Gauge Coupling Unification in Left–Right Symmetric Models

We explore possibilities of gauge coupling unification in left–right symmetric models with non–minimal particle content. In addition to unification we require the absence of anomalies and sufficient proton lifetime. Numerous previously unknown solutions are presented where unification occurs within the latest experimental errors. Solutions exist where the scale of left–right symmetry breaking can be as low as O(TeV ) or as high as the Planck scale. Email: [email protected] Email: [email protected] It is well known that gauge coupling unification is possible in the minimal left–right (LR) symmetric model [1] if the scale of LR symmetry breaking, MR, is chosen around 10 10 GeV (see e.g., [2]). Attempts to lower or rise MR sizably require a different, non–minimal particle content. Two possible directions for such changes which modify the β–functions (and thus gauge coupling unification) are: (i) supersymmetrization or (ii) new (“exotic”) fermionic and/or scalar representations. In the supersymmetric case a few solutions for gauge coupling unification with low MR are already known. Deshpande, Keith and Rizzo [3] investigated for example a SUSY–SO(10) scenario (which is supersymmetric both in the LR and the Standard Model sector) and found at two–loop level unification for MR = 1 TeV at the scale MX ≈ 10 16.2±0.4 GeV. Unfortunately this requires very high–dimensional SO(10) representations in the scalar sector. Two further solutions were recently presented by Ma, where the supersymmetric LR model is embedded into a larger supersymmetric gauge group: In one case [4] into the SUSY–SO(10) (with additional discrete symmetries) and SUSY– SO(10)⊗ SO(10), respectively, and in the other case [5] into the SUSY–E6. In both cases, however, new exotic fermions must be postulated in order to achieve gauge coupling unification for a low right–handed scale. We will discuss in this letter interesting solutions which emerge from new fermionic and scalar particles in left–right symmetric models even without supersymmetry. To our knowledge such solutions which achieve unification even with MR = O(TeV ) in non–supersymmetric left–right models were not published so far. Let us recall some attempts to modify the original minimal SU(5) embedding of the Standard Model where the proton life time, τP , and the weak mixing angle, sin (θW ), are too small. Frampton and Glashow [6] proposed originally to add a few chiral fermion multiplets in real representations with the same quantum numbers as the known quarks and leptons. In this way it was possible to increase τP and sin (θW ) by the necessary amounts. When more precise data became available Amaldi, de Boer, Frampton, Fürstenau, and Liu [8] repeated the analysis of the gauge coupling unification [7] for the Standard Model, the minimal supersymmetric Standard Model and an adequately modified SU(5) with exotic fermions and extra scalars. They investigated the running of gauge couplings for different combinations of new multiplets at the two–loop level where the contribution of exotic particles started at a common effective mass scale. This threshold scale was treated as a free parameter in the range of MZ ≤ Mthres ≤ 10 TeV. In this way they were able to find many unification solutions, even if they added only four multiplets. In all of these cases there is no contradiction with proton life time, and by using only real representations potential chiral anomalies are automatically avoided. Our aim is to perform a similar search for gauge coupling unification in the class of left– right symmetric models. We will therefore extend the minimal LR model and introduce new fermionic and scalar multiplets which we call “exotic”. The effects of these particles will be switched on at a common effective threshold which is essentially identical to the right handed scale MR. We calculate the relevant β–functions to one–loop order and restrict ourselves to cases where this is sufficient. We search only for gauge unification solutions with no specific