Matching_to_the_SM_in_SPheno.md

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-title: Matching to the SM in SPheno
-permalink: /Matching_to_the_SM_in_SPheno/
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+# Matching to the SM in SPheno
 
-[Category:Outputs](/Category:Outputs "wikilink") [Category:SPheno](/Category:SPheno "wikilink")
+ 
 
 General
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@@ -103,16 +100,7 @@ Here, `g1RBLFactor` which relates *g*<sub>*R*</sub> and *g*<sub>*Y*</sub><sup>*S
 
 Even much more complicated matching conditions can be imposed. For instance, the matching in the left-right symmetry model with two generations of bi-doublets are
 
-$\\begin{aligned}
-v_{u,1} &= v_L \\sin\\beta \\sin\\beta_u\\\\
-v_{d,1} &= v_L \\cos\\beta \\sin\\beta_d\\\\
-v_{u,2} &= v_L \\sin\\beta \\cos\\beta_u \\\\
-v_{d,2} &= v_L \\cos\\beta \\cos\\beta_d\\\\
-Y_{Q_1}&=-\\frac{Y_d\\sqrt{1+\\tan\\beta_d^2}  -Y_u\\sqrt{1+ \\tan\\beta_u^2} }{\\tan\\beta_d-\\tan\\beta_u}\\\\
-Y_{Q_2}&=\\frac{\\tan\\beta_u Y_d\\sqrt{1+\\tan\\beta_d^2} -Y_u\\tan\\beta_d\\sqrt{1+ \\tan\\beta_u^2}}{\\tan\\beta_d-\\tan\\beta_u}\\\\
-Y_{L_1}&=-\\frac{Y_e\\sqrt{1+\\tan\\beta_d^2}  -Y_\\nu\\sqrt{1+ \\tan\\beta_u^2} }{\\tan\\beta_d-\\tan\\beta_u}\\\\
-Y_{L_2}&=\\frac{\\tan\\beta_u Y_e\\sqrt{1+\\tan\\beta_d^2} -Y_\\nu\\tan\\beta_d\\sqrt{1+ \\tan\\beta_u^2}}{\\tan\\beta_d-\\tan\\beta_u}
-\\end{aligned}$
+$` v_{u,1}  = v_L \sin\beta \sin\beta_u\\ v_{d,1}  = v_L \cos\beta \sin\beta_d\\ v_{u,2}  = v_L \sin\beta \cos\beta_u \\ v_{d,2}  = v_L \cos\beta \cos\beta_d\\ Y_{Q_1} =-\frac{Y_d\sqrt{1+\tan\beta_d^2}  -Y_u\sqrt{1+ \tan\beta_u^2} }{\tan\beta_d-\tan\beta_u}\\ Y_{Q_2} =\frac{\tan\beta_u Y_d\sqrt{1+\tan\beta_d^2} -Y_u\tan\beta_d\sqrt{1+ \tan\beta_u^2}}{\tan\beta_d-\tan\beta_u}\\ Y_{L_1} =-\frac{Y_e\sqrt{1+\tan\beta_d^2}  -Y_\nu\sqrt{1+ \tan\beta_u^2} }{\tan\beta_d-\tan\beta_u}\\ Y_{L_2} =\frac{\tan\beta_u Y_e\sqrt{1+\tan\beta_d^2} -Y_\nu\tan\beta_d\sqrt{1+ \tan\beta_u^2}}{\tan\beta_d-\tan\beta_u} `$
 
 where three angles are introduced to parametrize all VEVs and the neutrino Yukawa coupling is considered to be given as input. These matching conditions together with the ones in the gauge sector are defined via