Scaling of Hadronic Form Factors in Point Form Kinematics

Abstract

The general features of baryon form factors calculated with point form kinematics are derived. With point form kinematics and spectator currents hadronic form factors are functions of $\eta :=\frac{1}{4}(v_{out}-v_{in}{)}^2$ and, over a range of $\eta$ values are insensitive to unitary scale transformations of the model wave functions when the extent of the wave function is small compared to the scale defined by the constituent mass, $<r^2>\ll 1/m^2$. The form factors are sensitive to the shape of such compact wave functions. Simple 3-quark proton wave functions are employed to illustrate these features. Rational and algebraic model wave functions lead to a reasonable representation of the empirical form factors, while Gaussian wave functions fail. For large values of $\eta$ point form kinematics with spectator currents leads to power law behavior of the wave functions.

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