diff --git a/draft.tex b/draft.tex index e4ca6b3..a4c07a8 100644 --- a/draft.tex +++ b/draft.tex @@ -175,7 +175,7 @@ $\bar{B}^{0} \to \bar{K}^{*0} \mu^{+}\mu^{-}$ has been recently reported~\cite{Aaij:2015oid,Wehle:2016yoi,Aaij:2013aln,Aaij:2014pli}, %notably in one of the observables with reduced form-factor uncertainties, notably in one of the observables with reduced theoretical uncertainties, -$P^{\prime}_{5}$~\cite{Descotes-Genon:2015uva}. +$P^{\prime}_{5}$~\cite{Aaij:2013qta,Descotes-Genon:2015uva}. Several models have been suggested in order to interpret these results as new physics (NP) signatures~\cite{Gauld:2013qja,Buras:2013qja,Altmannshofer:2013foa,Crivellin:2015era,Hiller:2014yaa,Biswas:2014gga,Gripaios:2014tna}. Nonetheless, the vector-like nature of this pattern could be also explained by @@ -194,12 +194,15 @@ The formalism of {\textit{b}} decays is commonly described within an effective field theory~\cite{Altmannshofer:2008dz}, which probes distinct energy scales; -with regimes classified into short-distance perturbative\footnote{ -At short-distance (high energies) quarks interact weakly, being considered in an asymptotic freedom, which -allows a pertubative calculation~\cite{PhysRevD.8.3633,Politzer:1974fr,Gross:1998jx}.} +with regimes classified into short-distance (high energies) perturbative +%\footnote{At short-distance (high energies) quarks interact weakly, being considered in an asymptotic freedom, which +%allows a pertubative calculation~\cite{PhysRevD.8.3633,Politzer:1974fr,Gross:1998jx}.} and non-calculable long-distance effects. -These can be parametrised in the weak Lagrangian in terms of induced couplings $\mathcal{C}_i$ - referred to as Wilson coefficients (WC) - -and effective vertex operators with different Lorentz structure, $\mathcal{O}_i$. +These can be parametrised in the weak Lagrangian in terms of +effective vertex operators with different Lorentz structures, $\mathcal{O}_i$, +with corresponding couplings $\mathcal{C}_i$ - referred to as Wilson coefficients (WC). +%induced couplings $\mathcal{C}_i$ - referred to as Wilson coefficients (WC) - +%and effective vertex operators with different Lorentz structure, $\mathcal{O}_i$. Only a subset of the operators that are most sensitive to NP is examined in this work~\cite{Bobeth:2017vxj}, \textit{i.e.} $\mathcal{O}_7$ (virtual photon exchanges), $\mathcal{O}_{9,10}$ (vector and axial currents) and corresponding right-handed couplings with flipped helicities. @@ -225,7 +228,7 @@ %or by using the analytical and dispersive properties of these correlators~\cite{Bobeth:2017vxj}. or by exploring properties (\textit{e.g.} analyticity) of the structure of these functions~\cite{Bobeth:2017vxj}. However, these models still have intrinsic limitations, in particular -in the assumptions that enter in parametrisation of the di-lepton invariant mass. +in the assumptions that enter in parametrisation of the di-lepton invariant mass distribution. In this Letter we propose a new \textit{model-independent} approach that from a simultaneous unbinned amplitude analysis of both @@ -234,7 +237,7 @@ This work builds on the generalisation of Ref.~\cite{Bobeth:2017vxj}, but it is insensitive to the model assumptions of the parametrisation. %This relies on the strong correlation {\color{red} between the two decay modes} when examining muons and electrons -This relies on the strong correlation between the muon and electron modes +This effect relies on the strong correlation between the muon and electron modes imposed by the lepton-flavour universality of the hadronic matrix elements. %when examining directly the difference in Wilson coefficients. Furthermore, in this method the full set of observables @@ -309,11 +312,10 @@ 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. Note -that an amplitude analysis of the electron mode only has been previously disregarded, +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. -Therefore, in a common framework these hadronic contributions are treated as +In a common framework the 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. For consistency the WC $\widetilde{C}_{7}$ is also shared in the fit @@ -537,7 +539,7 @@ %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] +\begin{figure}[t] \includegraphics[width=.4\textwidth]{plots/B2Kstll_summary.pdf} \caption{% Sensitivity to \texttt{BMP}$_{\WC_{9,10}}$ scenario for the expected statistics after the \lhcb Run II. @@ -549,7 +551,7 @@ %We acknowledge useful contributions from Gino Isidori, Danny van Dyk and Patrick Owen. -%This work is supported by the Swiss National Science Foundation (SNF) under contract PZ00P2-174182. +%This work is supported by the Swiss National Science Foundation (SNF) under contracts 173104 and 174182. %\newpage @@ -570,7 +572,7 @@ and $\WC^{\prime (\mu)}_9 = - \WC^{\prime (\mu)}_{10} = 0.3$. Notice that for the electron mode the $\WC_{9,10}^{\prime(e)}$ is set and fixed to the SM value $\WC^{\prime \rm{SM}}_{9,10} = 0$. -\begin{figure}[b] +\begin{figure}[t] \includegraphics[width=.4\textwidth]{plots/ellipses_CpMu_Hz.pdf} \caption{% Two-dimensional sensitivity scans for the pair of Wilson coefficients $\WC'^{(\mu)}_9$ and diff --git a/references.bib b/references.bib index 893c318..57de4b6 100644 --- a/references.bib +++ b/references.bib @@ -714,4 +714,20 @@ year = "2018", eprint = "[In preparation]", } +@article{Aaij:2013qta, + author = "Aaij, R and others", + title = "{Measurement of Form-Factor-Independent Observables in + the Decay $B^{0} \to K^{*0} \mu^+ \mu^-$}", + collaboration = "LHCb", + journal = "Phys. Rev. Lett.", + volume = "111", + year = "2013", + pages = "191801", + doi = "10.1103/PhysRevLett.111.191801", + eprint = "1308.1707", + archivePrefix = "arXiv", + primaryClass = "hep-ex", + reportNumber = "LHCB-PAPER-2013-037, CERN-PH-EP-2013-146", + SLACcitation = "%%CITATION = ARXIV:1308.1707;%%" +}