Abstract
Results are presented from an ongoing study of the ρ resonance. The focus is on CLS 2-flavour ensembles generated using O(a) improved Wilson fermions with pion masses ranging from 265 to 437 MeV. The energy levels are extracted by solving the GEVP of correlator matrices, created with the distillation approach involving ρ and ππ interpolators. The study is done in the centre-of-mass frame and several moving frames. One aim of this work is to extract the timelike pion form factor after applying the Lüscher formalism. We therefore plan to integrate this study with the existing Mainz programme for the calculation of the hadronic vacuum polarization contribution to the muon g – 2.
Highlights
The ρ resonance, whose principal decay is ρ → ππ, is the simplest QCD resonance to study on the lattice, yet very interesting for a number of reasons: Studying resonances is quite challenging and the ρ is the benchmark for Lüscher-style analyses [1,2,3]
The noise-to-signal ratio, which is proportional to e−(mρ−mπ)∆t, is more favourable compared to other hadronic states. Another reason to study the ρ resonance is that it gives access to an interesting physical quantit√y: Meyer [5] has shown that one can extract the pion form factor Fπ in the timelike region for 2mπ ≤ s ≤ 4mπ, by computing scattering phase shifts and matrix elements in the vector channel. This quantity is of particular interest because it is crucial to reduce the uncertainty in theoretical calculations of hadronic vacuum polarization part ahμvp in the anomalous magnetic moment of the muon (g − 2)μ [6]
The fit we perform to the phase shift points precisely takes into account their error, which is confined to the Lüscher curves
Summary
The ρ resonance, whose principal decay is ρ → ππ, is the simplest QCD resonance to study on the lattice, yet very interesting for a number of reasons: Studying resonances is quite challenging and the ρ is the benchmark for Lüscher-style analyses [1,2,3]. The noise-to-signal ratio, which is proportional to e−(mρ−mπ)∆t (where mπ denotes the mass of a pion at rest), is more favourable compared to other hadronic states Another reason to study the ρ resonance is that it gives access to an interesting physical quantit√y: Meyer [5] has shown that one can extract the pion form factor Fπ in the timelike region for 2mπ ≤ s ≤ 4mπ, by computing scattering phase shifts and matrix elements in the vector channel. This quantity is of particular interest because it is crucial to reduce the uncertainty in theoretical calculations of hadronic vacuum polarization part ahμvp in the anomalous magnetic moment of the muon (g − 2)μ [6]. The approach we use in this work and which is able to handle those is (stochastic) distillation using Laplacian-Heavyside (LapH) smearing [7, 8]
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