diff --git a/draft.tex b/draft.tex index c420e54..6cdf57d 100644 --- a/draft.tex +++ b/draft.tex @@ -308,7 +308,8 @@ %$\WC_9^{(\mu)} = -\WC_{10}^{(\mu)} = - 0.7$, referred to as \texttt{BMP}$_{\WC_9}$ and \texttt{BMP}$_{\WC_{9,10}}$, respectively. These points are favoured by several global fit -analyses with similar significance~\cite{Capdevila:2017bsm,Altmannshofer:2017yso,Hurth:2017hxg}. +analyses with similar significance~\cite{Capdevila:2017bsm,Altmannshofer:2017yso,Hurth:2017hxg}, +but chosen with reduced SM tension in order to examine a more conservative hypothesis. An extended unbinned maximum likelihood fit is performed to these simulated samples, in which multivariate Gaussian terms are added to the likelihood to incorporate prior knowledge @@ -456,36 +457,38 @@ % In conclusion, we propose a clean, robust 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 $\Delta\WC_9$ -and $\Delta\WC_{10}$, independent on any theoretical uncertainties. +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 ($\mathcal{H}_\lambda[q^2]$) +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. 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 projection for the current anomalous measurements alone given the benchmark points. +Therefore, this novel formalism can be the \textit{holy grail} to observe +NP in $\bar{B}\to \bar{K}^*\ell^+\ell^-$ decays in near future. -% -%the contribution of all the single constituents of -%the analysis and how the proposed method takes advantage of the complete description -%of the decay. -% A promising feature of this framework is the possibility to extend the analysis to include other decay channels involving flavour changing neutral currents. -For instance, the charged decay $B^+ \to K^{*+} \ellell$ underlies the same physics as -the examined neutral mode and is easily accessible at the $B$-factories, while other rare -semileptonic decays as the $B^+ \to K^+ \ellell$ presents a different phenomenology but -guarantees access to the same NP information by mean of the description in term of WCs. -Thus, a global simultaneous fit to all data involving $b \to s \ell^+ \ell^-$ transitions -would provide an historical comprehension of the underling physics. -Secondly, the parameter space of the investigated WCs can naturally be broadened to -incorporate direct measurement of the right-handed $\WC_i'$, currently only weakly -determined by global fits~\cite{Capdevila:2017bsm,Altmannshofer:2017yso,Hurth:2017hxg}, -and of possible phases in the WCs - appearing as $\Im \WC_i$ - by mean of a separate -analysis of the two opposite charge-conjugated modes. +For instance, the charged decay $B^+ \to K^{*+} \ellell$ undergoes the same physics +and is easily accessible at the $B$-factories, while other rare +semi-leptonic decays such as $B^+ \to K^+ \ellell$ and $\Lambda_{b} \to \Lambda^{(*)} \ell^+\ell^-$ +have a different phenomenology but access the same NP information in terms of WC description. +Thus, an unbinned global simultaneous fit to all data involving $b \to s \ell^+ \ell^-$ transitions +is a natural and appealing extension of this work. +Moreover, the parameter space of the investigated WCs can also be broadened to +incorporate direct measurement of the right-handed $\WC_i^{\prime}$ - +currently weakly constrained by global fits~\cite{Capdevila:2017bsm,Altmannshofer:2017yso,Hurth:2017hxg}. +%and of possible phases in the WCs - appearing as $\Im \WC_i$ - by mean of a separate +%analysis of the two opposite charge-conjugated modes. % \begin{figure}[b] \includegraphics[width=.4\textwidth]{plots/B2Kstll_summary.pdf} \caption{% - Sensitivity to the NP$_{\WC_9-\WC_{10}}$ scenario for the expected statistics after the \lhcb RunII. - The relative contribution ($1,\,2,\,3\,\sigma$ contours) of each step of the analysis is shown in different colors, together with the - result of full amplitude method proposed in this letter. + Sensitivity to \texttt{BMP}$_{\WC_{9,10}}$ scenario for the expected statistics after the \lhcb Run II. + The relative contribution ($1,\,2,\,3\,\sigma$ contours) of each step of the analysis is shown in different colours, + together with the result of full amplitude method proposed in this letter. \label{fig:allComponents} } \end{figure} @@ -503,10 +506,10 @@ \section{Supplemental material} -In this supplemental material we show an extension of the physics case of the proposed method -and investigate the sensitivity to the right-handed Wilson coefficients $\WC'^{(\mu)}_9$ and -$\WC'^{(\mu)}_{10}$. -We assume the primed WCs to be fixed at 0 (SM) for the electron mode and let free-floating the +An extension of the physics case of the proposed method +is to investigate the sensitivity to the chirality-flipped counterparts of the usual Wilson coefficients, +\textit{i.e.} $\WC'^{(\mu)}_9$ and $\WC'^{(\mu)}_{10}$. +We assume the primed WCs to be fixed to the SM value for electrons mode and let free-floating the muon channel. In the following, we consider different NP scenarios concerning the $\WC'^{(\mu)}_i$, while $\WC^{(\mu,e)}_i$ are set as for \texttt{BMP}$_{\WC_{9,10}}$. diff --git a/references.bib b/references.bib index d3fc2d1..258e6f8 100644 --- a/references.bib +++ b/references.bib @@ -593,3 +593,15 @@ reportNumber = "CERN-EP-2016-141, LHCB-PAPER-2016-012", SLACcitation = "%%CITATION = ARXIV:1606.04731;%%" } +@article{Albrecht:2017odf, + author = "Albrecht, Johannes and Bernlochner, Florian and Kenzie, + Matthew and Reichert, Stefanie and Straub, David and + Tully, Alison", + title = "{Future prospects for exploring present day anomalies in + flavour physics measurements with Belle II and LHCb}", + year = "2017", + eprint = "1709.10308", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + SLACcitation = "%%CITATION = ARXIV:1709.10308;%%" +}