LHC-scale left-right symmetry and unification

We construct a comprehensive list of nonsupersymmetric standard model extensions with a low-scale left-right (LR)-symmetric intermediate stage that may be obtained as simple low-energy effective theories within a class of renormalizable $SO(10)$ grand unified theories. Unlike the traditional “minimal” LR models many of our example settings support a perfect gauge coupling unification even if the LR scale is in the LHC domain at a price of only (a few copies of) one or two types of extra fields pulled down to the TeV-scale ballpark. We discuss the main aspects of a potentially realistic model building conforming the basic constraints from the quark and lepton sector flavor structure, proton decay limits, etc. We pay special attention to the theoretical uncertainties related to the limited information about the underlying unified framework in the bottom-up approach, in particular, to their role in the possible extraction of the LR-breaking scale. We observe a general tendency for the models without new colored states in the TeV domain to be on the verge of incompatibility with the proton stability constraints.

Figure 1

Gauge coupling unification, including the 2-loop $\beta$-coefficients, for two “minimal” left-right models, to the left “mLR,” to the right “$\mathrm{m}\mathrm{\Omega }\mathrm{LR}$” model. For definition of the models and discussion see text.

Figure 2

Gauge coupling unification at 2-loop level (full lines) and 1-loop level (dashed lines), for two LR models with a low scale of LR breaking. The figure to the left has the field content $\mathrm{SM}+{\mathrm{\Phi }}_{1,2,2,0}+3{\mathrm{\Phi }}_{1,1,3,0}+2{\mathrm{\Phi }}_{1,1,3,-2}$, while the model to the right is defined as $\mathrm{SM}+2{\mathrm{\Psi }}_{3,1,1,-2/3}+2{\mathrm{\Phi }}_{1,2,1,1}+2{\mathrm{\Phi }}_{1,1,3,-2}$. For discussion see text.

Figure 3

Two example models for which correct unification is found for a low value of the scale $m_{\mathrm{LR}}$. The model to the left has a rather low unification scale, see text. Note that these are the same two models already shown in Fig. 2 in the introduction.

Figure 4

One-loop estimated proton lifetime for “colorless models” as a function of $m_{\mathrm{LR}}$. The figure shows $T_{1/2}$ [y] estimated from $m_G$ defined as the point where ${\alpha }_2={\alpha }_3$ with from top to bottom: $\mathrm{\Delta }(b_2^{\mathrm{LR}})=0$, $\frac{1}{6}$, $\frac{1}{3}$ and $\frac{1}{2}$ and $\mathrm{\Delta }(b_3^{\mathrm{LR}})=0$ (“colorless models”), see text. The horizontal line is the experimental limit from Super-K [37, 41].

Figure 5

Evolution of the gauge couplings for the sliding-LR model example discussed in the text based on split SUSY. The plot to the left shows $m_{\mathrm{LR}}=10\mathrm{TeV}$, while the plot to the right has $m_{\mathrm{LR}}={10}^{10}\mathrm{GeV}$.

Figure 6

Evolution of the inverse gauge couplings in the second example of sliding-LR models: $2{\mathrm{\Psi }}_{3,2,1,1/3}+2{\mathrm{\Psi }}_{3,1,1,2/3}+2{\mathrm{\Phi }}_{1,1,1,2}+4{\mathrm{\Phi }}_{1,1,3,-2}$. This example is non-SUSY and with a CKM explained by VLQs (class [ii]).

Figure 7

Contour plot of the ${\chi }^2$ distribution in the plane ($m_{\mathrm{LR}},T_{1/2}$) for the model: $\mathrm{SM}+{\mathrm{\Phi }}_{1,2,2,0}+3{\mathrm{\Phi }}_{1,1,3,0}+2{\mathrm{\Phi }}_{1,1,3,-2}$, using the four different approaches to estimate the theoretical error, defined in the text: Top row: (i) left and (ii) right, bottom row (iii) left and (iv) right. The cyan (blue, red) region corresponds to the allowed region at 68% (95% and $3–\sigma$) CL. In all four cases the model is ruled out by proton decay constraints at one sigma, but allowed at $2–\sigma$ CL. For further discussion see text.

Figure 8

Contour plot of the ${\chi }^2$ distribution in the plane ($m_{\mathrm{LR}},m_G$) for the model: $\mathrm{SM}+2{\mathrm{\Psi }}_{3,1,1,-2/3}+2{\mathrm{\Phi }}_{1,2,1,1}+2{\mathrm{\Phi }}_{1,1,3,-2}$, using the four different approaches to estimate the theoretical error, defined in the text: (i) left and (iv) right. Methods (ii) and (iii) lead to results similar to (i) and (iv), respectively, and are therefore not shown.

Figure 9

Allowed range cyan (blue, red) of $T_{1/2}$ (left) and $m_{\mathrm{LR}}$ (right) at 1-, 2- and 3-$\sigma$ CL as a function of the error in $\mathrm{\Delta }({\alpha }^{-1})$. The plot is for the model $\mathrm{SM}+{\mathrm{\Phi }}_{1,2,2,0}+3{\mathrm{\Phi }}_{1,1,3,0}+2{\mathrm{\Phi }}_{1,1,3,-2}$. The horizontal line in the left plot is the experimental lower limit [37, 41], while the vertical line at $\mathrm{\Delta }({\alpha }^{-1})=0.76$ corresponds to the estimated uncertainty in this model using method (i).