The pion and an improved static bag model

Quark-model calculations involve an extended static object localized in space. We introduce new methods, involving momentum-space wave packets, which account for this localization. These methods have little effect on heavy states, whose sizes are large compared to their Compton size 1/m, but are very important for light particles such as the pion. In this treatment the pion's mass is naturally very small, and, in order to connect with a spontaneously broken chiral symmetry, we require that m_π vanish when the light quarks are massless. Expanding about this limit (and also readjusting the fit to other hadrons), we obtain mq=(mᵤ+md)2=33 MeV. We calculate F_π≈145 MeV (using a normalization such that F_π|ₑₓₚ=93 MeV), FKF_π≈1, and various corrections to static properties of baryons. In addition we explore the relationship of our methods with chiral perturbation theory, deriving the formula m_π²=(mᵤ+md)〈π(p)|q̄(0)q(0)|π(p)〉 in the appropriate approximation and commenting on the quark mass obtained from the nucleon's σ term. Finally we discuss the bag model's use of the scalar density q̄q as an order parameter describing the separation of the spontaneously broken vacuum phase from the perturbative vacuum of the bag's interior.