Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The Vector and Scalar Form Factors of the Pion to Two Loops

J. Bijnens, G. Colangelo, P. Talavera

Abstract

We calculate the vector and scalar form factors of the pion to two loops in Chiral Perturbation Theory. We estimate the unknown O(p^6) constants using resonance exchange. We make a careful comparison to the available data and determine two O(p^4) constants rather precisely, and two O(p^6) constants less precisely. We also use Chiral Perturbation Theory to two loops to extract in a model--independent manner the charge radius of the pion from the available data, and obtain \rpiV=0.437\pm 0.016 fm^2.

The Vector and Scalar Form Factors of the Pion to Two Loops

Abstract

We calculate the vector and scalar form factors of the pion to two loops in Chiral Perturbation Theory. We estimate the unknown O(p^6) constants using resonance exchange. We make a careful comparison to the available data and determine two O(p^4) constants rather precisely, and two O(p^6) constants less precisely. We also use Chiral Perturbation Theory to two loops to extract in a model--independent manner the charge radius of the pion from the available data, and obtain \rpiV=0.437\pm 0.016 fm^2.

Paper Structure

This paper contains 25 sections, 74 equations.

Table of Contents

  1. Introduction
  2. Definitions and Notation
  3. Form factors
  4. Chiral Perturbation Theory
  5. The calculation
  6. $F_\pi$ and $M_\pi^2$
  7. Scalar Form Factor
  8. Vector Form Factor
  9. Comparison with earlier work
  10. Resonance and $SU(3)$ estimates of the ${\cal O}(p^6)$ parameters
  11. Scalar contributions
  12. Vector contributions
  13. $SU(3)$ contributions
  14. Numerical results and comparison with experiment
  15. General input parameters
  16. ...and 10 more sections