Changes between Version 1 and Version 2 of FCHiggs


Ignore:
Timestamp:
09/03/13 21:19:20 (7 years ago)
Author:
stefankrastanov
Comment:

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  • FCHiggs

    v1 v2  
    1 blabla
     1== Top Quark Decay to a Higgs and a Light Quark Operator ==
     2
     3=== Motivation ===
     4
     5Neutral Flavor Changing couplings are absent in the Standard Model at tree
     6level. Moreover, at next-to-leading order they are supressed by the GIM
     7mechanism. Therefore a detection of such processes would be a strong hint at
     8new physics. Here we focus Neutral Flavor Change mediated by the Higgs boson
     9following [@zhang2013top].
     10
     11The lowest dimensional operators compatible with the symmetries of the Standard
     12Model are the following six-dimensional operators (for a comprehensive list of
     13all six-dimensional operators compatible with Standard Model symmetries consult
     14[@grzadkowski2010dimension]):
     15
     16- chromomagnetic operator $O_{uG}$
     17
     18{{{
     19#!latex
     20\begin{equation}
     21\begin{matrix}
     22O^{1,3}_{uG} = y_t g_s (\bar{q} \sigma^{\mu\nu} T^a t) \bar{\phi} G^a_{\mu\nu}; \\
     23 \\
     24O^{3,1}_{uG} = y_t g_s (\bar{Q} \sigma^{\mu\nu} T^a u) \bar{\phi} G^a_{\mu\nu};
     25\end{matrix}
     26\end{equation}
     27}}}
     28
     29- dimension-six Yukawa interaction $O_{u\phi}$
     30
     31{{{
     32#!latex
     33\begin{equation}
     34\begin{matrix}
     35O^{1,3}_{u\phi} = - y_t^3 (\phi^\dagger \phi) (\bar{q} t) \bar{\phi}; \\
     36 \\
     37O^{3,1}_{u\phi} = - y_t^3 (\phi^\dagger \phi) (\bar{Q} u) \bar{\phi};
     38\end{matrix}
     39\end{equation}
     40}}}
     41
     42- To each (1,3) operator corresponds a (3,1) operator where the flavors are
     43  reversed.
     44
     45- To each operator (e.g. (1,3)) corresponds another where the up quark is
     46  exchanged for a charm quark (e.g. (2,3)).
     47
     48- The hermitian conjugates of the above-mentioned operators contributing with
     49  the opposite chirality.
     50
     51Where we denoted:
     52
     53- $\phi$ is the Higgs doublet;
     54- $Q$ and $q$ are respectively the 1st (or 2nd) and the 3th left-handed quark
     55  doublet;
     56- $u$ (or $c$) and $t$ are the right-handed quarks;
     57- $\bar{\phi} = i \sigma^2 \phi$
     58- $y_t = \sqrt{2}\frac{m_t}{v}$ the top quark Yukawa coupling.
     59
     60The complete Lagrangian takes the form:
     61
     62{{{
     63#!latex
     64\begin{equation}
     65\mathcal{L}_{eff} = \mathcal{L}_{SM} + \sum_i \frac{c_i O_i}{\Lambda^2},
     66\end{equation}
     67}}}
     68
     69where $\Lambda$ is the new physics energy scale, $O_i$ is for the various
     70six-dimensional operators in consideration and  $c_i$ are relative couplings.
     71
     72The normalizations for the six-dimensional operators were chosen such that for
     73any new SM-like vertices the ratio of the new couplings to the SM couplings is
     74of the form $c_i\frac{m_t^2}{\Lambda^2}$.
     75
     76=== Implementation and Validation ===
     77
     78The implementation is a straightforward transcription of the Lagrangian into
     79`FeynRules` format as no new fields need to be defined.
     80
     81The model was validated using the build-in checks in `FeynRules` and
     82`MadGraph5`. Moreover the decay widths were confirmed through `MadGraph5` and
     83compared to the analytical results.
     84