Nambu--Jona-Lasinio model compared with chiral perturbation theory: The pion radius in SU(2) revisited
- Institut fuer Theoretische Physik, Philosophenweg 19, D-69120 Heidelberg (Germany)
A calculation of the pion radius to {ital O}(1/{ital N}{sub {ital c}}) in the Nambu--Jona-Lasinio model indicates that the chiral logarithmic term of chiral perturbation theory (CHPT) is recovered from the higher order corrections in the static limit in the Pauli-Villars regularization scheme, and with {Lambda}{r_arrow}{infinity}. This follows equivalently in the {ital O}(3) scheme under the assumption that {Lambda}{much_gt}{ital m}. The chiral logarithm is the leading contribution in the chiral limit. However, at the physical values of the current quark mass, the constant term due to the intrinsic structure of the pion plays the key role. This intrinsic term is the usual term that arises from the photon coupling to the internal quark and antiquark structure that makes up the pion, and corresponds to the tree level calculation in CHPT. At physical values of the current quark masses, it turns out that this term is the leading one, with the chiral logarithmic term being subleading. From the values obtained for {l_angle}{ital r}{sub {pi}}{sup 2}{r_angle}, we can also set an upper limit for the contribution expected from the {rho} meson. This is determined as {l_angle}{ital r}{sub {pi}}{sup 2}{r_angle}{sub {rho}}{lt}(0.4) fm{sup 2}. A redetermination of {ital {bar l}}{sub 6} including the higher order contribution gives {ital {bar l}}{sub 6}=16.07. The finite temperature dependence of the mean square charge radius is also examined, and its behavior is determined principally by the intrinsic part.
- OSTI ID:
- 118512
- Journal Information:
- Physical Review, C, Vol. 52, Issue 4; Other Information: PBD: Oct 1995
- Country of Publication:
- United States
- Language:
- English
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