DK I = 0, $$ D\overline{K} $$ I = 0, 1 scattering and the $$ {D}_{s0}^{\ast } $$(2317) from lattice QCD

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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 $$ {D}_0^{\ast } $$ D 0 ∗ 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 $$ {D}_{s0}^{\ast } $$ D s 0 ∗ , and $$ {D}_0^{\ast } $$ D 0 ∗ 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 $$ {D}_0^{\ast } $$ D 0 ∗ is consistently found well below that of the $$ {D}_{s0}^{\ast } $$ D s 0 ∗ , in contrast to the currently reported experimental result.

Section: Introductionmentioning

confidence: 78%

“…The reference amplitude from that work, 7 updated with an improved estimate of the D-meson mass from ref. [29], results in…”

Section: Light Quark Mass Dependencementioning

confidence: 92%

Section: Light Quark Mass Dependencementioning

confidence: 97%

“…[26] in S-wave Dπ scattering, and ref. [29] in S-wave DK scattering. The D * 0 resonance pole found in this study lies on the unphysical sheet with a large width.…”

Section: Light Quark Mass Dependencementioning

confidence: 99%

Section: Light Quark Mass Dependencementioning

confidence: 99%

See 3 more Smart Citations

Isospin-1/2 Dπ scattering and the lightest $$ {D}_0^{\ast } $$ resonance from lattice QCD

Gayer

Lang

Ryan

et al. 2021

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DK/Dπ scattering and an exotic virtual bound state at the SU(3) flavour symmetric point from lattice QCD

Yeo,

Thomas,

Wilson

2024

Elastic S-wave scattering of a charm meson with a light pseudoscalar meson in JP = 0+ is investigated in the flavour $$ \overline{\textbf{3}} $$ 3 ¯ , 6 and $$ \overline{\textbf{15}} $$ 15 ¯ sectors at the SU(3)f flavour point using lattice QCD, working on three volumes with mπ ≈ 700 MeV. Large bases of interpolating operators are employed to extract finite-volume spectra, which are subsequently used with the Lüscher method to provide constraints on infinite-volume scattering amplitudes. Examining the singularities of the amplitudes, the S-wave amplitude in the flavour $$ \overline{\textbf{3}} $$ 3 ¯ sector is found to contain a deeply bound state, strongly coupled to elastic threshold, corresponding to the $$ {J}^P={0}^{+}\ {D}_{s0}^{\ast }(2317) $$ J P = 0 + D s 0 ∗ 2317 . In the exotic flavour 6 sector a virtual bound state is found at $$ \sqrt{s_{\textrm{pole}}} $$ s pole = 2510 – 2610 MeV, roughly 40 – 140 MeV below threshold, whereas the $$ \overline{\textbf{15}} $$ 15 ¯ channel shows weak repulsion.

Two-particle scattering from finite-volume quantization conditions using the plane wave basis

Meng

Epelbaum

2021

We propose an alternative approach to Lüscher’s formula for extracting two-body scattering phase shifts from finite volume spectra with no reliance on the partial wave expansion. We use an effective-field-theory-based Hamiltonian method in the plane wave basis and decompose the corresponding matrix elements of operators into irreducible representations of the relevant point groups. The proposed approach allows one to benefit from the knowledge of the long-range interaction and avoids complications from partial wave mixing in a finite volume. We consider spin-singlet channels in the two-nucleon system and pion-pion scattering in the ρ-meson channel in the rest and moving frames to illustrate the method for non-relativistic and relativistic systems, respectively. For the two-nucleon system, the long-range interaction due to the one-pion exchange is found to make the single-channel Lüscher formula unreliable at the physical pion mass. For S-wave dominated states, the single-channel Lüscher method suffers from significant finite-volume artifacts for a L = 3 fm box, but it works well for boxes with L > 5 fm. However, for P-wave dominated states, significant partial wave mixing effects prevent the application of the single-channel Lüscher formula regardless of the box size (except for the near-threshold region). Using a toy model to generate synthetic data for finite-volume energies, we show that our effective-field-theory-based approach in the plane wave basis is capable of a reliable extraction of the phase shifts. For pion-pion scattering, we employ a phenomenological model to fit lattice QCD results at the physical pion mass. The extracted P-wave phase shifts are found to be in a good agreement with the experimental results.