TITLE:
New Approach to Pion Distribution Amplitude
AUTHORS:
Teruo Kurai
KEYWORDS:
Distribution Amplitude, ‘t Hooft Model
JOURNAL NAME:
Journal of Modern Physics,
Vol.16 No.6,
June
25,
2025
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.