The strong coupling, unification, and recent data

TL;DR

Unless higher-dimension operators are assumed to be suppressed, at present one cannot place strong constraints on the superheavy spectrum, and the prediction of strong coupling assuming (supersymmetric) coupling constant unification is reexamined.

Abstract

The prediction of the strong coupling assuming (supersymmetric) coupling constant unification is reexamined. We find, using the new electroweak data, $α_{s}(M_{Z}) \approx 0.129 \pm 0.010$. The implications of the large $α_{s}$ value are discussed. The role played by the $Z$ beauty width is stressed. It is also emphasized that high-energy (but not low-energy) corrections could significantly diminish the prediction. However, unless higher-dimension operators are assumed to be suppressed, at present one cannot place strong constraints on the super-heavy spectrum. Non-leading electroweak threshold corrections are also discussed.

Figures (4)

• Figure 1: MSSM evolution of $\alpha_{1,\,2}$ (solid lines) and of $\alpha_{3}$ (dashed lines) in the vicinity of the $\alpha_{1,\,2}$ unification point (the scale $M$ is in GeV). $\alpha_{s}(M_{Z})$ = 0.110, 0.115, 0.120, 0.125, 0.130; $m_{t}^{pole} = 160$ GeV; $\tan\beta = 4$; and $\Delta_{\alpha_{s}} = 0$.
• Figure 2: $M_{SUSY}$ as a function of the $\mu$ parameter. The different universal soft parameters and $\tan\beta$ are picked at random in the allowed parameter space (see text). $m_{t}^{pole} = 160$ GeV. $M_{SUSY} = M_{Z}$ is denoted for comparison. (All masses are in GeV.)
• Figure 3: Same as in Fig. 2 except a function of $\tan\beta$.
• Figure 4: The Z-pole weak angle and strong coupling are predicted as a function of the unification scale $M$. A given value of $s^2(M_{Z})$ corresponds to a fixed choice for $M$, e.g., $s^{2}(M_{Z})= 0.2359$ corresponds to $M = 10^{16}$ GeV. MSSM $\beta$-functions are assumed. Two-loop Yukawa corrections are taken into account assuming $m_{t}^{pole} = 160$ GeV and $\tan\beta = 4$. ($\Delta_{\alpha_{s}} = 0$.) $s^{2}(M_{Z}) = 0.2316 \pm 0.0003$ and $\alpha_{s}(M_{Z})= 0.12 \pm 0.01$ are indicated for comparison.