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

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:
 [1] ;  [2] ;  [1] ;  [3] ;  [1] ;  [4]
  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:
Grant/Contract Number:
FG02-95ER40907; SC0013065; AC05-00OR22725
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
Research Org:
The George Washington Univ., Washington, D.C. (United States); Univ. of Kentucky, Lexington, KY (United States); UT-Battelle, LLC, Oak Ridge, TN (United States)
Sponsoring Org:
USDOE Office of Science (SC)
Contributing Orgs:
χQCD Collaboration
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ρ resonance; leptonic decay constant; renormalization
OSTI Identifier:
1506458

Sun, Wei, Alexandru, Andrei, Chen, Ying, Draper, Terrence, Liu, Zhaofeng, and Yang, Yi -Bo. Anatomy of the ρ resonance from lattice QCD at the physical point. United States: N. p., Web. doi:10.1088/1674-1137/42/6/063102.
Sun, Wei, Alexandru, Andrei, Chen, Ying, Draper, Terrence, Liu, Zhaofeng, & Yang, Yi -Bo. Anatomy of the ρ resonance from lattice QCD at the physical point. United States. doi:10.1088/1674-1137/42/6/063102.
Sun, Wei, Alexandru, Andrei, Chen, Ying, Draper, Terrence, Liu, Zhaofeng, and Yang, Yi -Bo. 2018. "Anatomy of the ρ resonance from lattice QCD at the physical point". United States. doi:10.1088/1674-1137/42/6/063102. https://www.osti.gov/servlets/purl/1506458.
@article{osti_1506458,
title = {Anatomy of the ρ resonance from lattice QCD at the physical point},
author = {Sun, Wei and Alexandru, Andrei and Chen, Ying and Draper, Terrence and Liu, Zhaofeng and Yang, Yi -Bo},
abstractNote = {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.},
doi = {10.1088/1674-1137/42/6/063102},
journal = {Chinese Physics. C, High Energy Physics and Nuclear Physics},
number = 6,
volume = 42,
place = {United States},
year = {2018},
month = {4}
}