Nonlinear Chiral Symmetry and Partial Conservation of Axial-Vector Current—Bogoliubov-Parasiuk-Hepp-Zimmermann Renormalization

1973 ◽  
Vol 7 (10) ◽  
pp. 2950-2956 ◽  
Author(s):  
Yuk-Ming P. Lam
Keyword(s):  
Chiral Symmetry ◽  
Axial Vector ◽  
Vector Current ◽  
Axial Vector Current ◽  
Partial Conservation

scholarly journals Nuclear currents in chiral effective field theory

2020 ◽  
Vol 56 (9) ◽  
Author(s):  
Hermann Krebs
Keyword(s):  
Field Theory ◽  
Chiral Symmetry ◽  
Effective Field Theory ◽  
Unitary Transformation ◽  
Axial Vector ◽  
Vector Current ◽  
Effective Field ◽  
Axial Vector Current ◽  
Leading Order ◽  
Chiral Effective Field Theory

Abstract In this article, we review the status of the calculation of nuclear currents within chiral effective field theory. After formal discussion of the unitary transformation technique and its application to nuclear currents we give all available expressions for vector, axial-vector currents. Vector and axial-vector currents are discussed up to order Q with leading-order contribution starting at order $$Q^{-3}$$ Q - 3 . Pseudoscalar and scalar currents will be discussed up to order $$Q^0$$ Q 0 with leading-order contribution starting at order $$Q^{-4}$$ Q - 4 . This is a complete set of expressions in next-to-next-to-next-to-leading-order (N$$^3$$ 3 LO) analysis for nuclear scalar, pseudoscalar, vector and axial-vector current operators. Differences between vector and axial-vector currents calculated via transfer-matrix inversion and unitary transformation techniques are discussed. The importance of a consistent regularization is an additional point which is emphasized: lack of a consistent regularization of axial-vector current operators is shown to lead to a violation of the chiral symmetry in the chiral limit at order Q. For this reason a hybrid approach at order Q, discussed in various publications, is non-applicable. To respect the chiral symmetry the same regularization procedure needs to be used in the construction of nuclear forces and current operators. Although full expressions of consistently regularized current operators are not yet available, the isoscalar part of the electromagnetic charge operator up to order Q has a very simple form and can be easily regularized in a consistent way. As an application, we review our recent high accuracy calculation of the deuteron charge form factor with a quantified error estimate.

Partial conservation of axial-vector current effects in the MIT bag model

1979 ◽  
Vol 20 (3) ◽  
pp. 727-730 ◽  
Author(s):  
M. V. Barnhill ◽  
W. K. Cheng ◽  
A. Halprin
Keyword(s):  
Axial Vector ◽  
Vector Current ◽  
Axial Vector Current ◽  
Bag Model ◽  
Partial Conservation ◽  
Mit Bag Model
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