Changes between Version 7 and Version 8 of EffLRSM


Ignore:
Timestamp:
Oct 30, 2016, 11:15:24 PM (8 years ago)
Author:
Richard Ruiz
Comment:

Grammar edits and Notes formatting. Ready for public.

Legend:

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  • EffLRSM

    v7 v8  
    1818\begin{equation}
    1919\mathcal{L} = \mathcal{L}_{\rm SM} + \mathcal{L}_{\rm LRSM~Kin.} + \mathcal{L}_{\rm LRSM~Int.}
     20\nonumber
    2021\end{equation}
    2122}}}
    … …  
    2425#!latex
    2526\begin{equation}
    26 \mathcal{L}_{\rm LRSM~Kin.} \ni \frac{1}{2}\overline{N_k} i\!\not\!\partial N_k - \frac{1}{2}m_{N_k} \overline{N_k}N_k, \quad k=1,\dots,3,
     27\mathcal{L}_{\rm LRSM~Kin.} \ni \frac{1}{2}\overline{N_k} i\!\not\!\partial N_k - \frac{1}{2}m_{N_k} \overline{N_k}N_k, \quad k=1,\dots,3.
     28\nonumber
    2729\end{equation}
    2830}}}
    … …  
    3436\mathcal{L}_{Z_R-f-f}
    3537\end{equation}
     38\nonumber
    3639}}}
    3740The W,,R,, chiral coupling to quarks are
    … …  
    4043\begin{equation}
    4144 \mathcal{L}_{W_R-q-q'} = \frac{-\kappa_R^q g}{\sqrt{2}}\sum_{i,j=u,d,\dots}\overline{u}_i V_{ij}^{\rm CKM'}~W_{R \mu}^+ \gamma^\mu P_R~ d_j + \text{H.c.}
     45\nonumber
    4246\end{equation}
    4347}}}
    44 V,,ij,,^CKM'^ is the right-handed (RH) Cabbibo-Kobayashi-Masakawa (CKM) matrix, which is related to the SM CKM matrix. g=\sqrt{4\pi\alpha_{\rm EM}(M_Z)}/\sin\theta_W is the SM Weak coupling constant and
     48V,,ij,,^CKM'^ is the right-handed (RH) Cabbibo-Kobayashi-Masakawa (CKM) matrix and is related to the SM CKM matrix. g=\sqrt{4\pi\alpha_{\rm EM}(M_Z)}/\sin\theta_W is the SM Weak coupling constant and
    4549k,,R,,^q^ is an overall normalization for the W,,R,, interaction strength.
    4650For leptons, the W,,R,, coupling and leptonic mixing is parametrized by
    47 [ [#Atre 3], [#Han 4] ], .
    48 ~\cite{Atre:2009rg,Han:2012vk}
     51[ [#Atre 3], [#Han 4] ],
    4952{{{
    5053#!latex
    … …  
    5457 \sum_{m'=1}^3  \overline{N_{m'}} Y_{\ell m'}
    5558~W_{R \mu}^+ \gamma^\mu P_R~ \ell^-+\text{H.c.}
     59\nonumber
    5660\end{equation}
    5761}}}
    … …  
    6266 \mathcal{L}_{Z_R-f-f} = \frac{-\kappa_{R}^f g}{\sqrt{1 - \left(1/\kappa_{R}^f\right)^2 \tan^2\theta_W}}\sum_{f=u,e,\dots}
    6367 \overline{f} Z_{R \mu} \gamma^\mu \left(g_{L}^{Z_R,f}P_L + g_{R}^{Z_R,f}P_R\right)f.
     68\nonumber
    6469\end{equation}
    6570}}}
    … …  
    96101
    97102== Notes ==
    98 
     103 * '''Important''': Default parameters are set so "out-of-the-box" checks can be made with [ [#Mattelaer 1] ] and [ [#Mitra 2] ].
    99104
    100105 * Aside from the SM inputs, this model contains 28 free parameters:
    … …  
    103108  * Nine real (no CP violation) mixing parameters for RH quark mixing: VCKMR[u,d] for ''u'' = ''up (1), charm (2), top (3)'' and ''d'' = ''down (1), strange (2), bottom (3)''. Default values are VCKMR = Identity(3x3), i.e., VCKMR[1,1] = VCKMR[2,2] = VCKMR[3,3] = 1 and all others zero.
    104109  * Nine real (no CP violation) mixing parameters for RH leptonic mixing: YlN[l,N] for ''l'' = ''e (1), mu (2), tau (3)'' and ''N = N1 (1), N2 (2), N3 (3).'' Default values are YlN = Identity(3x3), i.e., YlN[1,1] = YlN[2,2] YlN[3,3] and all others zero.
     110 
     111 * Default model settings assumes five massless quarks, massless light neutrinos, and massless charged leptons. This is easily modifiable by regenerating UFO files.
    105112
    106  * '''Important''': Default parameters are set so "out-of-the-box" checks can be made with [ [#Mattelaer 1] ] and [ [#Mitra 2] ].
    107113
    108114