Resonance Parameters from Lattice QCD
Open AccessHadron-hadron scattering has long served as a tool to investigate the structure andinteractions of hadrons and ultimately to understand the nature of the strong force.A large experimental program is dedicated to mapping hadronic resonances. On thetheory side, quantum chromodynamics (QCD) which describes the strong interactionsof quarks and gluons, is believed to accurately describe all relevant dynamics. LatticeQCD, a non-perturbative formulation, can be used to investigate hadronic physicsin terms of quarks and gluons, but only recently it has become possible to use it toextract scattering parameters.In this work, we use lattice QCD to compute the resonance parameters of and mesons. We perform a high-precision calculation of the phase shifts for -scattering in the I = 1, J = 1 and I = 0, J = 0 channels in the elastic region usingelongated lattices with two dierent pion mass corresponding to m = 226MeV andm = 315MeV. To nely tune the momentum of the two pions state to map out theresonances accurately, we use both the elongated-box method which adjusts the lengthof the elongated direction and the boosted-frame method. To determine the resonanceparameters, we compute the scattering phase shifts from the two-pion spectrum usingLuscher's formula.In this work, we employed nHYP-smeared clover fermions with mass-degeneratequark avors (Nf = 2). We parameterize the resonance phase shifts using a Breit-Wigner form and a model from unitarized chiral perturbation theory (UchiPT) at twodierent quark masses and perform an extrapolation to the physical point. We nd thatthe extrapolated value, m = 720(1)(15)MeV, is signicantly lower that the physicalresult and we nd evidence that this this shift could be due to the absence of thestrange quark in our calculation. The resonance is parameterized using UchiPT and avconformal mapping parametrization. The pole for -resonance in the parametrizationprovided by UchiPT extrapolated to the physical point is m = (440+10-16-i240+20-20)MeV.This agrees well with estimates in the Particle Data Book based on the analysisof the experimental data. Our results are also compatible with other lattice QCDextractions.
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