Phy489_Lecture21-22_2013

2 note that 1 5 1 1 2 5 5 2 4 1

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Unformatted text preview: u L carries helicity =  ­1. However, this is sBll generally referred to as a le] ­handed spinor. For an anB ­parBcle, a similar exercise yields (again, in the massless limit) ⎡ ⎤ ⎛ 1− γ 5 ⎞ ⎢uL p = ⎜ ⎟u p⎥ ⎝2⎠ ⎢ ⎥ ⎣ ⎦ ⎛ 1+ γ 5 ⎞ vL p = ⎜ ⎟v p ⎝2⎠ () () () () The corresponding right handed spinors are: uR ⎛ 1+ γ 5 ⎞ p =⎜ up 2⎟ ⎝ ⎠ () () vR ⎛ 1− γ 5 ⎞ p =⎜ ⎟v p ⎝2⎠ () () 5 Adjoint Spinors (Chiral Fermions) Need also to know the expressions for of the corresponding adjoint spinors: 5⎞ ⎛1 − γ 5 ⎞ 0 ⎛ ⎛1 + γ 5 ⎞ 0 1+ γ uL = u γ = u ⎜ ⎟γ = u γ ⎜ ⎟ = u⎜ ⎟ 2⎠ 2⎠ 2⎠ ⎝ ⎝ ⎝ L 0 ⎛ 1 − γ55⎞⎞ vv = vv ⎛ 1 − γ ⎟ L=⎜ ⎜ 2⎟ L ⎝ ⎝ 2 ⎠⎠ ⎛ 1 − γ 55⎞⎞ ⎛ uR = u ⎜ 1 − γ ⎟ uR = u⎝ 2 ⎟⎠ ⎝2⎠ ⎛ 1+ γ 5 ⎛ 1 + γ 5 ⎞⎞ vv = vv ⎜ RR = 2 ⎠⎟ ⎝ 2 ⎟⎠ ⎝ 6 The Charged Current Weak InteracBon νe e Look now at charged weak interacBon vertex: W ⎛ 1− γ 5 ⎞ j − The contribuBon to the amplitude M from this vertex is µ = ν γ µ ⎜ ⎟ e 2⎠ ⎝ where, for the moment, we are using parBcle species (ν , e ) to label the spinors rather than uν , u e (the bar however sBll...
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This document was uploaded on 02/11/2014.

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