Loop_Masses.md

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-title: Loop Masses
-permalink: /Loop_Masses/
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+# Loop Masses
 
-[Category:Calculations](/Category:Calculations "wikilink") The information about the [one-](/One-Loop_Self-Energies_and_Tadpoles "wikilink") and [two-loop](/Two-Loop_Self-Energies_and_Tadpoles "wikilink") corrections to the one- and two-point functions can be used to calculate the loop corrected mass spectrum. The renormalized mass matrices (or masses) are related to the tree-level mass matrices (or masses) and the self-energies as follows.
+ The information about the [one-](/One-Loop_Self-Energies_and_Tadpoles "wikilink") and [two-loop](/Two-Loop_Self-Energies_and_Tadpoles "wikilink") corrections to the one- and two-point functions can be used to calculate the loop corrected mass spectrum. The renormalized mass matrices (or masses) are related to the tree-level mass matrices (or masses) and the self-energies as follows.
 
 ### Loop corrected masses
 
@@ -37,13 +34,7 @@ For vector bosons we have similar simple expressions as for scalar. The one-loop
 
 The one-loop mass matrix of a Majorana fermion*χ* is related to the tree-level mass matrix*m*<sub>*χ*</sub><sup>(*T*)</sup> and the different parts of the self-energies by
 
-$\\begin{aligned}
-m_\\chi^{(1L)} (p^2) &=& m_\\chi^{(T)} - \\frac{1}{2} \\bigg\[ \\Sigma^\\chi_S(p^2) + \\Sigma^{\\chi,T}_S(p^2)
- + \\left(\\Sigma^{\\chi,T}_L(p^2)+   \\Sigma^\\chi_R(p^2)\\right) m_\\chi^{(T)}
- \\nonumber \\\\
-&& \\hspace{16mm}
-+ m_{\\chi}^{(T)} \\left(\\Sigma^{\\chi,T}_R(p^2) +  \\Sigma^\\chi_L(p^2) \\right)
- \\bigg\]  \\end{aligned}$
+$` m_\chi^{(1L)} (p^2)  =  m_\chi^{(T)} - \frac{1}{2} \bigg\[ \Sigma^\chi_S(p^2) + \Sigma^{\chi,T}_S(p^2)  + \left(\Sigma^{\chi,T}_L(p^2)+   \Sigma^\chi_R(p^2)\right) m_\chi^{(T)}  \nonumber \\    \hspace{16mm} + m_{\chi}^{(T)} \left(\Sigma^{\chi,T}_R(p^2) +  \Sigma^\chi_L(p^2) \right)  \bigg\]  `$
 
 Note,(*T*) is used to assign tree-level values while*T* denotes a transposition. Eq. (\[eq:propagator\]) can also be used for fermions by taking the eigenvalues of*m*<sub>*χ*</sub><sup>2, (1*L*)</sup> = *m*<sub>*χ*</sub><sup>(1*L*)\*</sup>*m*<sub>*χ*</sub><sup>(1*L*)</sup>.
 
@@ -51,9 +42,7 @@ Note,(*T*) is used to assign tree-level values while*T* denotes a transposition.
 
 For a Dirac fermion*Ψ* one obtains the one-loop corrected mass matrix via
 
-$\\begin{aligned}
-\\label{eq:DiracLoop}
-m_\\Psi^{(1L)}(p^2) =  m_\\Psi^{(T)} - \\Sigma^+_S(p^2)  - \\Sigma^+_R(p^2) m_\\Psi^{(T)} - m_\\Psi^{(T)} \\Sigma^+_L(p^2) .\\end{aligned}$
+$`  m_\Psi^{(1L)}(p^2) =  m_\Psi^{(T)} - \Sigma^+_S(p^2)  - \Sigma^+_R(p^2) m_\Psi^{(T)} - m_\Psi^{(T)} \Sigma^+_L(p^2) .`$
 
 Here, the eigenvalues of(*m*<sub>*Ψ*</sub><sup>(1*L*)</sup>)<sup>†</sup>*m*<sub>*Ψ*</sub><sup>(1*L*)</sup> are used in eq. (\[eq:propagator\]) to get the pole masses.