Abstract
Isospin-1/2 Dπ scattering amplitudes are computed using lattice QCD, working in a single volume of approximately (3.6 fm)3 and with a light quark mass corresponding to mπ ≈ 239 MeV. The spectrum of the elastic Dπ energy region is computed yielding 20 energy levels. Using the Lüscher finite-volume quantisation condition, these energies are translated into constraints on the infinite-volume scattering amplitudes and hence enable us to map out the energy dependence of elastic Dπ scattering. By analytically continuing a range of scattering amplitudes, a \( {D}_0^{\ast } \) resonance pole is consistently found strongly coupled to the S-wave Dπ channel, with a mass m ≈ 2200 MeV and a width Γ ≈ 400 MeV. Combined with earlier work investigating the \( {D}_{s0}^{\ast } \), and \( {D}_0^{\ast } \) with heavier light quarks, similar couplings between each of these scalar states and their relevant meson-meson scattering channels are determined. The mass of the \( {D}_0^{\ast } \) is consistently found well below that of the \( {D}_{s0}^{\ast } \), in contrast to the currently reported experimental result.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Belle collaboration, Study of B → D**0π−(D**0 → D(*)+π−) decays, Phys. Rev. D 69 (2004) 112002 [hep-ex/0307021] [INSPIRE].
FOCUS collaboration, Measurement of masses and widths of excited charm mesons \( {D}_2^{\ast } \) and evidence for broad states, Phys. Lett. B 586 (2004) 11 [hep-ex/0312060] [INSPIRE].
BaBar collaboration, Dalitz Plot Analysis of B → D+π−π−, Phys. Rev. D 79 (2009) 112004 [arXiv:0901.1291] [INSPIRE].
LHCb collaboration, Amplitude analysis of B0 → \( {\overline{D}}^0{K}^{+}{\pi}^{-} \) decays, Phys. Rev. D 92 (2015) 012012 [arXiv:1505.01505] [INSPIRE].
LHCb collaboration, Dalitz plot analysis of B0 → \( {\overline{D}}^0{\pi}^{+}{\pi}^{-} \) decays, Phys. Rev. D 92 (2015) 032002 [arXiv:1505.01710] [INSPIRE].
S. Godfrey and N. Isgur, Mesons in a Relativized Quark Model with Chromodynamics, Phys. Rev. D 32 (1985) 189 [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, PTEP 2020 (2020) 083C01 [INSPIRE].
E. Eichten and C. Hughes, Exploring S-Wave Threshold Effects in QCD: A Heavy-Light Approach, Phys. Lett. B 802 (2020) 135250 [arXiv:1911.02024] [INSPIRE].
LHCb collaboration, A model-independent study of resonant structure in B+ → D+D−K+ decays, Phys. Rev. Lett. 125 (2020) 242001 [arXiv:2009.00025] [INSPIRE].
LHCb collaboration, Amplitude analysis of the B+ → D+D−K+ decay, Phys. Rev. D 102 (2020) 112003 [arXiv:2009.00026] [INSPIRE].
LHCb collaboration, Observation of structure in the J/ψ-pair mass spectrum, Sci. Bull. 65 (2020) 1983 [arXiv:2006.16957] [INSPIRE].
X. Feng, K. Jansen and D.B. Renner, Resonance Parameters of the rho-Meson from Lattice QCD, Phys. Rev. D 83 (2011) 094505 [arXiv:1011.5288] [INSPIRE].
Hadron Spectrum collaboration, Energy dependence of the ρ resonance in ππ elastic scattering from lattice QCD, Phys. Rev. D 87 (2013) 034505 [Erratum ibid. 90 (2014) 099902] [arXiv:1212.0830] [INSPIRE].
D.J. Wilson, R.A. Briceno, J.J. Dudek, R.G. Edwards and C.E. Thomas, 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].
J. Bulava, B. Fahy, B. Hörz, K.J. Juge, C. Morningstar and C.H. Wong, I = 1 and I = 2 π − π scattering phase shifts from Nf = 2 + 1 lattice QCD, Nucl. Phys. B 910 (2016) 842 [arXiv:1604.05593] [INSPIRE].
C. Alexandrou et al., P-wave ππ scattering and the ρ resonance from lattice QCD, Phys. Rev. D 96 (2017) 034525 [arXiv:1704.05439] [INSPIRE].
C. Andersen, J. Bulava, B. Hörz and C. Morningstar, The I = 1 pion-pion scattering amplitude and timelike pion form factor from Nf = 2 + 1 lattice QCD, Nucl. Phys. B 939 (2019) 145 [arXiv:1808.05007] [INSPIRE].
Extended Twisted Mass collaboration, Hadron-Hadron Interactions from Nf = 2 + 1 + 1 Lattice QCD: The ρ-resonance, Eur. Phys. J. A 56 (2020) 61 [arXiv:1907.01237] [INSPIRE].
F. Erben, J.R. Green, D. Mohler and H. Wittig, Rho resonance, timelike pion form factor, and implications for lattice studies of the hadronic vacuum polarization, Phys. Rev. D 101 (2020) 054504 [arXiv:1910.01083] [INSPIRE].
R.A. Briceno, 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].
R.A. Briceno, J.J. Dudek, R.G. Edwards and D.J. Wilson, Isoscalar ππ, \( K\overline{K} \), ηη scattering and the σ, f0, f2 mesons from QCD, Phys. Rev. D 97 (2018) 054513 [arXiv:1708.06667] [INSPIRE].
Hadron Spectrum collaboration, An a0 resonance in strongly coupled πη, \( K\overline{K} \) scattering from lattice QCD, Phys. Rev. D 93 (2016) 094506 [arXiv:1602.05122] [INSPIRE].
A.J. Woss, C.E. Thomas, J.J. Dudek, R.G. Edwards and D.J. Wilson, b1 resonance in coupled πω, πϕ scattering from lattice QCD, Phys. Rev. D 100 (2019) 054506 [arXiv:1904.04136] [INSPIRE].
Hadron Spectrum collaboration, Decays of an exotic 1−+ hybrid meson resonance in QCD, Phys. Rev. D 103 (2021) 054502 [arXiv:2009.10034] [INSPIRE].
Hadron Spectrum collaboration, Excited J−− meson resonances at the SU(3) flavor point from lattice QCD, Phys. Rev. D 103 (2021) 074502 [arXiv:2012.00518] [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].
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, R.A. Briceno, J.J. Dudek, R.G. Edwards and C.E. Thomas, The quark-mass dependence of elastic πK scattering from QCD, Phys. Rev. Lett. 123 (2019) 042002 [arXiv:1904.03188] [INSPIRE].
Hadron Spectrum collaboration, DKI = 0, \( D\overline{K}I \) = 0, 1 scattering and the D∗ (2317) from lattice QCD, JHEP 02 (2021) 100 [arXiv:2008.06432] [INSPIRE].
L. Liu, K. Orginos, F.-K. Guo, C. Hanhart and U.-G. Meissner, Interactions of charmed mesons with light pseudoscalar mesons from lattice QCD and implications on the nature of the \( {D}_{s0}^{\ast } \)(2317), Phys. Rev. D 87 (2013) 014508 [arXiv:1208.4535] [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].
G. Moir, M. Peardon, S.M. Ryan, C.E. Thomas and L. Liu, Excited spectroscopy of charmed mesons from lattice QCD, JHEP 05 (2013) 021 [arXiv:1301.7670] [INSPIRE].
P. Pérez-Rubio, S. Collins and G.S. Bali, Charmed baryon spectroscopy and light flavor symmetry from lattice QCD, Phys. Rev. D 92 (2015) 034504 [arXiv:1503.08440] [INSPIRE].
M. Kalinowski and M. Wagner, Masses of D mesons, Ds mesons and charmonium states from twisted mass lattice QCD, Phys. Rev. D 92 (2015) 094508 [arXiv:1509.02396] [INSPIRE].
K. Cichy, M. Kalinowski and M. Wagner, Continuum limit of the D meson, Ds meson and charmonium spectrum from Nf = 2 + 1 + 1 twisted mass lattice QCD, Phys. Rev. D 94 (2016) 094503 [arXiv:1603.06467] [INSPIRE].
Hadron Spectrum collaboration, Excited and exotic charmonium, Ds and D meson spectra for two light quark masses from lattice QCD, JHEP 12 (2016) 089 [arXiv:1610.01073] [INSPIRE].
M. Lüscher, Volume Dependence of the Energy Spectrum in Massive Quantum Field Theories. 2. Scattering States, Commun. Math. Phys. 105 (1986) 153 [INSPIRE].
R.A. Briceno, J.J. Dudek and R.D. Young, Scattering processes and resonances from lattice QCD, Rev. Mod. Phys. 90 (2018) 025001 [arXiv:1706.06223] [INSPIRE].
Hadron Spectrum collaboration, Excited and exotic charmonium spectroscopy from lattice QCD, JHEP 07 (2012) 126 [arXiv:1204.5425] [INSPIRE].
C. Morningstar and M.J. Peardon, Analytic smearing of SU(3) link variables in lattice QCD, Phys. Rev. D 69 (2004) 054501 [hep-lat/0311018] [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].
J.J. Dudek, R.G. Edwards, M.J. Peardon, D.G. Richards and C.E. Thomas, Highly excited and exotic meson spectrum from dynamical lattice QCD, Phys. Rev. Lett. 103 (2009) 262001 [arXiv:0909.0200] [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].
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. 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.C. Johnson, Angular momentum on a lattice, Phys. Lett. B 114 (1982) 147 [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. 74 (2006) 079905] [hep-lat/0507018] [INSPIRE].
A. Woss, C.E. Thomas, J.J. Dudek, R.G. Edwards and D.J. Wilson, Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD, JHEP 07 (2018) 043 [arXiv:1802.05580] [INSPIRE].
Hadron Spectrum collaboration, A Novel quark-field creation operator construction for hadronic physics in lattice QCD, Phys. Rev. D 80 (2009) 054506 [arXiv:0905.2160] [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].
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].
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].
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].
Z. Fu, Rummukainen-Gottlieb’s formula on two-particle system with different mass, Phys. Rev. D 85 (2012) 014506 [arXiv:1110.0319] [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].
M.T. Hansen and S.R. Sharpe, Multiple-channel generalization of Lellouch-Lüscher formula, Phys. Rev. D 86 (2012) 016007 [arXiv:1204.0826] [INSPIRE].
R.A. Briceno 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].
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].
R.A. Briceno, Two-particle multichannel systems in a finite volume with arbitrary spin, Phys. Rev. D 89 (2014) 074507 [arXiv:1401.3312] [INSPIRE].
Hadron Spectrum collaboration, Efficient solution of the multichannel Lüscher determinant condition through eigenvalue decomposition, Phys. Rev. D 101 (2020) 114505 [arXiv:2001.08474] [INSPIRE].
M.T. Hansen and S.R. Sharpe, Lattice QCD and Three-particle Decays of Resonances, Ann. Rev. Nucl. Part. Sci. 69 (2019) 65 [arXiv:1901.00483] [INSPIRE].
B. Hörz and A. Hanlon, Two- and three-pion finite-volume spectra at maximal isospin from lattice QCD, Phys. Rev. Lett. 123 (2019) 142002 [arXiv:1905.04277] [INSPIRE].
T.D. Blanton, F. Romero-López and S.R. Sharpe, I = 3 Three-Pion Scattering Amplitude from Lattice QCD, Phys. Rev. Lett. 124 (2020) 032001 [arXiv:1909.02973] [INSPIRE].
M. Mai, M. Döring, C. Culver and A. Alexandru, Three-body unitarity versus finite-volume π+π+π+ spectrum from lattice QCD, Phys. Rev. D 101 (2020) 054510 [arXiv:1909.05749] [INSPIRE].
C. Culver, M. Mai, R. Brett, A. Alexandru and M. Döring, Three pion spectrum in the I = 3 channel from lattice QCD, Phys. Rev. D 101 (2020) 114507 [arXiv:1911.09047] [INSPIRE].
M. Fischer, B. Kostrzewa, L. Liu, F. Romero-López, M. Ueding and C. Urbach, Scattering of two and three physical pions at maximal isospin from lattice QCD, Eur. Phys. J. C 81 (2021) 436 [arXiv:2008.03035] [INSPIRE].
Hadron Spectrum collaboration, Energy-Dependent π+π+π+ Scattering Amplitude from QCD, Phys. Rev. Lett. 126 (2021) 012001 [arXiv:2009.04931] [INSPIRE].
T.D. Blanton and S.R. Sharpe, Relativistic three-particle quantization condition for nondegenerate scalars, Phys. Rev. D 103 (2021) 054503 [arXiv:2011.05520] [INSPIRE].
G.F. Chew and S. Mandelstam, Theory of low-energy pion pion interactions, Phys. Rev. 119 (1960) 467 [INSPIRE].
J. Hofmann and M.F.M. Lutz, Open charm meson resonances with negative strangeness, Nucl. Phys. A 733 (2004) 142 [hep-ph/0308263] [INSPIRE].
F.-K. Guo, C. Hanhart, S. Krewald and U.-G. Meissner, Subleading contributions to the width of the \( {D}_{s0}^{\ast } \)(2317), Phys. Lett. B 666 (2008) 251 [arXiv:0806.3374] [INSPIRE].
F.-K. Guo, C. Hanhart and U.-G. Meissner, Interactions between heavy mesons and Goldstone bosons from chiral dynamics, Eur. Phys. J. A 40 (2009) 171 [arXiv:0901.1597] [INSPIRE].
M. Albaladejo, P. Fernandez-Soler, F.-K. Guo and J. Nieves, Two-pole structure of the \( {D}_0^{\ast } \)(2400), Phys. Lett. B 767 (2017) 465 [arXiv:1610.06727] [INSPIRE].
X.-Y. Guo, Y. Heo and M.F.M. Lutz, On chiral extrapolations of charmed meson masses and coupled-channel reaction dynamics, Phys. Rev. D 98 (2018) 014510 [arXiv:1801.10122] [INSPIRE].
Z.-H. Guo, L. Liu, U.-G. Meißner, J.A. Oller and A. Rusetsky, Towards a precise determination of the scattering amplitudes of the charmed and light-flavor pseudoscalar mesons, Eur. Phys. J. C 79 (2019) 13 [arXiv:1811.05585] [INSPIRE].
J.R. Peláez and A. Rodas, Dispersive πK → πK and ππ → \( K\overline{K} \) amplitudes from scattering data, threshold parameters and the lightest strange resonance κ or \( {K}_0^{\ast } \)(700), arXiv:2010.11222 [INSPIRE].
I. Danilkin, O. Deineka and M. Vanderhaeghen, Data-driven dispersive analysis of the ππ and πK scattering, Phys. Rev. D 103 (2021) 114023 [arXiv:2012.11636] [INSPIRE].
E. van Beveren and G. Rupp, Observed Ds(2317) and tentative D(2100–2300) as the charmed cousins of the light scalar nonet, Phys. Rev. Lett. 91 (2003) 012003 [hep-ph/0305035] [INSPIRE].
E. van Beveren and G. Rupp, New BABAR state DsJ(2860) as the first radial excitation of the \( {D}_{s0}^{\ast } \)(2317), Phys. Rev. Lett. 97 (2006) 202001 [hep-ph/0606110] [INSPIRE].
M.-L. Du, F.-K. Guo, C. Hanhart, B. Kubis and U.-G. Meißner, Where is the lightest charmed scalar meson?, Phys. Rev. Lett. 126 (2021) 192001 [arXiv:2012.04599] [INSPIRE].
LHCb collaboration, Amplitude analysis of B− → D+π−π− decays, Phys. Rev. D 94 (2016) 072001 [arXiv:1608.01289] [INSPIRE].
S. Weinberg, Evidence That the Deuteron Is Not an Elementary Particle, Phys. Rev. 137 (1965) B672 [INSPIRE].
D. Morgan, Pole counting and resonance classification, Nucl. Phys. A 543 (1992) 632 [INSPIRE].
D. Morgan and M.R. Pennington, New data on the \( K\overline{K} \) the f0(S*) threshold region and the nature of, Phys. Rev. D 48 (1993) 1185 [INSPIRE].
V. Baru, J. Haidenbauer, C. Hanhart, Y. Kalashnikova and A.E. Kudryavtsev, Evidence that the a0(980) and f0(980) are not elementary particles, Phys. Lett. B 586 (2004) 53 [hep-ph/0308129] [INSPIRE].
F. Aceti and E. Oset, Wave functions of composite hadron states and relationship to couplings of scattering amplitudes for general partial waves, Phys. Rev. D 86 (2012) 014012 [arXiv:1202.4607] [INSPIRE].
Z.-H. Guo and J.A. Oller, Probabilistic interpretation of compositeness relation for resonances, Phys. Rev. D 93 (2016) 096001 [arXiv:1508.06400] [INSPIRE].
T. Hyodo, Structure of Near-Threshold s-Wave Resonances, Phys. Rev. Lett. 111 (2013) 132002 [arXiv:1305.1999] [INSPIRE].
I. Matuschek, V. Baru, F.-K. Guo and C. Hanhart, On the nature of near-threshold bound and virtual states, Eur. Phys. J. A 57 (2021) 101 [arXiv:2007.05329] [INSPIRE].
SciDAC, LHPC and UKQCD collaborations, The Chroma software system for lattice QCD, Nucl. Phys. B Proc. Suppl. 140 (2005) 832 [hep-lat/0409003] [INSPIRE].
M.A. Clark, R. Babich, K. Barros, R.C. Brower and C. Rebbi, 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 SC 10 (Supercomputing 2010), (2010) [arXiv:1011.0024] [INSPIRE].
B. Joó et al., Lattice QCD on Intel® Xeon PhiTM Coprocessors, Lect. Notes Comput. Sci. 7905 (2013) 40.
J.C. Osborn et al., Multigrid solver for clover fermions, PoS LATTICE2010 (2010) 037 [arXiv:1011.2775] [INSPIRE].
R. Babich et al., Adaptive multigrid algorithm for the lattice Wilson-Dirac operator, Phys. Rev. Lett. 105 (2010) 201602 [arXiv:1005.3043] [INSPIRE].
J.A. Oller and U.G. Meissner, Chiral dynamics in the presence of bound states: Kaon nucleon interactions revisited, Phys. Lett. B 500 (2001) 263 [hep-ph/0011146] [INSPIRE].
Author information
Authors and Affiliations
Consortia
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2102.04973
Deceased. (David Tims)
Rights and permissions
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.
About this article
Cite this article
Gayer, L., Lang, N., Ryan, S.M. et al. Isospin-1/2 Dπ scattering and the lightest \( {D}_0^{\ast } \) resonance from lattice QCD. J. High Energ. Phys. 2021, 123 (2021). https://doi.org/10.1007/JHEP07(2021)123
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2021)123