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New Approach to Pion Distribution Amplitude

DOI: 10.4236/jmp.2025.166046, PP. 886-910

Keywords: Distribution Amplitude, ‘t Hooft Model

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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( 1x ) 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 1x 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.

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