Chiral states:

Lc

Rc

Based on spinor structure

 

Helicity states

LHH

RHH

Helicity is spin along z-axis where the z-axis is chosen along the momentum direction:

-

+

 

 

 

 

 

 

[The difference between a helicity and spin formalisms appears when there is more than one particle. Each particle will then define a new z-axis for spin projection]

 

There are two states that span the spin space for a particle and two states that span the space for an antiparticle. One can either use the helicity or the chiral basis.

 

In the limit of m0

particle

Left Handed

Right Handed

 

 

Right Handed

Left Handed

antiparticle

 

 

Momentum

Possible Spin

(conserve ang. Mom)

 

 

 

Possible spin for weak interation due to Lc for massless neutrino

 

Neutrino

Muon

 

 

Hel - LHH

Hel - LHH

Angular momentum

 

Chiral Lc

Chiral Lc

Weak interaction

 

 

Neutrino

M=0

mass= 0

 

Anti muon (electron)

Angular momentum conservation