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 lefthanded, 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 righthanded $\mathrm{Z}_R^0$ and $\mathrm{W}_R^{\pm}$ and righthanded 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 righthanded neutrinos instead of the ordinary lefthanded 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 righthanded 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 righthanded 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).