
M.T. Hansen and S.R. Sharpe, Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude, Phys. Rev. D 92 (2015) 114509 [arXiv:1504.04248] [INSPIRE].
K. Polejaeva and A. Rusetsky, Three particles in a finite volume, Eur. Phys. J. A 48 (2012) 67 [arXiv:1203.1241] [INSPIRE].
R.A. Briceño, M.T. Hansen and S.R. Sharpe, Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles, Phys. Rev. D 95 (2017) 074510 [arXiv:1701.07465] [INSPIRE].
H.W. Hammer, J.Y. Pang and A. Rusetsky, Three particle quantization condition in a finite volume: 2. General formalism and the analysis of data, JHEP 10 (2017) 115 [arXiv:1707.02176] [INSPIRE].
M. Mai and M. Döring, Three-body unitarity in the finite volume, Eur. Phys. J. A 53 (2017) 240 [arXiv:1709.08222] [INSPIRE].
M. Döring et al., Three-body spectrum in a finite volume: the role of cubic symmetry, Phys. Rev. D 97 (2018) 114508 [arXiv:1802.03362] [INSPIRE].
T. Barnes, N. Black and E.S. Swanson, Meson meson scattering in the quark model: Spin dependence and exotic channels, Phys. Rev. C 63 (2001) 025204 [nucl-th/0007025] [INSPIRE].
C. Michael, Adjoint sources in lattice gauge theory, Nucl. Phys. B 259 (1985) 58 [INSPIRE].
M. Lüscher and U. Wolff, How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation, Nucl. Phys. B 339 (1990) 222 [INSPIRE].
Hadron Spectrum collaboration, J.J. Dudek et al., An a 0 resonance in strongly coupled πη, \( K\overline{K} \) scattering from lattice QCD, Phys. Rev. D 93 (2016) 094506 [arXiv:1602.05122] [INSPIRE].
G. Moir et al., Coupled-Channel Dπ, Dη and \( {D}_s\overline{K} \) Scattering from Lattice QCD, JHEP 10 (2016) 011 [arXiv:1607.07093] [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].
D.J. Wilson et al., Coupled ππ, \( K\overline{K} \) scattering in P-wave and the ρ resonance from lattice QCD, Phys. Rev. D 92 (2015) 094502 [arXiv:1507.02599] [INSPIRE].
H.P. Stapp, T.J. Ypsilantis and N. Metropolis, Phase shift analysis of 310-MeV proton proton scattering experiments, Phys. Rev. 105 (1957) 302 [INSPIRE].
D.C. Moore and G.T. Fleming, Angular momentum on the lattice: the case of non-zero linear momentum, Phys. Rev. D 73 (2006) 014504 [Erratum ibid. D 74 (2006) 079905] [hep-lat/0507018] [INSPIRE].
R.C. Johnson, Angular momentum on a lattice, Phys. Lett. 114B (1982) 147 [INSPIRE].
M. Lüscher, Two particle states on a torus and their relation to the scattering matrix, Nucl. Phys. B 354 (1991) 531 [INSPIRE].
M. Lüscher, Signatures of unstable particles in finite volume, Nucl. Phys. B 364 (1991) 237 [INSPIRE].
Hadron Spectrum collaboration, J.J. Dudek et al., Energy dependence of the ρ resonance in ππ elastic scattering from lattice QCD, Phys. Rev. D 87 (2013) 034505 [arXiv:1212.0830] [INSPIRE].
R.A. Briceño, J.J. Dudek, R.G. Edwards and D.J. Wilson, Isoscalar ππ, \( K\overline{K} \) , ηη scattering and the σ, f 0 , f 2 mesons from QCD, Phys. Rev. D 97 (2018) 054513 [arXiv:1708.06667] [INSPIRE].
Hadron Spectrum collaboration, J.J. Dudek et al., Resonances in coupled πK − ηK scattering from quantum chromodynamics, Phys. Rev. Lett. 113 (2014) 182001 [arXiv:1406.4158] [INSPIRE].
J.J. Dudek et al., Toward the excited meson spectrum of dynamical QCD, Phys. Rev. D 82 (2010) 034508 [arXiv:1004.4930] [INSPIRE].
J.J. Dudek, R.G. Edwards, N. Mathur and D.G. Richards, Charmonium excited state spectrum in lattice QCD, Phys. Rev. D 77 (2008) 034501 [arXiv:0707.4162] [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].
R.A. Briceño, J.J. Dudek, R.G. Edwards and D.J. Wilson, Isoscalar ππ scattering and the σ meson resonance from QCD, Phys. Rev. Lett. 118 (2017) 022002 [arXiv:1607.05900] [INSPIRE].
Hadron Spectrum collaboration, G.K.C. Cheung et al., Tetraquark operators in lattice QCD and exotic flavour states in the charm sector, JHEP 11 (2017) 033 [arXiv:1709.01417] [INSPIRE].
J.J. Dudek et al., Isoscalar meson spectroscopy from lattice QCD, Phys. Rev. D 83 (2011) 111502 [arXiv:1102.4299] [INSPIRE].
Hadron Spectrum collaboration, L. Liu et al., Excited and exotic charmonium spectroscopy from lattice QCD, JHEP 07 (2012) 126 [arXiv:1204.5425] [INSPIRE].
A.J. Woss and C.E. Thomas, Utilising optimised operators and distillation to extract scattering phase shifts, PoS LATTICE2016 (2016) 134 [arXiv:1612.05437] [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 [arXiv:1107.1930] [INSPIRE].
J.J. de Swart, The octet model and its Clebsch-Gordan coefficients, Rev. Mod. Phys. 35 (1963) 916 [Erratum ibid. 37 (1965) 326] [INSPIRE].
S. Prelovsek, C.B. Lang, L. Leskovec and D. Mohler, Study of the Z + c channel using lattice QCD, Phys. Rev. D 91 (2015) 014504 [arXiv:1405.7623] [INSPIRE].
S. Prelovsek, U. Skerbis and C.B. Lang, Lattice operators for scattering of particles with spin, JHEP 01 (2017) 129 [arXiv:1607.06738] [INSPIRE].
R.G. Edwards, B. Joo and H.-W. Lin, Tuning for three-flavors of anisotropic clover fermions with Stout-link smearing, Phys. Rev. D 78 (2008) 054501 [arXiv:0803.3960] [INSPIRE].
Hadron Spectrum collaboration, H.-W. Lin et al., First results from 2 + 1 dynamical quark flavors on an anisotropic lattice: light-hadron spectroscopy and setting the strange-quark mass, Phys. Rev. D 79 (2009) 034502 [arXiv:0810.3588] [INSPIRE].
Hadron Spectrum collaboration, M. Peardon et al., A Novel quark-field creation operator construction for hadronic physics in lattice QCD, Phys. Rev. D 80 (2009) 054506 [arXiv:0905.2160] [INSPIRE].
Hadron Spectrum collaboration, R.G. Edwards et al., Flavor structure of the excited baryon spectra from lattice QCD, Phys. Rev. D 87 (2013) 054506 [arXiv:1212.5236] [INSPIRE].
Particle Data Group collaboration, C. Patrignani et al., Review of particle physics, Chin. Phys. C 40 (2016) 100001.
C.J. Shultz, J.J. Dudek and R.G. Edwards, Excited meson radiative transitions from lattice QCD using variationally optimized operators, Phys. Rev. D 91 (2015) 114501 [arXiv:1501.07457] [INSPIRE].
M. Gockeler et al., Scattering phases for meson and baryon resonances on general moving-frame lattices, Phys. Rev. D 86 (2012) 094513 [arXiv:1206.4141] [INSPIRE].
C.W. Andersen, J. Bulava, B. Hörz and C. Morningstar, Elastic I = 3/2p-wave nucleon-pion scattering amplitude and the Δ(1232) resonance from N f = 2 + 1 lattice QCD, Phys. Rev. D 97 (2018) 014506 [arXiv:1710.01557] [INSPIRE].
G.F. Chew and S. Mandelstam, Theory of low-energy pion pion interactions, Phys. Rev. 119 (1960) 467 [INSPIRE].
E852 collaboration, M. Nozar et al., A Study of the reaction π − p → ωπ − p at 18 GeV/c: the D and S decay amplitudes for b 1(1235) → ωπ, Phys. Lett. B 541 (2002) 35 [hep-ex/0206026] [INSPIRE].
SciDAC, LHPC, UKQCD collaboration, R.G. Edwards and B. Joo, The Chroma software system for lattice QCD, Nucl. Phys. Proc. Suppl. 140 (2005) 832 [hep-lat/0409003] [INSPIRE].
M.A. Clark et al., Solving Lattice QCD systems of equations using mixed precision solvers on GPUs, Comput. Phys. Commun. 181 (2010) 1517 [arXiv:0911.3191] [INSPIRE].
R. Babich, M.A. Clark and B. Joo, Parallelizing the QUDA Library for Multi-GPU Calculations in Lattice Quantum Chromodynamics, in the proceedings of the SC10 (Supercomputing 2010), November 13–19, New Orleans, U.S.A. (2010) arXiv:1011.0024 [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].
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Woss, A.J., Thomas, C.E., Dudek, J.J. et al. Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD. J. High Energ. Phys. 2018, 43 (2018). https://doi.org/10.1007/JHEP07(2018)043
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DOI: https://doi.org/10.1007/JHEP07(2018)043