%0 Journal Article
%T New Approach to Pion Distribution Amplitude
%A Teruo Kurai
%J Journal of Modern Physics
%P 886-910
%@ 2153-120X
%D 2025
%I Scientific Research Publishing
%R 10.4236/jmp.2025.166046
%X The usual pion distribution amplitude is typically constructed using functions based on one of the trial functions from the &#8216;t Hooft singular integral equation, specially of the form <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>x</mi><mrow><mo>(</mo>
   <mrow>
    <mn>1</mn><mo>&#x2212;</mo><mi>x</mi></mrow>
  <mo>)</mo></mrow></mrow>
</math>

 type. However, these of function are not exact solutions of the &#8216;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 &#8216;t Hooft model. Our distribution amplitude shows <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mfrac>
   <mrow>
    <mn>1</mn><mo>&#x2212;</mo><mi>x</mi></mrow>
   <mi>x</mi>
  </mfrac>
  </mrow>
</math>

 behavior as <i>x</i> approaches 1. Notably, asymptotic form of our distribution amplitude reveals an intriguing property: peak of our distribution amplitude shifts towards <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>x</mi><mo>=</mo><mn>1</mn></mrow>
</math>

 as the coupling constant <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <msup>
   <mi>g</mi>
   <mn>2</mn>
  </msup>
  </mrow>
</math>

 increases.
%K Distribution Amplitude
%K &#8216
%K t Hooft Model
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=143519