## Resonances gone topsy turvy – the charm of QCD or new physics in b -> s l+l-?

Preprint number: CP3-Origins-2014-21 DNRF90 and DIAS-2014-21
Authors: Lyon James (Edinburgh University) and Roman Zwicky (CP3-Origins & DIAS)
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 $$C^{eff}_9 + C^{‘ eff}_9$$. We devise strategies to investigate the microscopic structure in future measurements. We show that the charm-resonance effects can accommodate the $$B \to K^* ll$$-anomalies (e.g. $$P_5’$$). Hence our findings indicate that the interpretation of the anomaly through a $$Z’$$-boson, mediating between $$bs$$ and $$ll$$ fields, is disfavoured. More generally our results motivate investigations into $$b \to s\bar cc$$-physics.