TeV-scale scalar leptoquarks motivated by B anomalies improve Yukawa unification in SO(10) GUT

TL;DR

This work tackles the tension in minimal SO(10) GUTs between Yukawa unification and observed fermion masses by embedding TeV-scale scalar leptoquarks from the 126_H representation. The TeV LQs modify the RG evolution of the third-generation Yukawa couplings, enabling successful $b$-$\tau$ unification at $M_{ ext{GUT}}$ with only two inputs, $y_t(M_{ ext{GUT}})$ and $\tan\beta$. The LQ-fermion couplings exhibit infrared fixed-point behavior, yielding order-one couplings at the TeV scale compatible with explaining the $B$-anomaly data, while flavor-violating effects can be generated RG-amplified from tiny UV seeds. The framework suggests a UV-complete pathway linking TeV-scale LQ phenomenology to grand unification, and points to further work on including light colored states to enhance mixing and refine gauge coupling unification.

Abstract

It is common practice to explain deviations between data and Standard-Model (SM) predictions by postulating new particles at the TeV scale ad-hoc. This approach becomes much more convincing, if one successfully embeds the postulated particles into a UV completion which addresses other conceptual or phenomenological shortcomings of the SM. We present a study of an SO(10) grand unified theory which contains scalar leptoquark fields employed to explain the ``flavour anomalies'' in $b\rightarrow s$ and $b\rightarrow c$ decays. We find that the additional degrees of freedom improve the renormalization-group (RG) evolution of the SM parameters. In particular, the light leptoquarks modify the RG evolution of the Yukawa couplings such that successful bottom-tau unification becomes possible in a minimal SO(10) GUT with only a $126$-plet coupling to fermions. If we amend the Yukawa interaction of the minimal one-generation model with a second fermion multiplet and small flavor-violating terms, we find the flavour violation in the leptoquark couplings growing with the RG evolution while it stays small in the Yukawa interaction of the SM Higgs boson. By employing mass splittings among the members of the $126$-plet one can increase the effect and obtain large flavor violation in leptoquark couplings from tiny perturbations at the GUT scale, because the flavour-conserving limit is an unstable initial condition for the RG equations.

Figures (6)

• Figure 1: The small solid ellipse represents the landscape of minimal SO(10), which is a SM-like theory. The red star marks the SM itself. It is not consistent with the minimal theory and therefore lies in the GUT swampland (shown with the large solid ellipse). The dashed ellipse illustrates the reshaped landscape induced by TeV-scale LQs, within which the SM is now included.
• Figure 2: RG evolution of the third-generation charged fermions masses from $10^2$ to $10^{16}$ GeV. The solid (dotted) lines indicate the scenario with (without) LQs at TeV scale. We fix $y_t(M_{\text{GUT}})=0.56$ to get the correct value of $m_t$ and Yukawa unification implies $\tan\beta=42$. The gray vertical lines indicate $M_{\text{GUT}}$ and the light LQ threshold.
• Figure 3: RG evolution of the LQ-fermion coupling $y_1,y_2$ and $y_3$ (green, red, and blue, respectively) from $10^2$ to $10^{16}$ GeV. The right panel shows the scenario without $\widetilde{S}_1$ in the light spectrum, with $y_t(M_{\text{GUT}} )=0.62$. All other parameters are as in Figure \ref{['S3R2']}.
• Figure 4: Feynman diagrams illustrating the LQ contributions to the running of $y_b$ and $(\epsilon^{bs}y_b)$. The self-energy correction to $Q_L^3$, arising from $S_3$, is universal to both $y_b$ and $(\epsilon^{bs}y_b)$. $\widetilde{S}_1$ and $\widetilde{R}_2$ couple to $b_R$ only so only contribute to $y_b$. $s_R$ receives no self-energy corrections.
• Figure 5: RG evolution of $\epsilon^{bs}$ with $y_t(M_{\text{GUT}})=0.58$. The dashed line lies in the region where the Yukawa couplings become non-perturbative and thus may not reflect the physical reality.