The ρ-resonance from N = 2 lattice QCD including the physical pion mass

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.

Section: Jhep10(2021)051mentioning

confidence: 97%

Section: P-wave ππ Scattering From Lattice Qcd Data For Fv Energiesmentioning

confidence: 99%

Section: Jhep10(2021)051mentioning

confidence: 99%

“…energy levels below the 4M π threshold from the lattice QCD simulations of ref. [68] shown in figure 13.…”

Section: P-wave ππ Scattering From Lattice Qcd Data For Fv Energiesmentioning

confidence: 99%

See 2 more Smart Citations

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

Meng

Epelbaum

2021

“…The calculation of hadronic scattering processes constitutes a notoriously challenging task in lattice quantum chromodynamics (QCD), given the complications that ensue once multihadron dynamics are properly taken into account [1]. In the past years, significant improvement has been achieved mainly for ππ → ππ [2][3][4][5][6][7][8][9][10][11][12][13], the simplest hadronic scattering process, with computations even at physical pion mass available [14,15]. Meanwhile, the computation and analysis of more complicated processes remains challenging.…”

Section: Introductionmentioning

confidence: 99%

The γπ → ππ anomaly from lattice QCD and dispersion relations

Niehus¹,

Hoferichter

Kubis³

2021

We propose a formalism to extract the γπ → ππ chiral anomaly F3π from calculations in lattice QCD performed at larger-than-physical pion masses. To this end, we start from a dispersive representation of the γ(*)π → ππ amplitude, whose main quark-mass dependence arises from the ππ scattering phase shift and can be derived from chiral perturbation theory via the inverse-amplitude method. With parameters constrained by lattice calculations of the P-wave phase shift, we use this combination of dispersion relations and effective field theory to extrapolate two recent γ(*)π → ππ calculations in lattice QCD to the physical point. Our formalism allows us to extract the radiative coupling of the ρ(770) meson and, for the first time, the chiral anomaly F3π = 38(16)(11) GeV−3. The result is consistent with the chiral prediction albeit within large uncertainties, which will improve in accordance with progress in future lattice-QCD computations.

Particle-dimer approach for the Roper resonance in a finite volume

Severt¹,

Mai

Meißner

2023

Self Cite

We propose a new finite-volume approach which implements two- and three-body dynamics in a transparent way based on an Effective Field Theory Lagrangian. The formalism utilizes a particle-dimer picture and formulates the quantization conditions based on the self-energy of the decaying particle. The formalism is studied for the case of the Roper resonance, using input from lattice QCD and phenomenology. Finally, finite-volume energy eigenvalues are predicted and compared to existing results of lattice QCD calculations. This crucially provides initial guidance on the necessary level of precision for the finite-volume spectrum.