Changes between Version 6 and Version 7 of FCNC4F
 Timestamp:
 11/03/18 21:42:16 (23 months ago)
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FCNC4F
v6 v7 1 $wgUseTeX = true;2 3 1 == 4fermion EFT with FCNC implementation 4 2 … … 14 12 15 13 == Description of the model: 16 This is a Contact Interaction (CI)model.14 This is a Contact Interaction model. 17 15 18 16 The lagrangian of the model is described by: \\ … … 21 19 #!latex 22 20 \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}) 24 23 \end{eqnarray} 25 24 }}} 26 25 27 At the first model, only the offdiagonal elements for the bs admixtures are considered, since those are the ones related to the observed bsll anomalies.26 Only the offdiagonal elements for the bs admixtures are considered, since those are the ones related to the observed bsll anomalies. 28 27 The matrices take the form: 29 28 {{{ … … 34 33 , 35 34 C_{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} 39 C_{ij}^{U e} = 40 \begin{pmatrix} C_{u e} & 0 & 0 \\ 0 & C_{c e} & 0 \\ 0 & 0 & C_{t e} \end{pmatrix} 41 , 42 C_{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} 37 44 \end{eqnarray} 38 45 }}} 39 46 40 47 41 A more general model is also attached, contains the full terms: 48 A more general model is also attached, contains the full diagonal and nondiagonal terms. 49 {{{ 42 50 #!latex 43 51 \begin{eqnarray} 44 52 C_{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} 46 54 , 47 55 C_{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} 60 C_{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 , 63 C_{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} 49 65 \end{eqnarray} 50 66 }}} 51 52 Similar couplings to electrons are considered as well for complicity.53 54 67 55 68