Method to study complex systems of mesons in lattice QCD
Correlation functions involving many hadrons allow finite density systems to be explored with Lattice QCD. Recently, systems with up to 12 $$\pi^+$$'s or $K^+$'s have been studied to determine the the $3$$$\pi^+$$ and $3$$K^+$ interactions and the corresponding chemical potential has been determined as a function of density in each case. We derive recursion relations between correlation functions that allow us to extend this work to systems of arbitrary numbers of mesons and to systems containing arbitrary different types of mesons such as $$\pi^+$$'s, $K^+$'s, $D^0$'s and $B^+$'s. These relations allow for the study of finitedensity systems in arbitrary volumes, and the study of highdensity systems. Systems comprised of up to N=12 m mesons can be explored with Lattice QCD calculations utilizing $m$ different sources for the quark propagators. As the recursion relations require only a small, Nindependent, number of operations to derive the N+1 meson contractions from the N meson contractions, they are compuationally feasible.
 Authors:

^{[1]};
^{[2]}
 College of William and Mary, Williamsburg, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
 Univ. of Washington, Seattle, WA (United States)
 Publication Date:
 Report Number(s):
 JLABTHY101121; DOE/OR/231771068; arXiv:1001.2768
Journal ID: ISSN 15507998; PRVDAQ
 Grant/Contract Number:
 AC0506OR23177
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review. D, Particles, Fields, Gravitation and Cosmology
 Additional Journal Information:
 Journal Volume: 82; Journal Issue: 1; Journal ID: ISSN 15507998
 Publisher:
 American Physical Society (APS)
 Research Org:
 Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Nuclear Physics (NP) (SC26)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
 OSTI Identifier:
 1256901
Detmold, William, and Savage, Martin J. Method to study complex systems of mesons in lattice QCD. United States: N. p.,
Web. doi:10.1103/PhysRevD.82.014511.
Detmold, William, & Savage, Martin J. Method to study complex systems of mesons in lattice QCD. United States. doi:10.1103/PhysRevD.82.014511.
Detmold, William, and Savage, Martin J. 2010.
"Method to study complex systems of mesons in lattice QCD". United States.
doi:10.1103/PhysRevD.82.014511. https://www.osti.gov/servlets/purl/1256901.
@article{osti_1256901,
title = {Method to study complex systems of mesons in lattice QCD},
author = {Detmold, William and Savage, Martin J.},
abstractNote = {Correlation functions involving many hadrons allow finite density systems to be explored with Lattice QCD. Recently, systems with up to 12 $\pi^+$'s or $K^+$'s have been studied to determine the the $3$$\pi^+$ and $3$$K^+$ interactions and the corresponding chemical potential has been determined as a function of density in each case. We derive recursion relations between correlation functions that allow us to extend this work to systems of arbitrary numbers of mesons and to systems containing arbitrary different types of mesons such as $\pi^+$'s, $K^+$'s, $D^0$'s and $B^+$'s. These relations allow for the study of finitedensity systems in arbitrary volumes, and the study of highdensity systems. Systems comprised of up to N=12 m mesons can be explored with Lattice QCD calculations utilizing $m$ different sources for the quark propagators. As the recursion relations require only a small, Nindependent, number of operations to derive the N+1 meson contractions from the N meson contractions, they are compuationally feasible.},
doi = {10.1103/PhysRevD.82.014511},
journal = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},
number = 1,
volume = 82,
place = {United States},
year = {2010},
month = {7}
}