skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: b 1 resonance in coupled π ω , π ϕ scattering from lattice QCD

Journal Article · · Physical Review D
; ; ; ;

We present the first lattice QCD calculation of coupled $$\pi\omega$$ and $$\pi\phi$$ scattering, incorporating coupled $$S$$ and $$D$$-wave $$\pi\omega$$ in $J^P=1^+$. Finite-volume spectra in three volumes are determined via a variational analysis of matrices of two-point correlation functions, computed using large bases of operators resembling single-meson, two-meson and three-meson structures, with the light-quark mass corresponding to a pion mass of $$m_\pi \approx 391$$ MeV. Utilising the relationship between the discrete spectrum of finite-volume energies and infinite-volume scattering amplitudes, we find a narrow axial-vector resonance ($$J^{PC}=1^{+-}$$), the analogue of the $$b_1$$ meson, with mass $$m_{R}\approx1380$$ MeV and width $$\Gamma_{R}\approx 91$$ MeV. The resonance is found to couple dominantly to $$S$$-wave $$\pi\omega$$, with a much-suppressed coupling to $$D$$-wave $$\pi\omega$$, and a negligible coupling to $$\pi\phi$$ consistent with the `OZI rule'. No resonant behavior is observed in $$\pi\phi$$, indicating the absence of a putative low-mass $$Z_s$$ analogue of the $$Z_c$$ claimed in $$\pi J/\psi$$. In order to minimally present the contents of a unitary three-channel scattering matrix, we introduce an $$n$$-channel generalization of the traditional two-channel Stapp parameterization.

Research Organization:
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Nuclear Physics (NP)
Contributing Organization:
Hadron Spectrum Collaboration
Grant/Contract Number:
SC0018416; AC05-06OR23177; AC05-00OR22725; AC02-05CH11231; ST/P000681/1; ST/P002307/1; ST/R002452/1; ST/R00689X/1; UF160419
OSTI ID:
1562569
Alternate ID(s):
OSTI ID: 1567053
Report Number(s):
JLAB-THY-19-2910; DOE/OR/; 23177-4664; arXiv:1904.04136; DAMTP-2019-12; PRVDAQ; 054506
Journal Information:
Physical Review D, Journal Name: Physical Review D Vol. 100 Journal Issue: 5; ISSN 2470-0010
Publisher:
American Physical SocietyCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 30 works
Citation information provided by
Web of Science

References (75)

Volume dependence of the energy spectrum in massive quantum field theories: I. Stable particle states journal June 1986
Helicity operators for mesons in flight on the lattice journal January 2012
Finite-Volume Spectrum of π + π + and π + π + π + Systems journal February 2019
Coupled-channel scattering on a torus journal July 2013
Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles journal April 2017
Tuning for three flavors of anisotropic clover fermions with stout-link smearing journal September 2008
Multiple-channel generalization of Lellouch-Lüscher formula journal July 2012
S - and D -wave phase shifts in isospin-2 π π scattering from lattice QCD journal August 2012
Decay width of light quark hybrid meson from the lattice journal April 2006
Solving lattice QCD systems of equations using mixed precision solvers on GPUs journal September 2010
Toward the excited isoscalar meson spectrum from lattice QCD journal November 2013
Moving multichannel systems in a finite volume with application to proton-proton fusion journal November 2013
A study of the reaction π−p→ωπ−p at 18 GeV/c: the D and S decay amplitudes for b1(1235)→ωπ journal August 2002
Theory of the Low-Energy Pion-Pion Interaction journal July 1960
Three-particle quantization condition in a finite volume: 2. General formalism and the analysis of data journal October 2017
ρ and K * resonances on the lattice at nearly physical quark masses and N f = 2 journal March 2016
Resonance scattering phase shifts on a non-rest-frame lattice journal September 1995
P -wave π π scattering and the ρ resonance from lattice QCD journal August 2017
The I = 1 pion–pion scattering amplitude and timelike pion form factor from Nf = 2 + 1 lattice QCD journal February 2019
Review of Particle Physics journal August 2018
Novel quark-field creation operator construction for hadronic physics in lattice QCD journal September 2009
Relativistic, model-independent, three-particle quantization condition journal December 2014
Three particles in a finite volume journal May 2012
The Angular Distribution of Scattering and Reaction Cross Sections journal October 1952
Coupled π π , K K ¯ scattering in P -wave and the ρ resonance from lattice QCD journal November 2015
Three-particle scattering amplitudes from a finite volume formalism journal May 2013
Charmonium excited state spectrum in lattice QCD journal February 2008
Resonance parameters of the ρ meson from lattice QCD journal May 2011
Lattice QCD calculation of the ρ meson decay width journal November 2007
First results from 2 + 1 dynamical quark flavors on an anisotropic lattice: Light-hadron spectroscopy and setting the strange-quark mass journal February 2009
Toward the excited meson spectrum of dynamical QCD journal August 2010
Axial resonances a 1(1260), b 1(1235) and their decays from the lattice journal April 2014
How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation journal July 1990
Two-particle multichannel systems in a finite volume with arbitrary spin journal April 2014
Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude journal December 2015
Volume dependence of the energy spectrum in massive quantum field theories: II. Scattering states journal June 1986
Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD journal July 2018
Tetraquark operators in lattice QCD and exotic flavour states in the charm sector journal November 2017
Three-particle systems with resonant subprocesses in a finite volume journal January 2019
Observation of a Charged Charmoniumlike Structure in e + e − → π + π − J / ψ at s = 4.26     GeV journal June 2013
Study of e + e − → π + π − J / ψ and Observation of a Charged Charmoniumlike State at Belle journal June 2013
Two particle states and the S -matrix elements in multi-channel scattering journal July 2005
Coupled-channel Dπ, Dη and D s K ¯ $$ {D}_s\overline{K} $$ scattering from lattice QCD journal October 2016
Angular momentum on the lattice: The case of nonzero linear momentum journal January 2006
Excited state baryon spectroscopy from lattice QCD journal October 2011
Three-body unitarity in the finite volume journal December 2017
Erratum: Energy dependence of the ρ resonance in π π elastic scattering from lattice QCD [Phys. Rev. D 87 , 034505 (2013)] journal November 2014
Scattering phases for meson and baryon resonances on general moving-frame lattices journal November 2012
I = 1 and I = 2 π – π scattering phase shifts from N f = 2 + 1 lattice QCD journal September 2016
K π scattering and the K * decay width from lattice QCD journal September 2013
Resonances in Coupled π K − η K Scattering from Quantum Chromodynamics journal October 2014
Finite volume corrections to the two-particle decay of states with nonzero momentum journal December 2005
Resonances in coupled π K , η K scattering from lattice QCD journal March 2015
Numerical study of the relativistic three-body quantization condition in the isotropic approximation journal July 2018
Implementing the three-particle quantization condition including higher partial waves journal March 2019
Isoscalar π π ,   K K ¯ ,   η η scattering and the σ ,   f 0 ,   f 2 mesons from QCD journal March 2018
Rho resonance parameters from lattice QCD journal August 2016
An a 0 resonance in strongly coupled π η , K K ¯ scattering from lattice QCD journal May 2016
Energy dependence of the ρ resonance in π π elastic scattering from lattice QCD journal February 2013
X ( 3872 ) and Y ( 4140 ) using diquark-antidiquark operators with lattice QCD journal August 2015
Two-particle states on a torus and their relation to the scattering matrix journal May 1991
Three-body spectrum in a finite volume: The role of cubic symmetry journal June 2018
Adjoint sources in lattice gauge theory journal September 1985
Determination of s- and p-wave I = 1/2 Kπ scattering amplitudes in Nf = 2 + 1 lattice QCD journal July 2018
ρ meson decay in 2 + 1 flavor lattice QCD journal November 2011
Phase-Shift Analysis of 310-Mev Proton-Proton Scattering Experiments journal January 1957
Quark-Mass Dependence of Elastic π K Scattering from QCD journal July 2019
Erratum: Angular momentum on the lattice: The case of nonzero linear momentum [Phys. Rev. D 73 , 014504 (2006)] journal October 2006
Finite-volume effects for two-hadron states in moving frames journal October 2005
Isoscalar meson spectroscopy from lattice QCD journal June 2011
Search for a strangeonium-like structure Z s decaying into ϕ π and a measurement of the cross section e + e − → ϕ π π journal January 2019
Studying the ρ resonance parameters with staggered fermions journal August 2016
The Chroma Software System for Lattice QCD journal March 2005
Determination of s - and p -wave I  = 1/2 Kπ scattering amplitudes in N f  = 2 + 1 lattice QCD text January 2018
Scattering phases for meson and baryon resonances on general moving-frame lattices text January 2012

Cited By (1)

Mixing and m q dependence of axial vector mesons in the Coulomb gauge QCD model journal December 2019

Figures / Tables (35)

FIG. 1(p. 6)figure FIG. 1
FIG. 2(p. 6)figure FIG. 2
FIG. 3(p. 7)figure FIG. 3
TABLE I(p. 7)table TABLE I
TABLE II(p. 7)table TABLE II
TABLE III(p. 8)table TABLE III
TABLE IV(p. 8)table TABLE IV
FIG. 4(p. 9)figure FIG. 4
TABLE V.(p. 9)table TABLE V.
FIG. 5(p. 10)figure FIG. 5
FIG. 6(p. 11)figure FIG. 6
FIG. 7(p. 14)figure FIG. 7
FIG. 8(p. 14)figure FIG. 8
FIG. 10(p. 16)figure FIG. 10
FIG. 9(p. 16)figure FIG. 9
FIG. 11(p. 17)figure FIG. 11
FIG. 12(p. 18)figure FIG. 12
FIG. 13(p. 19)figure FIG. 13
FIG. 14(p. 20)figure FIG. 14
FIG. 15(p. 20)figure FIG. 15
FIG. 16(p. 21)figure FIG. 16
FIG. 17(p. 22)figure FIG. 17
FIG. 18(p. 23)figure FIG. 18
FIG. 19(p. 25)figure FIG. 19
TABLE IX(p. 26)table TABLE IX
TABLE VI(p. 26)table TABLE VI
TABLE VII(p. 26)table TABLE VII
TABLE VIII(p. 26)table TABLE VIII
TABLE X(p. 26)table TABLE X
TABLE XI(p. 27)table TABLE XI
TABLE XII(p. 27)table TABLE XII
TABLE XIII(p. 27)table TABLE XIII
TABLE XIV(p. 28)table TABLE XIV
TABLE XV.(p. 28)table TABLE XV.
TABLE XVI(p. 29)table TABLE XVI

Similar Records

Coupled ππ, KK¯ scattering in P-wave and the ρ resonance from lattice QCD
Journal Article · Mon Nov 02 00:00:00 EST 2015 · Physical Review. D, Particles, Fields, Gravitation and Cosmology · OSTI ID:1562569
+2 more
Isoscalar π π ,   K K ¯ ,   η η scattering and the σ ,   f 0 ,   f 2 mesons from QCD
Journal Article · Fri Mar 23 00:00:00 EDT 2018 · Physical Review D · OSTI ID:1562569
+1 more
ππ→πγ* amplitude and the resonant ρ→πγ* transition from lattice QCD
Journal Article · Wed Jun 01 00:00:00 EDT 2016 · Physical Review D · OSTI ID:1562569
+3 more

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS