1 | | blabla |
| 1 | == Top Quark Decay to a Higgs and a Light Quark Operator == |
| 2 | |
| 3 | === Motivation === |
| 4 | |
| 5 | Neutral Flavor Changing couplings are absent in the Standard Model at tree |
| 6 | level. Moreover, at next-to-leading order they are supressed by the GIM |
| 7 | mechanism. Therefore a detection of such processes would be a strong hint at |
| 8 | new physics. Here we focus Neutral Flavor Change mediated by the Higgs boson |
| 9 | following [@zhang2013top]. |
| 10 | |
| 11 | The lowest dimensional operators compatible with the symmetries of the Standard |
| 12 | Model are the following six-dimensional operators (for a comprehensive list of |
| 13 | all 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} |
| 22 | O^{1,3}_{uG} = y_t g_s (\bar{q} \sigma^{\mu\nu} T^a t) \bar{\phi} G^a_{\mu\nu}; \\ |
| 23 | \\ |
| 24 | O^{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} |
| 35 | O^{1,3}_{u\phi} = - y_t^3 (\phi^\dagger \phi) (\bar{q} t) \bar{\phi}; \\ |
| 36 | \\ |
| 37 | O^{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 | |
| 51 | Where 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 | |
| 60 | The 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 | |
| 69 | where $\Lambda$ is the new physics energy scale, $O_i$ is for the various |
| 70 | six-dimensional operators in consideration and $c_i$ are relative couplings. |
| 71 | |
| 72 | The normalizations for the six-dimensional operators were chosen such that for |
| 73 | any new SM-like vertices the ratio of the new couplings to the SM couplings is |
| 74 | of the form $c_i\frac{m_t^2}{\Lambda^2}$. |
| 75 | |
| 76 | === Implementation and Validation === |
| 77 | |
| 78 | The implementation is a straightforward transcription of the Lagrangian into |
| 79 | `FeynRules` format as no new fields need to be defined. |
| 80 | |
| 81 | The model was validated using the build-in checks in `FeynRules` and |
| 82 | `MadGraph5`. Moreover the decay widths were confirmed through `MadGraph5` and |
| 83 | compared to the analytical results. |
| 84 | |