Changes between Version 4 and Version 5 of EffLRSM


Ignore:
Timestamp:
Oct 30, 2016, 10:15:58 PM (8 years ago)
Author:
Richard Ruiz
Comment:

In-progress update of Lagrangian

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  • EffLRSM

    v4 v5  
    1919
    2020== Model Description ==
    21 This effective model extends the Standard Model (SM) field content by introducing heavy Left-Right symmetric gauge bosons W,,R,,^+-^, Z,,R,, with masses M,,WR,, and M,,ZR,,, as well as three heavy Majorana neutrinos N,,i,, with mass m,,Ni,,.
     21This effective model extends the Standard Model (SM) field content by introducing heavy Left-Right symmetric gauge bosons W,,R,,^+/-^, Z,,R,, with masses M,,WR,, and M,,ZR,,, as well as three heavy Majorana neutrinos N,,i,, with mass m,,Ni,,. The Lagrangian is given by,
    2222
    2323{{{
    2424#!latex
    2525\begin{equation}
    26 \mathcal{L} = \mathcal{L}_{\rm SM} + \mathcal{L}_{N} + \mathcal{L}_{N~\text{Int.}}
     26\mathcal{L} = \mathcal{L}_{\rm SM} + \mathcal{L}_{\rm LRSM~Kin.} + \mathcal{L}_{\rm LRSM~Int.}
    2727\end{equation}
    2828}}}
    … …  
    3131#!latex
    3232\begin{equation}
    33 \mathcal{L}_{N} = \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,
     33\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,
     34\end{equation}
     35}}}
     36The W,,R,,, Z,,R,,, couplings to fermions is separated into three pieces:
     37{{{
     38#!latex
     39\begin{equation}
     40\mathcal{L}_{\rm LRSM~Int.} = \mathcal{L}_{W_R-q-q'} + \mathcal{L}_{W_R-\ell-\nu/N} +
     41\mathcal{L}_{Z_R-f-f}
     42\end{equation}
     43}}}
     44The W,,R,, chiral coupling to quarks are
     45{{{
     46#!latex
     47\begin{equation}
     48 \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.}
     49\end{equation}
     50}}}
     51V^^CKM'^^ is the RH Cabbibo-Kobayashi-Masakawa (CKM) matrix, which is related to the SM CKM matrix.
     52g=\sqrt{4\pi\alpha_{\rm EM}(M_Z)}/\sin\theta_W is the SM Weak coupling constant and
     53\kappa_{R}^^{q}^^ is an overall real normalization for the W,,R,, interaction strength.
     54For leptons, the W,,R,, coupling and leptonic mixing is parametrized by~\cite{Atre:2009rg,Han:2012vk}
     55{{{
     56#!latex
     57\begin{equation}
     58 \mathcal{L}_{W_R-\ell-\nu/N} = \frac{-\kappa_R^\ell g}{\sqrt{2}}
     59 \sum_{\ell=e,\mu,\tau}
     60 \sum_{m'=1}^3  \overline{N_{m'}} Y_{\ell m'}
     61~W_{R \mu}^+ \gamma^\mu P_R~ \ell^-+\text{H.c.}
     62\end{equation}
     63}}}
     64For chiral fermion $f$, we parametrize the $\ZR$ neutral currents by
     65{{{
     66#!latex
     67\begin{equation}
     68 \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}
     69 \overline{f} Z_{R \mu} \gamma^\mu \left(g_{L}^{Z_R,f}P_L + g_{R}^{Z_R,f}P_R\right)f.
     70\end{equation}
     71}}}
     72$\kappa_{R}^{f}$ are the same $\kappa_{R}^{q,\ell}$ as for $\WR$.
     73In terms of electric and isospin charges, the chiral coefficients are
     74{{{
     75#!latex
     76\begin{equation}
     77c
    3478\end{equation}
    3579}}}
    3680
    37 and its interactions with the Weak gauge and Higgs bosons are given by
    38 {{{
    39 #!latex
    40 \begin{eqnarray}
    41 \mathcal{L}_{N~\text{Int}} =
    42 &-&\frac{g}{\sqrt{2}} W_{\mu}^{+}\sum_{k=1}^{3}\sum_{\ell=e}^{\tau} \overline{N_k}V_{\ell k}^{*}\gamma^{\mu}P_{L}\ell^{-}
    43 +{\rm H.c.}
    44 \\
    45 &-&\frac{g}{2\cos\theta_W}Z_{\mu}\sum_{k=1}^{3}\sum_{\ell=e}^{\tau} \overline{N_k}V_{\ell k}^{*}\gamma^{\mu}P_{L}\nu_\ell
    46 +{\rm H.c.}
    47 \\
    48 &-&\frac{g m_N}{2 M_W}         h \sum_{k=1}^{3}\sum_{\ell=e}^{\tau} \overline{N_k}V_{\ell k}^{*}P_{L}\nu_\ell
    49 +{\rm H.c.}
    50 \end{eqnarray}
    51 }}}
     81
     82
     83
    5284
    5385
    … …  
    108140[=#Mitra] [2] M. Mitra, D. Scott, and M. Spannowsky,
    109141''Neutrino Jets from High-Mass W,,R,, Gauge Bosons in TeV-Scale Left-Right Symmetric Models'', arXiv:1607.03504 [hep-ph]
     142
     143
     144[=#Atre] [3] A. Atre, T. Han, S. Pascoli and B. Zhang, ''The Search for Heavy Majorana Neutrinos,'' JHEP '''0905''', 030 (2009),  arXiv:0901.3589 [hep-ph]
     145
     146
     147[=#Han] [3] T. Han, I. Lewis, R. Ruiz, Z.-G. Si, ''Lepton Number Violation and W' Chiral Couplings at the LHC,'' PRD87, 035011 (2013)