Changes between Version 6 and Version 7 of FCNC4F


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Timestamp:
Nov 3, 2018, 9:42:16 PM (6 years ago)
Author:
Yoav Afik
Comment:

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  • FCNC4F

    v6 v7  
    1 $wgUseTeX = true;
    2 
    31== 4-fermion EFT with FCNC implementation
    42
    … …  
    1412
    1513== Description of the model:
    16 This is a Contact Interaction (CI) model.
     14This is a Contact Interaction model.
    1715
    1816The lagrangian of the model is described by: \\
    … …  
    2119#!latex
    2220\begin{eqnarray}
    23 \mathcal{L}_{eff} = \frac{C_{ij}^{U \mu}}{v^2} (\bar{u}_{L}^{i} \gamma_{\mu} u_{L}^{j}) (\bar{\mu}_{L} \gamma_{\mu} \mu_{L}) + \frac{C_{ij}^{D \mu}}{v^2} (\bar{d}_{L}^{i} \gamma_{\mu} d_{L}^{j}) (\bar{\mu}_{L} \gamma_{\mu} \mu_{L}),
     21\mathcal{L}_{eff} = \frac{C_{ij}^{U \mu}}{v^2} (\bar{u}_{L}^{i} \gamma_{\mu} u_{L}^{j}) (\bar{\mu}_{L} \gamma_{\mu} \mu_{L}) + \frac{C_{ij}^{D \mu}}{v^2} (\bar{d}_{L}^{i} \gamma_{\mu} d_{L}^{j}) (\bar{\mu}_{L} \gamma_{\mu} \mu_{L}) + \\
     22\frac{C_{ij}^{U e}}{v^2} (\bar{u}_{L}^{i} \gamma_{\mu} u_{L}^{j}) (\bar{e}_{L} \gamma_{\mu} e_{L}) + \frac{C_{ij}^{D e}}{v^2} (\bar{d}_{L}^{i} \gamma_{\mu} d_{L}^{j}) (\bar{e}_{L} \gamma_{\mu} e_{L})
    2423\end{eqnarray}
    2524}}}
    2625
    27 At the first model, only the off-diagonal elements for the b-s admixtures are considered, since those are the ones related to the observed b-s-l-l anomalies.
     26Only the off-diagonal elements for the b-s admixtures are considered, since those are the ones related to the observed b-s-l-l anomalies.
    2827The matrices take the form:
    2928{{{
    … …  
    3433,
    3534C_{ij}^{D \mu} =
    36 \begin{pmatrix} C_{d \mu} & 0 & 0 \\ 0 & C_{s \mu} & C_{b s \mu}^{*} \\ 0 & C_{b s \mu} & C_{t \mu} \end{pmatrix}
     35\begin{pmatrix} C_{d \mu} & 0 & 0 \\ 0 & C_{s \mu} & C_{b s \mu}^{*} \\ 0 & C_{b s \mu} & C_{b \mu} \end{pmatrix}
     36\end{eqnarray}
     37
     38\begin{eqnarray}
     39C_{ij}^{U e} =
     40\begin{pmatrix} C_{u e} & 0 & 0 \\ 0 & C_{c e} & 0 \\ 0 & 0 & C_{t e} \end{pmatrix}
     41,
     42C_{ij}^{D e} =
     43\begin{pmatrix} C_{d e} & 0 & 0 \\ 0 & C_{s e} & C_{b s e}^{*} \\ 0 & C_{b s e} & C_{b e} \end{pmatrix}
    3744\end{eqnarray}
    3845}}}
    3946
    4047
    41 A more general model is also attached, contains the full terms:
     48A more general model is also attached, contains the full diagonal and non-diagonal terms.
     49{{{
    4250#!latex
    4351\begin{eqnarray}
    4452C_{ij}^{U \mu} =
    45 \begin{pmatrix} C_{u \mu} & 0 & 0 \\ 0 & C_{c \mu} & 0 \\ 0 & 0 & C_{t \mu} \end{pmatrix}
     53\begin{pmatrix} C_{u \mu} & C_{c u \mu}^{*} & C_{t u \mu}^{*} \\ C_{c u \mu} & C_{c \mu} & C_{t c \mu}^{*} \\ C_{t u \mu} & C_{t c \mu} & C_{t \mu} \end{pmatrix}
    4654,
    4755C_{ij}^{D \mu} =
    48 \begin{pmatrix} C_{d \mu} & 0 & 0 \\ 0 & C_{s \mu} & C_{b s \mu}^{*} \\ 0 & C_{b s \mu} & C_{t \mu} \end{pmatrix}
     56\begin{pmatrix} C_{d \mu} & C_{s d \mu}^{*} & C_{b d \mu}^{*} \\ C_{s d \mu} & C_{s \mu} & C_{b s \mu}^{*} \\ C_{b d \mu} & C_{b s \mu} & C_{b \mu} \end{pmatrix}
     57\end{eqnarray}
     58
     59\begin{eqnarray}
     60C_{ij}^{U e} =
     61\begin{pmatrix} C_{u e} & C_{c u e}^{*} & C_{t u e}^{*} \\ C_{c u e} & C_{c e} & C_{t c e}^{*} \\ C_{t u e} & C_{t c e} & C_{t e} \end{pmatrix}
     62,
     63C_{ij}^{D e} =
     64\begin{pmatrix} C_{d e} & C_{s d e}^{*} & C_{b d e}^{*} \\ C_{s d e} & C_{s e} & C_{b s e}^{*} \\ C_{b d e} & C_{b s e} & C_{b e} \end{pmatrix}
    4965\end{eqnarray}
    5066}}}
    51 
    52 Similar couplings to electrons are considered as well for complicity.
    53 
    5467
    5568