Impact on $L$-observables of a new combined analysis of $B_{d,s}\to K^{(*)}$ form factors

TL;DR

This work assesses how a new, combined analysis of $B_{d,s}\to K^{(*)}$ form factors—melding LCSRs with $B$-meson DAs and lattice QCD—affects optimized non-leptonic observables called $L$-observables, which compare $B_s$ and $B_d$ decay rates to reduce hadronic uncertainties. Using a BSZ $z$-expansion within a Bayesian framework, the authors provide machine-readable form-factor results and correlations, revealing substantial shifts in SM predictions for $L_{K^*\bar{K}^*}$ and $L_{K\bar{K}}$ depending on the input set, and they introduce two new observables, $\tilde{L}_{K^*}$ and $\tilde{L}_K$, to enhance experimental access and NP discrimination. The study shows that LCSR-only inputs yield predictions close to prior results with larger uncertainties, while the LCSR+LQCD combination dramatically changes central values and tightens uncertainties, increasing the tension for $L_{K^*\bar{K}^*}$ to about $4.4\sigma$ and reducing the tension for $L_{K\bar{K}}$ to $<1\sigma$. The authors also develop a U-spin framework to interpret these observables, demonstrate how the form-factor choice drives the size of U-spin breaking, and propose an enhancement mechanism for the new tilde observables under NP. Overall, the paper provides a comprehensive, correlation-aware assessment of SM and NP in $B_{d,s}\to K^{(*)}$-driven $L$-observables and offers practical, machine-readable inputs to the community for further phenomenological exploration.

Abstract

We explore the impact of a combined analysis of $B_{d,s}\to K^{(*)}$ form factors on a set of $L$-observables. The $L$-observables are constructed from ratios of branching fractions in $B_{s}\to VV,PP,PV$ versus $B_d \to VV,PP,PV$ decays with $P=K^0,\bar{K}^0$ and $V=K^{*0},\bar{K}^{*0}$, thereby partially reducing their hadronic uncertainties. We show the change of the Standard Model predictions of the $L$-observables under different determinations of the ratio of the relevant form factors (with correlations) including lattice QCD data and a novel light-cone sum rule analysis. In addition, we provide precise results for all $B_{d,s} \to K^{(*)}$ form factors in machine-readable files. We find that the inclusion of our up-to-date results, as well as the use or omission of lattice QCD data for the form factors, has a significant impact on the $L$-observables. We also discuss how the New Physics interpretation is affected by the updated form factors and present revised predictions for the mechanism identified in our analysis of $B \to VP$ decays, now employing more suitable new experimental observables defined in this paper.

Figures (4)

• Figure 1: Plot of the $f_0^{B_d\to K}$, $f_0^{B_s\to K}$, $A_0^{B_d\to K^*}$, $A_0^{B_s\to K^*}$ form factors as a function of $q^2$. The data points show the central values and associated uncertainties of our LCSR (see Subsection \ref{['sec:LCSR']}), HPQCD 2013 Bouchard:2013eph, FNAL/MILC 2015 Bailey:2015dka, HPQCD 2022 Parrott:2022rgu, HLMW2015 Horgan:2015vla, and FLAG2024 FLAG:2024oxs.
• Figure 2: Allowed regions for the relevant Wilson coefficient pairs ${\cal C}^{\rm NP}_{4d}-{\cal C}^{\rm NP}_{4s}$ (left) and ${\cal C}^{\rm NP}_{8gd}-{\cal C}^{\rm NP}_{8gs}$ (right) considering $L_{\bar{K}^*K^*}$ and $L_{KK}$ observables together with the constraints from the individual branching ratios using our previous set of form factors but updated $\lambda_{B_d}$ (top), the new LCSR only (mid) and combined LCSR+Lattice (bottom).
• Figure 3: $\tilde{L}_{K^{(*)}}$ observables as a function of the NP coefficients ${\cal C}^{\rm NP}_{4d,4s,8gd,8gs}$. The top row displays the variation of $\tilde{L}_{K^{(*)}}$ w.r.t ${\cal C}^{\rm NP}_{4d}$ for a fixed value of ${\cal C}^{\rm NP}_{4s}$ (left), and vice versa (right) corresponding to the form factor values provided in rows 3 and 6 of Table \ref{['tab:table6']} (Only LCSR case). The second row follows the same order corresponding to the same form factors, but for ${\cal C}^{\rm NP}_{8gd,s}$. The value at which the non-varying NP Wilson coefficient is fixed in each case is displayed in the label for the vertical axis, and is chosen from the hatched magenta regions in Fig. \ref{['fig:figallowed']}. Shaded regions correspond to the allowed values considering the constraints from the other observables for a fixed value of ${\cal C}^{\rm NP}_{4d,4s,8gd,8gs}$.
• Figure 4: $\tilde{L}_{K^{(*)}}$ observables as a function of the NP coefficients ${\cal C}^{\rm NP}_{4d,4s,8gd,8gs}$ using the LCSR+lattice determination. Same conventions as in Fig.\ref{['fig:fig3a']}.