Resonances gone topsy turvy - the charm of QCD or new physics in $b\to s{\ell }^{+}{\ell }^{-}$?

Abstract

We investigate the interference pattern of the charm-resonances $\Psi (3370,4040,4160,4415)$ with the electroweak penguin operator $O_9$ in the branching fraction of $B^{+}\to K^{+}\mu \mu$. For this purpose we extract the charm vacuum polarisation via a standard dispersion relation from BESII-data on $e^{+}{e}^{-}\to hadrons$. In the factorisation approximation (FA) the vacuum polarisation describes the interference fully non-perturbatively. The observed interference pattern by the LHCb collaboration is opposite in sign and and significantly enhanced as compared to the FA. A change of the FA-result by a factor of -2.5, which correspond to a 350%-corrections, results in a reasonable agreement with the data. This raises the question on the size of non-factorisable corrections which are colour enhanced but loop-suppressed. In the parton picture it is found that the corrections are of relative size ~-0.5 when averaged over the open charm-region which is far below -3.5 needed to explain the observed effect. We present combined fits to the BESII- and the LHCb-data, testing for effects beyond the Standard Model (SM)-FA. We cannot find any significant evidence of the parton estimate being too small due to cancellations between the individual resonances. It seems difficult to accommodate the LHCb-result in the standard treatment of the SM or QCD respectively. In the SM the effect can be described in a $q^2$-dependent shift of the Wilson coefficient combination $C_9^{eff}+C_9^{{}^{\prime }eff}$. We devise strategies to investigate the microscopic structure in future measurements. We show that the charm-resonance effects can accommodate the $B\to K^{\ast }ll$-anomalies (e.g. $P_5^{\prime }$). Hence our findings indicate that the interpretation of the anomaly through a $Z^{\prime }$-boson, mediating between $bs$ and $ll$ fields, is disfavoured. More generally our results motivate investigations into $b\to s\bar{c}c$-physics.

arXiv comment28 pp, 13 figures, 5 tables

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