New Approach to Pion Distribution Amplitude

Abstract

The usual pion distribution amplitude is typically constructed using functions based on one of the trial functions from the ‘t Hooft singular integral equation, specially of the form x ( 1 − x ) type. However, these of function are not exact solutions of the ‘t Hooft equation, which means a pion distribution amplitude constructed in this manner may not accurately represent a real pion as described by Light Front QCD. In contrast, we have developed a pion distribution amplitude using solutions that correspond to zero-mass state wave functions of a bound system of 1 + 1 dimensional QCD derived from the ‘t Hooft model. Our distribution amplitude shows 1 − x x behavior as x approaches 1. Notably, asymptotic form of our distribution amplitude reveals an intriguing property: peak of our distribution amplitude shifts towards x = 1 as the coupling constant g 2 increases.