OnceSubtracted Dispersion Relations, Current Algebra, and K_{l3} Form Factors
Abstract
K_{l3} decay is treated using oncesubtracted dispersion relations, current algebra, and partial conservation of axialvector current. The dispersion integrals are evaluated by saturating them with the vector K^{*} and and scalar κ intermediate states. The subtraction point is chosen so that the subtraction constants may correspond to the softpion result. It is shown that if f_{+}(t) obeys oncesubtracted dispersion relations and f_{}(t) an unsubtracted one (scheme I), and if f_{K}f_{π}~=1.161.28, then f_{+}(0) cannot be close to 1 unless a κ meson exists. In this case it is also shown that both λ_{+} and λ_{} are small, while ξ=f_{}(0)f_{+}(0) is small and negative. We also consider the possibility of having oncesubtracted dispersion relations for both f_{+}(t) and f_{}(t) (scheme II). It is found that the results of schemes I and II are the same if either (a) there exists a κ meson with mass around 1 BeV and f_{+}(0)~=1, or (b) no κ meson exists, but f_{+}(0)~=f_{K}f_{π}. If, on the other hand, no κ meson exists, and if f_{+}(0)~=1, while f_{K}f_{π}~=1.28, then one is able to get λ_{} an order of magnitude bigger than λ_{+} in scheme II. Thus there is a possibility for large λ_{} only in scheme II. Furthermore, in scheme I, using partial conservation of vector current for the strangenesschanging vector current, we obtain (f_{K}f_{π})f_{+}^{ 1}(0)~=m_{κ}^{2}(m_{κ}^{2}m_{K}^{2}). For (f_{K}f_{π})f_{+}^{1}(0)~=1.28, we predict m_{κ}~=1.06 BeV.
 Publication:

Physical Review
 Pub Date:
 October 1968
 DOI:
 10.1103/PhysRev.174.2033
 Bibcode:
 1968PhRv..174.2033P