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)
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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.