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---
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title: Rotations in matter sector
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permalink: /Rotations_in_matter_sector/
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---
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# Rotations in matter sector
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[Category:Model](/Category:Model "wikilink")
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General
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-------
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... | ... | @@ -76,10 +73,7 @@ In that case two sets of old eigenstates (*O*<sub>1</sub>,*O*<sub>2</sub>) are r |
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{{{First Basis},{Second Basis}},{{First States,First Matrix},{Second States,Second Matrix}}}
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This is interpreted as
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$\\begin{aligned}
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O_1 &= M_1 N_1 \\\\
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O_2 &= M_2 N_2 \\\\
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\\end{aligned}$
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$` O_1 = M_1 N_1 \\ O_2 = M_2 N_2 \\ `$
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### Examples
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... | ... | @@ -115,13 +109,9 @@ If one uses the flag in the MSSM for the up-squark mixing |
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{{SuL, SuR}, {Su, ZU},NoFlavorMixing}
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the mixing is taken to be
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$\\begin{aligned}
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&\\left(\\begin{array}{c} \\tilde{d}_L^1 \\\\ \\tilde{d}_R^1 \\end{array}\\right)_k = Z^{D_1,\\dagger}_{kj} \\tilde{d}_{1j} \\\\
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&\\left(\\begin{array}{c} \\tilde{d}_L^2 \\\\ \\tilde{d}_R^2 \\end{array}\\right)_k = Z^{D_2,\\dagger}_{kj} \\tilde{d}_{2j} \\\\
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&\\left(\\begin{array}{c} \\tilde{d}_L^3 \\\\ \\tilde{d}_R^3 \\end{array}\\right)_k = Z^{D_3,\\dagger}_{kj} \\tilde{d}_{3j}
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\\end{aligned}$
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$` \left(\begin{array}{c} \tilde{d}_L^1 \\ \tilde{d}_R^1 \end{array}\right)_k = Z^{D_1,\dagger}_{kj} \tilde{d}_{1j} \\ \left(\begin{array}{c} \tilde{d}_L^2 \\ \tilde{d}_R^2 \end{array}\right)_k = Z^{D_2,\dagger}_{kj} \tilde{d}_{2j} \\ \left(\begin{array}{c} \tilde{d}_L^3 \\ \tilde{d}_R^3 \end{array}\right)_k = Z^{D_3,\dagger}_{kj} \tilde{d}_{3j} `$
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or more compact
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$\\left(\\begin{array}{c} \\tilde{d}_L^f \\\\ \\tilde{d}_R^f \\end{array}\\right)_k = Z^{D_f,\\dagger}_{kj} \\tilde{d}_{fj} \\\\$
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$`\left(\begin{array}{c} \tilde{d}_L^f \\ \tilde{d}_R^f \end{array}\right)_k = Z^{D_f,\dagger}_{kj} \tilde{d}_{fj} \\`$
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The consequences are
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1. There are three 2 × 2 rotation matrices which get labelled by a flavour index
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