Title: Anatomy of the ρ resonance from lattice QCD at the physical point

Abstract

We propose a strategy to access the $$q\bar{q}$$ component of the ρ resonance in lattice QCD. Through a mixed action formalism (overlap valence on domain wall sea), the energy of the $$q\bar{q}$$ component is derived at different valence quark masses, and shows a linear dependence on $${m}_{{\rm{\pi }}}^{2}$$. The slope is determined to be $${c}_{1}=0.505(3)\,{{\rm{GeV}}}^{-1}$$, from which the valence $${\rm{\pi }}{\rm{\rho }}$$ sigma term is extracted to be $${\sigma }_{{\rm{\pi }}{\rm{\rho }}}^{(\mathrm{val})}=9.82(6)$$ MeV using the Feynman-Hellman theorem. At the physical pion mass, the mass of the $$q\bar{q}$$ component is interpolated to be $${m}_{{\rm{\rho }}}=775.9\pm 6.0\pm 1.8\,{\rm{MeV}}$$, which is close to the ρ resonance mass. We also obtain the leptonic decay constant of the $$q\bar{q}$$ component to be $${f}_{{{\rm{\rho }}}^{-}}=208.5\pm 5.5\pm 0.9\,{\rm{MeV}}$$, which can be compared with the experimental value $${f}_{{\rm{\rho }}}^{{\rm{\exp }}}\approx 221\,{\rm{MeV}}$$ through the relation $${f}_{{\rm{\rho }}}^{{\rm{\exp }}}=\sqrt{{Z}_{{\rm{\rho }}}}{f}_{{{\rm{\rho }}}^{\pm }}$$, with $${Z}_{{\rm{\rho }}}\approx 1.13$$ being the on-shell wavefunction renormalization of ρ owing to the $${\rm{\rho }}-{\rm{\pi }}$$ interaction. We emphasize that $${m}_{{\rm{\rho }}}$$ and $${f}_{{\rm{\rho }}}$$ of the $$q\bar{q}$$ 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.

Authors:

Sun, Wei ^[1]; Alexandru, Andrei ^[2]; Chen, Ying ^[1]; Draper, Terrence ^[3]; Liu, Zhaofeng ^[1]; Yang, Yi -Bo ^[4]

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+ Show Author Affiliations

1. Chinese Academy of Sciences (CAS), Beijing (China)
2. George Washington Univ., Washington, DC (United States)
3. Univ. of Kentucky, Lexington, KY (United States)
4. Michigan State Univ., East Lansing, MI (United States)

Publication Date:

Fri Apr 27 00:00:00 EDT 2018

Research Org.:

Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); George Washington Univ., Washington, DC (United States); Univ. of Kentucky, Lexington, KY (United States); UT-Battelle LLC/ORNL, Oak Ridge, TN (United States)

Sponsoring Org.:

USDOE Office of Science (SC)

Contributing Org.:

χQCD Collaboration

OSTI Identifier:

1506458

Grant/Contract Number:  

FG02-95ER40907; SC0013065; AC05-00OR22725

Resource Type:

Accepted Manuscript

Journal Name:

Chinese Physics. C, High Energy Physics and Nuclear Physics

Additional Journal Information:

Journal Volume: 42; Journal Issue: 6; Journal ID: ISSN 1674-1137

Publisher:

IOP Publishing

Country of Publication:

United States

Language:

English

Subject:

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ρ resonance; leptonic decay constant; renormalization