Effective field theory approach to $b\to s\ell\ell^{(\prime)
Lorenzo Calibbi
Andreas Crivellin
Toshihiko Ota
LHCb reported anomalies in $B\to K^* \mu^+\mu^-$, $B_s\to\phi\mu^+\mu^-$ and $R(K)=B\to K \mu^+\mu^-/B\to K e^+e^-$. Furthermore, BaBar, BELLE and LHCb found hints for the violation of lepton flavour universality violation in $R(D^{(*))=B\to D^{(*)\tau\nu/B\to D^{(*)\ell\nu$. In this note we reexamine these decays and their correlations to $B\to K^{(*)\nu\bar{\nu$ using gauge invariant dim-6 operators. For the numerical analysis we focus on scenarios in which new physics couples, in the interaction eigenbasis, to third generation quarks and lepton only. We conclude that such a setup can explain the $b\to s\mu^+\mu^-$ data simultaneously with $R(D^{(*))$ for small mixing angles in the lepton sector (of the order of $\pi/16$) and very small mixing angles in the quark sector (smaller than $V_{cb$). In these region of parameter space $B\to K^{(*)\tau\mu$ and $B_s\to \tau\mu$ can be order $10^{-6$. Possible UV completions are briefly discussed.
EFT.tex
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\begin{document}
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\preprint{\vbox{\hbox{CERN-PH-TH-2015-134}\hbox{STUPP-15-222}}} 


\title{Effective field theory approach to $b\to s\ell\ell^{(\prime)}$, $B\to K^{(*)}\nu\bar{\nu}$ and $B\to D^{(*)}\tau\nu$\\ with third generation couplings}

\author{Lorenzo Calibbi}
\affiliation{State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, P.~R.~China}
\affiliation{Service de Physique Th\'eorique, Universit\'e Libre de Bruxelles,
C.P. 225, B-1050 Brussels, Belgium}
\author{Andreas Crivellin}
\affiliation{CERN Theory Division, CH--1211 Geneva 23, Switzerland}
\author{Toshihiko Ota}
\affiliation{Department of Physics, Saitama University, Shimo-Okubo 255, 338-8570 Saitama-Sakura, Japan}%

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\begin{abstract}
LHCb reported anomalies in $B\to K^* \mu^+\mu^-$, $B_s\to\phi\mu^+\mu^-$ and $R(K)=B\to K \mu^+\mu^-/B\to K e^+e^-$. Furthermore, BaBar, BELLE and LHCb found hints for the violation of lepton flavour universality violation in $R(D^{(*)})=B\to D^{(*)}\tau\nu/B\to D^{(*)}\ell\nu$. In this note we reexamine these decays and their correlations to $B\to K^{(*)}\nu\bar{\nu}$ using gauge invariant dim-6 operators. For the numerical analysis we focus on scenarios in which new physics couples, in the interaction eigenbasis, to third generation quarks and lepton only. We conclude that such a setup can explain the $b\to s\mu^+\mu^-$ data simultaneously with $R(D^{(*)})$ for small mixing angles in the lepton sector (of the order of $\pi/16$) and very small mixing angles in the quark sector (smaller than $V_{cb}$). In these region of parameter space $B\to K^{(*)}\tau\mu$ and $B_s\to \tau\mu$ can be order $10^{-6}$. Possible UV completions are briefly discussed.
\end{abstract}
\pacs{13.20.He, 14.40.Nd, 14.65.Fy, 14.80.Sv, 11.30.Hv}

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\maketitle

%%%%%%%%%%%
\section{Introduction}
\label{intro}
%%%%%%%%%%%

So far, the LHC completed the standard model (SM) of particle physics by discovering the last missing piece, the Higgs particle~\cite{Aad:2012tfa,Chatrchyan:2012ufa}.\footnote{We denote the SM scalar particle predicted by Brout, Englert and Higgs as the ''Higgs particle".} Furthermore, no significant direct evidence for physics beyond the SM has been found, i.e.~no new particles were discovered. However, LHCb observed indirect `hints' for new physics (NP) in $B\to K^*\mu^+\mu^-$, $B_s\to\phi\mu^+\mu^-$ and $R(K)\equiv{\rm Br}(B\to K \mu^+\mu^-)/{\rm Br}(B\to K e^+e^-)$. Furthermore, BaBar and also very recently BELLE and LHCb reported lepton flavour universality violation in $B\to D^{(*)}\tau\nu$. These observations can be used as a guideline in the exploration of possible physics beyond the SM.

In more detail, the current experimental situation is as follows: LHCb reported deviations from the SM predictions~\cite{Egede:2008uy} in $B\to K^* \mu^+\mu^-$~\cite{Aaij:2013qta,LHCb:2015dla} (mainly in an angular observable called $P_5^\prime$~\cite{Descotes-Genon:2013vna}) with a significance of $2$--$3\,\sigma$ depending on the assumptions of hadronic uncertainties~\cite{Descotes-Genon:2014uoa,Altmannshofer:2014rta,Jager:2014rwa}. Also in the decay $B_s\to\phi\mu^+\mu^-$~\cite{Aaij:2013aln} LHCb uncovered differences compared to the SM prediction based on lattice QCD~\cite{Horgan:2013pva,Horgan:2015vla} and light-cone sumrules~\cite{Straub:2015ica} of $3.1\,\sigma$ \cite{Altmannshofer:2014rta}.\footnote{Very recently, this discrepancy increased to $3.5\,\sigma$~\cite{BsphimumuFPCP}.}
Furthermore, LHCb~\cite{Aaij:2014ora} found indications for the violation of lepton flavour universality, namely
%
\begin{align}
	R(K)=0.745^{+0.090}_{-0.074}\pm 0.036\,,
\end{align}
%
in the range $1\,{\rm GeV^2}<q^2<6\,{\rm GeV^2}$. This measurement is in tension with the theoretically clean SM prediction $R_{\rm SM}(K)=1.0003 \pm 0.0001$~\cite{Bobeth:2007dw} by $2.6\,\sigma$. Combining these anomalies with all other observables for $b\to s \mu^+\mu^-$ transitions, it is found that a scenario with NP in $C_9^{\mu\mu}$ (corresponding to the operator $\bar s \gamma^\nu P_L b\,\bar\mu \gamma_\nu \mu$) but not in $C_9^{ee}$ is preferred compared to the SM by $4.3\,\sigma$~\cite{Altmannshofer:2015sma}. 

Hints for lepton flavour universality violating NP also comes from the BaBar collaboration that performed an analysis of the semileptonic $B$ decays $B\to D^{(*)}\tau\nu$~\cite{Lees:2012xj}. Recently, these decays have also been reanalyzed by BELLE~\cite{BDstaumuBELLE} and LHCb measured $B\to D^{*}\tau\nu$~\cite{BDstaumuLHCb}. In summary, these experiments have found for the ratios ${R}(D^{(*)})\equiv{\rm Br}(B\to D^{(*)} \tau \nu)/{\rm Br}(B\to D^{(*)} \ell \nu)$:
%
\begin{align}
R(D)_{\rm BaBar}\,&=\,0.440\pm0.058\pm0.042  \,,\\ 
R(D)_{\rm BELLE}\,&=\,0.375^{+0.064}_{-0.063}\pm0.026  \,,\\ 
R(D^*)_{\rm BaBar}\,&=\,0.332\pm0.024\pm0.018\,,\\
R(D^*)_{\rm BELLE}\,&=\,0.293^{+0.039}_{-0.037}\pm0.015  \,,\\
R(D^*)_{\rm LHCb}\,&=\,0.336\pm0.027\pm0.030  \,. 
\end{align}
%
Here the first (second) errors are statistical (systematic). Combining these measurements one finds~\cite{BDstaumuCOMBINED}
\begin{align}
R(D)_{\rm EXP}\,&=\,0.388\pm0.047\,,\nonumber\\ 
R(D^*)_{\rm EXP}\,&=\,0.321\pm0.021  \,. 
\label{RDEXP}
\end{align}
%
Comparing these measurements to the SM predictions~\cite{Fajfer:2012vx}
%
\begin{align}
R_{\rm SM}(D)\,&=\,0.297\pm0.017 \,,  \nonumber
\\ R_{\rm SM}(D^*) \,&=\,0.252\pm0.003 \,,
\label{RDSM}
\end{align}
%
we see that there is a discrepancy of 1.8\,$\sigma$ for $R(D)$ and 3.3\,$\sigma$ for $R(D^*)$ and the combination corresponds approximately to a $3.8\, \sigma$ deviation from the SM (compared to $3.4\, \sigma$ taking into account the BaBar results only~\cite{Lees:2012xj}).

Numerous models have been proposed in order to explain the anomalies in $b\to s\mu^+\mu^-$ transitions (see for example Refs.~\cite{Descotes-Genon:2013wba,Gauld:2013qba,Buras:2013qja,Gauld:2013qja,Buras:2013dea,Altmannshofer:2014cfa,Crivellin:2015mga,Crivellin:2015lwa,Niehoff:2015bfa,Sierra:2015fma,Celis:2015ara} for $Z^\prime$ models and Refs.~\cite{Becirevic:2015asa,Varzielas:2015iva} for models with leptoquarks) and the deviations from the SM predicitons in tauonic $B$ decays \cite{Crivellin:2012ye,Datta:2012qk,Crivellin:2013wna,Li:2013vlx,Faisel:2013nra,Atoui:2013zza,Sakaki:2013bfa,Celis:2013bya,Biancofiore:2014wpa}. 

Alternatively, a model independent approach using higher dimensional operators has been employed, as in the model independent fits~\cite{Descotes-Genon:2013vna,Hurth:2014vma,Altmannshofer:2014rta}. In this context, it has been argued that as $R(K)$ violates lepton flavour universality (LFU) also lepton flavour could be violated in $B$ decays~\cite{Glashow:2014iga} which might be linked to neutrino oscillations \cite{Boucenna:2015raa}.\footnote{Lepton flavour violating $B$ decays in leptoquark models have been studied in~\cite{Varzielas:2015iva} and in $Z^\prime$ models in~\cite{Crivellin:2015era}.}
While~\cite{Glashow:2014iga} considered the effect of operators at the $B$~meson scale which are invariant under electromagnetic gauge interactions only, also operators invariant under the full SM gauge group~\cite{Buchmuller:1985jz,Grzadkowski:2010es} have been considered in Ref.~\cite{Fajfer:2012jt,Bhattacharya:2014wla,Buras:2014fpa,Alonso:2015sja}.\footnote{For an analogous analysis in the lepton sector see~\cite{Crivellin:2013hpa,Crivellin:2014cta,Pruna:2014asa}.}
Here it has been claimed than an simultaneous explanation of $R(K)$, $R(D)$ and $R(D^*)$ using gauge invariant operators with left-handed fermions is possible~\cite{Bhattacharya:2014wla,Alonso:2015sja}. For this purpose, it was assumed that in the interaction eigenbasis only couplings to the third generation exist~\cite{Glashow:2014iga,Bhattacharya:2014wla} (or are enhanced by $m_\tau^2/m_\mu^2$ compared to the second one~\cite{Alonso:2015sja}), while all other couplings are generated by the misalignment between the mass and the interaction basis (or are suppressed by small lepton mass ratios~\cite{Alonso:2015sja}). 

In this article we reconsider the possibility of explaining $B\to D^{(*)}\tau\nu$ and the $b\to s\mu^+\mu^-$ data with higher dimensional gauge invariant operators, taking into account the constraints from $B\to K^{(*)}\nu\bar{\nu}$ and using the results of the global fit to $b\to s\mu\mu$ transitions. We extend the analysis of Ref.~\cite{Alonso:2015sja} and consider the possibility of lepton flavour violation (LFV) and compared to Ref.~\cite{Glashow:2014iga} we include the correlations due to $SU(2)_L$ gauge invariance and give quantitative predictions for $B\to K^{(*)}\tau\mu$ and $B_s\to \tau\mu$. 

The outline is as follows: In the next section we collect the necessary formulae for the flavour observables. Sec.~\ref{sec:GIO} discusses the gauge invariant higher dimensional operators relevant for our analysis and Sec.~\ref{sec:NA} presents our numerical results. 
Sec.~\ref{uvcomplete} briefly reviews some possible UV completions. Finally we conclude in Sec.~\ref{conclusion}.

\section{Flavour observables}
\label{flavour}
%
\subsection{$b\to s\mu^+\mu^-$ transitions}
%
$b\to s\ell_i\ell_j$ transitions are defined via the effective Hamiltonian
\bea
%
H_{\rm eff}^{\ell_i\ell_j} &=& - \dfrac{ 4 G_F }{\sqrt 2}
V_{tb}V_{ts}^{*} \sum\limits_{a = 9,10}
\left( {C_a^{\ell_i\ell_j} O_a^{\ell_i\ell_j} + C_a^{\prime\,\ell_i\ell_j}  O_a^{\prime\,\ell_i\ell_j} } \right)\,,\nn {O_{9(10)}^{\ell_i\ell_j}} &=& 
\dfrac{\alpha }{4\pi}[\bar s{\gamma ^\mu } P_L b]\,[\bar\ell_i{\gamma _\mu }(\gamma^5)\ell_j] \,,
\label{eq:effHam}
%
\eea
where the primed operators are obtained by exchanging $L\leftrightarrow R$.

Concerning \BKs, $B_s\to \phi\mu^+\mu^-$ and $B\to K\mu^+\mu^-/B\to K e^+ e^-$, as already noted in Ref.~\cite{Descotes-Genon:2013wba,Descotes-Genon:2013zva}, $C^{\mu\mu}_9<0$ and $C^{\prime\mu\mu}_9=0$ is preferred by data. However, also the possibility $C^{\mu\mu}_9=-C^{\mu\mu}_{10}<0$ gives a good fit to data. Using the global fit of Ref.~\cite{Altmannshofer:2014rta,Altmannshofer:2015sma} we see that at ($1\,\sigma$) $2\,\sigma$ level 
%
\bea
-0.53(-0.81) \geq & C_9^{\mu\mu}& \geq(-1.32)-1.54\,,\label{scenario1}\\
-0.18(-0.35) \geq & C_{9}^{\mu\mu}=-C_{10}^{\mu\mu}& \geq(-0.71)
-0.91\,.\label{scenario2}
\label{eq:C9fit}
\eea
%
Interestingly, the values of $C_9^{\mu\mu},\,C_{10}^{\mu\mu}$ favoured by $R(K)$ and \BKs lie approximately in the same range.\footnote{Note that the fit to \eq{scenario2} includes muon data only. However, as $B\to Ke^+e^-$ agrees rather well with the SM prediction, the effect on the global fit is expected to be small. Also the latest LHCb result for $B_s\to\phi\mu^+\mu^-$ \cite{BsphimumuFPCP}, which would slight increase the tension with the SM, is not included in the fit.}
Furthermore, a good fit to the current data does not require $C^{\prime\mu\mu}_9$, hence in the following we neglect operators with right-handed quark currents for simplicity. 

\subsection{$B\to K^{(*)}\nu\bar{\nu}$}

Following Ref.~\cite{Buras:2014fpa} we write the relevant effective Hamiltonian as
\begin{align}
{H_{\rm eff}^{\nu_i\nu_j} } &=  - \frac{{4{G_F}}}{{\sqrt 2 }}{V_{tb}}V_{ts}^*\left( {{C_L^{ij}}{O_L^{ij}} + {C_R^{ij}}{O_R^{ij}}} \right)\,\\
O_{L,R}^{ij} &= \frac{\alpha }{{4\pi }} [\bar s{\gamma ^\mu }{P_{L,R}}b][{{\bar \nu }_i}{\gamma _\mu }\left( {1 - {\gamma ^5}} \right){\nu _j}]\,,
\end{align}
and $C_L^{\rm SM}\approx-1.47/s_w^2$. In the limit of vanishing right-handed $sb$ current, the branching ratios normalized by the SM predictions read
\begin{equation}
{R_{K^{(*)}}^{\nu\bar{\nu}}} = 
\frac{1}{3}\sum\limits_{i,j=1}^3 \dfrac{ \left|  {C_L^{ij}} \right|^2}{\left| {C_L^{\rm SM}} \right|^2} \,.
\end{equation}
The current experimental limits are ${R_K^{\nu\bar{\nu}}} < 4.3$~\cite{Lees:2013kla} and ${R_{{K^*}}^{\nu\bar{\nu}}} < 4.4$~\cite{Lutz:2013ftz}.

\subsection{$B\to D^{(*)}\tau\nu$}

The effective Hamiltonian for semileptonic $b\to c$ transitions is
\begin{equation}
{H_{\text{eff}}} = \frac{{4{G_F}}}{{\sqrt 2 }}{V_{cb}}C_{L\,ij}^{cb} [\bar c{\gamma ^\mu }{P_L}b][\bar \ell_i {\gamma _\mu }P_L\nu_j]\,,
\end{equation}
with $C_{L\,ij}^{cb\,{\rm SM}}=\delta_{ij}$ (for massless neutrinos) taking into account only left handed vector currents. In this case the ratios of branching ratios are 
\begin{equation}
\dfrac{R(D^{(*)})_{\rm EXP}}{R(D^{(*)})_{\rm SM}} = 
 \dfrac{{\sum\limits_{j=1}^3} {{{\left| {C_{L\;3j}^{cb}} \right|}^2}}}{{\sum\limits_{j=1}^3}{{{\left| {C_{L\;\ell j}^{cb}} \right|}^2}}}\,,
\end{equation}
with $\ell=e,\mu$ which has to be compared to \eq{RDSM} and \eq{RDEXP}.

\subsection{Lepton-flavour violating \boldmath$B$\unboldmath\ decays}
\label{susec:H}

Here we give formulas for the branching ratios of LFV $B$ decays following the analysis of Ref.~\cite{Crivellin:2015era}. We take into account only contributions from the operators $O_{9}^{(\prime)\ell\ell^\prime}$ and $O_{10}^{(\prime)\ell\ell^\prime}$ while neglecting contributions from operators with scalar currents not relevant for our analysis. For $B_s\to\ell^+\ell^{\prime -}$ (with $\ell\neq \ell^\prime$) we use the results of Ref.~\cite{Dedes:2008iw} neglecting the mass of the lighter lepton. The branching ratios for $B\to K^{(*)}\tau^\pm\mu^\mp, B\to K^{(*)} \mu^\pm e^\mp$ are computed using form-factors obtained from lattice QCD in Ref.~\cite{Bouchard:2013eph} (see also Refs.~\cite{Horgan:2015vla,Horgan:2013hoa}). The final results read
%
\begin{widetext}
\bea
\Br\left[ B_s \to \ell^+ \ell^{\prime-} \right] &=& \dfrac{\tau_{B_s}
  m_\ell^2 M_{B_s} f_{B_s}^2}{32\pi^3} \alpha^2 G_F^2 \left| V_{tb}
V_{ts}^*\right|^2 \left(1 - \dfrac{{\rm
    Max}[m_\ell^2,m_{\ell^\prime}^2]}{M_{B_s}^2}\right)^2 \left(\left|
C_{9}^{\ell \ell^\prime}-C^{\prime\ell \ell^\prime}_{9}\right|^2 +
\left| C_{10}^{\ell \ell^\prime}-C^{\prime\ell \ell^\prime}_{10}
\right|^2 \right) ,\nonumber\\
%\Br\left[ B_s \to \ell^+ \ell \right] &=&\frac{{{\tau _{{B_s}}}m_\ell ^2{M_{{B_s}}}f_{{B_s}}^2}}{{8{\pi ^3}}}{\alpha ^2}G_F^2{\left| {{V_{tb}}V_{ts}^*} \right|^2}\sqrt {1 - \frac{{4m_\ell ^2}}{{{\rm{M}}{{\rm{B}}^2}}}} {\left| {C_{10}^{\ell \ell } - C_{10}^{\prime \ell \ell }} \right|^2}\,\\
\Br[B\to K^{(*)}\ell^+\ell^{\prime-}] &=& 10^{-9} \left(a_{K^{(*)}\ell\ell^\prime}\left|C_9^{\ell\ell^\prime} + C_9^{\prime\ell\ell^\prime} \right|^2 +
b_{K^{(*)}\ell\ell^\prime}\left|C_{10}^{\ell\ell^\prime} + C_{10}^{\prime\ell\ell^\prime} \right|^2 \right. \nn &\;\;\;&+\left.
c_{K^*\ell\ell^\prime}\left|C_9^{\ell\ell^\prime}
-C_9^{\prime\ell\ell^\prime} \right|^2 +d_{K^*\ell\ell^\prime}\left|C_{10}^{\ell\ell^\prime}-C_{10}^{\prime\ell\ell^\prime} \right|^2 \right)\,,
\label{bkstaumu}
\eea
%
with
%
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
$\ell\ell^\prime $ & $a_{K\ell\ell^\prime}$ & $b_{K\ell\ell^\prime}$ &
$a_{K^*\ell\ell^\prime}$ & $b_{K^*\ell\ell^\prime}$ &
$c_{K^*\ell\ell^\prime}$ & $d_{K^*\ell\ell^\prime}$ \\
\hline
$\;\tau\mu,\tau e\;$ & $\;9.6 \pm 1.0\;$ & $\;10.0 \pm 1.3\;$ & $\;3.0 \pm
0.8\;$ & $\;2.7 \pm 0.7\;$ & $\;16.4 \pm 2.1\;$ & $\;15.4 \pm 1.9\;$
\\
$\mu e$ & $15.4 \pm 3.1$ & $15.7 \pm 3.1$ & $5.6 \pm 1.9$ & $5.6 \pm
1.9$ & $29.1 \pm 4.9$ & $29.1 \pm 4.9$ \\
\hline
\end{tabular}
\end{center}
\end{widetext}
%
The formula for the branching ratio of $B_s \to \ell^+ \ell^{\prime-}$ is symmetric with respect to the exchange of 
$C_9^{(\prime)\ell\ell^\prime}\leftrightarrow C_{10}^{(\prime)\ell\ell^\prime}$, while in the case of $B \to K^{(*)}\ell^+ \ell^{\prime-}$
this symmetry is broken by lepton-mass effects. There is a small difference between the theoretical prediction for 
the charged mode $B^+\to K^{(*)+}\ell^+ \ell^{\prime-}$ and the neutral one $B^0\to K^{(*)0}\ell^+ \ell^{\prime-}$ due to the different $B$-meson lifetime $\tau_B$ which we neglected fixing the numerical value of $\tau_B$ to the one of the neutral meson. Note that the results above are given for $\ell^-\ell^{\prime+}$ final states and not for the sum $\ell^\pm\ell^{\prime\mp}=\ell^-\ell^{\prime+}+\ell^+\ell^{\prime-}$ to which the experimental constraints apply~\cite{Amhis:2014hma}. The only channel with $\tau\mu$ final states for which an experimental upper limit exists is
%
\bea
{\rm Br}\left[B^+\to K^+\tau^\pm\mu^\mp \right]_{\rm exp}\le 4.8\times 10^{-5} \,.
\eea

\section{Gauge invariant operators}
\label{sec:GIO}

As we have previously seen, a scenario with left-handed currents only gives a good fit to data, cf.~\eq{scenario2}. In such a scenario $SU(2)_L$ relations are necessarily present. These relations are automatically taken into account once gauge invariant operators are considered. Therefore, let us focus on 4-fermion operators with left-handed quarks and leptons. There are two such 4-fermion operators in the effective Lagrangian
\begin{equation}
	{\cal L_{\rm dim6}}=\dfrac{1}{\Lambda^2}\sum{O_X C_X}\,,
\end{equation}
where $\Lambda$ is the scale of NP, which can contribute to $b\to s\ell\ell$ transitions at tree-level \cite{Buchmuller:1985jz,Grzadkowski:2010es}:
\begin{align}
\label{Q1-Q3}
Q_{\ell q}^{\left( 1 \right)} = \left( {\bar L{\gamma ^\mu }L} \right)\left( {\bar Q{\gamma _\mu }Q} \right)\,,~~
Q_{\ell q}^{\left( 3 \right)} = \left( {\bar L{\gamma ^\mu }{\tau _I}L} \right)\left( {\bar Q{\gamma _\mu }{\tau ^I}Q} \right)\,,
\end{align}
where $L$ is the lepton doublet and $Q$ the quark doublet and the flavour indices are not explicitly shown here. Writing these operators in terms of their $SU(2)_L$ components (i.e.~up-quarks, down-quarks, charged leptons and neutrinos) we find for the terms relevant for the processes discussed in the last section (before EW symmetry breaking)
\begin{align}
{\cal L} \supset & \frac{{C_{ijkl}^{\left( 1 \right)}}}{{{\Lambda ^2}}}\left( {{{\bar \ell }_i}{\gamma ^\mu }{P_L}{\ell _j}{{\bar d}_k}{\gamma _\mu }{P_L}{d_l} + {{\bar \nu }_i}{\gamma ^\mu }{P_L}{\nu _j}{{\bar d}_k}{\gamma _\mu }{P_L}{d_l}} \right) +\nonumber\\
 &\frac{C_{ijkl}^{\left( 3 \right)}}{{{\Lambda ^2}}}\left( {2{{\bar \ell }_i}{\gamma ^\mu }{P_L}{\nu _j}{{\bar u}_k}{\gamma _\mu }{P_L}{d_l} - {{\bar \nu }_i}{\gamma ^\mu }{P_L}{\nu _j}{{\bar d}_k}{\gamma _\mu }{P_L}{d_l}}\right.\nonumber\\ 
 &+\left.{ {{\bar \ell }_i}{\gamma ^\mu }{P_L}{\ell _j}{{\bar d}_k}{\gamma _\mu }{P_L}{d_l}} \right)\,,
\end{align}
where $C^{(1,3)}_{ijkl}$ are the dimensionless coefficients of the operators of Eq.~(\ref{Q1-Q3}). After EW symmetry breaking the following redefinitions of the fields are performed in order to render the mass matrices diagonal
\begin{equation}
{d_L} \to D_{}^\dag {d_L},\;{u_L} \to U_{}^\dag {u_L},\;\;{\ell _L} \to L_{}^\dag {\ell _L},\;\nu  \to L_{}^\dag \nu \,.
\end{equation}
We define for future convenience
\begin{equation}
\lambda^{(1,3)}\tilde X_{ij}^{\left( {1,3} \right)}\tilde Y_{kl}^{\left( {1,3} \right)} = L_{i'i}^*{L_{j'j}}D_{k'k}^*{D_{l'l}}C_{i'j'k'l'}^{\left( {1,3} \right)}\,,
\end{equation}
where $\lambda^{(1,3)}$ are overall constants. Using constraints from the measured CKM matrix, i.e.~$V = U^\dag D$, we finally obtain
\begin{align}
C_9^{ij} =&  -C_{10}^{ij}
\nonumber 
\\ =& \frac{\pi }{{\sqrt 2 {\Lambda ^2}{G_F}\alpha {V_{tb}}V_{ts}^*}}\left( {{\lambda ^{(1)}}\tilde X_{ij}^{(1)}\tilde Y_{23}^{(1)} + {\lambda ^{(3)}}\tilde X_{ij}^{(3)}\tilde Y_{23}^{(3)}} \right)\nonumber\\
C_L^{ij} 
=& 
\frac{\pi }{{\sqrt 2 {\Lambda ^2}{G_F}\alpha {V_{tb}}V_{ts}^*}}\left( {{\lambda ^{(1)}}\tilde X_{ij}^{(1)}\tilde Y_{23}^{(1)} - {\lambda ^{(3)}}\tilde X_{ij}^{(3)}\tilde Y_{23}^{(3)}} \right)\nonumber\,,
\\
C_{L\;ij}^{cb} &=  - {\frac{\lambda^{(3)}}{{\sqrt 2 {\Lambda ^2}{G_F}}}}\frac{{{{\tilde X}_{ij}^{(3)}}}}{{{V_{cb}}}}\sum\limits_k {\left( {{V_{2k}}{{\tilde Y}_{k3}^{(3)}}} \right)}\,,\label{C9C10CL}
\end{align}
for the Wilson coefficients relevant for $b\to s\mu^+\mu^-$,  $B\to K^{(*)}\nu\bar{\nu}$ and $B\to D^{(*)}\tau\nu$ respectively.
Note that in the limit $C^{(1)}=C^{(3)}$ the contribution to $B\to K^{(*)}\nu\bar{\nu}$ vanishes. 

\begin{figure}[t]
\begin{center}
\begin{tabular}{cp{7mm}c}
\includegraphics[width=0.43\textwidth]{C1plot} &&
\end{tabular}
\end{center}
\caption{Allowed regions in the $\lambda^{(1)}$--$\alpha_{\mu\tau}$ plane from
 $b\to s \mu^+\mu^-$ data (blue) and $B\to K \nu\bar{\nu}$ (yellow) for $\alpha_{sb}={\rm ArcSin}[V_{cb}]$ and $\Lambda=1\,$TeV. Note that here changing $\alpha_{sb}$ only has the effect of an overall scaling of $\lambda^{(1)}$. The contour lines denote ${\rm Br}[B\to K^*\tau\mu]$ in units of $10^{-6}$.
\label{Plot1}}
\end{figure}

\section{Numerical analysis}
\label{sec:NA}
%
\begin{figure*}[t]
\begin{center}
\begin{tabular}{cp{7mm}c}
\includegraphics[width=0.32\textwidth]{C3plot05}
\includegraphics[width=0.32\textwidth]{C3plot1}
\includegraphics[width=0.32\textwidth]{C3plot2}
\end{tabular}
\end{center}
\caption{Allowed regions in the $\alpha_{\mu\tau}$--$\alpha_{sb}$ plane from $B\to K\nu\bar{\nu}$ (yellow), $R(D^*)$ (red) and $b\to s \mu^+\mu^-$ (blue) for $\Lambda=1\,$TeV and $\lambda^{(3)}=-0.5$ (left plot), $\lambda^{(3)}=-1$ (middle) and $\lambda^{(3)}=-2$ (right). Note that $\alpha_{sb}=\pi/64$ roughly corresponds to the angle needed to generate $V_{cb}$ and that if $\lambda^{(3)}$ is positive, $R(D^*)$ and $b\to s\mu^+\mu^-$ cannot be explained simultaneously. \label{Plot2}}
\end{figure*}
%
Since we have $C_9^{\tau\mu}=-C_{10}^{\tau\mu}$ we find for the LFV $B$ decays
\begin{align}
{\rm Br}\left[B\to K\tau^\pm\mu^\mp \right]/{\rm Br}\left[B\to K^*\tau^\pm\mu^\mp \right]&\approx 1\,,\\
{\rm Br}\left[B_s\to \tau^\pm\mu^\mp \right]/{\rm Br}\left[B\to K^*\tau^\pm\mu^\mp \right]&\approx 0.5\,.
\end{align}
Therefore in the following, we will just present the numerical evaluation of ${\rm Br}\left[B\to K^*\tau^\pm\mu^\mp \right]$ while ${\rm Br}\left[B_s\to \tau^\pm\mu^\mp \right]$ and ${\rm Br}\left[B\to K\tau^\pm\mu^\mp \right]$ can be obtained by the appropriate rescaling.

We also note that $B\to K\nu\bar{\nu}$ imposes an upper limit on the absolute value of $C_9^{\tau\tau}=-C_{10}^{\tau\tau}$ and $C_9^{\tau\mu}=-C_{10}^{\tau\mu}$ valid for $C^{(3)}$ and $C^{(1)}$ separately. Neglecting the small NP contribution to $C_L^{\mu\mu}$ and assuming no NP in the electron channel we find:
\begin{align}
\dfrac{|C_9^{\tau\mu}|}{C_L^{\rm SM}}&\le\sqrt{4.3\times3/2}\approx 2.5\,,\label{C9tautau}\\
\dfrac{|C_9^{\tau\tau}|}{C_L^{\rm SM}}&\le\sqrt{3\times4.3\times3/2-2}+1\approx 5.2\,.
\end{align}
This leads to the following upper limits valid in any model generating only $C^{(3)}$ or $C^{(1)}$:
\begin{align}
{\rm Br}[B\to K\tau\mu]\leq 8.3\times 10^{-6}\,.
\end{align}
However, this limit can be evaded for $C^{(3)}=C^{(1)}$. In Ref.~\cite{Alonso:2015sja} it was proposed that the MFV-like relation $\tilde Y_{22}/\tilde Y_{33}=m_\tau^2/m_\mu^2$ could explain $R(D^{(*)})$ and $b\to s\mu^+\mu^-$ data simultaneously. From \eq{C9tautau} we see that this ansatz is only possible for $C^{(3)}=C^{(1)}$ but not if $C^{(3)}$ or $C^{(1)}$ are separately different from zero.

Therefore, we will focus in the following on scenarios with third generation couplings in the EW basis only, which correspond to a general rank 1 matrix in the mass eigenbasis, as suggested in Ref.~\cite{Glashow:2014iga,Bhattacharya:2014wla}. In other words we have
\begin{align}
C_{ijkl}^{(1,3)}&=\lambda^{(1,3)}\tilde X_{ij}\tilde Y_{kl}\,,\\
\tilde X &= {L^\dag }XL,\;\tilde Y = {D^\dag }YD\,,\;\;\;
X &= Y = \left( {\begin{array}{*{20}{c}}0&0&0\\0&0&0\\0&0&1\end{array}} \right)\,.\nonumber
\end{align}
Taking into account only rotations among the second and third generation one finds
\begin{align}
\tilde X =& \left( {\begin{array}{*{20}{c}}
0&0&0\\
0&{{{\sin }^2}\left( \alpha_{\mu\tau}  \right)}&{ - \sin \left( \alpha_{\mu\tau}  \right)\cos \left( \alpha_{\mu\tau}  \right)}\\
0&{ - \sin \left( \alpha_{\mu\tau}  \right)\cos \left( \alpha_{\mu\tau}  \right)}&{{{\cos }^2}\left( \alpha_{\mu\tau}  \right)}
\end{array}} \right)\,,\nonumber\\
\tilde Y =& \left( {\begin{array}{*{20}{c}}
0&0&0\\
0&{{{\sin }^2}\left( \alpha_{sb}  \right)}&{ - \sin \left( \alpha_{sb}  \right)\cos \left( \alpha_{sb}  \right)}\\
0&{ - \sin \left( \alpha_{sb}  \right)\cos \left( \alpha_{sb}  \right)}&{{{\cos }^2}\left( \alpha_{sb}  \right)}
\end{array}} \right)\,.\nonumber
\end{align}
Note that a rotation $\sin(\alpha_{sb})\gg V_{cb}$ would require fine-tuning with the up sector in order to obtain the correct CKM matrix.

\subsubsection{$Q_{\ell q}^{\left( 1 \right)}$ operator}
%
In this case we have neutral currents only. As a consequence, there is obviously no effect in $R(D^{(*)})$, but $b\to s \mu^+\mu^-$ is directly correlated to $B\to K^{(*)}\nu\bar{\nu}$ depending on the angle $\alpha_{\mu\tau}$. Note that a change in $\alpha_{sb}$ can be compensated by a change in $\lambda^{(1)}$ and therefore does not affect the correlations among $B\to K^{(*)}\nu\bar{\nu}$ and $b\to s \mu^+\mu^-$ transitions. In Fig.~\ref{Plot1} the regions favoured by $b\to s\mu^+\mu^-$ (blue) and allowed by $B\to K\nu\bar{\nu}$ (yellow) are shown together with contour lines for $B\to K^*\tau\mu$ in units of $10^{-6}$. Note that $B\to K\nu\bar{\nu}$ rules out branching ratios for $B\to K^*\tau\mu$ above approximately $1\times10^{-6}$ and that the constraint from $B\to K\nu\bar{\nu}$, being inclusive in the neutrino flavours, is independent of $\alpha_{\mu\tau}$.

\subsubsection{$Q_{\ell q}^{\left( 3 \right)}$ operator}
%
Here we have also charged currents that are related to the neutral current processes via CKM rotations. In Fig.~\ref{Plot2} 
the regions allowed by $B\to K\nu\bar{\nu}$ (yellow) and giving a good fit to data for $b\to s\mu^+\mu^-$ (blue) and (at the $2\,\sigma$ level) for $B\to D^*\tau\nu$ (red) are shown for different values of $\lambda^{(3)}$. Note that $b\to s\mu^+\mu^-$ data can be explained simultaneously with $R(D^{(*)})$ for negative $\mathcal{O}(1)$ values of $\lambda^{(3)}$ without violating the bounds from $B\to K\nu\bar{\nu}$. Again, in the regions compatible with all experimental constraints, the branching rations of LFV $B$ decays to $\tau\mu$ final states can only be up to $\approx10^{-6}$.

\subsubsection{$Q_{\ell q}^{\left( 1 \right)}$ and $Q_{\ell q}^{\left(3 \right)}$ with $\lambda^{(1)}=\lambda^{(3)}$}
%
In this case the phenomenology is then rather similar to the case of $C^{(3)}$ only. The major differences are that, as already mentioned before, the bounds from $B\to K\nu\bar{\nu}$ are evaded and the relative contribution to $b\to s\mu\mu$ compared to $R(D^{(*)})$ is a factor of 2 larger. In Fig.~\ref{PlotC3C1} we show the analogous plot to the central panel of Fig.~\ref{Plot2} ($\lambda^{(3)}=\lambda^{(1)}=-1$) for this scenario. Note that again $R(D^{(*)})$ rules out very large branching ratios for lepton flavour violating $B$ decays in the regions compatible with $b\to s\mu^+\mu^-$ data. We also consider the MFV-like ansatz \cite{Alonso:2015sja} with additional flavour rotations (light blue) which however differs only slightly for the ansatz with third generation couplings.

\section{UV completions}
\label{uvcomplete}
%
Let us briefly discuss UV completions which can give the desired coupling structure. As discussed previously, the 4-Fermi operator $Q_{\ell q}^{(3)}$ is relevant both for $R(K)$ and $R(D^{(*)})$. If $Q_{\ell q}^{(3)}$ is mediated by a single field, then there are only four possibilities:
(i) Vector boson (VB) with the SM charges $(SU(3)_{c}, SU(2)_{L}, U(1)_{Y})=({\bf 1},{\bf 3},0)$,
(ii) Scalar leptoquark (SLQ) with ({\bf 3},{\bf 3},$-1/3$),
(iii) Vector leptoquark (VLQ) with ({\bf 3},{\bf 1},2/3),
and (iv) Vector leptoquark with ({\bf 3},{\bf 3},2/3). 
The vector boson ({\bf 1},{\bf 3},0) induces only $Q_{\ell q}^{(3)}$.
On the other hand, the leptoquark fields result in 
particular combinations of $Q_{\ell q}^{(1)}$ and 
$Q_{\ell q}^{(3)}$~\cite{Alonso:2015sja}.
With the assumption of the third generation coupling,
the relative size of the effective couplings $\lambda^{(1,3)}$
and the signs are determined as 
\begin{align}
\text{VB({\bf 1},{\bf 3},$0$) : }& 
\lambda^{(3)}\text{ both positive and negative} ,%\\
\end{align}
\begin{align}
\text{SLQ({\bf 3},{\bf 3},$-1/3$) : }& 
\lambda^{(1)} = 3 \lambda^{(3)},  
 \quad 
\lambda^{(3)}>0,
\\
\text{VLQ({\bf 3},{\bf 1},2/3) : }&
\lambda^{(1)} = \lambda^{(3)},
\quad 
\lambda^{(3)} < 0,
\\
%%%%%
\text{VLQ({\bf 3},{\bf 3},2/3) : }&
\lambda^{(1)} = -3 \lambda^{(3)},
\quad
\lambda^{(3)}
>0.
\end{align}
The coefficient $C_{9}^{ij}$ is proportional to $\lambda^{(1)}+\lambda^{(3)}$ and a negative value is favoured by $R(K)$. Therefore, the scalar leptoquark is rejected as a candidate. To explain $R(D^{(*)})$ simultaneously, $\lambda^{(3)}$ itself must also be negative. This condition excludes the triplet vector leptoquark. If the experimental results are explained by the operator $Q_{\ell q}^{(3)}$ under the assumption of third generation coupling only, the possible mediators are the triplet vector boson or the singlet vector leptoquark.
According to the analysis of the previous section, a good fit to flavour data requires a mediator mass of $\mathcal{O}$(1) TeV. 
This opens interesting prospects for the LHC, especially in the case of leptoquarks that can be produced in proton-proton collisions 
via colour interactions and would decay to one lepton ($\tau$ or more interestingly $\mu$) and one jet (possibly a $b$-jet).
%
\begin{figure}[tb]
\begin{center}
\begin{tabular}{cp{7mm}c}
\includegraphics[width=0.43\textwidth]{C3C1plot} &&
\end{tabular}
\end{center}
\caption{
Allowed regions in the $\alpha_{\mu\tau}$--$\alpha_{sb}$ plane from $R(D^*)$ (red) and $b\to s \mu^+\mu^-$ (dark blue) for $\Lambda=\,$TeV and $\lambda^{(3)}=\lambda^{(1)}=-1$. The light blue region corresponds to the MFV-like ansatz for the lepton masses. Note that $\alpha_{sb}=\pi/64$ roughly corresponds to the angle needed to generate $V_{cb}$ and that the MFV-like Ansatz only differs marginally from the one with third generation couplings only in the region compatible with $R(D)$. The contour lines denote ${\rm Br}[B\to K^*\tau\mu]$ in units of $10^{-6}$.           
\label{PlotC3C1}}
\end{figure}

\section{Conclusions}
\label{conclusion}
%
In this article we considered the effect of gauge invariant dim-$6$ operators with left-handed fermions on $b\to s\mu^+\mu^-$, $B\to K^{(*)}\nu\bar{\nu}$, $B\to D^{(*)}\tau\nu$, $B\to K^{(*)}\tau\mu$ and $B_s\to \tau\mu$. For operators with left-handed quarks and leptons we find the correlations ${\rm Br}\left[B\to K\tau^\pm\mu^\mp \right]\approx {\rm Br}\left[B\to K^*\tau^\pm\mu^\mp \right]\approx 2 {\rm Br}\left[B_s\to \tau^\pm\mu^\mp \right]$. We showed that the anomalies in $b\to s\mu\mu$ data can be explained simultaneously with $R(D^*)$. For this we considered scenarios in which third generation couplings in the EW basis are present only: $\lambda^{(1)}\neq0$, $\lambda^{(3)}\neq0$ and $\lambda^{(3)}=\lambda^{(1)}\neq0$. Taking into account $\lambda^{(1)}\neq0$ only, $b\to s\mu^+\mu^-$ data can be explained without violating bounds from $B\to K^{(*)}\nu\bar{\nu}$. However, in the allowed regions of parameter space, ${\rm Br}[B\to K^{(*)}\tau\mu]$ can only be up to $1\times 10^{-6}$. In the case of $\lambda^{(3)}\neq0$, $b\to s\mu^+\mu^-$ data can be explained simultaneously with $R(D^*)$. In these regions ${\rm Br}[B\to K^{(*)}\tau\mu]$ can again be only up to $10^{-6}$. Finally we considered $\lambda^{(3)}=\lambda^{(1)}\neq0$. Such a scenario can be realized with a leptoquark in the singlet representation of $SU(2)_L$ (making an MFV-like ansatz for the lepton couplings possible) and constraints from $B\to K^{(*)}\nu\bar{\nu}$ are avoided. Again, LFV $B$ decays turn out to be of the same order as in the other scenarios.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\medskip
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
{\it Note added} --- During the completion of this work, an article presenting a dynamical model with additional vector bosons and third generation couplings appeared in which $Q_{\ell q}^{(3)}$  is generated~\cite{Greljo:2015mma}.

{\it Acknowledgments} --- {\small A.C.~and T.O.~thank the ULB for hospitality during their visit in Brussels. A.C.~is supported by a Marie Curie Intra-European Fellowship of the European Community's 7th Framework Programme under contract number PIEF-GA-2012-326948. T.O.~is supported by Japan Society for the Promotion of Science under KAKENHI Grant Number 26105503.
L.C.~thanks the Munich Institute for Astro- and Particle Physics and the organizers of the workshop ``Indirect Searches for New Physics in the LHC and Flavour Precision Era'' for hospitality and partial financial support during the completion of this work.}

\bibliography{BIB}

\end{document}

EFT.bbl
\begin{thebibliography}{65}
\expandafter\ifx\csname natexlab\endcsname\relax\def\natexlab#1{#1}\fi
\expandafter\ifx\csname bibnamefont\endcsname\relax
  \def\bibnamefont#1{#1}\fi
\expandafter\ifx\csname bibfnamefont\endcsname\relax
  \def\bibfnamefont#1{#1}\fi
\expandafter\ifx\csname citenamefont\endcsname\relax
  \def\citenamefont#1{#1}\fi
\expandafter\ifx\csname url\endcsname\relax
  \def\url#1{\texttt{#1}}\fi
\expandafter\ifx\csname urlprefix\endcsname\relax\def\urlprefix{URL }\fi
\providecommand{\bibinfo}[2]{#2}
\providecommand{\eprint}[2][]{\url{#2}}

\bibitem[{\citenamefont{Aad et~al.}(2012)}]{Aad:2012tfa}
\bibinfo{author}{\bibfnamefont{G.}~\bibnamefont{Aad}} \bibnamefont{et~al.}
  (\bibinfo{collaboration}{ATLAS Collaboration}), \bibinfo{journal}{Phys.Lett.}
  \textbf{\bibinfo{volume}{B716}}, \bibinfo{pages}{1} (\bibinfo{year}{2012}),
  \eprint{1207.7214}.

\bibitem[{\citenamefont{Chatrchyan et~al.}(2012)}]{Chatrchyan:2012ufa}
\bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Chatrchyan}}
  \bibnamefont{et~al.} (\bibinfo{collaboration}{CMS Collaboration}),
  \bibinfo{journal}{Phys.Lett.} \textbf{\bibinfo{volume}{B716}},
  \bibinfo{pages}{30} (\bibinfo{year}{2012}), \eprint{1207.7235}.

\bibitem[{\citenamefont{Egede et~al.}(2008)\citenamefont{Egede, Hurth, Matias,
  Ramon, and Reece}}]{Egede:2008uy}
\bibinfo{author}{\bibfnamefont{U.}~\bibnamefont{Egede}},
  \bibinfo{author}{\bibfnamefont{T.}~\bibnamefont{Hurth}},
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Matias}},
  \bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Ramon}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{W.}~\bibnamefont{Reece}},
  \bibinfo{journal}{JHEP} \textbf{\bibinfo{volume}{0811}}, \bibinfo{pages}{032}
  (\bibinfo{year}{2008}), \eprint{0807.2589}.

\bibitem[{\citenamefont{Aaij et~al.}(2013{\natexlab{a}})}]{Aaij:2013qta}
\bibinfo{author}{\bibfnamefont{R.}~\bibnamefont{Aaij}} \bibnamefont{et~al.}
  (\bibinfo{collaboration}{LHCb collaboration}),
  \bibinfo{journal}{Phys.Rev.Lett.} \textbf{\bibinfo{volume}{111}},
  \bibinfo{pages}{191801} (\bibinfo{year}{2013}{\natexlab{a}}),
  \eprint{1308.1707}.

\bibitem[{\citenamefont{Collaboration}(2015)}]{LHCb:2015dla}
\bibinfo{author}{\bibfnamefont{T.~L.} \bibnamefont{Collaboration}}
  (\bibinfo{collaboration}{LHCb}) (\bibinfo{year}{2015}).

\bibitem[{\citenamefont{Descotes-Genon
  et~al.}(2013{\natexlab{a}})\citenamefont{Descotes-Genon, Hurth, Matias, and
  Virto}}]{Descotes-Genon:2013vna}
\bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Descotes-Genon}},
  \bibinfo{author}{\bibfnamefont{T.}~\bibnamefont{Hurth}},
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Matias}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Virto}},
  \bibinfo{journal}{JHEP} \textbf{\bibinfo{volume}{1305}}, \bibinfo{pages}{137}
  (\bibinfo{year}{2013}{\natexlab{a}}), \eprint{1303.5794}.

\bibitem[{\citenamefont{Descotes-Genon
  et~al.}(2014)\citenamefont{Descotes-Genon, Hofer, Matias, and
  Virto}}]{Descotes-Genon:2014uoa}
\bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Descotes-Genon}},
  \bibinfo{author}{\bibfnamefont{L.}~\bibnamefont{Hofer}},
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Matias}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Virto}},
  \bibinfo{journal}{JHEP} \textbf{\bibinfo{volume}{1412}}, \bibinfo{pages}{125}
  (\bibinfo{year}{2014}), \eprint{1407.8526}.

\bibitem[{\citenamefont{Altmannshofer and
  Straub}(2014)}]{Altmannshofer:2014rta}
\bibinfo{author}{\bibfnamefont{W.}~\bibnamefont{Altmannshofer}}
  \bibnamefont{and} \bibinfo{author}{\bibfnamefont{D.~M.} \bibnamefont{Straub}}
  (\bibinfo{year}{2014}), \eprint{1411.3161}.

\bibitem[{\citenamefont{J{\"a}ger and Martin~Camalich}(2014)}]{Jager:2014rwa}
\bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{J{\"a}ger}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Martin~Camalich}}
  (\bibinfo{year}{2014}), \eprint{1412.3183}.

\bibitem[{\citenamefont{Aaij et~al.}(2013{\natexlab{b}})}]{Aaij:2013aln}
\bibinfo{author}{\bibfnamefont{R.}~\bibnamefont{Aaij}} \bibnamefont{et~al.}
  (\bibinfo{collaboration}{LHCb}), \bibinfo{journal}{JHEP}
  \textbf{\bibinfo{volume}{1307}}, \bibinfo{pages}{084}
  (\bibinfo{year}{2013}{\natexlab{b}}), \eprint{1305.2168}.

\bibitem[{\citenamefont{Horgan et~al.}(2014{\natexlab{a}})\citenamefont{Horgan,
  Liu, Meinel, and Wingate}}]{Horgan:2013pva}
\bibinfo{author}{\bibfnamefont{R.~R.} \bibnamefont{Horgan}},
  \bibinfo{author}{\bibfnamefont{Z.}~\bibnamefont{Liu}},
  \bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Meinel}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Wingate}},
  \bibinfo{journal}{Phys.Rev.Lett.} \textbf{\bibinfo{volume}{112}},
  \bibinfo{pages}{212003} (\bibinfo{year}{2014}{\natexlab{a}}),
  \eprint{1310.3887}.

\bibitem[{\citenamefont{Horgan et~al.}(2015)\citenamefont{Horgan, Liu, Meinel,
  and Wingate}}]{Horgan:2015vla}
\bibinfo{author}{\bibfnamefont{R.}~\bibnamefont{Horgan}},
  \bibinfo{author}{\bibfnamefont{Z.}~\bibnamefont{Liu}},
  \bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Meinel}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Wingate}}
  (\bibinfo{year}{2015}), \eprint{1501.00367}.

\bibitem[{\citenamefont{Bharucha et~al.}(2015)\citenamefont{Bharucha, Straub,
  and Zwicky}}]{Straub:2015ica}
\bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Bharucha}},
  \bibinfo{author}{\bibfnamefont{D.~M.} \bibnamefont{Straub}},
  \bibnamefont{and} \bibinfo{author}{\bibfnamefont{R.}~\bibnamefont{Zwicky}}
  (\bibinfo{year}{2015}), \eprint{1503.05534}.

\bibitem[{\citenamefont{Aaij et~al.}(2014)}]{Aaij:2014ora}
\bibinfo{author}{\bibfnamefont{R.}~\bibnamefont{Aaij}} \bibnamefont{et~al.}
  (\bibinfo{collaboration}{LHCb collaboration}),
  \bibinfo{journal}{Phys.Rev.Lett.} \textbf{\bibinfo{volume}{113}},
  \bibinfo{pages}{151601} (\bibinfo{year}{2014}), \eprint{1406.6482}.

\bibitem[{\citenamefont{Bobeth et~al.}(2007)\citenamefont{Bobeth, Hiller, and
  Piranishvili}}]{Bobeth:2007dw}
\bibinfo{author}{\bibfnamefont{C.}~\bibnamefont{Bobeth}},
  \bibinfo{author}{\bibfnamefont{G.}~\bibnamefont{Hiller}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{G.}~\bibnamefont{Piranishvili}},
  \bibinfo{journal}{JHEP} \textbf{\bibinfo{volume}{0712}}, \bibinfo{pages}{040}
  (\bibinfo{year}{2007}), \eprint{0709.4174}.

\bibitem[{\citenamefont{Altmannshofer and
  Straub}(2015)}]{Altmannshofer:2015sma}
\bibinfo{author}{\bibfnamefont{W.}~\bibnamefont{Altmannshofer}}
  \bibnamefont{and} \bibinfo{author}{\bibfnamefont{D.~M.} \bibnamefont{Straub}}
  (\bibinfo{year}{2015}), \eprint{1503.06199}.

\bibitem[{\citenamefont{Lees et~al.}(2012)}]{Lees:2012xj}
\bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Lees}} \bibnamefont{et~al.}
  (\bibinfo{collaboration}{BaBar}), \bibinfo{journal}{Phys.Rev.Lett.}
  \textbf{\bibinfo{volume}{109}}, \bibinfo{pages}{101802}
  (\bibinfo{year}{2012}), \eprint{1205.5442}.

\bibitem[{\citenamefont{Chur}(2015)}]{BDstaumuBELLE}
\bibinfo{author}{\bibfnamefont{T.}~\bibnamefont{Chur}}
  (\bibinfo{collaboration}{BELLE}), \bibinfo{journal}{Talk at the FPCP
  conference 2015,
  \url{https://agenda.hepl.phys.nagoya-u.ac.jp/indico/getFile.py/access?contribId=22&sessionId=4&resId=0&materialId=slides&confId=170}}
   (\bibinfo{year}{2015}).

\bibitem[{\citenamefont{Ciezarek}(2015)}]{BDstaumuLHCb}
\bibinfo{author}{\bibfnamefont{G.}~\bibnamefont{Ciezarek}}
  (\bibinfo{collaboration}{LHCb}), \bibinfo{journal}{Talk at the FPCP
  conference 2015,
  \url{https://agenda.hepl.phys.nagoya-u.ac.jp/indico/getFile.py/access?contribId=21&sessionId=4&resId=0&materialId=slides&confId=170}}
   (\bibinfo{year}{2015}).

\bibitem[{\citenamefont{Rotondo}(2015)}]{BDstaumuCOMBINED}
\bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Rotondo}},
  \bibinfo{journal}{Talk of Zoltan Ligeti at the FPCP conference 2015,
  \url{https://agenda.hepl.phys.nagoya-u.ac.jp/indico/getFile.py/access?contribId=9&sessionId=19&resId=0&materialId=slides&confId=170}}
   (\bibinfo{year}{2015}).

\bibitem[{\citenamefont{Fajfer et~al.}(2012{\natexlab{a}})\citenamefont{Fajfer,
  Kamenik, and Nisandzic}}]{Fajfer:2012vx}
\bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Fajfer}},
  \bibinfo{author}{\bibfnamefont{J.~F.} \bibnamefont{Kamenik}},
  \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{I.}~\bibnamefont{Nisandzic}},
  \bibinfo{journal}{Phys.Rev.} \textbf{\bibinfo{volume}{D85}},
  \bibinfo{pages}{094025} (\bibinfo{year}{2012}{\natexlab{a}}),
  \eprint{1203.2654}.

\bibitem[{\citenamefont{Descotes-Genon
  et~al.}(2013{\natexlab{b}})\citenamefont{Descotes-Genon, Matias, and
  Virto}}]{Descotes-Genon:2013wba}
\bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Descotes-Genon}},
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Matias}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Virto}},
  \bibinfo{journal}{Phys.Rev.} \textbf{\bibinfo{volume}{D88}},
  \bibinfo{pages}{074002} (\bibinfo{year}{2013}{\natexlab{b}}),
  \eprint{1307.5683}.

\bibitem[{\citenamefont{Gauld et~al.}(2014{\natexlab{a}})\citenamefont{Gauld,
  Goertz, and Haisch}}]{Gauld:2013qba}
\bibinfo{author}{\bibfnamefont{R.}~\bibnamefont{Gauld}},
  \bibinfo{author}{\bibfnamefont{F.}~\bibnamefont{Goertz}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{U.}~\bibnamefont{Haisch}},
  \bibinfo{journal}{Phys.Rev.} \textbf{\bibinfo{volume}{D89}},
  \bibinfo{pages}{015005} (\bibinfo{year}{2014}{\natexlab{a}}),
  \eprint{1308.1959}.

\bibitem[{\citenamefont{Buras and Girrbach}(2013)}]{Buras:2013qja}
\bibinfo{author}{\bibfnamefont{A.~J.} \bibnamefont{Buras}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Girrbach}},
  \bibinfo{journal}{JHEP} \textbf{\bibinfo{volume}{1312}}, \bibinfo{pages}{009}
  (\bibinfo{year}{2013}), \eprint{1309.2466}.

\bibitem[{\citenamefont{Gauld et~al.}(2014{\natexlab{b}})\citenamefont{Gauld,
  Goertz, and Haisch}}]{Gauld:2013qja}
\bibinfo{author}{\bibfnamefont{R.}~\bibnamefont{Gauld}},
  \bibinfo{author}{\bibfnamefont{F.}~\bibnamefont{Goertz}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{U.}~\bibnamefont{Haisch}},
  \bibinfo{journal}{JHEP} \textbf{\bibinfo{volume}{1401}}, \bibinfo{pages}{069}
  (\bibinfo{year}{2014}{\natexlab{b}}), \eprint{1310.1082}.

\bibitem[{\citenamefont{Buras et~al.}(2014)\citenamefont{Buras, De~Fazio, and
  Girrbach}}]{Buras:2013dea}
\bibinfo{author}{\bibfnamefont{A.~J.} \bibnamefont{Buras}},
  \bibinfo{author}{\bibfnamefont{F.}~\bibnamefont{De~Fazio}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Girrbach}},
  \bibinfo{journal}{JHEP} \textbf{\bibinfo{volume}{1402}}, \bibinfo{pages}{112}
  (\bibinfo{year}{2014}), \eprint{1311.6729}.

\bibitem[{\citenamefont{Altmannshofer et~al.}(2014)\citenamefont{Altmannshofer,
  Gori, Pospelov, and Yavin}}]{Altmannshofer:2014cfa}
\bibinfo{author}{\bibfnamefont{W.}~\bibnamefont{Altmannshofer}},
  \bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Gori}},
  \bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Pospelov}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{I.}~\bibnamefont{Yavin}},
  \bibinfo{journal}{Phys.Rev.} \textbf{\bibinfo{volume}{D89}},
  \bibinfo{pages}{095033} (\bibinfo{year}{2014}), \eprint{1403.1269}.

\bibitem[{\citenamefont{Crivellin
  et~al.}(2015{\natexlab{a}})\citenamefont{Crivellin, D'Ambrosio, and
  Heeck}}]{Crivellin:2015mga}
\bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Crivellin}},
  \bibinfo{author}{\bibfnamefont{G.}~\bibnamefont{D'Ambrosio}},
  \bibnamefont{and} \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Heeck}}
  (\bibinfo{year}{2015}{\natexlab{a}}), \eprint{1501.00993}.

\bibitem[{\citenamefont{Crivellin
  et~al.}(2015{\natexlab{b}})\citenamefont{Crivellin, D'Ambrosio, and
  Heeck}}]{Crivellin:2015lwa}
\bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Crivellin}},
  \bibinfo{author}{\bibfnamefont{G.}~\bibnamefont{D'Ambrosio}},
  \bibnamefont{and} \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Heeck}}
  (\bibinfo{year}{2015}{\natexlab{b}}), \eprint{1503.03477}.

\bibitem[{\citenamefont{Niehoff et~al.}(2015)\citenamefont{Niehoff, Stangl, and
  Straub}}]{Niehoff:2015bfa}
\bibinfo{author}{\bibfnamefont{C.}~\bibnamefont{Niehoff}},
  \bibinfo{author}{\bibfnamefont{P.}~\bibnamefont{Stangl}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{D.~M.} \bibnamefont{Straub}}
  (\bibinfo{year}{2015}), \eprint{1503.03865}.

\bibitem[{\citenamefont{Sierra et~al.}(2015)\citenamefont{Sierra, Staub, and
  Vicente}}]{Sierra:2015fma}
\bibinfo{author}{\bibfnamefont{D.~A.} \bibnamefont{Sierra}},
  \bibinfo{author}{\bibfnamefont{F.}~\bibnamefont{Staub}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Vicente}}
  (\bibinfo{year}{2015}), \eprint{1503.06077}.

\bibitem[{\citenamefont{Celis et~al.}(2015)\citenamefont{Celis, Fuentes-Martin,
  Jung, and Serodio}}]{Celis:2015ara}
\bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Celis}},
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Fuentes-Martin}},
  \bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Jung}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{H.}~\bibnamefont{Serodio}}
  (\bibinfo{year}{2015}), \eprint{1505.03079}.

\bibitem[{\citenamefont{Becirevic et~al.}(2015)\citenamefont{Becirevic, Fajfer,
  and Kosnik}}]{Becirevic:2015asa}
\bibinfo{author}{\bibfnamefont{D.}~\bibnamefont{Becirevic}},
  \bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Fajfer}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{N.}~\bibnamefont{Kosnik}}
  (\bibinfo{year}{2015}), \eprint{1503.09024}.

\bibitem[{\citenamefont{Varzielas and Hiller}(2015)}]{Varzielas:2015iva}
\bibinfo{author}{\bibfnamefont{I.~d.~M.} \bibnamefont{Varzielas}}
  \bibnamefont{and} \bibinfo{author}{\bibfnamefont{G.}~\bibnamefont{Hiller}}
  (\bibinfo{year}{2015}), \eprint{1503.01084}.

\bibitem[{\citenamefont{Crivellin et~al.}(2012)\citenamefont{Crivellin, Greub,
  and Kokulu}}]{Crivellin:2012ye}
\bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Crivellin}},
  \bibinfo{author}{\bibfnamefont{C.}~\bibnamefont{Greub}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Kokulu}},
  \bibinfo{journal}{Phys.Rev.} \textbf{\bibinfo{volume}{D86}},
  \bibinfo{pages}{054014} (\bibinfo{year}{2012}), \eprint{1206.2634}.

\bibitem[{\citenamefont{Datta et~al.}(2012)\citenamefont{Datta, Duraisamy, and
  Ghosh}}]{Datta:2012qk}
\bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Datta}},
  \bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Duraisamy}},
  \bibnamefont{and} \bibinfo{author}{\bibfnamefont{D.}~\bibnamefont{Ghosh}},
  \bibinfo{journal}{Phys.Rev.} \textbf{\bibinfo{volume}{D86}},
  \bibinfo{pages}{034027} (\bibinfo{year}{2012}), \eprint{1206.3760}.

\bibitem[{\citenamefont{Crivellin et~al.}(2013)\citenamefont{Crivellin, Kokulu,
  and Greub}}]{Crivellin:2013wna}
\bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Crivellin}},
  \bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Kokulu}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{C.}~\bibnamefont{Greub}},
  \bibinfo{journal}{Phys.Rev.} \textbf{\bibinfo{volume}{D87}},
  \bibinfo{pages}{094031} (\bibinfo{year}{2013}), \eprint{1303.5877}.

\bibitem[{\citenamefont{Li et~al.}(2014)\citenamefont{Li, Yang, and
  Yuan}}]{Li:2013vlx}
\bibinfo{author}{\bibfnamefont{X.-Q.} \bibnamefont{Li}},
  \bibinfo{author}{\bibfnamefont{Y.-D.} \bibnamefont{Yang}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{X.-B.} \bibnamefont{Yuan}},
  \bibinfo{journal}{Phys.Rev.} \textbf{\bibinfo{volume}{D89}},
  \bibinfo{pages}{054024} (\bibinfo{year}{2014}), \eprint{1311.2786}.

\bibitem[{\citenamefont{Faisel}(2014)}]{Faisel:2013nra}
\bibinfo{author}{\bibfnamefont{G.}~\bibnamefont{Faisel}},
  \bibinfo{journal}{Phys.Lett.} \textbf{\bibinfo{volume}{B731}},
  \bibinfo{pages}{279} (\bibinfo{year}{2014}), \eprint{1311.0740}.

\bibitem[{\citenamefont{Atoui et~al.}(2014)\citenamefont{Atoui, Morénas,
  Bečirevic, and Sanfilippo}}]{Atoui:2013zza}
\bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Atoui}},
  \bibinfo{author}{\bibfnamefont{V.}~\bibnamefont{Morénas}},
  \bibinfo{author}{\bibfnamefont{D.}~\bibnamefont{Bečirevic}},
  \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{F.}~\bibnamefont{Sanfilippo}},
  \bibinfo{journal}{Eur.Phys.J.} \textbf{\bibinfo{volume}{C74}},
  \bibinfo{pages}{2861} (\bibinfo{year}{2014}), \eprint{1310.5238}.

\bibitem[{\citenamefont{Sakaki et~al.}(2013)\citenamefont{Sakaki, Tanaka,
  Tayduganov, and Watanabe}}]{Sakaki:2013bfa}
\bibinfo{author}{\bibfnamefont{Y.}~\bibnamefont{Sakaki}},
  \bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Tanaka}},
  \bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Tayduganov}},
  \bibnamefont{and} \bibinfo{author}{\bibfnamefont{R.}~\bibnamefont{Watanabe}},
  \bibinfo{journal}{Phys.Rev.} \textbf{\bibinfo{volume}{D88}},
  \bibinfo{pages}{094012} (\bibinfo{year}{2013}), \eprint{1309.0301}.

\bibitem[{\citenamefont{Celis}(2013)}]{Celis:2013bya}
\bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Celis}}, \bibinfo{journal}{PoS}
  \textbf{\bibinfo{volume}{EPS-HEP2013}}, \bibinfo{pages}{334}
  (\bibinfo{year}{2013}), \eprint{1308.6779}.

\bibitem[{\citenamefont{Biancofiore et~al.}(2014)\citenamefont{Biancofiore,
  Colangelo, and De~Fazio}}]{Biancofiore:2014wpa}
\bibinfo{author}{\bibfnamefont{P.}~\bibnamefont{Biancofiore}},
  \bibinfo{author}{\bibfnamefont{P.}~\bibnamefont{Colangelo}},
  \bibnamefont{and} \bibinfo{author}{\bibfnamefont{F.}~\bibnamefont{De~Fazio}},
  \bibinfo{journal}{Phys.Rev.} \textbf{\bibinfo{volume}{D89}},
  \bibinfo{pages}{095018} (\bibinfo{year}{2014}), \eprint{1403.2944}.

\bibitem[{\citenamefont{Hurth et~al.}(2014)\citenamefont{Hurth, Mahmoudi, and
  Neshatpour}}]{Hurth:2014vma}
\bibinfo{author}{\bibfnamefont{T.}~\bibnamefont{Hurth}},
  \bibinfo{author}{\bibfnamefont{F.}~\bibnamefont{Mahmoudi}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Neshatpour}},
  \bibinfo{journal}{JHEP} \textbf{\bibinfo{volume}{1412}}, \bibinfo{pages}{053}
  (\bibinfo{year}{2014}), \eprint{1410.4545}.

\bibitem[{\citenamefont{Glashow et~al.}(2014)\citenamefont{Glashow, Guadagnoli,
  and Lane}}]{Glashow:2014iga}
\bibinfo{author}{\bibfnamefont{S.~L.} \bibnamefont{Glashow}},
  \bibinfo{author}{\bibfnamefont{D.}~\bibnamefont{Guadagnoli}},
  \bibnamefont{and} \bibinfo{author}{\bibfnamefont{K.}~\bibnamefont{Lane}}
  (\bibinfo{year}{2014}), \eprint{1411.0565}.

\bibitem[{\citenamefont{Boucenna et~al.}(2015)\citenamefont{Boucenna, Valle,
  and Vicente}}]{Boucenna:2015raa}
\bibinfo{author}{\bibfnamefont{S.~M.} \bibnamefont{Boucenna}},
  \bibinfo{author}{\bibfnamefont{J.~W.~F.} \bibnamefont{Valle}},
  \bibnamefont{and} \bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Vicente}}
  (\bibinfo{year}{2015}), \eprint{1503.07099}.

\bibitem[{\citenamefont{Buchmuller and Wyler}(1986)}]{Buchmuller:1985jz}
\bibinfo{author}{\bibfnamefont{W.}~\bibnamefont{Buchmuller}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{D.}~\bibnamefont{Wyler}},
  \bibinfo{journal}{Nucl.Phys.} \textbf{\bibinfo{volume}{B268}},
  \bibinfo{pages}{621} (\bibinfo{year}{1986}).

\bibitem[{\citenamefont{Grzadkowski et~al.}(2010)\citenamefont{Grzadkowski,
  Iskrzynski, Misiak, and Rosiek}}]{Grzadkowski:2010es}
\bibinfo{author}{\bibfnamefont{B.}~\bibnamefont{Grzadkowski}},
  \bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Iskrzynski}},
  \bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Misiak}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Rosiek}},
  \bibinfo{journal}{JHEP} \textbf{\bibinfo{volume}{1010}}, \bibinfo{pages}{085}
  (\bibinfo{year}{2010}), \eprint{1008.4884}.

\bibitem[{\citenamefont{Fajfer et~al.}(2012{\natexlab{b}})\citenamefont{Fajfer,
  Kamenik, Nisandzic, and Zupan}}]{Fajfer:2012jt}
\bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Fajfer}},
  \bibinfo{author}{\bibfnamefont{J.~F.} \bibnamefont{Kamenik}},
  \bibinfo{author}{\bibfnamefont{I.}~\bibnamefont{Nisandzic}},
  \bibnamefont{and} \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Zupan}},
  \bibinfo{journal}{Phys.Rev.Lett.} \textbf{\bibinfo{volume}{109}},
  \bibinfo{pages}{161801} (\bibinfo{year}{2012}{\natexlab{b}}),
  \eprint{1206.1872}.

\bibitem[{\citenamefont{Bhattacharya et~al.}(2014)\citenamefont{Bhattacharya,
  Datta, London, and Shivashankara}}]{Bhattacharya:2014wla}
\bibinfo{author}{\bibfnamefont{B.}~\bibnamefont{Bhattacharya}},
  \bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Datta}},
  \bibinfo{author}{\bibfnamefont{D.}~\bibnamefont{London}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Shivashankara}}
  (\bibinfo{year}{2014}), \eprint{1412.7164}.

\bibitem[{\citenamefont{Buras et~al.}(2015)\citenamefont{Buras, Girrbach-Noe,
  Niehoff, and Straub}}]{Buras:2014fpa}
\bibinfo{author}{\bibfnamefont{A.~J.} \bibnamefont{Buras}},
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Girrbach-Noe}},
  \bibinfo{author}{\bibfnamefont{C.}~\bibnamefont{Niehoff}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{D.~M.} \bibnamefont{Straub}},
  \bibinfo{journal}{JHEP} \textbf{\bibinfo{volume}{1502}}, \bibinfo{pages}{184}
  (\bibinfo{year}{2015}), \eprint{1409.4557}.

\bibitem[{\citenamefont{Alonso et~al.}(2015)\citenamefont{Alonso, Grinstein,
  and Camalich}}]{Alonso:2015sja}
\bibinfo{author}{\bibfnamefont{R.}~\bibnamefont{Alonso}},
  \bibinfo{author}{\bibfnamefont{B.}~\bibnamefont{Grinstein}},
  \bibnamefont{and} \bibinfo{author}{\bibfnamefont{J.~M.}
  \bibnamefont{Camalich}} (\bibinfo{year}{2015}), \eprint{1505.05164}.

\bibitem[{\citenamefont{Descotes-Genon
  et~al.}(2013{\natexlab{c}})\citenamefont{Descotes-Genon, Matias, and
  Virto}}]{Descotes-Genon:2013zva}
\bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Descotes-Genon}},
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Matias}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Virto}},
  \bibinfo{journal}{PoS} \textbf{\bibinfo{volume}{EPS-HEP2013}},
  \bibinfo{pages}{361} (\bibinfo{year}{2013}{\natexlab{c}}),
  \eprint{1311.3876}.

\bibitem[{\citenamefont{Lees et~al.}(2013)}]{Lees:2013kla}
\bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Lees}} \bibnamefont{et~al.}
  (\bibinfo{collaboration}{BaBar}), \bibinfo{journal}{Phys.Rev.}
  \textbf{\bibinfo{volume}{D87}}, \bibinfo{pages}{112005}
  (\bibinfo{year}{2013}), \eprint{1303.7465}.

\bibitem[{\citenamefont{Lutz et~al.}(2013)}]{Lutz:2013ftz}
\bibinfo{author}{\bibfnamefont{O.}~\bibnamefont{Lutz}} \bibnamefont{et~al.}
  (\bibinfo{collaboration}{Belle}), \bibinfo{journal}{Phys.Rev.}
  \textbf{\bibinfo{volume}{D87}}, \bibinfo{pages}{111103}
  (\bibinfo{year}{2013}), \eprint{1303.3719}.

\bibitem[{\citenamefont{Crivellin
  et~al.}(2015{\natexlab{c}})\citenamefont{Crivellin, Hofer, Matias, Nierste,
  Pokorski et~al.}}]{Crivellin:2015era}
\bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Crivellin}},
  \bibinfo{author}{\bibfnamefont{L.}~\bibnamefont{Hofer}},
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Matias}},
  \bibinfo{author}{\bibfnamefont{U.}~\bibnamefont{Nierste}},
  \bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Pokorski}},
  \bibnamefont{et~al.} (\bibinfo{year}{2015}{\natexlab{c}}),
  \eprint{1504.07928}.

\bibitem[{\citenamefont{Dedes et~al.}(2009)\citenamefont{Dedes, Rosiek, and
  Tanedo}}]{Dedes:2008iw}
\bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Dedes}},
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Rosiek}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{P.}~\bibnamefont{Tanedo}},
  \bibinfo{journal}{Phys.Rev.} \textbf{\bibinfo{volume}{D79}},
  \bibinfo{pages}{055006} (\bibinfo{year}{2009}), \eprint{0812.4320}.

\bibitem[{\citenamefont{Bouchard et~al.}(2013)\citenamefont{Bouchard, Lepage,
  Monahan, Na, and Shigemitsu}}]{Bouchard:2013eph}
\bibinfo{author}{\bibfnamefont{C.}~\bibnamefont{Bouchard}},
  \bibinfo{author}{\bibfnamefont{G.~P.} \bibnamefont{Lepage}},
  \bibinfo{author}{\bibfnamefont{C.}~\bibnamefont{Monahan}},
  \bibinfo{author}{\bibfnamefont{H.}~\bibnamefont{Na}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Shigemitsu}}
  (\bibinfo{collaboration}{HPQCD Collaboration}), \bibinfo{journal}{Phys.Rev.}
  \textbf{\bibinfo{volume}{D88}}, \bibinfo{pages}{054509}
  (\bibinfo{year}{2013}), \eprint{1306.2384}.

\bibitem[{\citenamefont{Horgan et~al.}(2014{\natexlab{b}})\citenamefont{Horgan,
  Liu, Meinel, and Wingate}}]{Horgan:2013hoa}
\bibinfo{author}{\bibfnamefont{R.~R.} \bibnamefont{Horgan}},
  \bibinfo{author}{\bibfnamefont{Z.}~\bibnamefont{Liu}},
  \bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Meinel}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Wingate}},
  \bibinfo{journal}{Phys.Rev.} \textbf{\bibinfo{volume}{D89}},
  \bibinfo{pages}{094501} (\bibinfo{year}{2014}{\natexlab{b}}),
  \eprint{1310.3722}.

\bibitem[{\citenamefont{Amhis et~al.}(2014)}]{Amhis:2014hma}
\bibinfo{author}{\bibfnamefont{Y.}~\bibnamefont{Amhis}} \bibnamefont{et~al.}
  (\bibinfo{collaboration}{Heavy Flavor Averaging Group (HFAG)})
  (\bibinfo{year}{2014}), \eprint{1412.7515}.

\bibitem[{\citenamefont{Greljo et~al.}(2015)\citenamefont{Greljo, Isidori, and
  Marzocca}}]{Greljo:2015mma}
\bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Greljo}},
  \bibinfo{author}{\bibfnamefont{G.}~\bibnamefont{Isidori}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{D.}~\bibnamefont{Marzocca}}
  (\bibinfo{year}{2015}), \eprint{1506.01705}.

\bibitem[{\citenamefont{Linn}(2015)}]{BsphimumuFPCP}
\bibinfo{author}{\bibfnamefont{C.}~\bibnamefont{Linn}}
  (\bibinfo{collaboration}{LHCb}), \bibinfo{journal}{Talk at the FPCP
  conference 2015,
  \url{https://agenda.hepl.phys.nagoya-u.ac.jp/indico/getFile.py/access?contribId=19&sessionId=4&resId=0&materialId=slides&confId=170}}
   (\bibinfo{year}{2015}).

\bibitem[{\citenamefont{Crivellin
  et~al.}(2014{\natexlab{a}})\citenamefont{Crivellin, Najjari, and
  Rosiek}}]{Crivellin:2013hpa}
\bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Crivellin}},
  \bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Najjari}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Rosiek}},
  \bibinfo{journal}{JHEP} \textbf{\bibinfo{volume}{1404}}, \bibinfo{pages}{167}
  (\bibinfo{year}{2014}{\natexlab{a}}), \eprint{1312.0634}.

\bibitem[{\citenamefont{Crivellin
  et~al.}(2014{\natexlab{b}})\citenamefont{Crivellin, Hoferichter, and
  Procura}}]{Crivellin:2014cta}
\bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Crivellin}},
  \bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Hoferichter}},
  \bibnamefont{and} \bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Procura}},
  \bibinfo{journal}{Phys.Rev.} \textbf{\bibinfo{volume}{D89}},
  \bibinfo{pages}{093024} (\bibinfo{year}{2014}{\natexlab{b}}),
  \eprint{1404.7134}.

\bibitem[{\citenamefont{Pruna and Signer}(2014)}]{Pruna:2014asa}
\bibinfo{author}{\bibfnamefont{G.~M.} \bibnamefont{Pruna}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{A.}~\bibnamefont{Signer}},
  \bibinfo{journal}{JHEP} \textbf{\bibinfo{volume}{1410}}, \bibinfo{pages}{14}
  (\bibinfo{year}{2014}), \eprint{1408.3565}.

\end{thebibliography}
