Changes between Version 3 and Version 4 of topBSM


Ignore:
Timestamp:
Sep 3, 2013 9:19:53 PM (5 years ago)
Author:
stefankrastanov
Comment:

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  • topBSM

    v3 v4  
    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 
    851== Beyond-SM Operators with the Top Quark ==
    862