arXiv : A new $B$-flavour anomaly in $B_{d,s}\to K^{*0}\bar{K}^{*0}$: anatomy and interpretation

Algueró, Marcel; Crivellin, Andreas; Descotes-Genon, Sébastien; Matias, Joaquim; Novoa-Brunet, Martín

doi:10.1007/JHEP04(2021)066

Article
Report number	arXiv:2011.07867
Title	*A new $B$-flavour anomaly in $B_{d,s}\to K^{0}\bar{K}^{0}$: anatomy and interpretation*
Author(s)	Algueró, Marcel (Barcelona, IFAE ; BIST, Barcelona ; Barcelona, Autonoma U.) ; Crivellin, Andreas (CERN ; Zurich U. ; PSI, Villigen) ; Descotes-Genon, Sébastien (IJCLab, Orsay) ; Matias, Joaquim (Barcelona, IFAE ; BIST, Barcelona ; Barcelona, Autonoma U.) ; Novoa-Brunet, Martín (IJCLab, Orsay)
Publication	2021-04-08
Imprint	2020-11-16
Number of pages	26
Note	Final version to appear in JHEP. 25 pages, 5 figures
In:	JHEP 2104 (2021) 066
DOI	10.1007/JHEP04(2021)066
Subject category	hep-ph ; Particle Physics - Phenomenology
Abstract	In the context of the recently measured non-leptonic decays $B_{d}\to K^{0}\bar{K}^{0}$ and $B_{s}\to K^{0}\bar{K}^{0}$ we analyse the anatomy of the $L_{VV}$ observable that compares the longitudinal components of $B_s \to VV$ and $B_d \to VV$ decays. This observable is cleaner than the longitudinal polarisation fraction as it is afflicted only at subleading order in a $1/m_b$ expansion by the theoretical uncertainties arising in the transverse components entering the polarisation fraction. Focusing on the particular case of $B_{d}\to K^{0}\bar{K}^{0}$ and $B_{s}\to K^{0}\bar{K}^{0}$, we discuss the main sources of hadronic uncertainty in the SM. We find for the SM prediction $L_{K^\bar{K}^}=19.5^{+9.3}_{-6.8}$, which implies a $2.6\sigma$ tension with respect to the most recent data, pointing to a deficit in the $b \to s$ transition of the non-leptonic decay versus the corresponding $b \to d$ transition. We discuss possible New Physics explanations for this deviation, first at the level of the Weak Effective Theory and we identify that the two Wilson coefficients ${\cal C}_{4}$ and ${\cal C}_{8g}$ can play a central role in explaining this anomaly. Finally, we briefly explore two different simplified New Physics models which can explain the anomaly through a contribution either in ${\cal C}_4$ (Kaluza-Klein gluon) or in ${\cal C}_{8g}$, with a significant amount of fine tuning, but possible connections to the $b \to s \ell \ell$ anomalies.
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0)

$The tension between the theoretical prediction (blue) and the experimental value (orange) is reduced below $1\sigma$ for ${\cal C}^{\rm NP}_{4s}\simeq 0.25{\cal C}^{\rm SM}_{4s}$ (upper plot) or ${\cal C}^{\rm eff,NP}_{8gs}\simeq -{\cal C}^{\rm eff,SM}_{8gs}$ (lower plot). The predictions are given for ${\cal C}^{\rm NP}_{4s}$ and ${\cal C}^{\rm eff,NP}_{8gs}$ for a range corresponding to 100\% of their respective SM values. The plots for the remaining Wilson coefficients can be found in Appendix~\ref{app:plots}.$ $The tension between the theoretical prediction (blue) and the experimental value (orange) is reduced below $1\sigma$ for ${\cal C}^{\rm NP}_{4s}\simeq 0.25{\cal C}^{\rm SM}_{4s}$ (upper plot) or ${\cal C}^{\rm eff,NP}_{8gs}\simeq -{\cal C}^{\rm eff,SM}_{8gs}$ (lower plot). The predictions are given for ${\cal C}^{\rm NP}_{4s}$ and ${\cal C}^{\rm eff,NP}_{8gs}$ for a range corresponding to 100\% of their respective SM values. The plots for the remaining Wilson coefficients can be found in Appendix~\ref{app:plots}.$ $1$\sigma$ and $2\sigma$ CL regions from $L_{K^{*}\bar{K}^{*}}$ allowing NP contributions to both ${\cal C}_{4s}$ and ${\cal C}_{4d}$.$ Show more plots

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