Selection Rule delta_I = 1/2 in the strangeness-changing weak currents

[zq460]

I read in a paper that delta_I = 1/2 rule of the strangeness-changing weak current implies the ratio of cross section of proton->Sigma0 process to neutron->Sigma- process to be 1/2. I do not understand what is this selection rule and how does it effect the cross section ratio of the 2 processes. Is delta_I = 1/2 rule is the change in the isospin of initial and final particle which has to be 1/2 for these processes? Will be great if somebody could explain. Thank you.

 

[Bill_K]

zq460, Could you be more specific about what reactions you have in mind? The only references I can find about a ΔI = 1/2 rule apply to K → ππ decay.

 

[zq460]

yes, I should have posted the reference paper. Sorry my first time ever on this forum. Here you can see an old paper http://nngroup.physics.sunysb.edu/~nngroup/misc/Documents/NeutrinoReactionsAtAcceleratorEnergies.pdf. The delta_I = 1/2 rule is mentioned just before equation (3.40) on page 317.

I am talking about the cabbibo suppressed 'charged current processes', where when a neutrino interacts with a nucleon, converts to a lepton producing a W-, which converts a u-quark in the nucleon to a s-quark. So this is a strangness changing process (delta_S = 1) where a 'proton converts to a Sigma0' or a 'neutron converts to a Sigma-', both processes are written in equation (3.39) and their cross section ratio is written to be 1/2 accodording to delta_I = 1/2 rule in equation (3.40). I do not understand the rule and also how it effects the ratio of the cross sections of the 2 processes?

Thanks much for the help!