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---
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title: Rotations angles in SPheno
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permalink: /Rotations_angles_in_SPheno/
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---
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[Category:Model](/Category:Model "wikilink") [Category:SPheno](/Category:SPheno "wikilink")
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General
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-------
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If a rotation angle is used to parametrise the [mixing in the gauge sector](/Rotations_in_gauge_sector "wikilink") a relation must be given how SPheno can calculate this angle from the numerical values of the rotation matrix. For this purpose, the flag `DependenceSPheno` must be used in [parameters.m](/parameters.m "wikilink")
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### Example
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1. **The Weinberg angle in the SM**: the angle can be calculated from the diagonalisation matrix of the neutral gauge bosons *Z* (called `ZZ`) via
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*Θ*<sub>*W*</sub> = acos|*Z*<sub>11</sub>|
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That's done in [parameters.m](/parameters.m "wikilink")
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{ZZ, { Description -> "Weinberg-Angle",
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...
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DependenceSPheno -> ArcCos[Abs[ZZ[1,1]]] }}
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2. **Models with extra gauge bosons**: for models with a *Z*′ gauge bosons stemming from a *U*(1) tensored to the SM gauge groups, the rotation matrix reads in general
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$\\left(\\begin{array}{ccc}
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\\cos\\Theta&-\\sin\\Theta \\cos\\Theta'& \\sin\\Theta \\sin\\Theta' \\\\
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\\sin\\Theta&\\cos\\Theta \\cos\\Theta'&-\\cos\\Theta \\sin\\Theta'\\\\
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0& \\sin\\Theta'& \\cos\\Theta'
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\\end{array}\\right)$
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and the angles can be calculate from
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$\\begin{aligned}
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\\Theta &=& \\text{acos}|Z_{11}|\\\\
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\\Theta' &=& \\text{acos}|Z_{33}|
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\\end{aligned}$
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All of that is defined in [parameters.m](/parameters.m "wikilink") via
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{ZZ,{
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Dependence -> {{Cos[ThetaW],-Sin[ThetaW] Cos[ThetaWp], Sin[ThetaW] Sin[ThetaWp] },
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{Sin[ThetaW],Cos[ThetaW] Cos[ThetaWp],-Cos[ThetaW] Sin[ThetaWp]},
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{0, Sin[ThetaWp], Cos[ThetaWp]}},
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...};
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{ThetaW,{
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DependenceSPheno -> ArcCos[Abs[ZZ[1,1]]],
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...
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};
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{ThetaWp, {
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DependenceSPheno -> ArcCos[Abs[ZZ[3,3]]],
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...
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};
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See also
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-------- |
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\ No newline at end of file |