Anatomy of the ρ resonance from lattice QCD at the physical point**Supported in part by the U.S. DOE Grant No. DE-SC0013065, the National Nature Science Foundation of China (NSFC) (11335001, 11575196, 11575197, 11621131001) (CRC110 by DFG and NSFC), A. A. is supported in part by the National Science Foundation CAREER (PHY-1151648) and by U.S. DOE (DE-FG02-95ER40907), Y. C. thanks the

Wei Sun,Yi-Bo Yang,Ying Chen,Terrence Draper,Andrei Alexandru,Zhaofeng Liu

doi:10.1088/1674-1137/42/6/063102

Abstract

We propose a strategy to access the component of the ρ resonance in lattice QCD. Through a mixed action formalism (overlap valence on domain wall sea), the energy of the component is derived at different valence quark masses, and shows a linear dependence on . The slope is determined to be , from which the valence sigma term is extracted to be MeV using the Feynman-Hellman theorem. At the physical pion mass, the mass of the component is interpolated to be , which is close to the ρ resonance mass. We also obtain the leptonic decay constant of the component to be , which can be compared with the experimental value through the relation , with being the on-shell wavefunction renormalization of ρ owing to the interaction. We emphasize that and of the component, which are obtained for the first time from QCD, can be taken as the input parameters of ρ in effective field theory studies where ρ acts as a fundamental degree of freedom.

Highlights

The vector meson ρ is a well-known hadron resonance which appears in the I =1 and L=1 ππ system with the resonance parameters mρ =775 MeV and Γρ =149 MeV
As far as the ρ meson is concerned, there is a confined channel corresponding to the quark model ρ and its excited states, as well as an open channel of ππ scattering states. The coupling between both channels results in the ρ resonance of an O(1/Nc) width. This argument coincides with the result of a chiral perturbation theory study of ρ [2] which shows that while the ρ mass keeps almost constant, the width decreases with increasing Nc
We argue that the qqwall source operator in a fixed gauge can strongly suppress P -wave scattering states such that the qqcomponent of an ordinary meson, such as ρ, can be accessed in a lattice QCD study

Summary

Introduction

The vector meson ρ is a well-known hadron resonance which appears in the I =1 and L=1 ππ system with the resonance parameters mρ =775 MeV and Γρ =149 MeV. The bare mass parameters are chosen as am(qval) = 0.00170,0.00240,0.00300,0.00455,0.00600 and 0.02030, which give a pion mass ranging from 114 to 371 MeV In this way we can discern the chiral behaviors of the mass and the leptonic decay constant of the ρ meson. This corresponds to using the Coulomb gauge fixed wall-source operator for the charged ρ, OV(w,i)(t)= u(y,t)γid(z,t) In principle, this operator couples to all the eigenstates of the lattice Hamiltonian, which can be taken as the linear superpositions of ππ(I = 1) scattering states and the confined qqstates. In order to reduce the excited-state contamination, we linearly combine the two correlation functions as Cmix(t) = C(0,t)+ωC(4.58a,t) with an optimal mixing parameter ω≈10, by which we can get a very flat effective mass plateau starting from t/a = 3, as shown in the figure (red points). One can deterπρ mine the disconnected part from a direct calculation of the mψψ matrix element in the disconnected three-point correlator

Leptonic decay constant of the ρ meson

Conclusion