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PHY431 Homework Set 6Reading:Lecture NotesHomework:See below:Due date:Wednesday March 8Hints and SolutionsProblem VI.1Using the isospin-lowering operator I-, and starting at the "fully stretched" state ∆++= |uuu⟩,derive the representation of the three other ∆states in terms of quark states.Hints:no hintsSolution:I-∆++= I-|uuu⟩= N{|duu⟩+|udu⟩+|uud⟩} = ∆+, with Na normalization constant.Clearly N= 1/√3 here.I-∆+= N{|ddu⟩+|dud⟩+|udd⟩} = ∆0, with again N= 1/√3 .I-∆0= N{|ddd⟩} = ∆-, with N= 1 .Problem VI.2Calculate the Isospin-3 (I3) eigenvalues (of the I3operator) of the bottom and the topquarks.Hints:no hintsSolution:I3(b) = Q- 1/2(B+S+C+B+T) = -1/3- 1/2(1/3+0+0-1+0) = 0I3(t) = Q- 1/2(B+S+C+B+T) = +2/3- 1/2(1/3+0+0+0+1) = 0, as expected for any quark not auor dquark.Problem VI.3Show that the states |π0⟩and |η⟩are othonormal, assuming that the |
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