diff --git a/draft.tex b/draft.tex index e7ef9c9..9769bb5 100644 --- a/draft.tex +++ b/draft.tex @@ -135,8 +135,15 @@ \begin{abstract} Rare semileptonic $b \to s \ell^+ \ell^-$ transitions provide some of the most promising framework to search for new physics effects. - Recent analyses have indicated an anomalous pattern in measurements of lepton-flavour-universality observables. - We propose a novel approach to independently and complementary clarify the nature of these effects + %Recent analyses have indicated an anomalous pattern in measurements + %of angulepton-flavour-universality observables. +Recent analyses of these decays have indicated an anomalous behaviour in measurements + of angular distributions of the decay $B^0\to + K^*\mu^+\mu^-$ and lepton-flavour-universality observables. +Unambiguously establishing if these deviations have a common nature + is of paramount importance in order to understand the observed pattern. + We propose a novel approach to independently and complementary + probe this hypothesis by performing a simultaneous amplitude analysis of $\bar{B}^0 \to \bar{K}^{*0} \mu^+\mu^-$ and $\bar{B}^0 \to \bar{K}^{*0} e^+e^-$ decays. This method enables the direct determination of observables that encode potential non-equal couplings of muons and electrons, @@ -146,7 +153,12 @@ %of the Wilson Coefficients ${\cal{C}}_{9}$ and ${\cal{C}}_{10}$ %between electrons and muons, and are found to be insensitive to non-perturbative QCD effects. - We show that considering the current preferred New Physics scenario a first observation of LFU breaking in a single measurement is possible with LHCb Run-II dataset. +%Our method combines the full information in $B^0\to K^*\ell^+\ell^-$ +%decays and, +If current hints of new physics are confirmed, our approach could +allow an early discovery of physics beyond the Standard +Model with LHCb Run-II datasets. +% We show that considering the current preferred New Physics scenario a first observation of LFU breaking in a single measurement is possible with LHCb Run-II dataset. \end{abstract} \maketitle @@ -296,9 +308,10 @@ The key feature of this strategy is to realise that all hadronic matrix elements are known to be lepton-flavour universal, and thus are shared among both semileptonic decays. This benefits from the large statistics available for $\bar{B}^0 \to \bar{K}^{*0} \mu^+\mu^-$ decays -that is sufficient to enable the determination of these multi-space parameters.\footnote{Note +that is sufficient to enable the determination of these multi-space +parameters. Note that an amplitude analysis of the electron mode only has been previously disregarded, -given the limited dataset foreseen in either LHCb or Belle-II experiments.} +given the limited dataset foreseen in either LHCb or Belle-II experiments. Therefore, in a common framework these hadronic contributions are treated as nuisance parameters, while only the Wilson coefficients $\widetilde{\WC}_9^{(\mu,e)}$ and $\widetilde{\WC}_{10}^{(\mu,e)}$ are kept separately for the two channels. @@ -455,7 +468,8 @@ in the electron mode; the size and asymmetry of such smearing is naively chosen to reproduce the mass fits of Ref.~\cite{Aaij:2017vbb}. Despite the low \qsq asymmetric tail, the determination of $\Delta\WC_9$ and -$\Delta\WC_{10}$ remains unbiased. +$\Delta\WC_{10}$ remains unbiased, even if no-correction is +applied. Moreover, the differential decay width can receive additional complex amplitudes from signal-like backgrounds, \textit{e.g.} $K\pi$ S-wave from a non-resonant decay and/or a scalar resonance (see detailed discussion in Ref.~\cite{Hurth:2017hxg}). These contributions are in general expected to be small~\cite{Aaij:2015oid,Aaij:2016flj}, @@ -483,19 +497,26 @@ % -In conclusion, we propose a clean, robust and model-independent method to combine +In conclusion, we propose a clean and model-independent method to combine all the available information from $\bar{B}\to \bar{K}^*\ell^+\ell^-$ decays for a precise determination of LFU-breaking differences of WCs, \textit{i.e.} $\Delta\WC_9$ and $\Delta\WC_{10}$. This relies on a shared parametrisation of the local (form-factors) and non-local ($\mathcal{H}_\lambda[z^n]$) hadronic matrix elements between the muonic and electronic channels, -that in turn enables the determination of the observables of interest free from any theoretical uncertainty. +that in turn enables the determination of the observables of interest +free from any theoretical uncertainty. +In addition, this simultaneous analysis is more robust against +experimental effects such +as mismodeling of the detector resolution, since most parameters are +effectively determined from the muon mode. This would be an important +benefit for LHCb where the electron resolution is significantly worse +than that of muons. Figure~\ref{fig:allComponents} illustrates the usefulness of the newly-proposed observables by combining the different information from angular analysis to branching ratio measurements. Due to the inclusiveness of the approach, the expected sensitivity surpasses any of the projections for the foreseen measurements of \textit{e.g.} $R_{K^{*}}$ or $P^{\prime}_{5}$ alone - given the benchmark points. %of projection for the current anomalous measurements alone given the benchmark points. -Therefore, this novel formalism can be the most immediate method to observe unambigously +Therefore, this novel formalism can be the most immediate method to observe unambiguously NP in $\bar{B}\to \bar{K}^*\ell^+\ell^-$ decays. A promising feature of this framework is the possibility to extend the analysis to