\(\varvec{B^0\rightarrow K^{*0}\mu ^+\mu ^}\) decay in the aligned twoHiggsdoublet model
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Abstract
In the aligned twoHiggsdoublet model, we perform a complete oneloop computation of the shortdistance Wilson coefficients \(C_{7,9,10}^{(\prime )}\), which are the most relevant ones for \(b\rightarrow s\ell ^+\ell ^\) transitions. It is found that, when the model parameter \(\left \varsigma _{u}\right \) is much smaller than \(\left \varsigma _{d}\right \), the charged scalar contributes mainly to chiralityflipped \(C_{9,10}^\prime \), with the corresponding effects being proportional to \(\left \varsigma _{d}\right ^2\). Numerically, the chargedscalar effects fit into two categories: (A) \(C_{7,9,10}^\mathrm {H^\pm }\) are sizable, but \(C_{9,10}^{\prime \mathrm {H^\pm }}\simeq 0\), corresponding to the (large \(\left \varsigma _{u}\right \), small \(\left \varsigma _{d}\right \)) region; (B) \(C_7^\mathrm {H^\pm }\) and \(C_{9,10}^{\prime \mathrm {H^\pm }}\) are sizable, but \(C_{9,10}^\mathrm {H^\pm }\simeq 0\), corresponding to the (small \(\left \varsigma _{u}\right \), large \(\left \varsigma _{d}\right \)) region. Taking into account phenomenological constraints from the inclusive radiative decay \(B\rightarrow X_{s}{\gamma }\), as well as the latest modelindependent global analysis of \(b\rightarrow s\ell ^+\ell ^\) data, we obtain the much restricted parameter space of the model. We then study the impact of the allowed model parameters on the angular observables \(P_2\) and \(P_5'\) of \(B^0\rightarrow K^{*0}\mu ^+\mu ^\) decay, and we find that \(P_5'\) could be increased significantly to be consistent with the experimental data in case B.
1 Introduction
The rare \(B\rightarrow K^{*}\ell ^+\ell ^\) decays, being the flavorchanging neutralcurrent (FCNC) processes, do not arise at tree level and are highly suppressed at higher orders within the Standard Model (SM), due to the Glashow–Iliopoulos–Maiani (GIM) mechanism [1]. However, new TeVscale particles in many extensions of the SM could affect the decay amplitude at a similar level as the SM does. These decays play, therefore, a crucial role in testing the SM and probing various NP scenarios beyond it [2]. It is particularly interesting to note that, based on these decays, observables with a very limited sensitivity to hadronic uncertainties can be constructed, enhancing therefore the discovery potential for NP [3, 4, 5, 6, 7, 8, 9, 10].
Experimentally, several interesting deviations from the SM predictions have been observed in these decays. In 2013, the formfactorindependent angular observable \(P'_5\) [8, 9] of \(B^0\rightarrow K^{*0}\mu ^+\mu ^\) decay was measured by the LHCb collaboration [11], showing a \(3.7\sigma \) disagreement with the SM expectation [12, 13, 14, 15]. Recently, the LHCb collaboration has released new measurements of the angular observables in this decay, based on the dataset of \(3~\mathrm {fb}^{1}\) of integrated luminosity, and still found a \(3.4\sigma \) deviation for \(P'_5\) [16]. Moreover, being in agreement with the LHCb measurements, a deviation with a significance of \(2.1\sigma \) was also reported by the Belle collaboration [17]. Besides the \(P'_5\) anomaly, there are some other slight deviations beyond the \(2\sigma \) level, such as the observables \(P_2\) in \(q^2\in [2,4.3]~\mathrm {GeV}^2\) and \(P'_4\) in \(q^2\in [14.18,16]~\mathrm {GeV}^2\) [18, 19, 20]. These anomalies have triggered lots of theoretical studies both within the SM and in various NP models [8, 9, 10, 12, 13, 14, 15, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44].
As a minimal extension of the SM scalar sector, the twoHiggsdoublet model (2HDM) [45] can easily satisfy the electroweak (EW) precision data and, at the same time, lead to a very rich phenomenology [46]. The scalar spectrum consists of two charged scalars \(H^\pm \) and three neutral ones \(h,\,H\), and A, one of which is to be identified with the SMlike Higgs boson found at the LHC [47, 48]. The direct search for these additional scalar states would be an important task for highenergy colliders in the next few years. It should be noted that, complementary to the direct searches, indirect constraints on the 2HDM could also be obtained from the rare FCNC decays like \(B\rightarrow K^{*}\ell ^+\ell ^\), since these scalars can affect these processes through the penguin and box diagrams. These studies are also very helpful to gain further insights into the scalar sector of supersymmetry and other models that have similar scalar contents [49, 50, 51].
In a generic 2HDM, the nondiagonal couplings of neutral scalars to fermions lead to treelevel FCNC interactions, which can be avoided by imposing on the Lagrangian an ad hoc discrete \(\mathcal {Z}_2\) symmetry. Depending on the \(\mathcal {Z}_2\) charge assignments to the scalars and fermions, this results in four types of 2HDMs (types I, II, X, Y) [46, 52] under the hypothesis of natural flavor conservation (NFC) [53]. In the aligned twoHiggsdoublet model (A2HDM) [54], on the other hand, the absence of treelevel FCNCs is automatically guaranteed by assuming the alignment in flavor space of the Yukawa matrices for each type of righthanded fermions. Interestingly, the A2HDM can recover as particular cases all known specific implementations of the 2HDMs based on \(\mathcal {Z}_2\) symmetries. The model also features possible new sources of CP violation beyond that of the Cabibbo–Kobayashi–Maskawa (CKM) matrix [55, 56]. These features make the A2HDM very attracting both in highenergy collider physics [57, 58, 59, 60, 61, 62, 63] and in lowenergy flavor physics [64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74].
In this paper, we will study the decay \(B^0\rightarrow K^{*0}\mu ^+\mu ^\) in the A2HDM. Our paper is organized as follows: in Sect. 2, we give a brief overview of the A2HDM, focusing mainly on the scalar and Yukawa sectors. In Sect. 3, a complete oneloop computation of the shortdistance (SD) Wilson coefficients \(C_{7,9,10}^{(\prime )}\) is presented, and the final analytical expressions are given both within the SM and in the A2HDM. The angular observables of \(B^0\rightarrow K^{*0}\mu ^+\mu ^\) decay are also introduced in this section. In Sect. 4, taking into account phenomenological constraints from the inclusive radiative decay \(B\rightarrow X_s\gamma \) and the latest modelindependent global analysis of \(b\rightarrow s\ell ^+\ell ^\) data, we study the impact of the allowed model parameters on the angular observables \(P_2\) and \(P_5'\) of \(B^0\rightarrow K^{*0}\mu ^+\mu ^\) decay. Finally, our conclusions are drawn in Sect. 5. Some relevant functions for the Wilson coefficients are collected in the appendices.
2 The aligned twoHiggsdoublet model
2.1 Scalar sector
2.2 Yukawa sector
The onetoone correspondence between different specific choices of the couplings \(\varsigma _{f}\) and the 2HDMs based on discrete \(\mathcal {Z}_2\) symmetries
Model  \(\varsigma _{d}\)  \(\varsigma _{u}\)  \(\varsigma _{\ell }\) 

Type I  \(\cot {\beta }\)  \(\cot {\beta }\)  \(\cot {\beta }\) 
Type II  \(\tan {\beta }\)  \(\cot {\beta }\)  \(\tan {\beta }\) 
Type X  \(\cot {\beta }\)  \(\cot {\beta }\)  \(\tan {\beta }\) 
Type Y  \(\tan {\beta }\)  \(\cot {\beta }\)  \(\cot {\beta }\) 
Inert  0  0  0 
3 \(\varvec{B^0\rightarrow K^{*0}\mu ^+\mu ^}\) in the A2HDM
3.1 Effective weak Hamiltonian
Within the SM, the electromagnetic dipole operator \(O_7\) and the semileptonic operators \(O_{9,10}\) play the leading role in the decay \(B^0\rightarrow K^{*0}\mu ^+\mu ^\). Besides modifying the values of the SD Wilson coefficients \(C_{7,9,10}\), the chargedscalar contributions could also make the chiralityflipped operators \(O_{7,9,10}^{\prime }\) defined above to contribute in a significant manner, especially in some regions of the parameter spaces discussed later.
3.2 Wilson coefficients in the SM
3.3 Wilson coefficients in the A2HDM
Our results for the chiralityflipped Wilson coefficients \(C_{7,9,10}^{\prime \mathrm {H^\pm }}\) are presented for the first time in the A2HDM. In the particular cases of the \(\mathcal {Z}_2\) symmetric 2HDMs, our results agree with the ones calculated in Refs. [89, 90, 91, 92]. It is also noted that the nexttoleading order QCD corrections to \(C_{7,9,10}^\mathrm {H^\pm }\) in the supersymmetry and typeII 2HDM have already been calculated in Refs. [93, 94, 95, 96, 97].
3.4 Angular observables in \({B^0\rightarrow K^{*0}\mu ^+\mu ^}\) decay
4 Numerical results and discussions
4.1 Choice of the model parameters

The chargedscalar mass is assumed to lie in the range \(M_{H^{\pm }} \in [80,1000]~\mathrm {GeV}\), where the lower bound comes from the LEP direct search [101], while the upper bound from the unitarity and stability of the scalar potential [102, 103, 104, 105].

The alignment parameter \(\varsigma _{u}\) is assumed to lie in the range \(\varsigma _{u}\le 2\), to be compatible with the current data of loopinduced processes, such as \(Z\rightarrow b\bar{b}\), \(b\rightarrow s \gamma \), \(B_{s,d}^0\)–\(\bar{B}_{s,d}^0\) mixings, as well as the h(125) decays [62, 63, 65, 66, 67, 68, 69].

The alignment parameter \(\varsigma _{d}\) is only mildly constrained through phenomenological requirements that involve additionally other model parameters. So we let it to be a free parameter.

In the 2HDMs with discrete \(\mathcal {Z}_2\) symmetries, the parameters \(\varsigma _{u}\) and \(\varsigma _{d}\) are not independent but are related to each other through the ratio of the VEVs \(\tan \beta =v_2/v_1\). The upper limit for \(\tan \beta \) also comes from the unitarity and stability of the scalar potential [102, 103, 104, 105]; we assume here \(\tan \beta \le 50\).
4.2 Constraints on the model parameters
For the other input parameters, we take \(M_Z=91.1876~\mathrm {GeV}\), \(M_{W}=80.385~\mathrm {GeV}\), \(m_{t}=(174.2\pm 1.4)~\mathrm {GeV}\), \(m_{b}=(4.78\pm 0.06)~\mathrm {GeV}\), and \(\bar{m}_{s}(2~\mathrm {GeV})=(96^{+8}_{4})~\mathrm {MeV}\) [106]. Since \(C_7^{\prime \mathrm {H}^\pm }=\bar{m}_{s}/\bar{m}_{b} C_7^{\mathrm {H}^\pm }\) and \(\bar{m}_{s} \ll \bar{m}_{b}\), the contribution from \(O_7'\) will be safely neglected.
Under the constraint from Eq. (4.3), we show in Fig. 2 the allowed regions in the \(\varsigma _{u}\)–\(\varsigma _{d}\) plane (\(\varsigma _{d}>0\)), with three representative values of the chargedscalar mass, \(M_{H^\pm }=80\), 300 and \(500~\mathrm {GeV}\) as benchmarks. The case with \(\varsigma _{d}<0\) is obtained from Fig. 2 with the changes \(\varsigma _{u}\rightarrow \varsigma _{u}\) and \(\varsigma _{d}\rightarrow \varsigma _{d}\). It is observed that the allowed range of \(\varsigma _{d}\) becomes quite large when \(\varsigma _{u}\) tends to 0; particularly, when \(\varsigma _{u}=0\), no constraint on \(\varsigma _{d}\) is obtained, because in this limit the SM result is recovered. When \(\varsigma _{d}=0\), on the other hand, a bound on \(\varsigma _{u}\) can be set with the allowed range of \(\varsigma _{u}\) further strengthened for smaller values of the chargedscalar mass. These qualitative observations are consistent with those observed previously in Refs. [64, 65, 66]. However, the allowed regions for \(\varsigma _{u}\) and \(\varsigma _{d}\) are further reduced compared to those obtained in Refs. [64, 65, 66], because the updated SM prediction (cf. Eq. (4.2)) becomes now more compatible with the current experimental data (cf. Eq. (4.1)). It is also found that the preset maximum value \(\left \varsigma _{u}\right =2\) is reached when \(\left \varsigma _{d}\right \) varies within a range away from 0, rather than at \(\varsigma _{d}=0\); for example, taking \(M_{H^\pm }=80~\mathrm {GeV}\), we find that \(\left \varsigma _{u}\right \) approaches 2 when \(0.6<\left \varsigma _{d}\right <0.8\). This novel observation motivates us to display the \(\varsigma _{d}\)axis in the logarithmic coordinate, making clear the correlation between \(\varsigma _{u}\) and \(\varsigma _{d}\) in the range \(\left \varsigma _{d}\right <1\). The inversely proportional and parabolic boundary curves in the first quadrant indicate that the NP contribution to \(C_{7}^\mathrm {H^\pm }\) (cf. Eq. (3.14)) is dominated by the \(\varsigma _{d}\varsigma _{u}^*\) and \(\left \varsigma _{u}\right ^2\) terms, respectively. As the large samesign solutions for \(\varsigma _{u}\) and \(\varsigma _{d}\) obtained in Refs. [64, 65], corresponding to the case when the NP influence is about twice the size of the SM contribution but with an opposite sign, are already excluded by the isospin asymmetry of \(B\rightarrow K^*\gamma \) decays [66, 116], they are not shown in Fig. 2.
It is also interesting to note that, under the constraint from Eq. (4.3) as well as the bounds on \(C_{9,10}^{\mathrm {H^\pm }}\) and \(C_{9,10}^{\prime \mathrm {H^\pm }}\) from Eqs. (4.4) and (4.5), we could obtain a bound on \(\varsigma _{d}\) even when \(\varsigma _{u}\) equals 0. Such a bound arises entirely from the information on \(C_{9,10}^{\prime \mathrm {H^\pm }}\) due to the \(\left \varsigma _{d}\right ^2\) terms in these two Wilson coefficients (cf. Eqs. (3.18) and (3.19)). For illustration, the allowed regions in the \(\varsigma _{d}\)–\(M_{H^\pm }\) plane when \(\varsigma _{u}=0\) and in the \(\varsigma _{u}\)–\(M_{H^\pm }\) plane when \(\varsigma _{d}=0\) are shown in Fig. 4. Numerically, we obtain \(\left \varsigma _{u}\right \le 0.506\), 0.763 and 0.990, and \(\left \varsigma _{d}\right \le 212\), 476 and 622, corresponding to \(M_{H^\pm }=80\), 300 and \(500~\mathrm {GeV}\), respectively. This means that the more accurate \(C_{9,10}^{\prime \mathrm{NP}}\) can be better used to restrict the parameter \(\varsigma _{d}\).
4.3 \(P_2\) and \(P_5'\) in the A2HDM
In this subsection, with the constrained parameter space for \(\varsigma _{u}\) and \(\varsigma _{d}\), we investigate the impact of A2HDM on the angular observables \(P_2\) and \(P_5'\) in the decay \(B^0\rightarrow K^{*0}\mu ^+\mu ^\). As there are involved only three model parameters \(\varsigma _{u}\), \(\varsigma _{d}\) and \(M_{H^\pm }\) in Eqs. (3.14)–(3.19), the five Wilson coefficients (\(C_7^{\prime \mathrm {H^\pm }}\) is neglected because \(\bar{m}_{s} \ll \bar{m}_{b}\)) are expected to be highly correlated with each other. Using the allowed values of \(\varsigma _{u}\) and \(\varsigma _{d}\) with three benchmark values of chargedscalar mass obtained in the previous subsection, we show in Fig. 5 the correlations among these five Wilson coefficients. One can see that, while \(C_7^\mathrm {H^\pm }\) is hardly correlated with the other four Wilson coefficients (Fig. 5a–d), \(C_9^\mathrm {H^\pm }\) and \(C_{10}^\mathrm {H^\pm }\) are obviously linearly correlated with each other and the slope depends only on the chargedscalar mass \(M_{H^\pm }\) (Fig. 5e), with the blue, red, and green lines obtained with \(M_{H^\pm }=80\), 300, and \(500~\mathrm {GeV}\), respectively. In addition, \(C_9^{\prime \mathrm {H^\pm }}\) and \(C_{10}^{\prime \mathrm {H^\pm }}\) are found to be approximately linearly correlated with each other (Fig. 5f), and the slope starts to be nearly a constant when \(M_{H^\pm }\ge 250~\mathrm {GeV}\), which explains why the two lines with \(M_{H^\pm }=300\) and \(500~\mathrm {GeV}\) almost overlap completely in Fig. 5f. In fact, from the analytic expressions for these Wilson coefficients (cf. Eqs. (3.15)–(3.16) and (3.18)–(3.19), together with (B.3)–(B.10)), we find that \(C_{9}^\mathrm {H^\pm }/C_{10}^\mathrm {H^\pm }\rightarrow 1+4\sin ^{2}\theta _{W}\,\left[ 1+4/(9x_{t})\right] \) and \(C_{9}^{\prime \mathrm {H^\pm }}/C_{10}^{\prime \mathrm {H^\pm }}\rightarrow 1+4\sin ^{2}\theta _{W}\) when \(M_{H^\pm }\) goes to infinity. This explains why the lines shown in Fig. 5e, f get closer to each other with larger \(M_{H^\pm }\).
The zerocrossing points of \(P_2\) (nonzero one) and \(P_5'\) both within the SM and in the A2HDM
SM  Case A  Case B  

\(q^2_0(P_2)\)  \(3.43^{+0.33}_{0.32}\)  \((3.02,\,3.90)\)  \((3.02,\,4.79)\) 
\(q^2_0(P_5')\)  \(2.02^{+0.19}_{0.15}\)  \((1.77,\,2.32)\)  \((1.79,\,4.85)\) 
4.4 2HDMs with \(\mathcal {Z}_2\) symmetries
In the generic 2HDMs with discrete \(\mathcal {Z}_2\) symmetries, the three alignment parameters \(\varsigma _{f}\) will be reduced to a single parameter \(\tan \beta =v_2/v_1\ge 0\), as indicated in Table 1. There are, therefore, only two model parameters, \(\tan \beta \) and \(M_{H^\pm }\), in the Wilson coefficients \(C_{7,9,10}^{(\prime )\mathrm {H^\pm }}\). We show in Fig. 7 the allowed regions in the \(\tan \beta \)–\(M_{H^\pm }\) plane corresponding to the four different types of 2HDMs with \(\mathcal {Z}_2\) symmetries. As \(C_{7,9,10}^{(\prime )\mathrm {H^\pm }}\) do not depend on the parameter \(\varsigma _\ell \), the type I (II) and type X (Y) models are indistinguishable from each other. However, one can clearly distinguish types I and X from types II and Y models. As shown in Fig. 7, the bound \(M_{H^\pm }>432\,\mathrm{GeV}\) is obtained for types II and Y 2HDMs, while there is no further bound found for \(M_{H^\pm }\) in types I and X 2HDMs with sizable \(\tan \beta \).
With the constrained model parameters shown in Fig. 7, we then show in Fig. 8 the \(q^2\) dependence of \(P_2\) and \(P_5'\) in the four different types of 2HDMs with \(\mathcal {Z}_2\) symmetries. One can see that, compared with the SM predictions, both \(P_2\) and \(P_5'\) are reduced in the types I and X (the green band), but increased in the types II and Y (the blue band) 2HDMs, only by a small amount. This is because the chargedscalar effect on the left and righthanded semileptonic operators is controlled by the same parameter \(\tan \beta \) and, under the constraint shown in Fig. 7, sizable \(C_{9,10}^{\prime \mathrm {H^\pm }}\) are not allowed in these models. It is, therefore, concluded the 2HDMs with \(\mathcal {Z}_2\) symmetries cannot explain the socalled \(P_5'\) anomaly.
5 Conclusions
In this paper, we have presented a complete oneloop calculation of the SD Wilson coefficients \(C_{7,9,10}^{(\prime )\mathrm {H^\pm }}\) due to the chargedscalar exchanges through the \(Z^0\) and \(\gamma \)penguin diagrams within the A2HDM. For \(C_{9,10}^{\prime \mathrm {H^\pm }}\), although being suppressed by the factor \(\bar{m}_{b}\,\bar{m}_{s}/M_{W}^2\), they could play an important role in interpreting the observed \(P_5'\) anomaly in the decay \(B^0\rightarrow K^{*0}\mu ^+\mu ^\), when the model parameter \(\varsigma _{d}\) is large.
Under the constraints from the branching ratio \(\mathcal {B}(B\rightarrow X_{s}\gamma )\) and the recent global fit results of \(b\rightarrow s\ell ^+\ell ^\) data, we have obtained the allowed parameter spaces in the \(\varsigma _{u}\)–\(\varsigma _{d}\) plane, corresponding to three representative chargedscalar masses. We found that \(C_{9,10}^\mathrm {H^\pm }\) play a major role in the small \(\left \varsigma _{d}\right \) region (\(\left \varsigma _{d}\right <1\)), while \(C_{9,10}^{\prime \mathrm {H^\pm }}\) are most important when the model parameter \(\varsigma _{u}\) approaches 0. When \(\varsigma _{u}\) is far away from 0 and \(\left \varsigma _{d}\right \ge 1\), on the other hand, the impact of \(C_{7}^\mathrm {H^\pm }\) will become more significant. Within the constrained parameter space, numerically, the effects of these NP Wilson coefficients can be divided into the following two cases: (A) \(C_{7,9,10}^\mathrm {H^\pm }\) are sizable, but \(C_{9,10}^{\prime \mathrm {H^\pm }}\simeq 0\), corresponding to the (large \(\left \varsigma _{u}\right \), small \(\left \varsigma _{d}\right \)) region; (B) \(C_7^\mathrm {H^\pm }\) and \(C_{9,10}^{\prime \mathrm {H^\pm }}\) are sizable, but \(C_{9,10}^\mathrm {H^\pm }\simeq 0\), corresponding to the (small \(\left \varsigma _{u}\right \), large \(\left \varsigma _{d}\right \)) region. We have then discussed their impacts on the angular observables \(P_2\) and \(P_5'\) in the decay \(B^0\rightarrow K^{*0}\mu ^+\mu ^\). It is found that there is only a small impact on \(P_2\) and \(P_5'\) in case A, while case B could obviously increase \(P_5'\) to be consistent with the experimental data and reduce \(P_2\) when the dimuon invariant mass squared \(q^2\) is higher than the zerocrossing point.
Finally, we have explored the constraints on \(\tan \beta \) and \(M_{H^\pm }\) in four types of \(\mathcal {Z}_2\)symmetric 2HDMs. The role of chiralityflipped operators \(O_{9,10}'\) becomes much more important for large values of \(\tan \beta \). Even with the current data, the types I and X and types II and Y could be clearly distinguished from each other. However, the chargedscalar effect on \(P_2\) and \(P_5'\) in these models is found to be small and does not help to explain the socalled \(P_5'\) anomaly.
Future precise measurements of the angular observables in \(b\rightarrow s\ell ^+\ell ^\) decays, especially with a finer binning of \(q^2\), would be very helpful to provide a more definite answer concerning the observed anomalies by the LHCb and Belle collaborations, restricting further or even deciphering the NP models.
Notes
Acknowledgements
The work is supported by the National Natural Science Foundation of China (NSFC) under contract Nos. 11675061, 11435003, 11225523 and 11521064. Q.H. is supported by the Excellent Doctorial Dissertation Cultivation Grant from CCNU, under contract number 2013YBZD19.
References
 1.S.L. Glashow, J. Iliopoulos, L. Maiani, Weak interactions with lepton–hadron symmetry. Phys. Rev. D 2, 1285–1292 (1970)ADSCrossRefGoogle Scholar
 2.T. Blake, G. Lanfranchi, D.M. Straub, Rare B decays as tests of the standard model. Prog. Part. Nucl. Phys. 92, 50–91 (2017). arXiv:1606.00916
 3.M. Beneke, T. Feldmann, D. Seidel, Systematic approach to exclusive \(B \rightarrow V l^+ l^\), \(V \gamma \) decays. Nucl. Phys. B 612, 25–58 (2001). arXiv:hepph/0106067 ADSCrossRefGoogle Scholar
 4.M. Beneke, T. Feldmann, D. Seidel, Exclusive radiative and electroweak \(b \rightarrow d\) and \(b \rightarrow s\) penguin decays at NLO. Eur. Phys. J. C 41, 173 (2005). arXiv:hepph/0412400 ADSCrossRefGoogle Scholar
 5.B. Grinstein, D. Pirjol, Exclusive rare \(B \rightarrow K^*\ell ^+\ell ^\) decays at low recoil: controlling the longdistance effects. Phys. Rev. D 70, 114005 (2004). arXiv:hepph/0404250 ADSCrossRefGoogle Scholar
 6.W. Altmannshofer, P. Ball, A. Bharucha, A.J. Buras, D.M. Straub, M. Wick, Symmetries and asymmetries of \(B \rightarrow K^{*} \mu ^{+} \mu ^{}\) decays in the standard model and beyond. JHEP 01, 019 (2009). arXiv:0811.1214 ADSCrossRefGoogle Scholar
 7.M. Beylich, G. Buchalla, T. Feldmann, Theory of \(B \rightarrow K^{(*)}\ell ^+ \ell ^\) decays at high \(q^2\): OPE and quark–hadron duality. Eur. Phys. J. C 71, 1635 (2011). arXiv:1101.5118 ADSCrossRefGoogle Scholar
 8.S. DescotesGenon, J. Matias, M. Ramon, J. Virto, Implications from clean observables for the binned analysis of \(B \rightarrow K^\ast \mu ^+\mu ^\) at large recoil. JHEP 01, 048 (2013). arXiv:1207.2753 ADSCrossRefGoogle Scholar
 9.S. DescotesGenon, T. Hurth, J. Matias, J. Virto, Optimizing the basis of \(B\rightarrow K^\ast \ell ^+\ell ^\) observables in the full kinematic range. JHEP 05, 137 (2013). arXiv:1303.5794 ADSCrossRefGoogle Scholar
 10.J. Gratrex, M. Hopfer, R. Zwicky, Generalised helicity formalism, higher moments and the \(B \rightarrow K_{J_K}(\rightarrow K \pi ) \bar{\ell }_1 \ell _2\) angular distributions. Phys. Rev. D 93(5), 054008 (2016). arXiv:1506.03970
 11.LHCb Collaboration, R. Aaij et al., Measurement of formfactorindependent observables in the decay \(B^{0} \rightarrow K^{*0} \mu ^+ \mu ^\). Phys. Rev. Lett. 111, 191801 (2013). arXiv:1308.1707
 12.S. DescotesGenon, L. Hofer, J. Matias, J. Virto, On the impact of power corrections in the prediction of \(B \rightarrow K^*\mu ^+\mu ^\) observables. JHEP 12, 125 (2014). arXiv:1407.8526 ADSCrossRefGoogle Scholar
 13.A. Bharucha, D.M. Straub, R. Zwicky, \(B\rightarrow V\ell ^+\ell ^\) in the standard model from lightcone sum rules. JHEP 08, 098 (2016). arXiv:1503.05534
 14.S. Jäger, J. Martin Camalich, On \(B \rightarrow V \ell \ell \) at small dilepton invariant mass, power corrections, and new physics. JHEP 05, 043 (2013). arXiv:1212.2263
 15.S. Jäger, J. Martin Camalich, Reassessing the discovery potential of the \(B \rightarrow K^{*} \ell ^+\ell ^\) decays in the largerecoil region: SM challenges and BSM opportunities. Phys. Rev. D 93(1), 014028 (2016). arXiv:1412.3183
 16.LHCb Collaboration, R. Aaij et al., Angular analysis of the \(B^{0} \rightarrow K^{*0} \mu ^{+} \mu ^{}\) decay using 3 fb\(^{1}\) of integrated luminosity. JHEP02, 104 (2016). arXiv:1512.04442
 17.Belle Collaboration, A. Abdesselam et al., Angular analysis of \(B^0 \rightarrow K^\ast (892)^0 \ell ^+ \ell ^\). In: Proceedings, LHCSki 2016—a first discussion of 13 TeV results: Obergurgl, Austria, April 10–15, 2016 (2016). arXiv:1604.04042
 18.W. Altmannshofer, D.M. Straub, New physics in \(b\rightarrow s\) transitions after LHC run 1. Eur. Phys. J. C 75(8), 382 (2015). arXiv:1411.3161
 19.S. DescotesGenon, L. Hofer, J. Matias, J. Virto, Global analysis of \(b\rightarrow s\ell \ell \) anomalies. JHEP 06, 092 (2016). arXiv:1510.04239
 20.T. Hurth, F. Mahmoudi, S. Neshatpour, On the anomalies in the latest LHCb data. Nucl. Phys. B 909, 737–777 (2016). arXiv:1603.00865
 21.T. Hurth, F. Mahmoudi, On the LHCb anomaly in B \(\rightarrow K^*\ell ^+\ell ^\). JHEP 04, 097 (2014). arXiv:1312.5267 ADSCrossRefGoogle Scholar
 22.S. DescotesGenon, J. Matias, J. Virto, Understanding the \(B\rightarrow K^*\mu ^+\mu ^\) Anomaly. Phys. Rev. D 88, 074002 (2013). arXiv:1307.5683 ADSCrossRefGoogle Scholar
 23.W. Altmannshofer, D.M. Straub, New physics in \(B \rightarrow K^*\mu \mu \)? Eur. Phys. J. C 73, 2646 (2013). arXiv:1308.1501 ADSCrossRefGoogle Scholar
 24.F. Beaujean, C. Bobeth, D. van Dyk, Comprehensive Bayesian analysis of rare (semi)leptonic and radiative \(B\) decays. Eur. Phys. J. C 74, 2897 (2014). arXiv:1310.2478. (Erratum: Eur. Phys. J. C 74, 3179 (2014))
 25.R.R. Horgan, Z. Liu, S. Meinel, M. Wingate, Calculation of \(B^0 \rightarrow K^{*0} \mu ^+ \mu ^\) and \(B_s^0 \rightarrow \phi \mu ^+ \mu ^\) observables using form factors from lattice QCD. Phys. Rev. Lett. 112, 212003 (2014). arXiv:1310.3887 ADSCrossRefGoogle Scholar
 26.T. Hurth, F. Mahmoudi, S. Neshatpour, Global fits to \(b \rightarrow s\ell \ell \) data and signs for lepton nonuniversality. JHEP 12, 053 (2014). arXiv:1410.4545 ADSCrossRefGoogle Scholar
 27.D. Du, A.X. ElKhadra, S. Gottlieb, A.S. Kronfeld, J. Laiho, E. Lunghi, R.S. Van de Water, R. Zhou, Phenomenology of semileptonic Bmeson decays with form factors from lattice QCD. Phys. Rev. D 93(3), 034005 (2016). arXiv:1510.02349
 28.M. Ciuchini, M. Fedele, E. Franco, S. Mishima, A. Paul, L. Silvestrini, M. Valli, \(B\rightarrow K^* \ell ^+ \ell ^\) decays at large recoil in the standard model: a theoretical reappraisal. JHEP 06, 116 (2016). arXiv:1512.07157
 29.S. Meinel, D. van Dyk, Using \(\Lambda _b\rightarrow \Lambda \mu ^+\mu ^\) data within a Bayesian analysis of \(\Delta B = \Delta S = 1\) decays. Phys. Rev. D94(1), 013007 (2016). arXiv:1603.02974
 30.A. Khodjamirian, T. Mannel, A.A. Pivovarov, Y.M. Wang, Charmloop effect in \(B \rightarrow K^{(*)} \ell ^{+} \ell ^{}\) and \(B\rightarrow K^*\gamma \). JHEP 09, 089 (2010). arXiv:1006.4945 ADSCrossRefMATHGoogle Scholar
 31.S. Braß, G. Hiller, I. Nisandzic, Zooming in on \(B\rightarrow K^*\ell \ell \) decays at low recoil. Eur. Phys. J. C 77(1), 16 (2017). arXiv:1606.00775
 32.B. Capdevila, S. DescotesGenon, J. Matias, J. Virto, Assessing leptonflavour nonuniversality from \(B\rightarrow K^*\ell \ell \) angular analyses. JHEP 10, 075 (2016). arXiv:1605.03156
 33.A. Karan, R. Mandal, A. K. Nayak, R. Sinha, T.E. Browder, Signal of righthanded currents using \(B\rightarrow K^*\ell ^+\ell ^\) observables at the kinematic endpoint. arXiv:1603.04355
 34.I. Ahmed, M.J. Aslam, M.A. Paracha, Asymmetries in \(B \rightarrow K^\ast \ell ^+ \ell ^\) decays and two Higgs doublet model. arXiv:1602.02400
 35.C.W. Chiang, X.G. He, G. Valencia, \(Z^\prime \) model for \(b \rightarrow s \ell \bar{\ell }\) flavor anomalies. Phys. Rev. D 93(7), 074003 (2016). arXiv:1601.07328
 36.A. Celis, W.Z. Feng, D. Lüst, Stringy explanation of \(b\rightarrow s \ell ^{+}\ell ^{}\) anomalies. JHEP 02, 007 (2016). arXiv:1512.02218
 37.S.M. Boucenna, A. Celis, J. FuentesMartin, A. Vicente, J. Virto, Nonabelian gauge extensions for Bdecay anomalies. Phys. Lett. B 760, 214–219 (2016). arXiv:1604.03088
 38.A. Crivellin, J. FuentesMartin, A. Greljo, G. Isidori, Lepton flavor nonuniversality in b decays from dynamical Yukawas. Phys. Lett. B 766, 77–85 (2017). arXiv:1611.02703
 39.R. Barbieri, C.W. Murphy, F. Senia, Bdecay anomalies in a composite leptoquark model. Eur. Phys. J. C 77(1), 8 (2017). arXiv:1611.04930
 40.F. Mahmoudi, T. Hurth, S. Neshatpour, Present status of \(b \rightarrow s \ell ^+ \ell ^\) anomalies (2016). arXiv:1611.05060
 41.A. Crivellin, G. D’Ambrosio, J. Heeck, Explaining \(h\rightarrow \mu ^\pm \tau ^\mp \), \(B\rightarrow K^* \mu ^+\mu ^\) and \(B\rightarrow K \mu ^+\mu ^/B\rightarrow K e^+e^\) in a twoHiggsdoublet model with gauged \(L_\mu L_\tau \). Phys. Rev. Lett. 114, 151801 (2015). arXiv:1501.00993
 42.A. Crivellin, G. D’Ambrosio, J. Heeck, Addressing the LHC flavor anomalies with horizontal gauge symmetries. Phys. Rev. D 91(7), 075006 (2015). arXiv:1503.03477
 43.L. Calibbi, A. Crivellin, T. Ota, Effective field theory approach to \(b\rightarrow s\ell \ell ^{(\prime )}\), \(B\rightarrow K^{(\ast )}\nu \bar{\nu }\) and \(B\rightarrow D^{(\ast )}\tau \nu \) with third generation couplings. Phys. Rev. Lett. 115, 181801 (2015). arXiv:1506.02661
 44.P. Arnan, L. Hofer, F. Mescia, A. Crivellin, Loop effects of heavy new scalars and fermions in \(b\rightarrow s\mu ^+\mu ^\). arXiv:1608.07832
 45.T.D. Lee, A theory of spontaneous T violation. Phys. Rev. D 8, 1226–1239 (1973)ADSCrossRefGoogle Scholar
 46.G.C. Branco, P.M. Ferreira, L. Lavoura, M.N. Rebelo, M. Sher, J.P. Silva, Theory and phenomenology of twoHiggsdoublet models. Phys. Rept. 516, 1–102 (2012). arXiv:1106.0034 ADSCrossRefGoogle Scholar
 47.ATLAS Collaboration, G. Aad et al., Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC. Phys. Lett. B 716, 1–29 (2012). arXiv:1207.7214
 48.C.M.S. Collaboration, S. Chatrchyan et al., Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC. Phys. Lett. B 716, 30–61 (2012). arXiv:1207.7235 ADSCrossRefGoogle Scholar
 49.H.E. Haber, G.L. Kane, The search for supersymmetry: probing physics beyond the standard model. Phys. Rept. 117, 75–263 (1985)ADSCrossRefGoogle Scholar
 50.J.E. Kim, Light pseudoscalars. Particle physics and cosmology. Phys. Rept. 150, 1–177 (1987)ADSCrossRefGoogle Scholar
 51.M. Trodden, Electroweak baryogenesis: a brief review. In: Proceedings, 33rd rencontres de Moriond 98 electrowek interactions and unified theories: Les racs, France, Mar 14–21, 1998, pp. 471–480 (1998). arXiv:hepph/9805252
 52.J.F. Gunion, H.E. Haber, G.L. Kane, S. Dawson, The Higgs hunter’s guide. Front. Phys. 80, 1–404 (2000)Google Scholar
 53.S.L. Glashow, S. Weinberg, Natural conservation laws for neutral currents. Phys. Rev. D 15, 1958 (1977)ADSCrossRefGoogle Scholar
 54.A. Pich, P. Tuzón, Yukawa alignment in the twohiggsdoublet model. Phys. Rev. D 80, 091702 (2009). arXiv:0908.1554 ADSCrossRefGoogle Scholar
 55.N. Cabibbo, Unitary symmetry and leptonic decays. Phys. Rev. Lett. 10, 531–533 (1963)ADSCrossRefGoogle Scholar
 56.M. Kobayashi, T. Maskawa, CP violation in the renormalizable theory of weak interaction. Prog. Theor. Phys. 49, 652–657 (1973)ADSCrossRefGoogle Scholar
 57.W. Altmannshofer, S. Gori, G.D. Kribs, A minimal flavor violating 2HDM at the LHC. Phys. Rev. D 86, 115009 (2012). arXiv:1210.2465 ADSCrossRefGoogle Scholar
 58.Y. Bai, V. Barger, L.L. Everett, G. Shaughnessy, General two Higgs doublet model (2HDMG) and large hadron collider data. Phys. Rev. D 87, 115013 (2013). arXiv:1210.4922 ADSCrossRefGoogle Scholar
 59.V. Barger, L.L. Everett, H.E. Logan, G. Shaughnessy, Scrutinizing the 125 GeV Higgs boson in two Higgs doublet models at the LHC, ILC, and muon collider. Phys. Rev. D88(11), 115003 (2013). arXiv:1308.0052
 60.D. LópezVal, T. Plehn, M. Rauch, Measuring extended Higgs sectors as a consistent free couplings model. JHEP 10, 134 (2013). arXiv:1308.1979 ADSCrossRefGoogle Scholar
 61.L. Wang, X.F. Han, Status of the aligned twoHiggsdoublet model confronted with the Higgs data. JHEP 04, 128 (2014). arXiv:1312.4759 ADSCrossRefGoogle Scholar
 62.A. Celis, V. Ilisie, A. Pich, LHC constraints on twoHiggs doublet models. JHEP 07, 053 (2013). arXiv:1302.4022 ADSCrossRefGoogle Scholar
 63.A. Celis, V. Ilisie, A. Pich, Towards a general analysis of LHC data within twoHiggsdoublet models. JHEP 12, 095 (2013). arXiv:1310.7941 ADSCrossRefGoogle Scholar
 64.M. Jung, A. Pich, P. Tuzón, ChargedHiggs phenomenology in the aligned twoHiggsdoublet model. JHEP 11, 003 (2010). arXiv:1006.0470 ADSCrossRefMATHGoogle Scholar
 65.M. Jung, A. Pich, P. Tuzón, The \(\bar{B}\rightarrow X_s\gamma \) rate and CP asymmetry within the aligned twohiggsdoublet model. Phys. Rev. D 83, 074011 (2011). arXiv:1011.5154 ADSCrossRefGoogle Scholar
 66.M. Jung, X.Q. Li, A. Pich, Exclusive radiative Bmeson decays within the aligned twoHiggsdoublet model. JHEP 10, 063 (2012). arXiv:1208.1251 ADSCrossRefGoogle Scholar
 67.A. Celis, M. Jung, X.Q. Li, A. Pich, Sensitivity to charged scalars in \(B\rightarrow D^{(*)}\tau \nu _\tau \) and \(B\rightarrow \tau \nu _\tau \) decays. JHEP 01, 054 (2013). arXiv:1210.8443 ADSCrossRefGoogle Scholar
 68.L. Duarte, G.A. GonzálezSprinberg, J. Vidal, Top quark anomalous tensor couplings in the twoHiggsdoublet models. JHEP 11, 114 (2013). arXiv:1308.3652 ADSCrossRefGoogle Scholar
 69.M. Jung, A. Pich, Electric dipole moments in twoHiggsdoublet models. JHEP 04, 076 (2014). arXiv:1308.6283 ADSCrossRefGoogle Scholar
 70.X.Q. Li, J. Lu, A. Pich, \(B_{s, d}^0 \rightarrow \ell ^+\ell ^\) decays in the aligned twoHiggsdoublet model. JHEP 06, 022 (2014). arXiv:1404.5865 ADSGoogle Scholar
 71.V. Ilisie, New Barr–Zee contributions to \((g2)_\mu \) in twoHiggsdoublet models. JHEP 04, 077 (2015). arXiv:1502.04199
 72.G. Abbas, A. Celis, X.Q. Li, J. Lu, A. Pich, Flavourchanging top decays in the aligned twoHiggsdoublet model. JHEP 06, 005 (2015). arXiv:1503.06423
 73.T. Han, S.K. Kang, J. Sayre, Muon \(g2\) in the aligned two Higgs doublet model. JHEP 02, 097 (2016). arXiv:1511.05162
 74.L. Wang, S. Yang, X.F. Han, \(h\rightarrow \mu \tau \) and muon g2 in the alignment limit of twoHiggsdoublet model. arXiv:1606.04408
 75.S. Davidson, H.E. Haber, Basisindependent methods for the twoHiggsdoublet model. Phys. Rev. D 72, 035004 (2005). arXiv:hepph/0504050. (Erratum: Phys. Rev.D 72, 099902 (2005))
 76.H.E. Haber, D. O’Neil, Basisindependent methods for the twoHiggsdoublet model. II. The significance of tan\(\beta \). Phys. Rev. D 74, 015018 (2006). arXiv:hepph/0602242. (Erratum: Phys. Rev. D 74(5), 059905 (2006))
 77.H.E. Haber, D. O’Neil, Basisindependent methods for the twoHiggsdoublet model III: the CPconserving limit, custodial symmetry, and the oblique parameters S, T, U. Phys. Rev. D 83, 055017 (2011). arXiv:1011.6188 ADSCrossRefGoogle Scholar
 78.G. Buchalla, A.J. Buras, M.E. Lautenbacher, Weak decays beyond leading logarithms. Rev. Mod. Phys. 68, 1125–1144 (1996). arXiv:hepph/9512380 ADSCrossRefGoogle Scholar
 79.T. Inami, C.S. Lim, Effects of superheavy quarks and leptons in lowenergy weak processes \(K_L\rightarrow \mu {\bar{\mu }}\), \(K^+\rightarrow \pi ^+\nu {\bar{\nu }}\) and \(K^0\leftrightarrow {\bar{K}}^0\). Prog. Theor. Phys. 65, 297 (1981). (Erratum: Prog. Theor. Phys. 65, 1772 (1981)) Google Scholar
 80.M. Misiak, The \(b \rightarrow se^+ e^\) and \(b \rightarrow s\gamma \) decays with nexttoleading logarithmic QCD corrections. Nucl. Phys. B 393, 23–45 (1993). (Erratum: Nucl. Phys. B 439, 461 (1995)) Google Scholar
 81.N.G. Deshpande, G. Eilam, Flavorchanging electromagnetic transitions. Phys. Rev. D 26, 2463 (1982)ADSCrossRefGoogle Scholar
 82.N.G. Deshpande, M. Nazerimonfared, Flavor changing electromagnetic vertex in a nonlinear \(R_\xi \) gauge. Nucl. Phys. B 213, 390–408 (1983)ADSCrossRefGoogle Scholar
 83.S.P. Chia, An exact calculation of \(\bar{d} s g\) vertex. Phys. Lett. B 130, 315–320 (1983)ADSCrossRefGoogle Scholar
 84.S.P. Chia, G. Rajagopal, An exact calculation of the flavor changing quark–photon vertex. Phys. Lett. B 156, 405–410 (1985)ADSCrossRefGoogle Scholar
 85.S.P. Chia, Radiative decay of the bottom quark and the \(W W \gamma \) coupling. Phys. Lett. B 240, 465–470 (1990)ADSCrossRefGoogle Scholar
 86.L.S. Wu, Z.J. Xiao, Exact calculations of vertex \(\bar{s}\gamma b\) and \(\bar{s} Z b\) in the unitary gauge. Commun. Theor. Phys. 48, 502–508 (2007). arXiv:hepph/0612326 ADSCrossRefGoogle Scholar
 87.X.G. He, J. Tandean, G. Valencia, Penguin and box diagrams in unitary gauge. Eur. Phys. J. C 64, 681–687 (2009). arXiv:0909.3638 ADSMathSciNetCrossRefMATHGoogle Scholar
 88.A.J. Buras, Climbing NLO and NNLO summits of weak decays. arXiv:1102.5650
 89.B. Grinstein, R.P. Springer, M.B. Wise, Strong interaction effects in weak radiative \(\bar{B}\) meson decay. Nucl. Phys. B 339, 269–309 (1990)ADSCrossRefGoogle Scholar
 90.S. Bertolini, F. Borzumati, A. Masiero, G. Ridolfi, Effects of supergravity induced electroweak breaking on rare \(B\) decays and mixings. Nucl. Phys. B 353, 591–649 (1991)ADSCrossRefGoogle Scholar
 91.P.L. Cho, M. Misiak, D. Wyler, \(K_L\rightarrow \pi ^0 e^+ e^\) and \(B\rightarrow X_sl^+l^\) decay in the MSSM. Phys. Rev. D 54, 3329–3344 (1996). arXiv:hepph/9601360 ADSCrossRefGoogle Scholar
 92.P.H. Chankowski, L. Slawianowska, \(B^0_{d, s}\rightarrow \mu ^\mu ^+\) decay in the MSSM. Phys. Rev. D 63, 054012 (2001). arXiv:hepph/0008046 ADSCrossRefGoogle Scholar
 93.M. Ciuchini, G. Degrassi, P. Gambino, G.F. Giudice, Nexttoleading QCD corrections to \(B \rightarrow X_s \gamma \): standard model and two Higgs doublet model. Nucl. Phys. B 527, 21–43 (1998). arXiv:hepph/9710335 ADSCrossRefGoogle Scholar
 94.F. Borzumati, C. Greub, Two Higgs doublet model predictions for \(\bar{B}\rightarrow X_s\gamma \) in NLO QCD. Phys. Rev. D 58, 074004 (1998). arXiv:hepph/9802391. (Addendum: Phys. Rev. D 59, 057501 (1999))
 95.C. Bobeth, M. Misiak, J. Urban, Matching conditions for \(b \rightarrow s \gamma \) and \(b \rightarrow s gluon\) in extensions of the standard model. Nucl. Phys. B 567, 153–185 (2000). arXiv:hepph/9904413 ADSCrossRefGoogle Scholar
 96.C. Bobeth, A.J. Buras, F. Krüger, J. Urban, QCD corrections to \(\bar{B} \rightarrow X_{d, s} \nu \bar{\nu }\), \(\bar{B}_{d, s} \rightarrow \ell ^{+} \ell ^{}\), \(K \rightarrow \pi \nu \bar{\nu }\) and \(K_{L} \rightarrow \mu ^{+} \mu ^{}\) in the MSSM. Nucl. Phys. B 630, 87–131 (2002). arXiv:hepph/0112305 ADSCrossRefGoogle Scholar
 97.S. Schilling, C. Greub, N. Salzmann, B. Töedtli, QCD corrections to the Wilson coefficients \(C_9\) and \(C_{10}\) in twoHiggs doublet models. Phys. Lett. B 616, 93–100 (2005). arXiv:hepph/0407323 ADSCrossRefGoogle Scholar
 98.F. Krüger, L.M. Sehgal, N. Sinha, R. Sinha, Angular distribution and CP asymmetries in the decays \(\bar{B}\rightarrow K^\pi ^+e^e^+\) and \(\bar{B}\rightarrow \pi ^\pi ^+e^e^+\). Phys. Rev. D 61, 114028 (2000). arXiv:hepph/9907386. (Erratum: Phys. Rev. D 63, 019901 (2001))
 99.D. Bečirević, E. Schneider, On transverse asymmetries in \(B\rightarrow K^\ast \ell ^+\ell ^\). Nucl. Phys. B 854, 321–339 (2012). arXiv:1106.3283 ADSCrossRefMATHGoogle Scholar
 100.J. Matias, F. Mescia, M. Ramon, J. Virto, Complete anatomy of \(\bar{B}_d \rightarrow \bar{K}^{* 0} (\rightarrow K \pi )\ell ^+\ell ^\) and its angular distribution. JHEP 04, 104 (2012). arXiv:1202.4266 ADSCrossRefGoogle Scholar
 101.OPAL, DELPHI, L3, ALEPH, LEP Higgs Working Group for Higgs boson searches Collaboration, Search for charged Higgs bosons: preliminary combined results using LEP data collected at energies up to 209GeV. In: Lepton and photon interactions at high energies. Proceedings, 20th international symposium, LP 2001, Rome, Italy, July 23–28, 2001 (2001). arXiv:hepex/0107031
 102.A. Barroso, P.M. Ferreira, I.P. Ivanov, R. Santos, Metastability bounds on the two Higgs doublet model. JHEP 06, 045 (2013). arXiv:1303.5098 ADSCrossRefGoogle Scholar
 103.P.S. Bhupal Dev, A. Pilaftsis, Maximally symmetric two higgs doublet model with natural standard model alignment. JHEP12, 024 (2014). arXiv:1408.3405. (Erratum: JHEP 1511, 147 (2015))
 104.D. Das, New limits on tan \(\beta \) for 2HDMs with Z\(_2\) symmetry. Int. J. Mod. Phys. A 30(26), 1550158 (2015). arXiv:1501.02610
 105.I. Chakraborty, A. Kundu, Scalar potential of twoHiggs doublet models. Phys. Rev. D 92(9), 095023 (2015). arXiv:1508.00702
 106.C. Patrignani, Review of particle physics. Chin. Phys. C 40(10), 100001 (2016)Google Scholar
 107.CLEO Collaboration, S. Chen et al., Branching fraction and photon energy spectrum for \(b \rightarrow s \gamma \). Phys. Rev. Lett. 87, 251807 (2001). arXiv:hepex/0108032
 108.Belle Collaboration, A. Limosani et al., Measurement of inclusive radiative Bmeson decays with a photon energy threshold of 1.7GeV. Phys. Rev. Lett. 103, 241801 (2009). arXiv:0907.1384
 109.Belle Collaboration, T. Saito et al., Measurement of the \(\bar{B} \rightarrow X_s \gamma \) branching fraction with a sum of exclusive decays. Phys. Rev. D 91(5), 052004 (2015). arXiv:1411.7198
 110.BaBar Collaboration, B. Aubert et al., Measurement of the \(B \rightarrow X_s \gamma \) branching fraction and photon energy spectrum using the recoil method. Phys. Rev. D 77, 051103 (2008). arXiv:0711.4889 ADSCrossRefGoogle Scholar
 111.BaBar Collaboration, J.P. Lees et al., Precision measurement of the \(B \rightarrow X_s \gamma \) photon energy spectrum, branching fraction, and direct CP asymmetry \(A_{CP}(B \rightarrow X_{s+d}\gamma )\). Phys. Rev. Lett. 109, 191801 (2012). arXiv:1207.2690
 112.BaBar Collaboration, J.P. Lees et al., Measurement of B(\(B\rightarrow X_s \gamma \)), the \(B\rightarrow X_s \gamma \) photon energy spectrum, and the direct CP asymmetry in \(B\rightarrow X_{s+d} \gamma \) decays. Phys. Rev. D 86, 112008 (2012). arXiv:1207.5772
 113.BaBar Collaboration, J.P. Lees et al., Exclusive measurements of \(b \rightarrow s\gamma \) transition rate and photon energy spectrum. Phys. Rev. D 86, 052012 (2012). arXiv:1207.2520
 114.Heavy Flavor Averaging Group (HFAG) Collaboration, Y. Amhis et al., Averages of bhadron, chadron, and \(\tau \)lepton properties as of summer 2014. arXiv:1412.7515
 115.M. Misiak et al., Updated NNLO QCD predictions for the weak radiative Bmeson decays. Phys. Rev. Lett. 114(22), 221801 (2015). arXiv:1503.01789
 116.X.Q. Li, Y.D. Yang, X.B. Yuan, Exclusive radiative Bmeson decays within minimal flavorviolating twoHiggsdoublet models. Phys. Rev. D 89, 054024 (2014). arXiv:1311.2786 ADSCrossRefGoogle Scholar
 117.P. Gambino, M. Gorbahn, U. Haisch, Anomalous dimension matrix for radiative and rare semileptonic B decays up to three loops. Nucl. Phys. B 673, 238–262 (2003). hepph/0306079ADSCrossRefGoogle Scholar
 118.BaBar Collaboration, J.P. Lees et al., Measurement of angular asymmetries in the decays \(B \rightarrow K^\ast \ell ^+\ell ^\). Phys. Rev. D 93(5), 052015 (2016). arXiv:1508.07960
 119.B. Capdevila, S. DescotesGenon, L. Hofer, J. Matias, Hadronic uncertainties in \(B\rightarrow K^*\mu ^+\mu ^\): a stateoftheart analysis. arXiv:1701.08672
 120.V.G. Chobanova, T. Hurth, F. Mahmoudi, D. Martinez Santos, S. Neshatpour, Large hadronic power corrections or new physics in the rare decay \(B\rightarrow K^\ast \mu ^+\mu ^\)? arXiv:1702.02234
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