Tensor-current contributions to B Anomalies

TL;DR

This work assesses whether tensor-current operators $C_T$ and $C_{T5}$ can explain the $B$-meson anomalies within a model-independent EFT for $b\to s\ell^+\ell^-$. By incorporating the full $q^2$ range and updating form factors, the authors perform Bayesian global fits under five LFU NP scenarios, ranging from tensor-only to a full 14-parameter framework. The main finding is that tensor currents provide only mild adjustments and do not lift the tension in $\Delta C_9$; the best-fit tensor effects remain small with $|C_T|,|C_{T5}|$ around $0.02-0.03$, and a strong 95% CL bound $F(x,y)|^{\text{S-I}}_{x=\Delta C_T,y=\Delta C_{T5}}\le 0.003$ is derived. The study reinforces that the observed $C_9$ anomaly likely requires more than tensor contributions and offers stringent constraints to guide future leptoquark/GUT-based model building.

Abstract

Tensor-current operators, potentially generated by scalar leptoquarks in grand unified theories (GUTs), are among the plausible new physics (NP) candidates suggested by the anomalies observed in $B$-meson decays. As experimental data continue to accumulate, exploring this possibility remains timely and well motivated. In this work, we present a systematic analysis of representative tensor-current Wilson coefficients ($C_T, C_{T5}$) in $b \to s \ell^+ \ell^-$ transitions. By incorporating contributions from the high-$q^2$ region, our framework fully exploits the available experimental data across the entire $q^2$ range. Within this setup, five distinct lepton-flavor-universal (LFU) scenarios are proposed and tested through global fits. Our results show that it is difficult to resolve the tension between experimental measurements and theoretical predictions using only $C_T$ and $C_{T5}$. Meanwhile, the significance of $ΔC_9$ remains essentially unchanged, even in the presence of tensor contributions. In one representative scenario (S-III), we obtain $[C_9,C_{10}, C_T, C_{T5}] \simeq [-1.05,\,0.22,\,0.02,\,0.01]$, with a reduced chi-squared statistic $\tildeχ^2 \equiv χ^2_{\rm min}/{\rm d.o.f.} = 708.7/486 = 1.46$. Furthermore, we derive a stringent 95$\%$ C.L. constraint on tensor operators, $$ F(x,y)\Big|^{\text{S-I}}_{x=ΔC_T,\,y=ΔC_{T5}} = x^2 + 0.063\,xy + 0.989\,y^2 + 0.034\,x + 0.043\,y \leq 0.003, $$ which provides one of the strongest bounds to date on $C_T$ and $C_{T5}$.

Figures (3)

• Figure 1: Plots of the confidence region of $C_T$ and $C_{T5}$ under the terms of scenario I. Panels on the diagonal denote their own density (black steps), where the darker steps represent the full-$q^2$ data, and the others are from both low-$q^2$ and high-$q^2$. The panel in the lower left corner of the diagonal represents the correlations between $C_T$ and $C_{T5}$ and preferred regions. The other description is detailed in the \ref{['app:sup_materials']} for reference.
• Figure 2: Constraints on the Wilson coefficients $C_{T}$ and $C_{T5}$. The panel on the left provides the comparison of other works prior to the 2022-$R_{K^{(\ast)}}$ release and our this analysis. The right panel presents a zoomed-in image, exclusively depicting the boundary points of 95% C.L. and elliptic curves in S-I (solid blue) as well as S-III (dashed purple).
• Figure 3: Complete plots of the confidence regions of various WCs under different scenarios settings (S-II to S-V), represented by subplots (a to d). The diagonal panels in each subplot contain the density depicted by steps, KDE in a blue curve, and two red dot-dashed lines indicating the boundary of the region at 68% C.L. The panels in the lower left corner of the diagonal represent the correlations and preferred regions, where those regions using the full data are highlighted in a darker color. The other plotting conventions are the same as the settings in \ref{['fig:lfus1']}.