Changes between Version 1 and Version 2 of FCHiggs

Timestamp:

Sep 3, 2013, 9:19:20 PM (12 years ago)

Author:

stefankrastanov

Comment:

--

FCHiggs

@@ -1 @@
-blabla
+== Top Quark Decay to a Higgs and a Light Quark Operator ==
+
+=== Motivation ===
+
+Neutral Flavor Changing couplings are absent in the Standard Model at tree
+level. Moreover, at next-to-leading order they are supressed by the GIM
+mechanism. Therefore a detection of such processes would be a strong hint at
+new physics. Here we focus Neutral Flavor Change mediated by the Higgs boson
+following [@zhang2013top].
+
+The lowest dimensional operators compatible with the symmetries of the Standard
+Model are the following six-dimensional operators (for a comprehensive list of
+all six-dimensional operators compatible with Standard Model symmetries consult
+[@grzadkowski2010dimension]):
+
+- chromomagnetic operator $O_{uG}$
+
+{{{
+#!latex
+\begin{equation}
+\begin{matrix}
+O^{1,3}_{uG} = y_t g_s (\bar{q} \sigma^{\mu\nu} T^a t) \bar{\phi} G^a_{\mu\nu}; \\
+ \\
+O^{3,1}_{uG} = y_t g_s (\bar{Q} \sigma^{\mu\nu} T^a u) \bar{\phi} G^a_{\mu\nu};
+\end{matrix}
+\end{equation}
+}}}
+
+- dimension-six Yukawa interaction $O_{u\phi}$
+
+{{{
+#!latex
+\begin{equation}
+\begin{matrix}
+O^{1,3}_{u\phi} = - y_t^3 (\phi^\dagger \phi) (\bar{q} t) \bar{\phi}; \\
+ \\
+O^{3,1}_{u\phi} = - y_t^3 (\phi^\dagger \phi) (\bar{Q} u) \bar{\phi};
+\end{matrix}
+\end{equation}
+}}}
+
+- To each (1,3) operator corresponds a (3,1) operator where the flavors are
+  reversed.
+
+- To each operator (e.g. (1,3)) corresponds another where the up quark is
+  exchanged for a charm quark (e.g. (2,3)).
+
+- The hermitian conjugates of the above-mentioned operators contributing with
+  the opposite chirality.
+
+Where we denoted:
+
+- $\phi$ is the Higgs doublet;
+- $Q$ and $q$ are respectively the 1st (or 2nd) and the 3th left-handed quark
+  doublet;
+- $u$ (or $c$) and $t$ are the right-handed quarks;
+- $\bar{\phi} = i \sigma^2 \phi$
+- $y_t = \sqrt{2}\frac{m_t}{v}$ the top quark Yukawa coupling.
+
+The complete Lagrangian takes the form:
+
+{{{
+#!latex
+\begin{equation}
+\mathcal{L}_{eff} = \mathcal{L}_{SM} + \sum_i \frac{c_i O_i}{\Lambda^2},
+\end{equation}
+}}}
+
+where $\Lambda$ is the new physics energy scale, $O_i$ is for the various
+six-dimensional operators in consideration and  $c_i$ are relative couplings.
+
+The normalizations for the six-dimensional operators were chosen such that for
+any new SM-like vertices the ratio of the new couplings to the SM couplings is
+of the form $c_i\frac{m_t^2}{\Lambda^2}$. 
+
+=== Implementation and Validation ===
+
+The implementation is a straightforward transcription of the Lagrangian into
+`FeynRules` format as no new fields need to be defined. 
+
+The model was validated using the build-in checks in `FeynRules` and
+`MadGraph5`. Moreover the decay widths were confirmed through `MadGraph5` and
+compared to the analytical results.
+