Changes between Version 6 and Version 7 of anomalyfreeZprime


Ignore:
Timestamp:
06/05/20 16:22:19 (4 months ago)
Author:
martinbauer
Comment:

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  • anomalyfreeZprime

    v6 v7  
    2727between the lepton and baryon numbers
    2828
     29The $Z'$ couplings to currents of SM fermionsare given by:[[BR]]
     30
     31{{{#!latex
     32\begin{alignat}{9}
     33\mathcal{L}_\text{fermion} = -g_{Z'} j'_\mu & {Z'}^\mu \notag \\
     34j'_\mu&= 0 \qquad && U(1)_X \notag  \\
     35j'_\mu&= \bar L_i \gamma_\mu L_i
     36          + \bar \ell_i\gamma_\mu \ell_i
     37          - \bar L_j \gamma_\mu L_j -\bar\ell_j\gamma_\mu \ell_j
     38            \qquad && U(1)_{L_i-L_j} \notag \\
     39j'_\mu&=  \frac{1}{3}\bar Q \gamma_\mu Q
     40          + \frac{1}{3}\bar u_R\gamma_\mu u_R
     41          + \frac{1}{3}\bar d_R\gamma_\mu d_R
     42          - \bar L \gamma_\mu L
     43          + \bar \ell\gamma_\mu \ell
     44            \qquad && U(1)_{B-L} \; ,
     45\end{alignat}
     46}}}
     47
     48where $g_{Z'}$ denotes the dark gauge coupling.  The different
     49coupling structures shown above can be understood in terms of a flavor
     50structure of a dark gauge coupling matrix.
     51
     52The fermion current structure can be
     53generalized to include the dark matter current. To couple to the gauge
     54mediator the dark matter fermion has to be a Dirac fermion. To avoid
     55new anomalies, the dark matter candidate cannot be chiral and its
     56charges under the new gauge group are $q_{\chi_L}=q_{\chi_R}$. This
     57defines a dark fermion Lagrangian with a vector mass term
     58
     59
     60{{{#!latex
     61\begin{align*}
     62\mathcal{L}_\text{DM}= i \bar \chi \not{D} \chi - m_\chi \bar \chi \chi \; ,
     63\end{align*}
     64}}}
     65
     66with the covariant derivative of the SM-singlet fermion
     67{{{#!latex
     68$D_\mu=\partial_\mu -ig_{Z'} q_\chi \hat Z'_\mu$.
     69}}}
     70
     71In all cases, the kinetic term for the $U(1)$ gauge bosons is not canonically normalized
     72
    2973{{{#!latex
    3074$\mbox{Var}[\tau(X_p,X_d)]=\mbox{Var}[E(\tau(X_p,X_d)|X_p)]+E[\mbox{Var}(\tau(X_p,X_d)|X_p)]$
    3175}}}
     76