Left-Right Symmetry and Doubly Charged Higgs Bosons

ISUB =

341	$\ell_i \ell_j \to \H _L^{\pm\pm}$
342	$\ell_i \ell_j \to \H _R^{\pm\pm}$
343	$\ell_i \gamma \to \H _L^{\pm\pm} \mathrm{e}^{\mp}$
344	$\ell_i \gamma \to \H _R^{\pm\pm} \mathrm{e}^{\mp}$
345	$\ell_i \gamma \to \H _L^{\pm\pm} \mu^{\mp}$
346	$\ell_i \gamma \to \H _R^{\pm\pm} \mu^{\mp}$
347	$\ell_i \gamma \to \H _L^{\pm\pm} \tau^{\mp}$
348	$\ell_i \gamma \to \H _R^{\pm\pm} \tau^{\mp}$
349	$\mathrm{f}_i \overline{\mathrm{f}}_i \to \H _L^{++} \H _L^{--}$
350	$\mathrm{f}_i \overline{\mathrm{f}}_i \to \H _R^{++} \H _R^{--}$
351	$\mathrm{f}_i \mathrm{f}_j \to \mathrm{f}_k f_l \H _L^{\pm\pm}$ ( $\mathrm{W}\mathrm{W}$ fusion)
352	$\mathrm{f}_i \mathrm{f}_j \to \mathrm{f}_k f_l \H _R^{\pm\pm}$ ( $\mathrm{W}\mathrm{W}$ fusion)
353	$\mathrm{f}_i \overline{\mathrm{f}}_i \to \mathrm{Z}_R^0$
354	$\mathrm{f}_i \overline{\mathrm{f}}_i \to \mathrm{W}_R^{\pm}$

At current energies, the world is left-handed, i.e. the Standard Model contains an SU(2)$_L$ group. Left-right symmetry at some larger scale implies the need for an SU(2)$_R$ group. Thus the particle content is expanded by right-handed $\mathrm{Z}_R^0$ and $\mathrm{W}_R^{\pm}$ and right-handed neutrinos. The Higgs fields have to be in a triplet representation, leading to doubly-charged Higgs particles, one set for each of the two SU(2) groups. Also the number of neutral and singly-charged Higgs states is increased relative to the Standard Model, but a search for the lowest-lying states of this kind is no different from e.g. the freedom already accorded by the MSSM Higgs scenarios.

PYTHIA implements the scenario of [Hui97]. The expanded particle content with default masses is:

KF	name	$m$ (GeV)
9900012	$\nu_{R\mathrm{e}}$	500
9900014	$\nu_{R\mu}$	500
9900016	$\nu_{R\tau}$	500
9900023	$\mathrm{Z}_R^0$	1200
9900024	$\mathrm{W}_R^+$	750
9900041	$\H _L^{++}$	200
9900042	$\H _R^{++}$	200

The main decay modes implemented are $\H _L^{++} \to \mathrm{W}_L^+ \mathrm{W}_L^+, \ell_i^+ \ell_j^+$ ($i, j$ generation indices) and $\H _R^{++} \to \mathrm{W}_R^+ \mathrm{W}_R^+, \ell_i^+ \ell_j^+$. The physics parameters of the scenario are found in PARP(181) - PARP(192).

The $W_R^{\pm}$ has been implemented as a simple copy of the ordinary $\mathrm{W}^{\pm}$, with the exception that it couple to right-handed neutrinos instead of the ordinary left-handed ones. Thus the standard CKM matrix is used in the quark sector, and the same vector and axial coupling strengths, leaving only the mass as free parameter. The $\mathrm{Z}_R^0$ implementation (without interference with $\gamma$ or the ordinary $\mathrm{Z}^0$) allows decays both to left- and right-handed neutrinos, as well as other fermions, according to one specific model ansatz [Fer00]. Obviously both the $W_R^{\pm}$ and the $\mathrm{Z}_R^0$ descriptions are likely to be simplifications, but provide a starting point.

The right-handed neutrinos can be allowed to decay further [Riz81,Fer00]. Assuming them to have a mass below that of $\mathrm{W}_R^+$, they decay to three-body states via a virtual $\mathrm{W}_R^+$, $\nu_{R\ell} \to \ell^+ \mathrm{f}\overline{\mathrm{f}}'$ and $\nu_{R\ell} \to \ell^- \overline{\mathrm{f}}\mathrm{f}'$, where both choices are allowed owing to the Majorana character of the neutrinos. If there is a significant mass splitting, also sequential decays $\nu_{R\ell} \to \ell^{\pm} {\ell'}^{\mp} {\nu'}_{R\ell}$ are allowed. Currently the decays are isotropic in phase space. If the neutrino masses are close to or above the $\mathrm{W}_R$ ones, this description has to be substituted by a sequential decay via a real $\mathrm{W}_R$ (not implemented, but actually simpler to do than the one here).