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 | | |