





title: Tadpole Equations



permalink: /Tadpole_Equations/







# Tadpole Equations






[Category:Calculations](/Category:Calculations "wikilink") During the evaluation of a model, SARAH calculates ’on the fly’ all minimum conditions of the treelevel potential, the so called tadpole equations. In the case of no CP violation, in which complex scalars are decomposed as



During the evaluation of a model, SARAH calculates ’on the fly’ all minimum conditions of the treelevel potential, the so called tadpole equations. In the case of no CP violation, in which complex scalars are decomposed as






$S_i \\to \\frac{1}{\\sqrt{2}}(v_i + \\phi_i + i \\sigma_i) \\,,$



$`S_i \to \frac{1}{\sqrt{2}}(v_i + \phi_i + i \sigma_i) \,,`$






the expressions






$0 = \\frac{\\partial V}{\\partial \\phi_i} \\equiv T_i$



$`0 = \frac{\partial V}{\partial \phi_i} \equiv T_i`$






are calculated. These are equivalent to $\\frac{\\partial V}{\\partial v_i}$. For models with CP violation in the Higgs sector, i.e. where either complex phases appear between the real scalars or where the VEVs have an imaginary part, SARAH calculates the minimum conditions with respect to the CPeven and CPodd components:



are calculated. These are equivalent to $`\frac{\partial V}{\partial v_i}`$. For models with CP violation in the Higgs sector, i.e. where either complex phases appear between the real scalars or where the VEVs have an imaginary part, SARAH calculates the minimum conditions with respect to the CPeven and CPodd components:






$0 = \\frac{\\partial V}{\\partial \\phi_i} \\equiv T_{\\phi_i} \\,,\\hspace{1cm} 0 = \\frac{\\partial V}{\\partial \\sigma_i} \\equiv T_{\\sigma_i}$



$`0 = \frac{\partial V}{\partial \phi_i} \equiv T_{\phi_i} \,,\hspace{1cm} 0 = \frac{\partial V}{\partial \sigma_i} \equiv T_{\sigma_i}`$






The set of all tadpole equations is in this case *T*<sub>*i*</sub> = {*T*<sub>*ϕ*<sub>*i*</sub></sub>, *T*<sub>*σ*<sub>*i*</sub></sub>}.




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