... | @@ -43,8 +43,9 @@ Example |
... | @@ -43,8 +43,9 @@ Example |
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1. **Scalar potential in the SM**: the terms
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1. **Scalar potential in the SM**: the terms
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$V_H = \\mu |H|^2 + \\frac12 \\lambda |H|^4$
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$`V_H = \mu |H|^2 + \frac{1}{2} \lambda |H|^4`$
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in the SM are defined via
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in the SM are defined via
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LagHiggs = Mu2 conj[H].H - 1/2 \[Lambda] conj[H].H.conj[H].H;
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LagHiggs = Mu2 conj[H].H - 1/2 \[Lambda] conj[H].H.conj[H].H;
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DEFINITION[GaugeES][LagrangianInput]= {
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DEFINITION[GaugeES][LagrangianInput]= {
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... | @@ -52,19 +53,21 @@ Example |
... | @@ -52,19 +53,21 @@ Example |
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...
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...
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};
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};
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SARAH adds automatically the *S**U*(2) indices and contracts them. Therefore, the short input above is interpreted as:
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SARAH adds automatically the SU(2) indices and contracts them. Therefore, the short input above is interpreted as:
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Mu2 Delta[lef1,lef2] conj[H[{lef1}]].H[{lef2}] - 1/2 \[Lambda] Delta[lef1,lef2] Delta[lef3,lef4] conj[H[{lef1}]].H[{lef2}].conj[H[{lef3}]].H[{lef4}]
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Mu2 Delta[lef1,lef2] conj[H[{lef1}]].H[{lef2}] - 1/2 \[Lambda] Delta[lef1,lef2] Delta[lef3,lef4] conj[H[{lef1}]].H[{lef2}].conj[H[{lef3}]].H[{lef4}]
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2. **Yukawa interactions in the SM**: the terms
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2. **Yukawa interactions in the SM**: the terms
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*V*<sub>*Y*</sub> = *Y*<sub>*d*</sub>*H*<sup>\*</sup>*d**q* + *Y*<sub>*e*</sub>*H*<sup>\*</sup>*e**l* + *Y*<sub>*u*</sub>*H**u**q*
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$`V_Y = Y_d H^\dagger\bar{d} q + Y_e H^\dagger\bar{e} l + Y_u H\bar{u} q `$
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in the SM are defined via
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in the SM are defined via
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LagYukawa = - (Yd conj[H].d.q + Ye conj[H].e.l + Yu H.u.q);
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LagYukawa = - (Yd conj[H].d.q + Ye conj[H].e.l + Yu H.u.q);
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DEFINITION[GaugeES][LagrangianInput]= {
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DEFINITION[GaugeES][LagrangianInput]= {
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{LagYukawa,{AddHC -> True}},
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{LagYukawa,{AddHC -> True}},
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...
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...
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};
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};
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(note that $`e, u`$ and $`d`$ are defined as their complex conjugates in the model file and hence there are nor `conj[e]` etc but `e`)
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SARAH adds automatically all indices and contracts them. For instance, `Yd conj[H].d.q` is interpreted as
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SARAH adds automatically all indices and contracts them. For instance, `Yd conj[H].d.q` is interpreted as
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