diff --git a/draft.tex b/draft.tex index a40a08d..c78227b 100644 --- a/draft.tex +++ b/draft.tex @@ -150,7 +150,7 @@ 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 non-perturbative QCD contributions from $b\to s c{\bar{c}}$ operators ({\textit{i.e.}} charm loops) -that are able to either mimic or camouflage NP effects~\cite{Jager:2012uw,Jager:2014rwa}. +that are able to either mimic or camouflage NP effects~\cite{Jager:2012uw,Jager:2014rwa,Ciuchini:2015qxb}. Non-standard measurement in ratios of $b \to s \ell^+ \ell^-$ processes - such as of $R_{K}$~\cite{Aaij:2014ora} and $R_{K^{*}}$~\cite{Aaij:2017vbb} - indicate a suppression of the muon channel which is also compatible with the $P^{\prime}_{5}$ anomaly. @@ -158,7 +158,7 @@ suggested due to the small theoretical uncertainties in their predictions~\cite{Hiller:2003js,Bordone:2016gaq}. Whilst the individual level of significance of the present anomalies is still inconclusive, there is an appealing non-trivial consistent pattern shown in -global analysis fits~\cite{Capdevila:2017bsm,Altmannshofer:2017yso,Hurth:2017hxg}. +global analysis fits~\cite{Capdevila:2017bsm,Altmannshofer:2017yso,Hurth:2017hxg,Ciuchini:2017mik,Alok:2017sui}. The formalism of {\textit{b}} decays is commonly described within an effective field theory~\cite{Altmannshofer:2008dz}, @@ -275,9 +275,12 @@ sample size corresponding roughly to the yields foreseen in LHCb Run-II [$8\,$fb$^{-1}$] and future upgrades [$50\,$-$\,300\,$fb$^{-1}$]~\cite{Aaij:2244311}, and Belle II [$50\,$ab$^{-1}$]. These are extrapolated from Refs.~\cite{Aaij:2015oid,Aaij:2017vbb,Wehle:2016yoi} -by scaling respectively with $\sigma_{b\bar{b}} \propto \sqrt{s}$ and $\sigma_{b\bar{b}} \propto s$ -for LHCb and Belle II, where $s$ denotes the designed centre-of-mass -energy of the $b$-quark pair. +by scaling respectively with luminosity and $\sigma_{b\bar{b}} \propto \sqrt{s}$ +for LHCb, where $s$ denotes the designed centre-of-mass energy of the $b$-quark pair, +and exclusively with luminosity for Belle II. +%by scaling respectively with $\sigma_{b\bar{b}} \propto \sqrt{s}$ and $\sigma_{b\bar{b}} \propto s$ +%for LHCb and Belle II, where $s$ denotes the designed centre-of-mass +%energy of the $b$-quark pair. Note that for brevity most of the results are shown for the representative scenario of LHCb Run-II. The studied \qsq range corresponds to @@ -300,7 +303,7 @@ analyses with similar significance~\cite{Capdevila:2017bsm,Altmannshofer:2017yso,Hurth:2017hxg}. 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 +in which multivariate Gaussian terms are added to the log-likelihood to incorporate prior knowledge on the nuisance parameters. In order to probe the model-independence of the framework, the non-local hadronic parametrisation is modified in several ways, \textit{i.e.} @@ -346,7 +349,7 @@ $\widetilde{\mathcal{C}}_9^{(\mu)}$ and $\widetilde{\mathcal{C}}_9^{(e)}$ for different non-local hadronic parametrisation models evaluated at \texttt{BMP}$_{\WC_9}$, and with the expected statistics after \lhcb Run II. - The contours correspond to $3\,\sigma$ statistical-only uncertainty bands and + The contours correspond to 99\% confidence level statistical-only uncertainty bands and the dotted black line indicates the LFU hypothesis. } \label{fig:C9ellipse} @@ -366,7 +369,7 @@ for different non-local hadronic parametrisation models evaluated at (top) \texttt{BMP}$_{\WC_9}$ and (bottom) \texttt{BMP}$_{\WC_{9,10}}$, and with the expected statistics after \lhcb Run II. - The contours correspond to $3\,\sigma$ statistical-only uncertainty bands. + The contours correspond to 99\% confidence level statistical-only uncertainty bands. \label{fig:DeltaC9C10} } %\end{center} @@ -379,7 +382,8 @@ Realistic experimental effects are necessary to determine the exact sensitivity achievable. Nevertheless, these results suggest that a first observation (with a single measurement) of LFU breaking appears to be feasible with the expected recorded statistics by the end of LHCb Run II. -Furthermore, it is interesting to examine the prospects for confirming this evidence in the upcoming LHCb/Belle upgrades. +Furthermore, it is interesting to examine the prospects for confirming this evidence in the upcoming LHCb/Belle +upgrades~\cite{Albrecht:2017odf}. Figure~\ref{fig:DeltaC9C10_Upgrade} summarises the two-dimensional statistical-only significances for the designed luminosities. Both LHCb Upgrade and Belle II experiments have comparable sensitivities (within $8.0-10\,\sigma$), @@ -394,7 +398,7 @@ \caption{% Two-dimensional sensitivity scans for the proposed observables $\Delta\WC_9$ and $\Delta\WC_{10}$ for the two considered NP scenarios: (green) \texttt{BMP}$_{\WC_9}$ and (red) \texttt{BMP}$_{\WC_{9,10}}$. - The contours correspond to $3\,\sigma$ statistical-only uncertainty bands expected for the (dashed) \belle II 50~ab$^{-1}$ + The contours correspond to 99\% confidence level statistical-only uncertainty bands expected for the (dashed) \belle II 50~ab$^{-1}$ and \lhcb Upgrade (dotted) $50\,$fb$^{-1}$ and (solid) $\,300\,$fb$^{-1}$ statistics. \label{fig:DeltaC9C10_Upgrade} } @@ -429,7 +433,7 @@ It is worth mentioning that a hypothetical determination of the individual $\widetilde{\WC}_9^{(\mu,e)}$ and $\widetilde{\WC}_{10}^{(\mu,e)}$ WCs can also produce a shift in their central values -that mimics the behaviour of NP~\cite{Mauri:2018}.% and makes impossible any claim in this direction. +that mimics the behaviour of NP~\cite{Chrzaszcz:2018yza}.% and makes impossible any claim in this direction. % @@ -470,7 +474,7 @@ \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. - The relative contribution ($1,\,2,\,3\,\sigma$ contours) of each step of the analysis is shown in different colours, + The relative contribution (68, 95, 99\% confidence level 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} } @@ -505,7 +509,7 @@ Two-dimensional sensitivity scans for the pair of Wilson coefficients $\WC'^{(\mu)}_9$ and $\WC'^{(\mu)}_{10}$ for different non-local hadronic parametrisation models for a NP scenario with $\WC'^{(\mu)}_9 = \WC'^{(\mu)}_{10} = 0.3$. - The contours correspond to $3\,\sigma$ statistical-only uncertainty bands evaluated with + The contours correspond to 99\% confidence level statistical-only uncertainty bands evaluated with the expected statistics after \lhcb Run II. \label{fig:Cp_Hz} } @@ -531,7 +535,7 @@ Two-dimensional sensitivity scans for the pair of Wilson coefficients $\WC'^{(\mu)}_9$ and $\WC'^{(\mu)}_{10}$ for three NP scenarios: (blue) $\WC'^{(\mu)}_9 = \WC'^{(\mu)}_{10} = 0$, (orange) $\WC'^{(\mu)}_9 = \WC'^{(\mu)}_{10} = 0.3$ and (magenta) $\WC'^{(\mu)}_9 = - \WC'^{(\mu)}_{10} = 0.3$. - The contours correspond to $3\,\sigma$ statistical-only uncertainty bands expected for the LHCb Upgrade (dotted) + The contours correspond to 99\% confidence level statistical-only uncertainty bands expected for the LHCb Upgrade (dotted) $50\,$fb$^{-1}$ and (solid) $\,300\,$fb$^{-1}$ statistics. \label{fig:Cp} } diff --git a/references.bib b/references.bib index 57de4b6..3963f7f 100644 --- a/references.bib +++ b/references.bib @@ -1,3 +1,66 @@ +@article{Chrzaszcz:2018yza, + author = "Chrzaszcz, Marcin and Mauri, Andrea and Serra, Nicola and + Silva Coutinho, Rafael and van Dyk, Danny", + title = "{Prospects for disentangling long- and short-distance + effects in the decays $B\to K^* \mu^+\mu^-$}", + year = "2018", + eprint = "1805.06378", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + reportNumber = "TUM-HEP-1108-17, ZU-TH-25-17", + SLACcitation = "%%CITATION = ARXIV:1805.06378;%%" +} +@article{Alok:2017sui, + author = "Alok, Ashutosh Kumar and Bhattacharya, Bhubanjyoti and + Datta, Alakabha and Kumar, Dinesh and Kumar, Jacky and + London, David", + title = "{New Physics in $b \to s \mu^+ \mu^-$ after the + Measurement of $R_{K^*}$}", + journal = "Phys. Rev.", + volume = "D96", + year = "2017", + number = "9", + pages = "095009", + doi = "10.1103/PhysRevD.96.095009", + eprint = "1704.07397", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + reportNumber = "UDEM-GPP-TH-17-256, WSU-HEP-1708", + SLACcitation = "%%CITATION = ARXIV:1704.07397;%%" +} +@article{Ciuchini:2017mik, + author = "Ciuchini, Marco and Coutinho, Antonio M. and Fedele, + Marco and Franco, Enrico and Paul, Ayan and Silvestrini, + Luca and Valli, Mauro", + title = "{On Flavourful Easter eggs for New Physics hunger and + Lepton Flavour Universality violation}", + journal = "Eur. Phys. J.", + volume = "C77", + year = "2017", + number = "10", + pages = "688", + doi = "10.1140/epjc/s10052-017-5270-2", + eprint = "1704.05447", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + SLACcitation = "%%CITATION = ARXIV:1704.05447;%%" +} +@article{Ciuchini:2015qxb, + author = "Ciuchini, Marco and Fedele, Marco and Franco, Enrico and + Mishima, Satoshi and Paul, Ayan and Silvestrini, Luca and + Valli, Mauro", + title = "{$B\to K^* \ell^+ \ell^-$ decays at large recoil in the + Standard Model: a theoretical reappraisal}", + journal = "JHEP", + volume = "06", + year = "2016", + pages = "116", + doi = "10.1007/JHEP06(2016)116", + eprint = "1512.07157", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + SLACcitation = "%%CITATION = ARXIV:1512.07157;%%" +} @article{Grossman:1996ke, author = "Grossman, Yuval and Worah, Mihir P.", title = "{CP asymmetries in B decays with new physics in decay