Dynamicallycoupled partialwaves in ρπ isospin2 scattering from lattice QCD
Abstract
We present the first determination of ρπ scattering, incorporating dynamicallycoupled partialwaves, using lattice QCD, a firstprinciples numerical approach to QCD. Considering the case of isospin2 ρπ, we calculate partialwave amplitudes with J ≤ 3 and determine the degree of dynamical mixing between the coupled S and Dwave channels with J^{P} = 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 mesonmeson operators. Calculations are performed with degenerate light and strange quarks tuned to the physical strange quark mass so that m_{π} ~700 MeV, ensuring that the ρ is stable against strong decay. Furthermore, this work demonstrates the successful application of techniques, opening the door to calculations of scattering processes that incorporate the effects of dynamicallycoupled partialwaves, including those involving resonances or bound states.
 Authors:

 Univ. of Cambridge, Cambridge (United Kingdom)
 College of William and Mary, Williamsburg, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
 Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
 Trinity College, Dublin (Ireland)
 Publication Date:
 Research Org.:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Nuclear Physics (NP)
 Contributing Org.:
 for the Hadron Spectrum collaboration
 OSTI Identifier:
 1462038
 Report Number(s):
 JLABTHY182643; DOE/OR/231774345; arXiv:1802.05580; DAMTP20186
Journal ID: ISSN 10298479; PII: 8577; TRN: US1902093
 Grant/Contract Number:
 AC0506OR23177
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 7; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Lattice field theory simulation; QCD Phenomenology
Citation Formats
Woss, Antoni J., Thomas, Christopher E., Dudek, Jozef J., Edwards, Robert G., and Wilson, David J. Dynamicallycoupled partialwaves in ρπ isospin2 scattering from lattice QCD. United States: N. p., 2018.
Web. doi:10.1007/JHEP07(2018)043.
Woss, Antoni J., Thomas, Christopher E., Dudek, Jozef J., Edwards, Robert G., & Wilson, David J. Dynamicallycoupled partialwaves in ρπ isospin2 scattering from lattice QCD. United States. doi:https://doi.org/10.1007/JHEP07(2018)043
Woss, Antoni J., Thomas, Christopher E., Dudek, Jozef J., Edwards, Robert G., and Wilson, David J. Fri .
"Dynamicallycoupled partialwaves in ρπ isospin2 scattering from lattice QCD". United States. doi:https://doi.org/10.1007/JHEP07(2018)043. https://www.osti.gov/servlets/purl/1462038.
@article{osti_1462038,
title = {Dynamicallycoupled partialwaves in ρπ isospin2 scattering from lattice QCD},
author = {Woss, Antoni J. and Thomas, Christopher E. and Dudek, Jozef J. and Edwards, Robert G. and Wilson, David J.},
abstractNote = {We present the first determination of ρπ scattering, incorporating dynamicallycoupled partialwaves, using lattice QCD, a firstprinciples numerical approach to QCD. Considering the case of isospin2 ρπ, we calculate partialwave amplitudes with J ≤ 3 and determine the degree of dynamical mixing between the coupled S and Dwave 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 mesonmeson 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. Furthermore, this work demonstrates the successful application of techniques, opening the door to calculations of scattering processes that incorporate the effects of dynamicallycoupled partialwaves, including those involving resonances or bound states.},
doi = {10.1007/JHEP07(2018)043},
journal = {Journal of High Energy Physics (Online)},
number = 7,
volume = 2018,
place = {United States},
year = {2018},
month = {7}
}
Web of Science
Works referenced in this record:
Scalar mesons in a finite volume
journal, January 2011
 Bernard, V.; Lage, M.; Meißner, U. G.
 Journal of High Energy Physics, Vol. 2011, Issue 1
Aharonov–Bohm effect and nucleon–nucleon phase shifts on the lattice
journal, July 2004
 Bedaque, Paulo F.
 Physics Letters B, Vol. 593, Issue 14
Mesonmeson scattering in the quark model: Spin dependence and exotic channels
journal, January 2001
 Barnes, T.; Black, N.; Swanson, E. S.
 Physical Review C, Vol. 63, Issue 2
Volume dependence of the energy spectrum in massive quantum field theories: I. Stable particle states
journal, June 1986
 Lüscher, M.
 Communications in Mathematical Physics, Vol. 104, Issue 2
Coupledchannel Dπ, Dη and D s K ¯ $$ {D}_s\overline{K} $$ scattering from lattice QCD
journal, October 2016
 Moir, Graham; Peardon, Michael; Ryan, Sinéad M.
 Journal of High Energy Physics, Vol. 2016, Issue 10
Angular momentum on the lattice: The case of nonzero linear momentum
journal, January 2006
 Moore, David C.; Fleming, George T.
 Physical Review D, Vol. 73, Issue 1
Threebody unitarity in the finite volume
journal, December 2017
 Mai, M.; Döring, M.
 The European Physical Journal A, Vol. 53, Issue 12
Solving lattice QCD systems of equations using mixed precision solvers on GPUs
journal, September 2010
 Clark, M. A.; Babich, R.; Barros, K.
 Computer Physics Communications, Vol. 181, Issue 9
Angular momentum on a lattice
journal, July 1982
 Johnson, R. C.
 Physics Letters B, Vol. 114, Issue 23
Two particle states in an asymmetric box and the elastic scattering phases
journal, July 2004
 Feng, Xu; Li, Xin; Liu, Chuan
 Physical Review D, Vol. 70, Issue 1
A method to measure the antikaon–nucleon scattering length in lattice QCD
journal, November 2009
 Lage, Michael; Meißner, UlfG.; Rusetsky, Akaki
 Physics Letters B, Vol. 681, Issue 5
Isoscalar $\pi \pi $ Scattering and the $\sigma $ Meson Resonance from QCD
journal, January 2017
 Briceño, Raul A.; Dudek, Jozef J.; Edwards, Robert G.
 Physical Review Letters, Vol. 118, Issue 2
Finite volume corrections to the twoparticle decay of states with nonzero momentum
journal, December 2005
 Christ, Norman H.; Kim, Changhoan; Yamazaki, Takeshi
 Physical Review D, Vol. 72, Issue 11
Scattering processes and resonances from lattice QCD
journal, April 2018
 Briceño, Raúl A.; Dudek, Jozef J.; Young, Ross D.
 Reviews of Modern Physics, Vol. 90, Issue 2
Theory of the LowEnergy PionPion Interaction
journal, July 1960
 Chew, Geoffrey F.; Mandelstam, Stanley
 Physical Review, Vol. 119, Issue 1
Threeparticle quantization condition in a finite volume: 2. General formalism and the analysis of data
journal, October 2017
 Hammer, HansWerner; Pang, JinYi; Rusetsky, Akaki
 Journal of High Energy Physics, Vol. 2017, Issue 10, 31 p.
Resonance scattering phase shifts on a nonrestframe lattice
journal, September 1995
 Rummukainen, K.; Gottlieb, Steven
 Nuclear Physics B, Vol. 450, Issue 12
Signatures of unstable particles in finite volume
journal, October 1991
 Lüscher, Martin
 Nuclear Physics B, Vol. 364, Issue 1
Twoparticle states on a torus and their relation to the scattering matrix
journal, May 1991
 Lüscher, Martin
 Nuclear Physics B, Vol. 354, Issue 23
Utilising optimised operators and distillation to extract scattering phase shifts
conference, March 2017
 Woss, Antoni; Thomas, Christopher
 Proceedings of 34th annual International Symposium on Lattice Field Theory — PoS(LATTICE2016)
Three particles in a finite volume
journal, May 2012
 Polejaeva, K.; Rusetsky, A.
 The European Physical Journal A, Vol. 48, Issue 5
Adjoint sources in lattice gauge theory
journal, September 1985
 Michael, C.
 Nuclear Physics B, Vol. 259, Issue 1
PhaseShift Analysis of 310Mev ProtonProton Scattering Experiments
journal, January 1957
 Stapp, H. P.; Ypsilantis, T. J.; Metropolis, N.
 Physical Review, Vol. 105, Issue 1
Multiparticle states and the hadron spectrum on the lattice
journal, September 2006
 Moore, David C.; Fleming, George T.
 Physical Review D, Vol. 74, Issue 5
Twonucleon systems in a finite volume. II. ${}^{3}S_{1}\mathrm{\text{\u2212}}{}^{3}D_{1}$ coupled channels and the deuteron
journal, December 2013
 Briceño, Raúl A.; Davoudi, Zohreh; Luu, Thomas C.
 Physical Review D, Vol. 88, Issue 11
Finitevolume effects for twohadron states in moving frames
journal, October 2005
 Kim, C. H.; Sachrajda, C. T.; Sharpe, Stephen R.
 Nuclear Physics B, Vol. 727, Issue 12
Axial resonances a 1(1260), b 1(1235) and their decays from the lattice
journal, April 2014
 Lang, C. B.; Leskovec, Luka; Mohler, Daniel
 Journal of High Energy Physics, Vol. 2014, Issue 4
Lattice operators for scattering of particles with spin
journal, January 2017
 Prelovsek, S.; Skerbis, U.; Lang, C. B.
 Journal of High Energy Physics, Vol. 2017, Issue 1
How to calculate the elastic scattering matrix in twodimensional quantum field theories by numerical simulation
journal, July 1990
 Lüscher, Martin; Wolff, Ulli
 Nuclear Physics B, Vol. 339, Issue 1
Volume dependence of the energy spectrum in massive quantum field theories: II. Scattering states
journal, June 1986
 Lüscher, M.
 Communications in Mathematical Physics, Vol. 105, Issue 2
The Octet Model and its ClebschGordan Coefficients
journal, October 1963
 de Swart, J. J.
 Reviews of Modern Physics, Vol. 35, Issue 4
The Chroma Software System for Lattice QCD
journal, March 2005
 Edwards, Robert G.; Joó, Bálint
 Nuclear Physics B  Proceedings Supplements, Vol. 140
Parallelizing the QUDA Library for MultiGPU Calculations in Lattice Quantum Chromodynamics
conference, November 2010
 Babich, Ronald; Clark, Michael A.; Joó, Balint
 2010 SC  International Conference for High Performance Computing, Networking, Storage and Analysis, 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
Works referencing / citing this record:
Implementing the threeparticle quantization condition including higher partial waves
journal, March 2019
 Blanton, Tyler D.; RomeroLópez, Fernando; Sharpe, Stephen R.
 Journal of High Energy Physics, Vol. 2019, Issue 3
Numerical exploration of three relativistic particles in a finite volume including twoparticle resonances and bound states
journal, October 2019
 RomeroLópez, Fernando; Sharpe, Stephen R.; Blanton, Tyler D.
 Journal of High Energy Physics, Vol. 2019, Issue 10
Scattering phase shifts and mixing angles for an arbitrary number of coupled channels on the lattice
journal, December 2019
 Bovermann, Lukas; Epelbaum, Evgeny; Krebs, Hermann
 Physical Review C, Vol. 100, Issue 6
Scattering amplitudes from finitevolume spectral functions
journal, August 2019
 Bulava, John; Hansen, Maxwell T.
 Physical Review D, Vol. 100, Issue 3
${b}_{1}$ resonance in coupled $\pi \omega $ , $\pi \varphi $ scattering from lattice QCD
journal, September 2019
 Woss, Antoni J.; Thomas, Christopher E.; Dudek, Jozef J.
 Physical Review D, Vol. 100, Issue 5
Unitarity of the infinitevolume threeparticle scattering amplitude arising from a finitevolume formalism
journal, September 2019
 Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.
 Physical Review D, Vol. 100, Issue 5
Consistency checks for twobody finitevolume matrix elements: Conserved currents and bound states
journal, December 2019
 Briceño, Raúl A.; Hansen, Maxwell T.; Jackura, Andrew W.
 Physical Review D, Vol. 100, Issue 11
Longrange electroweak amplitudes of single hadrons from Euclidean finitevolume correlation functions
journal, January 2020
 Briceño, Raúl A.; Davoudi, Zohreh; Hansen, Maxwell T.
 Physical Review D, Vol. 101, Issue 1
Threebody unitarity versus finitevolume ${\pi}^{+}{\pi}^{+}{\pi}^{+}$ spectrum from lattice QCD
journal, March 2020
 Mai, M.; Döring, M.; Culver, C.
 Physical Review D, Vol. 101, Issue 5
Variational approach to $N$ body interactions in finite volume
journal, November 2018
 Guo, Peng; Döring, Michael; Szczepaniak, Adam P.
 Physical Review D, Vol. 98, Issue 9
Threeparticle systems with resonant subprocesses in a finite volume
journal, January 2019
 Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.
 Physical Review D, Vol. 99, Issue 1
FiniteVolume Spectrum of ${\pi}^{+}{\pi}^{+}$ and ${\pi}^{+}{\pi}^{+}{\pi}^{+}$ Systems
journal, February 2019
 Mai, M.; Döring, M.
 Physical Review Letters, Vol. 122, Issue 6
QuarkMass Dependence of Elastic $\pi K$ Scattering from QCD
journal, July 2019
 Wilson, David J.; Briceño, Raúl A.; Dudek, Jozef J.
 Physical Review Letters, Vol. 123, Issue 4
$I=3$ ThreePion Scattering Amplitude from Lattice QCD
journal, January 2020
 Blanton, Tyler D.; RomeroLópez, Fernando; Sharpe, Stephen R.
 Physical Review Letters, Vol. 124, Issue 3
Hadrons and nuclei
journal, November 2019
 Detmold, William; Edwards, Robert G.; Dudek, Jozef J.
 The European Physical Journal A, Vol. 55, Issue 11
Phenomenology of relativistic $$\mathbf {3}\rightarrow \mathbf {3}$$ 3 → 3 reaction amplitudes within the isobar approximation
journal, January 2019
 Jackura, A.; FernándezRamírez, C.; Mathieu, V.
 The European Physical Journal C, Vol. 79, Issue 1