The Large N Limit with Vanishing Leading Order Condensate for Zero Pion Mass
It is conventionally assumed that the negative mass squared term in the linear sigma model version of the pion Lagrangian is M ^{2}~Λ ^{2} _{QCD} in powers of N _{c} [1]. We consider the case where M ^{2}~Λ ^{2} _{QCD}/N _{c} so that to leading order in N _{c} this symmetry breaking term vanishes. We present some arguments why this might be plausible. One might think that such a radical assumption would contradict lattice Monte Carlo data on QCD as function of N _{c}. We show that the linear sigma model gives a fair description of the data of DeGrand and Liu both for N _{c} = 3, and for variable N _{c}. The values of quark masses considered by DeGrand and Liu, and by Bali et. al. turn out to be too large to resolve the case we consider from that of the conventional large N _{c} limit [2, 3]. We argue that for quark masses m _{q}»Λ _{QCD}/N _{c} ^{3/2}, both the baryon mass and nucleon size scale as √N _{c}. For m _{q} >> Λ _{QCD}/N _{c} ^{3/2} the conventional largeN _{c} counting holds. The physical values of quark masses for QCD (N _{c} = 3) correspondmore »
 Authors:

^{[1]};
^{[2]}
 Univ. of Washington, Seattle, WA (United States). Institute for Nuclear Theory,; China Central Normal University, Wuhan (China)
 Brookhaven National Lab. (BNL), Upton, NY (United States). RIKEN Research Center
 Publication Date:
 Report Number(s):
 BNL2031972018JAAM; RBRC1240
Journal ID: ISSN 05874254
 Grant/Contract Number:
 SC0012704; FG0200ER41132
 Type:
 Accepted Manuscript
 Journal Name:
 Acta Physica Polonica. Series B
 Additional Journal Information:
 Journal Volume: 49; Journal ID: ISSN 05874254
 Publisher:
 Jagiellonian University
 Research Org:
 Brookhaven National Laboratory (BNL), Upton, NY (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Nuclear Physics (NP) (SC26); RIKEN
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS
 OSTI Identifier:
 1425165
McLerran, Larry, and Skokov, Vladimir. The Large N Limit with Vanishing Leading Order Condensate for Zero Pion Mass. United States: N. p.,
Web. doi:10.5506/APhysPolB.49.1513.
McLerran, Larry, & Skokov, Vladimir. The Large N Limit with Vanishing Leading Order Condensate for Zero Pion Mass. United States. doi:10.5506/APhysPolB.49.1513.
McLerran, Larry, and Skokov, Vladimir. 2017.
"The Large N Limit with Vanishing Leading Order Condensate for Zero Pion Mass". United States.
doi:10.5506/APhysPolB.49.1513. https://www.osti.gov/servlets/purl/1425165.
@article{osti_1425165,
title = {The Large N Limit with Vanishing Leading Order Condensate for Zero Pion Mass},
author = {McLerran, Larry and Skokov, Vladimir},
abstractNote = {It is conventionally assumed that the negative mass squared term in the linear sigma model version of the pion Lagrangian is M2~Λ2QCD in powers of Nc [1]. We consider the case where M2~Λ2QCD/Nc so that to leading order in Nc this symmetry breaking term vanishes. We present some arguments why this might be plausible. One might think that such a radical assumption would contradict lattice Monte Carlo data on QCD as function of Nc. We show that the linear sigma model gives a fair description of the data of DeGrand and Liu both for Nc = 3, and for variable Nc. The values of quark masses considered by DeGrand and Liu, and by Bali et. al. turn out to be too large to resolve the case we consider from that of the conventional large Nc limit [2, 3]. We argue that for quark masses mq»ΛQCD/Nc3/2, both the baryon mass and nucleon size scale as √Nc. For mq >> ΛQCD/Nc3/2 the conventional largeNc counting holds. The physical values of quark masses for QCD (Nc = 3) correspond to the small quark mass limit. We nd pion nucleon coupling strengths are reduced to order O(1) rather than O(Nc). Under the assumption that in the large Nc limit the sigma meson mass is larger than that of the omega, and that the omeganucleon coupling constant is larger than that of the sigma, we argue that the nucleonnucleon large range potential is weakly attractive and admits an interaction energy of order ΛQCD/Nc5/2~10 MeV. With these assumptions on coupling and masses, there is no strong long range attractive channel for nucleonnucleon interactions, so that nuclear matter at densities much smaller than that where nucleons strongly interact is a weakly interacting con guration of nucleons with strongly interacting localized cores. This situation is unlike the case in the conventional large Nc limit, where nuclear matter is bound with binding energies of order the nucleon mass and forms a Skyrme crystal.},
doi = {10.5506/APhysPolB.49.1513},
journal = {Acta Physica Polonica. Series B},
number = ,
volume = 49,
place = {United States},
year = {2017},
month = {5}
}