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title: Checks of implemented models
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permalink: /Checks_of_implemented_models/
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---
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# Checks of implemented models
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[Category:Model](/Category:Model "wikilink")
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Running the check for a newly implemented model
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... | ... | @@ -19,15 +16,11 @@ Performed Checks |
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Gauge anomalies are caused by triangle diagrams with three external gauge bosons and internal fermions . The corresponding conditions for all *S**U*(*N*)<sub>*A*</sub> groups to be anomaly free are
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$\\begin{aligned}
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\\sum_i \\mbox{Tr}\\left\[T_{Ar}^a(\\psi_i) T_{Ar}^a(\\psi_i) T_{Ar}^a(\\psi_i)\\right\] = 0 \\end{aligned}$
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$` \sum_i \mbox{Tr}\left[T_{Ar}^a(\psi_i) T_{Ar}^a(\psi_i) T_{Ar}^a(\psi_i)\right] = 0 `$
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Again,*T*<sub>*A**r*</sub><sup>*a*</sup>(*ψ*<sub>*i*</sub>) are the generators for a fermion *ψ*<sub>*i*</sub> transforming as irreducible representation*r* under the gauge group /math>SU(N)_A</math>. The sum is taken over all chiral superfields. In the Abelian sector several conditions have to be fulfilled depending on the number of*U*(1) gauge groups
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$\\begin{aligned}
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U(1)_A^3 &:& \\sum_i (Q^A_{\\psi_i})^3 = 0 \\\\
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U(1)_A\\times U(1)_B^2 &:& \\thinspace \\sum_i Q^A_{\\psi_i} (Q^B_{\\psi_i})^2 = 0 \\\\
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U(1)_A\\times U(1)_B\\times U(1)_C &:& \\thinspace \\sum_i Q^A_{\\psi_i} Q^B_{\\psi_i} Q^C_{\\psi_i}= 0\\end{aligned}$
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$` U(1)_A^3 : \sum_i (Q^A_{\psi_i})^3 = 0 \\ U(1)_A\times U(1)_B^2 : \thinspace \sum_i Q^A_{\psi_i} (Q^B_{\psi_i})^2 = 0 \\ U(1)_A\times U(1)_B\times U(1)_C : \thinspace \sum_i Q^A_{\psi_i} Q^B_{\psi_i} Q^C_{\psi_i}= 0`$
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The mixed condition involving Abelian and non-Abelian groups is
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... | ... | @@ -35,10 +28,7 @@ The mixed condition involving Abelian and non-Abelian groups is |
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Finally, conditions involving gravity𝔊 are
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$\\begin{aligned}
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\\mathfrak{G} \\times U(1)_A^2 &:& \\sum_i (Q^A_{\\psi_i})^2 = 0 \\\\
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\\mathfrak{G} \\times U(1)_A\\times U(1)_B &:& \\thinspace \\sum_i Q^A_{\\psi_i} Q^B_{\\psi_i} = 0 \\\\
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\\mathfrak{G}^2 \\times U(1)_A &:& \\sum_i Q^A_{\\psi_i} = 0 \\end{aligned}$
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$` \mathfrak{G} \times U(1)_A^2 : \sum_i (Q^A_{\psi_i})^2 = 0 \\ \mathfrak{G} \times U(1)_A\times U(1)_B : \thinspace \sum_i Q^A_{\psi_i} Q^B_{\psi_i} = 0 \\ \mathfrak{G}^2 \times U(1)_A : \sum_i Q^A_{\psi_i} = 0 `$
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If one if these conditions is not-fulfilled a warning is printed by SARAH. If some *U*(1) charges were defined as variable, the conditions on these variables for anomaly cancellation are printed.
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... | ... | |