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---
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title: VEVs
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permalink: /VEVs/
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---
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# VEVs
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[Category:Model](/Category:Model "wikilink") The particles responsible for breaking a gauge symmetry receive a VEV. After the symmetry breaking, these particles are parametrized by a scalar *ϕ* and a pseudo scalar *σ* part and the VEV *v*:
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The particles responsible for breaking a gauge symmetry receive a VEV. After the symmetry breaking, these particles are parametrized by a scalar ϕ and a pseudo scalar σ part and the VEV v:
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$S = \\frac{1}{\\sqrt{2}} \\left( \\phi_S + i \\sigma_S + v_S \\right)$
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$`S = \frac{1}{\sqrt{2}} \left( \phi_S + i \sigma_S + v_S \right)`$
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#### Implementation in SARAH
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... | ... | @@ -28,8 +25,7 @@ All indices carried by the particle receiving the VEV are automatically added to |
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In the MSSM, the Higgs*H*<sub>*d*</sub><sup>0</sup> and*H*<sub>*u*</sub><sup>0</sup> get VEVs*v*<sub>*d*</sub> and*v*<sub>*u*</sub>:
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$H_u^0 = \\frac{1}{\\sqrt{2}} \\left(v_u + i \\sigma_u +\\phi_u \\right) \\, , \\hspace{1cm}
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H_d^0 = \\frac{1}{\\sqrt{2}} \\left(v_d + i \\sigma_d +\\phi_d \\right)$
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$`H_u^0 = \frac{1}{\sqrt{2}} \left(v_u + i \sigma_u +\phi_u \right) \, , \hspace{1cm} H_d^0 = \frac{1}{\sqrt{2}} \left(v_d + i \sigma_d +\phi_d \right)`$
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This is done in SARAH by using
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... | ... | @@ -47,8 +43,7 @@ To add a relative phase, use |
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This is interpreted as
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$H_u^0 = \\frac{e^{i \\eta}}{\\sqrt{2}} \\left(v_u + i \\sigma_u +\\phi_u \\right) \\, , \\hspace{1cm}
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H_d^0 = \\frac{1}{\\sqrt{2}} \\left(v_d + i \\sigma_d +\\phi_d \\right)$
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$`H_u^0 = \frac{e^{i \eta}}{\sqrt{2}} \left(v_u + i \sigma_u +\phi_u \right) \, , \hspace{1cm} H_d^0 = \frac{1}{\sqrt{2}} \left(v_d + i \sigma_d +\phi_d \right)`$
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#### Aligned VEVs
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... | ... | @@ -77,7 +72,7 @@ To define complex VEVs, it is possible to give the phase as last argument: |
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{{SHd0, {vd, 1/Sqrt[2]}, {sigmad,I/Sqrt[2]},{phid,1/Sqrt[2]}},
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{SHu0, {vu, 1/Sqrt[2]}, {sigmau,I/Sqrt[2]},{phiu,1/Sqrt[2]},{eta}}};
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This is understood as $H_u^0 \\to \\frac{\\exp(i \\eta)}{\\sqrt{2}} \\left(v_u + i \\sigma_u + \\phi_u\\right)$. Another possibility to define complex VEVs is to define
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This is understood as $`H_u^0 \to \frac{\exp(i \eta)}{\sqrt{2}} \left(v_u + i \sigma_u + \phi_u\right)`$. Another possibility to define complex VEVs is to define
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DEFINITION[EWSB][VEVs]=
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{{SHd0, {vdR, 1/Sqrt[2]}, {vdI, I/Sqrt[2]},
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... | ... | @@ -88,8 +83,7 @@ This is understood as $H_u^0 \\to \\frac{\\exp(i \\eta)}{\\sqrt{2}} \\left(v_u + |
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which is understood as
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$H_d^0 \\to \\frac{1}{\\sqrt{2}}\\left(v_d^R + i v_d^I + i \\sigma_d + \\phi_d \\right)\\,,\\hspace{1cm}
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H_u^0 \\to \\frac{1}{\\sqrt{2}}\\left(v_u^R + i v_u^I + i \\sigma_u + \\phi_u \\right) \\, .$
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$`H_d^0 \to \frac{1}{\sqrt{2}}\left(v_d^R + i v_d^I + i \sigma_d + \phi_d \right)\,,\hspace{1cm} H_u^0 \to \frac{1}{\sqrt{2}}\left(v_u^R + i v_u^I + i \sigma_u + \phi_u \right) \, .`$
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This format has the advantage that the tree-level tadpole equations are also in the complex case are purely polynomials and can be used numerically with dedicated codes like <span>HOM4PS2</span> which is used by <span>Vevacious</span> .
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