next up previous contents
Next: 5.5 Partial wave expansion Up: 5 decays Previous: 5.3 Decay rates

5.4 Isospin decomposition

The decays (5.2) and (5.3) involve the same form factors as displayed in Eq. (5.12). We denote by , and the current matrix elements of the processes (5.1)-(5.3). These are related by isospin symmetry gif,

 

This relation also holds for the individual form factors, which may be decomposed into a symmetric and an antisymmetric part under . Because of Bose symmetry and of the rule of the relevant weak currents, one has

 

where

 

and is defined in Eq. (5.12).

The isospin relation for the decay rates is

 

Isospin violating contributions affect the matrix elements and phase space, as a result of which this relation is modified. In order to illustrate the (substantial) effects from asymmetries in phase space, we take constant form factors F,G and set R=0,H=0. Eq. (5.26) then reads (with physical masses for and with MeV in )

in the electron mode and

in the muon mode.



Carlos E.Piedrafita