Status of the semileptonic B decays and muon g-2 in general 2HDMs with right-handed neutrinos

Journal of High Energy Physics, May 2018

Abstract In this paper, we study the extended Standard Model (SM) with an extra Higgs doublet and right-handed neutrinos. If the symmetry to distinguish the two Higgs doublets is not assigned, flavor changing neutral currents (FCNCs) involving the scalars are predicted even at the tree level. We investigate the constraints on the FCNCs at the one-loop level, and especially study the semileptonic B meson decays, e.g. B → D(∗)τ ν and B → K(∗)ll processes, where the SM predictions are more than 2σ away from the experimental results. We also consider the flavor-violating couplings involving right-handed neutrinos and discuss if the parameters to explain the excesses of the semileptonic B decays can resolve the discrepancy in the anomalous muon magnetic moment. Based on the analysis, we propose the smoking-gun signals of our model at the LHC.

A PDF file should load here. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser.

Alternatively, you can download the file locally and open with any standalone PDF reader:

https://link.springer.com/content/pdf/10.1007%2FJHEP05%282018%29173.pdf

Status of the semileptonic B decays and muon g-2 in general 2HDMs with right-handed neutrinos

Revised: May Status of the semileptonic B decays and muon g-2 in Syuhei Iguro 1 Yuji Omura 0 0 Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University 1 Department of Physics, Nagoya University In this paper, we study the extended Standard Model (SM) with an extra Higgs doublet and right-handed neutrinos. If the symmetry to distinguish the two Higgs doublets is not assigned, avor changing neutral currents (FCNCs) involving the scalars are predicted even at the tree level. We investigate the constraints on the FCNCs at the one-loop level, and especially study the semileptonic B meson decays, e.g. B ! D( ) Beyond Standard Model; Higgs Physics - and B ! K( )ll processes, where the SM predictions are more than 2 away from the experimental results. We also consider the avor-violating couplings involving right-handed neutrinos and discuss if the parameters to explain the excesses of the semileptonic B decays can resolve the discrepancy in the anomalous muon magnetic moment. Based on the analysis, we propose the smoking-gun signals of our model at the LHC. 1 Introduction Type-III 2HDM 2.1 Setup of the texture 2 3 4 5 6 3.1 3.2 4.1 4.2 4.3 The summary of the experimental constraints The experimental constraints on u The experimental constraints on e and The (semi)leptonic B decays The bounds from the B ! l decays Summary of the capabilities to explain the excesses Our signals at the LHC Summary A Various parameters for our numerical analysis 1 Introduction The Standard Model (SM) succeeds in describing almost all of the experimental results. There is one Higgs doublet to break the electroweak (EW) symmetry, and the non-vanishing vacuum expectation value (VEV) of the Higgs eld generates the masses of the gauge bosons and the fermions. We do not still understand the reasons why the EW scale is around a few hundred GeV and why the couplings between the Higgs eld and the fermions are so hierarchical. The Higgs particle is, however, discovered at the LHC experiment, and the signal is consistent with the SM prediction [1, 2]. Thus, we are certain that the SM describes our nature up to the EW scale. On the other hand, it would be true that the structure of the SM is so mysterious. In addition to the mystery of the origin of the Higgs potential and couplings, the structure of the gauge symmetry is also very non-trivial. The anomaly-free conditions are miraculously satis ed: it is not easy to add extra chiral fermions to the SM. In the bottom-up approach been actually discussed since about 40 years ago [3{10]. The extended SM, besides, has other interesting aspects, from the viewpoint of the top-down approach. If we consider the new physics that can solve the mysteries of the SM, we often nd extra Higgs doublets. For instance, the supersymmetric extension predicts at least one more Higgs doublet. If we consider the extended gauge symmetry, such as SU(2)R, we nd extra Higgs doublets that couple to the SM fermions in the e ective lagrangian. If we assume that there are avor symmetries at high energy, there would be many Higgs doublets that couple to the SM fermions avor-dependently. Thus, it would be very interesting and important to study and summarize the predictions and the experimental constraints of the extended SM with extra Higgs doublets. Based on this background, we investigate not only the experimental constraints but also the predictions for the observables relevant to the future experiments, in the extended SM with one Higgs doublet (2HDM). We adopt the bottom-up approach. In our model, we do not assign any symmetry to distinguish the two Higgs doublets, so that there are tree-level Flavor Changing Neutral Currents (FCNCs) involving scalars [11]. This kind of general 2HDM has been discussed, and often called the Type-III 2HDM [7{10, 12{18]. Hereafter, we abbreviate such a generic 2HDM with tree-level FCNCs as the Type-III 2HDM. We note that this kind of setup is predicted as the e ective model of the extended SM with the extended gauge symmetry; e.g., the left-right symmetric model [19] and the SO(10) grand uni ed theory [20]. In our model, we also introduce right-handed neutrinos and allow the coupling between the right-handed neutrinos and both Higgs doublets. We simply assume that the light neutrinos are Dirac fermions, and the tiny masses are given by the small Yukawa couplings. Although the ne-tuning may be required, the Yukawa couplings between the neutrino and the extra scalars could be sizable in principle.1 Recently, the Type-III 2HDM is attracting a lot of attention, since it is one of the good candidates to explain the excesses reported by the BaBar, Belle, and LHCb collaborations. In the experiments, the semileptonic B decays, B ! D( ) , have been measured and the results largely deviate from the SM predictions [21{28]. The B decays in the Type-III 2HDM have been studied in refs. [29{42]. Although we recently nd that the explanation of B ! D contradicts the leptonic Bc decay [ 43, 44 ], the Type-III 2HDM is still one of the plausible and attractive candidates to achieve the explanation of the excess in B ! D [37]. In addition, another semileptonic B decay, i.e. B ! K( ) , is also discussed recently in the 2HDM [38{40]. In the process, the LHCb collaboration has reported the deviations from the SM predictions in the measurements concerned with the angular observables [45, 46] and the lepton universality [47, 48]. Moreover, it is known that the Type-III 2HDM can accomplish the explanation of the anomalous muon magnetic moment ((g 2) ) deviated from the SM prediction [49, 50]. 1We note that the right-handed neutrino can have the Majorana mass term. Our discussion, however, nd a parameter set to explain the all excesses. In this paper, we discuss the compatibility between each of the explanations. Compared to the previous works [37{40], we take into consideration the constraint from the lepton universality of B ! D( )l (l = e; ). The compatibility of those excesses in the B decays with the (g 2) discrepancy has not been also studied before. We also consider the contributions of the avor violating couplings involving the right-handed neutrinos. This paper is organized as follows. In section 2, we introduce our model and the simpli ed setup to evade the strong experimental constraints. In section 3, we summarize III 2HDM in section 4. We also propose our signals at the LHC in section 5. Section 6 is devoted to the summary. 2 Type-III 2HDM 1 2 ! = cos sin sin cos ! h H ! : { 3 { L = QiLH1ydidiR LiLH1yeeR i i QiLH2 idj djR LiLH2 iej ejR j j QiL(V y)ij He1yuuR LiL(V )ij He1y j i R QiL(V y)ij He2 jukukR LiL(V )ij He2 jk k R ; where i, j and k represent avor indices, and Q = (V yuL; dL)T , LL = (V L; eL)T are de ned. He1;2 denote He1;2 = i 2H1;2, where 2 is the Pauli matrix. V is the CabbiboKobayashi-Maskawa (CKM) matrix and V is the Maki-Nakagawa-Sakata (MNS) matrix. Fermions (fL; fR) (f = u; d; e; of the SM fermion mass matrices. denote the fermion masses, are de ned. ifj are the Yukawa couplings that are independent ) are mass eigenstates, and yif = p 2mfi =v, where mfi There are three types of the scalars: the charged Higgs (H ), the CP-odd scalar (A) and the two CP-even scalars ( 1;2). The CP-even scalars are not mass eigenstates, although the mixing should be tiny not to disturb the SM prediction. The mixing is de ned as We introduce the Type-III 2HDM with right-handed neutrinos. There are two Higgs doublets in our model. When the Higgs elds are written in the basis where only one Higgs doublet obtains the nonzero VEV, the elds can be decomposed as [51] G+ v+ p1+iG 2 ! ; H1 = H2 = H+ ! 2p+iA 2 ; where G+ and G are Nambu-Goldstone bosons, and H+ and A are a charged Higgs boson and a CP-odd Higgs boson, respectively. v is the VEV: v ' 246 GeV. In this base, we write down the Yukawa couplings with the SM fermions. In the mass basis of the fermions, the Yukawa interactions are expressed by [51] (2.1) (2.2) (2.3) The masses of the heavy scalars can be evaluated as m2H ' m2A + 5v2; m2H ' m2A 4 2 5 are the dimensionless couplings in the Higgs potential: V (Hi) = 4(H1yH2)(H2yH1) + 25 (H1yH2)2 + : : : The mass di erences are relevant to the electro-weak precision observables (EWPOs) and the explanation of the (g 2) anomaly [49, 50]. 2.1 Setup of the texture f are 3 3 matrices and the each element is the free parameter that is constrained by the avor physics and the collider experiments. The comprehensive study about the phenomenology in the Type-III 2HDM has been done in ref. [32]. There are many choices for the matrix alignment, but actually only a few elements are allowed to be sizable according to the stringent experimental bounds [32]. First, let us discuss the physics concerned with u and d. The all o -diagonal elements of d are strongly constrained by the F = 2 processes. uuc and cuu have to be small to avoid the stringent constraint that comes from the D-D mixing. Besides, we nd that the size of the Yukawa coupling involving the light quarks are limited by the direct search at the collider experiments. Even uut and tu may be constrained by the bounds from the u collider experiment, e.g., the upper limit from the same-sign top signal.2 Moreover, uut and tuu are strongly constrained by the K-K mixing at the one-loop level. Thus, it is di cult to expect that the couplings between the light quarks (u; d; s) and the other quarks are larger than O(0:01). The diagonal elements, on the other hand, could be O(0:1), unless the o -diagonal elements are not sizable [54]. Based on the examination, we consider the case that j cutj and/or j tucj are sizable. One of our motivations of this study is to investigate the compatibility among the explanations of the excesses in the Type-III 2HDM. It is pointed out that the sizable tuc can improve the discrepancies in the b ! sll and b ! cl processes [37]. Eventually, we consider the following simple textures of f from the phenomenological point of view: 0 ij 0 tuc cutttAC ; j d j u O(0:1): (2.6) The other elements of u are assumed to be at most O(0:01), so that the physics involving cut, tuc, and tut is mainly discussed in this paper. Note that we ignore all elements of d and assume that all sizable Yukawa couplings are real, through our paper. Next, we discuss the Yukawa couplings with leptons. We can also nd the strong upper bounds on the Yukawa couplings in the lepton sector. The lepton avor violating (LFV) 2Note that there is a way to avoid the strong constraint, considering the degenerate masses of the scalars [52, 53]. { 4 { HJEP05(218)73 processes are predicted by the neutral scalar exchanging, if the o -diagonal elements of e are sizable. In the case that the extra Yukawa couplings involving electron are large, the LEP experiment can easily exclude our model. Interestingly, the authors of refs. [49, 50] have pointed out that the large e and e can achieve the explanation of the (g that is largely deviated from the SM prediction. The explanation, however, requires the other Yukawa couplings to be small [49, 50]. Then, we especially consider the following texture of e 0 1 e CA : 0 (2.7) Note that the diagonal elements, e and e , are also strongly constrained, as far as e and e are sizable [50]. In our study, we also consider the contribution of to avor physics. This investigation has not been done well in the type-III 2HDM. This is because the tiny Dirac neutrino masses predict small Yukawa couplings so that is also naively expected to be small. however, does not contribute to the active neutrino masses, directly. If both sizable, would contribute to the neutrino masses radiatively. Otherwise, and e are could be large compared to yi , in the bottom-up approach. The unique texture as in eq. (2.7) may also allow to be sizable. Based on this consideration, we study the upper bound on and discuss the impact on the physical observables in avor physics. 3 The summary of the experimental constraints In this section, we discuss the physics triggered by the Yukawa couplings in eq. (2.6) and eq. (2.7). The contribution of is also studied. Note that we are interested in the light scalar scenario. In order to avoid the exotic decay, e.g. t ! Hc, and enlarge the new physics contributions maximumly, the extra scalar masses are set to 200 GeV or 250 GeV below. 3.1 The experimental constraints on u To begin with, we summarize the experimental constraints on u. In our study, the texture of u is approximately given by eq. (2.6). Then, we can evade the strong bound from the F = 2 processes at the tree level. The measurements of the meson mixings are, however, very sensitive to new physics contributions, so that we need to study the bounds carefully, taking into account the loop corrections. In our setup, the one-loop corrections involving the charged Higgs and the W -boson, that are described in gure 1, contribute to the B-B mixing and the Bs-Bs mixing. The operators induced by the one-loop corrections are He F =2 = CLqL(q PLb)(q PLb); (3.1) { 5 { 128 2m2H+ k;l 1 m2H+ where q = s, d. The new physics contribution to the coe cient, CLL, is evaluated at the one-loop level as q CLL = X(V y u)qk( yuV )lb ( yuV )kb(V y u)qlG1(xk; xl) 4g2muk mul VkbVlqG2(xk; xl; xW ) + g2muk mul VkbVlqG3(xk; xl; xW ) ; where xk = m2uk =m2H+ and xW = m2W =m2H+ . The functions Gi (i = 1; 2; 3) are de ned as where mBdi , FBdi and BBdI are a mass, a decay constant and the bag parameter of Bdi meson, respectively. We note that CLL includes the SM correction. The deviations of the neutral B(s) meson mixing will be evaluated including the SM corrections, but it is certain that there are non-negligible uncertainties in the theoretical predictions. In our analysis, we calculate our predictions, using the input parameters in appendix A. In order to draw the constraints on the Yukawa couplings, we require that the deviations induced by the charged Higgs contributions are within the 2 errors of the SM predictions and the experimental results. We simply adopt the SM predictions ( given by ref. [55]: 0:45 [ps 1] CL). Then, we de ne ( MB(s) ) = MBSM values: M Bexp = 0:5064 0:0019 [ps 1] and M Bex(sp) 0:78 [ps 1] and 16:2 [ps 1] MBSMs MBSM(s) , where M Bexsp = 17:757 M Bex(sp) are the experimental 0:021 [ps 1] [56]. Taking into account the 2 uncertainties, ( MB(s) ) are within the following ranges: 0:27 ( MB)[ps 1] 0:06; 4:1 ( MBs )[ps 1] 1:6: (3.7) { 6 { (3.2) (3.3) (3.4) (3.5) (3.6) MBSM(s) ) 21:9 (95% If the magnitudes of the Yukawa couplings are below the upper bounds in table 1 when mH = 200 GeV and 250 GeV, the charged Higgs contributions are within these ranges in eq. (3.7). The results in table 1 are consistent with the ones in ref. [57]. Next, we consider the rare decays of the mesons, such as B ! Xs . The b ! s transition is given by the C7 operator, according to the diagram in gure 2, Heb!s = 4GF VtbVts 16 2 mbC7F (sL e p2 bR) + h:c:; where C7 in our model is evaluated at the one-loop level as follows: C7 = 1 4p2GFm2H+VtbVts i X(V y u)si( yuV )ib 23 G71(xi) + G27(xi) : B Mixing Bs Bs Mixing j tucj G71(x) and G72(x) are de ned as G17(x) = G27(x) = 2 + 3x 6x2 + x3 + 6x log x 12(1 x)4 1 6x + 3x2 + 2x3 6x2 log x 12(1 x)4 ; : The b ! s has been experimentally measured and the result is consistent with the SM prediction [58]. Then, this process becomes a stringent bound on our model. For instance, the size of C7 at the bottom quark mass scale should be within the range, 0:055 0:02, according to the global tting [34]. In table 2, we derive the upper bounds on the up-type Yukawa couplings using the value in ref. [34]. The charged Higgs mass, mH , is xed at mH = 200 GeV or 250 GeV. These results are consistent with the ones derived from the values in refs. [56, 59]. { 7 { j cutj j tucj j tutj 200 [GeV] 1.03 BR(t ! hc) = j tucj2 + j cutj2 cos2 where t is de ned as t = 1:41 GeV. Based on the results in refs. [60{62], we derive the following upper bound: j cos j pj tucj2 + j cutj2 9:1 In our study, we survey the parameter region with O(1) tuc and/or cut. In addition, e and e are large in some cases. As we discuss below, the avor-violating Higgs decay, such at most O(10 3) and ignore the corrections that depend on cos . as h ! , also signi cantly constraints cos . Then, we simply assume that j cos j is 3.2 The experimental constraints on e and In this section, we summarize the constraints on e and . Interestingly, the texture of e in eq. (2.7) can evade the strong experimental bounds from the LFV processes. On the other hand, the discrepancy of (g 2) can be resolved by the sizable ( ; ) Yukawa couplings [49, 50]. Let us discuss the tree-level contributions to the physical observables, that are given by e , e and . In the type-III 2HDM, the charged Higgs boson exchanging induces ! l (l = ; e) at the tree level. We de ne the following observable: (3.12) (3.13) (3.14) g ge 2 BR( BR( ! ! e )=f (y ) )=f (ye) ; { 8 { where yl ml2=m2 (l = e; ; ) are de ned and f (y) is a phase space function. This measurement has been experimentally given as g =ge = 1:0018 0:0014 [63]. In our model, the extra contribution to the each branching ratio of l1 ! l2 decay is proportional to jgl1l2 j 2 X ij ( )l2i 2 e e . Allowing the 2 deviation of g =ge, we obtain the upper = 200(250) GeV as follows: j g j 0:25 (0:4); jge j Next, we study the constraints from the michel parameter of the lepton decays. As discussed above, the charged Higgs exchanging contributes to l1 ! l 2 decays. The constraints derived from the michel parameters are summarized in ref. [63]. Following ref. [63], we derive the bounds on and e as 0:76 gl1l2 0:76 e gl1l2 200 mH 200 mH 2 2 cl1l2 cle1l2 : and cl1l2 and cle1l2 are the upper bounds from l1 ! l2 (0:55; 2:01; 2:01) and (ce e; cee; ce ) = (0:035; 0:70; 0:72). bounds on g e and gee: jg ej 0:73(1:13) and jgeej The other elements, on the other hand, can be O(1). , introduced in ref. [63]: (c e; c e; c ) = Thus, we obtain the strong 0:046(0:072) at mH = 200(250) GeV. Note that in our texture as eq. (2.7), e and eee are assumed to be vanishing, so that the stringent constraints from the LFV decays of the charged leptons can be evaded. In our setup with e in eq. (2.7), the scalar mixing, cos , enhances the LFV decay, according to the neutral scalar exchanging. In order to avoid the current experimental bound, Br( ! 3 ) < 2:1 10 8 [63], we obtain the bound as j cos j of e can be larger than O(0:1) when j cos j is suppressed. In the case that e and eee are sizable, the upper bounds on the parameters are estimated as O(10 4) when the CP j e j2 + j e j2 is de ned. Then we can conclude that the ( , ) elements even scalar mass is O(100) GeV and e is O(1) [50]. We can derive the constraint from the avor-violating decay of 125 GeV neutral scalar. In our model, the branching ratio of the decay to two fermions (fi, fj ) is given by BR(h ! fifj ) = (h ! fifj ) + (h ! fifj ) = cos2 h j ifj j2 + j f j ji 2 16 h mh ; { 9 { (3.17) (3.18) ! 3 , (3.19) (3.20) h is the total decay width of h whose mass is around 125 GeV and h = 4:1 MeV. Following the upper bound on BR(h ! ) [64{66], we nd the upper limit on the - coupling at 2 : j cos j e 2:3 be at most O(10 3) and the contributions to the avor physics are ignored in our analysis. We consider the one-loop contributions to the LFV process and the Z-boson decay. The correction involving only e is summarized in ref. [50]. Assuming that the all elements of e are vanishing, we derive the constraints on bounds from l0 ! l are summarized in table 3. from the LFV processes. The upper ll0 is de ned as ll0 = P j j( e )lj ( )l0j . j e As we see in table 3, e is strongly constrained, while the other elements can be large. In addition, the decay of the Z boson may be largely deviated from the SM prediction, according to the extra scalars, at the one-loop level. In our work, we consider the case that either e or is sizable. Then, the contribution to the Z boson decay through the penguin diagrams is suppressed. We have calculated the deviation of BR(Z ! ), but it is not so large. We nd that the upper bounds on the deviation of BR(Z ! ) is required to be within 2 . e and j j can reach O(1), even if Note that would be strongly constrained by the cosmological observation, depending on the mass spectrum of the right-handed neutrino. We comment on the bound in section 4.3.3. 4 The (semi)leptonic B decays Based on the studies in section 3, we investigate the impact of our Type-III 2HDM on the (semi)leptonic B-meson decays. As discussed in refs. [35, 37, 38], the 2HDMs potentially have a great impact on B ! D( )l and B ! K( )ll processes (l = e; ; ), where the discrepancies between the experimental results and the SM predictions are reported. In particular, the global analyses on B ! K( )ll suggest that C9 and C10 operators may be deviated from the SM values. Besides, the avor universality of B ! K( )ll is also inconsistent with the SM prediction in the experimental results. In our model, can contribute to the C9 and C10 operators, avor-dependently. Thus, it becomes very important to nd how well the tension can be relaxed, taking into account the contribution. 4.1 First, we discuss the leptonic decays of the B meson: B ! l . In our model, the charged Higgs exchanging contributes to the B meson decays as HBlq = l0l tuq (V )l0jVtb( LjlR)(bLqR) e ( )lj tuq Vtb( RjlL)(bLqR): em2H The avor of the neutrino in the nal state can not be distinguished, so that let us de ne the parameters, X j jel tuq 2 ; j lqj 2 X ( ) e j lj tuq 2 ; and discuss the constraints on those products. In our setup, the (t, c)-elements of u are sizable, so that the leptonic decay of Bc is deviated from the SM prediction. The leptonic decay has not been measured by any experiments, but we can derive the constraint from the total decay width of Bc [ 43 ] and the measurement at the LEP experiment [44]. Adopting the severe constraint, BR(Bc ! ) 10% [44], we obtain the upper bounds on the lepton Yukawa couplings as follows: m2H j e;u j j e;u j 0:99 1:18 are linear to j leuj2 and j luj2. These products at mH the leptonic Bu decays as In our assumption, the (t, u) elements are less than O(0:01). Even in such a case, the may largely contribute the Bu decays. The contributions to Bu ! l = 200(250) GeV are constrained by We could also derive the bound from Bs ! . The error of the experimental measurement is still so large that it is di cult to draw a stringent bound on our model. The branching ratio of this rare decay, however, relates to the semi-leptonic B decay, B ! K( ) 4.2 , so that we give a discussion about this process below. We investigate the constraints from the semileptonic B decay; e.g., B ! D( )l (l = e; ; ). There is a discrepancy in B ! D( ) , although B ! D( )e and B ! D( ) are consistent with the SM predictions. In our model, the charged Higgs exchanging avordependently contributes to these processes via e and u couplings, as shown in eq. (4.1). Then, the discrepancy of B ! D( ) diagram in gure 3 [37], although the avor universality of B ! D( )l (l = e; ) may constrain our setup strongly. We de ne the observables to measure the universality as follow: could be ameliorated by the contribution of the R(D( ))e = BR(B ! D( )e ) BR(B ! D( ) ) : (4.1) (4.2) process, B ! D (D)l , is labeled as D (D) on the rst column. The deviations should not exceed a few percent: R(D )e = 1:04 0:05 0:01 [67]. Fixing the charged Higgs mass at mH the table 4, the upper bounds on e;c with mH = 200(250) GeV, we derive the upper bounds on e;c . In = 200 GeV and 250 GeV are summarized. The calculation is based on ref. [37]. Note that, roughly speaking, only BR(B ! D( ) ) is always enhanced, so the only lower limit on R(D( ))e is shown in table 4. We impose the bounds as R(D( ))e > 0:95 and R(D( ))e > 0:98 [67]. The semileptonic B decay associated with lepton in the nal state is also deviated from the SM prediction, in our model. In ref. [37], R(D( )) are well studied in the TypeIII 2HDM with only e , d and u, and we nd that at least R(D) can be enhanced so much that it is consistent with the experimental result. The lowest value to achieve the world average of R(D) (R(D)=0.407 0.046) and R(D ) (R(D )=0.304 0.015) at the 1 level [56] is when the charged Higgs mass is xed at mH R(D) = 0:299 and R(D ) = 0:253 with BR(Bc ! = 200 GeV. Note that our SM prediction is ) = 2:2% in our parameter set [68]. This lowest value for R(D) is very close to the upper bound from Bc ! in eq. (4.3). We can nd that the value required by R(D ) is totally excluded by the Bc decay. Besides, the lepton universality of this semileptonic decay provides the stringent bounds on e;c , as shown in table 4. Thus, we concluded that either j e cj or j cj should be O(1) 10 2 to achieve the discrepancy of R(D) without any con ict with the other observables concerned with the B decay. Otherwise, the anomaly of R(D) cannot be resolved in our model. 4.3 Finally, we consider B ! K( )ll in our model. In the so-called aligned 2HDM, this process has been discussed in ref. [38]. The Type-III 2HDM case with only e has also been shortly studied in ref. [37]. In our study, we include the box diagrams induced by e and and take into account the consistency with the explanations of (g 2) and R(D), that has not been done before. In the B ! K( )ll processes, there are several interesting observables where the discrepancies between the SM predictions and the experimental results are reported by the LHCb collaboration. One is P50 that is concerned with the angular distribution of the process [45, 46], and another is R(K ) [47] and R(K) [48] that measure the lepton universalities of B ! K =ee and B ! K are governed by C9l and C1l0 operators de ned as =ee, respectively. The observables l HBs = gSM nC9l(sL bL)(l l) + C1l0(sL bL)(l 5l) + h:c:o ; where gSM is the factor from the SM contribution: gSM = e2 4GF VtbVts 16 2 p2 : In our model, the Wilson coe cients C9l and C1l0 consist of the SM and the new physics contributions as C9l = (C9)SM + C9l and C1l0 = (C10)SM + C1l0. C9l and C1l0 are given by C9(l) = C10(l) = p 4 + 4 1 1 VtbVts 1 VtbVts 2 i 1 2 2 2GFm2H+ VtbVts i X(V y u)si( yuV )ib 2 3 G 1(xi) + G 2(xi) + 2s2W X(V y u)si( yuV )ibGZ (xi); i 1 X(V y u)si( yuV )ibGZ (xi); where sW corresponds to the Weinberg angle and the functions are de ned as G 1(x) = G 2(x) = GZ (x) = 16 2 45x + 36x2 7x3 + 6(2 3x) log x 36(1 x)4 9x + 18x2 11x3 + 6x3 log x 36(1 x)4 ; ; x(1 x + log x) 2(1 x)2 : (4.9) (4.10) (4.11) (4.12) (4.13) (4.14) (4.15) We note that the SM predictions are avor universal and the size of the each coe cient at the bottom mass scale is estimated as (C9)SM 4 and (C10)SM 4, respectively. The excesses in both P50 and R(K( )) require destructive interferences with the SM predictions; for instance, the 1 0:81 C 9 0:48 (1 ) and 1:00 region of j C9 j suggested by the global analysis is C 9 0:32 (2 ), assuming C 9 = C10 [74]. There are a lot of works on the global tting [69{77]. The results are consistent with each other and the excesses require large contributions to the muon couplings: ( C9l)=(C9)SM ' while such a large 0:2 and ( C1l0)=(C10)SM ' 0:2. We note that C1l0 need not be large, C9l is favored. In fact, the scenario with vanishing C1l0 can t the experimental results at the 2 level [75]. It is important that these observables have di erent characteristics: R(K( )) requires the violation of the avor universality, but P50 does not need the violation. In our study, HJEP05(218)73 we concentrate on the three cases: (A) iej = 0 and ij = 0, (B) e 6= 0, e 6= 0 and ij = 0, (C) iej = 0 and ( ) j 6= 0. e In the case (A), the extra scalars do not couple to leptons, so that we can not expect the realized, if tuc, cut and tut are sizable. violation of the lepton universality. P50 in this framework has been studied in refs. [37, 38], and we nd the sizable tuc, cut and tut lead large C9 and C10. In the case (B), e and e are only non-vanishing. In such a case, we can expect that the discrepancy of (g 2) is explained by the one-loop correction involving the neutral scalars [49, 50]. Besides, the violation of the lepton universality in B ! K( )ll would be In the case (C), we assume that ( ) j is only sizable. In this case, the box diagram involving the charged Higgs leads the destructive interference with the SM prediction in C9 and C10, so that the anomaly of R(K( )) may be resolved. Below, we discuss the induced C9, C10 and the relevant constraints in the each case. We do not consider the case that both ( ) j and e ; are sizable, in order to avoid the left-right mixing couplings of leptons induced by the one-loop diagrams involving the e e extra scalars. 4.3.1 Case (A): iej = 0 and In the case (A), the violation of the lepton universality can not be expected, but large C10 may be induced by the loop diagrams involving the scalars. In our setup, the main contributions to the operators are given by the couplings, tuc, cut, and tut. Then, the charged Higgs plays a crucial role in C9 and C10. The dominant contribution is given by the penguin diagram in gure 4. We note that this type diagram is allowed in all cases. Bs mixing and the red lines correspond to the borders. The dashed purple lines denote the predictions of C9 (left) and C10 (right). Setting the charged Higgs mass at mH = 200 GeV, we draw the predicted C9 and C10 in gure 5. The relevant constraints are shown in those plots. The gray region is excluded by the Bs Bs mixing in gure 5. Note that the constraint from the b ! s process is out of the gures. The dashed purple lines denote the predictions of C9 and C10 on the left and right panels. The size of the deviation is denoted on the each line. In the gures on the upper (lower) line, cut ( tut) is assumed to be vanishing. We see that tut does not help the enhancement of C9, but either tuc or cut can achieve C9 P50 excess within 1 level. We note that tuc is not sensitive to C10. 1, that can explain the the Bs ! suppression is about 2.4%. Let us comment on the contribution to the Bs ! process. The positive (negative) C10 coe cient suppresses (enhances) the branching ratio, compared to the SM prediction. The experimental result still has a large uncertainty, and the central value is below the SM prediction [78]. Thus, the positive C10 is, in e ect, favored, taking into account process as well [75]. If we chose the parameter to predict C10 ' 0:1, the (dotted green lines). The dashed green lines and dashed purple lines denote the predictions of and C10 for the each case. The size of the deviation is shown on the each line. = C9 with B ! D( )l processes, if e ; , is evaluated at the one-loop level as 4.3.2 Case (B): e 6 = 0, e 6 = 0 and In the case (B), we consider the scenario that both e and e are sizable, motivated by the (g 2) anomaly. Note that the mass di erence between H and A is also required to explain the excess [49, 50]. As discussed in section 4.1 and section 4.2, tuc leads the con ict are sizable. The deviation of (g 2) , denoted by when (mA; mH ) is xed at (mA; mH ) = (200 GeV; 250 GeV). The value experimentally required [79]3 is = (2:61 0:8) 10 9, so that e e should be about 0:03 to explain the discrepancy at the 1 level. In gure 6, we investigate the sizes of C 9 and C10, setting e (mA; mH ; mH ) = (200 GeV; 250 GeV; 200 GeV). e is xed at e = = 1, 0:1 and 0:034; 0:34 that correspond to 10 9. In the plots, the tut and cut dependences are shown, to see the contribution of the box diagram in gure 7. tuc is vanishing on the both panels. The gray region is excluded by the Bs-Bs mixing (red lines) and ! process (dotted green lines). The dashed green lines and dashed purple lines denote the predictions of C 9 and C10 for the each case. In this case, the deviations of C9 and C10 can be sizable, according to the diagrams in gure 4 and gure 7. In particular, the box diagram in gure 7 can lead the avor universality violation in the B ! K( )ll processes. In the case (B), however, the box diagram in gure 7 predicts two muons in the nal state to be right-handed, so that 3See also refs. [80{82] for a recent development. in case (B) and case (C). the relation, C 9 = in 1 GeV2 C C10, is predicted. According to the recent global analyses [74, 75], C10 is favored. R(K) is, in fact, estimated as R(K) = 1+0:23 C 9 0:233 unit. Thus, we conclude that it is di cult to achieve the explanations of the R(K( )) anomaly in the case (B). Such a positive C10 is disfavored by Bs ! . As mentioned above, it is also di cult that the explanation of R(D) is compatible with the one of (g 2) , because of the constraint from the lepton universality of B ! D( )l : Note that C9 is small on this plane in gure 6. If tuc is not vanishing, sizable C9 can be derived as shown in gure 5, although the C9 is avor universal. Then, it is possible that we explain both the R(D) and P50 anomalies by the one parameter set, but R(K( )) is not compatible with the explanation. 4.3.3 Finally, we study the case (C). The all elements of e are vanishing and some elements of are sizable in this case. As discussed in section 3.2, the LFV processes strictly constrain e ( )ij , and then we assume that the only sizable element is ( ) j . This assumption principally forbids the avor violating processes. ( ) j is also constrained by the (semi)leptonic B decays, as shown in section 4.1 and section 4.2, when tuc is large. Let us de ne the e following parameter, j e = sX ( ) j j2; j e and draw gure 8 xing = 1; 2 on the left and right panels, respectively. Based on ref. [ 83 ], we evaluate R(K), that is the ratio between BR(B+ ! K+ of two leptons in the nal state [48]. In particular, the result in B+ BR(B+ ! K+ ee). R(K) is reported in each bin of q2 GeV2, which is the invariant mass q 2 6 GeV2 is smaller than the SM predictions: R(K) = 0:745+00::009704 lepton universality is measured in B0 ! K shows the similar sign about the lepton universality violation [47]. as well, and the experimental result also In our model, R(K) is deviated by the diagram in gure 7 via the leptonic Yukawa couplings. In the case (C), the leptons in the nal state can be left-handed, so that C9 = C10 is predicted. In gure 8, the predicted R(K) is drawn by the dashed purple lines. The number on the each line corresponds to the size of R(K). The relevant parameters are xed at = 1(left panel); 2(right panel) and (mA; mH ; mH ) = ! K+ with 1 GeV2 0:036 [48]. The (4.17) ) and tut vs. cut in the case (C) with = 1(left); 2(right) and (mA; mH; mH ) = (200 GeV; 200 GeV; 200 GeV). The gray region is excluded by the Bs Bs mixing (solid red lines) and b ! s (dotted-dashed blue lines). The dashed purple lines denote the predictions of R(K). (200 GeV; 200 GeV; 200 GeV). The gray region is excluded by the Bs Bs mixing (solid red lines) and b ! s (dotted-dashed blue lines). As we see in gure 8, large is required even in the light charged Higgs scenario. The strongest constraint comes from Bs-Bs mixing, and then R(K) can reach 0:8, that is within 1 region, when = 2 and mH = 200 GeV. In such a case with large , the cosmological observations and the neutrino experiments will severely constrain our model. Let us simply assume that the active neutrinos consist of right-handed and left-handed neutrinos: they are Dirac neutrinos. In the case e i (4.18) (C), the coupling with muon, e i, is large and the others are small. This means that the only one right-handed neutrino that couples to muon is introduced e ectively. In our scenario, the right-handed neutrino interacts with the SM particles through the coupling, and it is in the thermal equilibrium up to a few MeV, when e e ective number, Ne , of neutrinos in our universe is measured by the Planck experiment: i is O(1). The Ne = 3:36 0:34 (CMB only) [84]. If the decoupling temperature of the right-handed neutrino is small, Ne could be estimated as Ne 4, that is excluded by the recent cosmological observation. In order to raise the decoupling temperature and decrease Ne , may be required to be less than O(0:1) [ 85 ]. The right-handed neutrino, on the other hand, is not needed to be an active neutrino, in our setup. In gure 8, the right-handed neutrino mass is vanishing, but the result would not be modi ed so much even if the small Majorana mass of the right-handed neutrino is introduced. Let us de ne the right-handed neutrino that couples to muon as R1. Then, the relevant terms are given by LiL(V )ijHe1yj Ri + mR R1c R1 + e 1 LLHe2 R1 + h:c:: Here, y1 can be assumed to be vanishing without con ict with the neutrino observables. As far as H2 does not develop non-vanishing VEV, e the active neutrinos, even if mR is sizable. The decay of R1 may be suppressed according to 1 does not contribute to the masses of through ij ,4 as far as R1 is heavier than above the QCD phase transition temperature.5 the alignment of . It would be interesting to discuss the compatibility between the dark matter abundance and RK , as discussed in ref. [86]. In our case, R1 can decay to leptons R2 and R3, that decouple with the thermal bath The neutrino scattering with nuclei also strongly constrains our model. The relevant ! process is the neutrino trident production: N [89]. In our model with sizable e 1, the charged Higgs exchanging enlarges the cross section but the contribution does not interfere with the SM correction, so that the prediction is not deviated from the SM predicso that we obtain the limit on the deviation of RK and RK . When mH tion so much. e 1, however, is very large to violate the lepton universality of B ! K( )ll, is set to 200 GeV, 1 is about 1 to avoid the 2 deviation of the experimental result [90]. the upper bound on Thus, the e e 1 2 scenario is totally excluded, as far as mR is not introduced. We conclude that the scenario with large R1 coupling is excluded by the cosmological observations and the neutrino experiments, if R1 is a part of the active neutrinos. We can easily introduce the mass term of R1, i.e. mR, since R1 is neutral under the SM gauge symmetry. Then, the bound from the trident production can be evaded, since R1 is not an active neutrino in this case. When small other elements of ( and R1 is heavier than R2;3, R1 can decay to the SM leptons in association with R2;3. 2;3 R can be interpreted as the active neutrinos, if the Majorana masses of R2;3 are vanishing. e e )i2 and ( )i3 are allowed Then, (e )ij , except for (e ) 1, should be smaller than O(0:1). If the decay of R1 is much suppressed, the abundance of R1 would be constrained by the cosmology. The cold dark matter case is similar to the result in ref. [86]. In this paper, the consistency with the cosmological observation in such a dark matter case is beyond our scope. In section 5, we propose the direct search for R1 at the LHC. Summary of the capabilities to explain the excesses 6]GeV2) [48], if is O(1). The Dirac neutrino case predicts Ne We summarize the possibility that our model can explain the excesses in the avor physics, choosing the proper parameter set. In table 5, our conclusion about the each excess is shown. On the rst, second and third rows, tut, tuc and cut are only sizable in the case (B) and (C), respectively. The each column corresponds to the capability to explain the each excess denoted on the top row. The symbol, \ ", means that our predictions are within the 1 regions of the experimental results. In the box with \ ", our prediction is of the experimental results, i.e., P50 and R(K) = 0:745+00::009704 out of the 2 region. In the box with \4", the predictions can be within the 2 region 0:036 ' 0:745+00::009872(q2 [1, 4 and is in tension with the recent cosmological observation. The neutrino trident production also excludes the case with > 1. We can also introduce the small Majorana mass term, mR, to decrease Ne . In the end, it is di cult to explain all of the excesses in our parameterization. The explanations of P50 and R(D) can be done by the sizable tuc and the e , but cannot be 4 i2 and ei3 are negligibly small, but not vanishing. e 5Recently, the model with light R that strongly couples to leptons is discussed, motivated by the R(D( )) anomaly [87, 88]. HJEP05(218)73 tt u tc u ct u tt u tc u ct u R(K( )) (B) e 6= 0, = 0 (C) e = 0, ", \4" and \ ". The meanings are explained in the text. compatible with the solutions to the (g 2) and R(K( )) anomalies. This is because the charged Higgs that couple to b, c and largely violate the lepton universality of B ! D( )l . 5 Our signals at the LHC Before closing our paper, we discuss the possibility that our 2HDM is tested by the LHC experiments. In our scenarios, the extra scalars are relatively light: we x the masses at 200 GeV or 250 GeV. Thus, the main targets to prove our model are the direct signals originated from the scalars. In the case (A), there are Yukawa couplings between the scalars and heavy quarks, denoted by tuc, cut and tut. If either tuc or cut is O(1), we obtain large C9, that can explain the P50 excess. In this case, the neutral and charged scalars are produced in association with top quark or bottom quark in the nal state. The produced scalars dominantly decay to heavy quarks, so that there are tt/bb/tb quarks in the nal state. Such a case has been studied in ref. [37].6 In the case (B), the neutral scalars can decay to and , and the charged Higgs the production cross sections of the scalars at the LHC with p decays to or with one neutrino. The scalars are produced via cut coupling, and then s = 13 TeV (8 TeV) are estimated in table 6, using CALCHEP [104]. Note that cteq6l1 is applied to the parton distribution function. Here, we quantitatively study our signal on the benchmark points in gure 6.We put the green x-marks on the gures. On the benchmark point (B1), the parameters are aligned as mH ( tut; cut) = (0:005; 0:2); ( e ; e ) = (1; 0:0341): (5.1) 6See also refs. [91{103]. = 200 [GeV] m = 200 [GeV] ( = H; A ) m = 250 [GeV] (b + c ! H ) (g + s ! t + H ) (g + g ! s + t + H ) (g + c ! t + ) (g + g ! c + t + ) (g + c ! t + ) (g + g ! c + t + ) 792 j tucj2 sections, just as adding (g + s ! t + H ) and (g + s ! t + H+) and denote as (g + s ! t + H ). This parameter set leads a sizable deviation of (g the charged Higgs mainly decays to through the diagram in gure 9 and the heavy neutral scalar decays to : BR(H ! ! ts) 99:3%; 96:9%; Following table 6, the production cross section of the charged Higgs is estimated as 2.46 pb at the LHC with p s = 13 TeV. The search for a new heavy resonance decaying to e= and neutrino has been developed recently [105] and the upper bound on the production is about 0.6 pb, that naively leads the upper bound on j cutj as j cutj . 0:2. In our model, however, there are top quarks in the nal state, so that the top quark will make the signals fuzzy. The search for a new resonance decaying to / is also attractive, because the decay is predicted by the charged Higgs and the neutral Higgs. It is challenging and actually the heavy mass region is surveyed by the ATLAS [106] and CMS collaborations [107, 108]. As discussed in section 4.2, the excesses in B ! D( ) require rather large Yukawa couplings, so that we expect that the direct search for the resonance at the LHC can reach the favored parameter region near future. The detail analysis is work in progress. On the benchmark point (B2), the parameters are xed at mH Then, the sizable deviation of (g 2) is estimated as sizable, the charged Higgs decays to : BR(H ! ) In this case, the charged Higgs mainly decays to , and can evade the bound from the resonance search. In the case (C), the scalars are produced due to the large cut. The produced neutral scalars decay to two neutrinos in this case, so that they predict the invisible signal. The charged scalar decays to one muon and one neutrino. This signal is similar to the case (B). On the benchmark point in gure 8, the parameters satisfy mH = mA = mH = 200 GeV; ( tut; cut) = ( 0:04; 0:2); 2 = 1: These parameters lead the following branching ratios, BR(H ! BR( h ! ) ) 99%; BR(H ! ts) 1%; 99%; BR( h ! tc) 1% ( h = H; A): The invisible decay of the heavy neutral scalars, produced by the diagram in gure 10, leads LHC with p the mono-top signal: pp ! ht ! s = 8 TeV is (pp ! t + missing) Based on the results in table 6, the mono-top signal on this benchmark point is about 0.3 pb, so that it is just below the current upper bound. In our model, the same-sign top signal is also predicted by the diagrams in gure 11, depending on the mass spectrum of the scalars. If the neutral scalars, H and A, are not current upper bound on the cross section is 1.2 pb at the LHC with p degenerate, the same-sign top signal, pp ! tt, is enhanced by cut, tuc couplings. The s = 13 TeV [111]. When mA = 200 GeV and mH = 250 GeV, the each cross section is estimated as t. The current upper bound on the cross section at the 0:8 [pb] [109, 110] when mH = 200 GeV. (pp ! tt + tt) = 4:23 (pp ! ttc + ttc) = 4:13 (pp ! ttcc + ttcc) = 1:14 10 3j tucj4[pb]; 10 1j tucj4[pb]; 10 1j tucj4[pb]: = 2:61 BR(H ! ts) 5:6%; (5.3) (5.4) (5.5) (5.6) (5.7) Then, our predictions on the benchmark points are below the experimental bound. We note that the same-sign top signal is produced by the process, pp ! ttc + ttc, rather than pp ! cc ! tt + tt, because of the production processes as shown in gure 11. 6 We have studied the avor physics in type-III 2HDM. In this model, there are many possible parameter choices, so we adopt some simple parameter sets motivated by the physical observables where the deviations from the SM predictions are reported. In our scenario, the avor violating Yukawa couplings for up-type quarks, tuc and cut, play an important role in enhancing/suppressing the semileptonic B decays, e.g. B ! K ll. In particular, cut can evade the strong bound from the avor physics and the collider experiments, so that cut is expected to be larger than O(0:1). In addition, we introduce the avor violating Yukawa couplings to the lepton sector as well: e and e . As discussed in refs. [49, 50], those avor violating couplings deviate (g 2) , as far as the extra neutral scalars are not degenerate. In our paper, we have discussed the compatibility between the explanations of (g 2) , of the B ! K( )ll and of the B ! D( ) excesses. As shown in table 5, the explanations of (g 2) and R(D) require relatively large Yukawa couplings, so the constraint from the lepton universality of B ! D( )l easily excludes our model. In order to explain the R(K) excess, we need the sizable lepton avor universality violation in the B ! K( )ll processes. Then, we introduce the avor violating Yukawa couplings involving right-handed neutrino, and discuss the capability to explain the R(K) excess in our model. In this case, we can evade the strong experimental bounds, as far as the appropriate alignment of the Yukawa couplings is chosen. Thus, the explanation of the R(K) deviation is achieved by the box diagram involving the right-handed neutrinos via the avor violating neutrino Yukawa couplings. This scenario, however, can not be compatible with the other explanations, because of the stringent constraint from the lepton universality of B ! D( )l . In addition, the Dirac neutrino case is excluded by the recent cosmological observation. Then, the sizable Majorana mass term for the right-handed neutrino is required to decrease the e ective neutrino number. The possible parameter choices and the capabilities of the each setup are summarized in table 5. Finally, we have investigated the possibility that the LHC experiments directly test our model. Interestingly, the direct search for new physics at the LHC can reach the parameter region that is favored by the excesses in the avor physics [37, 91{97, 100{103]. In our scenario, the scalar are enough light to be produced by the proton-proton collider. In the case that the charged Higgs mainly decays to one muon and one neutrino, the heavy resonance search at the LHC could widely cover our parameter region. The neutral scalar decays to two neutrinos, if the neutrino Yukawa couplings are large. In this case, the monotop signal could be our promising one, although the current bound has not yet reached our parameter region. The sizable cut predicts the same-sign top signal, if the neutral scalars are not degenerate. We have con rmed that our prediction of the cross section is below the current upper bound, but we can expect that our region could be covered near future. Acknowledgments The work of Y.O. is supported by Grant-in-Aid for Scienti c research from the Ministry of Education, Science, Sports, and Culture (MEXT), Japan, No. 17H05404. The authors thank to Kazuhiro Tobe, Tomomi Kawaguchi, Makoto Tomoto and Yasuyuki Horii for variable discussions. Various parameters for our numerical analysis Here, we summarize numerical values of various parameters we use in our numerical cal Quantity CKM parameters parameters for hadronic matrix elements B and D meson parameters culation below. Quantity A mBd mB mBs MBc mD mD Bd B fB Bs p Bc fBc fBdpBBd fBs BBs Value [116] [63] HJEP05(218)73 Open Access. Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. [1] ATLAS collaboration, 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 (2012) 1 [arXiv:1207.7214] [INSPIRE]. [2] CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE]. [3] T.D. Lee, A Theory of Spontaneous T Violation, Phys. Rev. D 8 (1973) 1226 [INSPIRE]. Higgs Bosons on Experimental Observables, Nucl. Phys. B 161 (1979) 493 [INSPIRE]. Higgs bosons to ! e , Phys. Rev. D 48 (1993) 217 [hep-ph/9302267] [INSPIRE]. e+e collisions, Phys. Rev. D 53 (1996) 1199 [hep-ph/9506243] [INSPIRE]. [10] D. Atwood, L. Reina and A. Soni, Phenomenology of two Higgs doublet models with avor changing neutral currents, Phys. Rev. D 55 (1997) 3156 [hep-ph/9609279] [INSPIRE]. [11] S.L. Glashow and S. Weinberg, Natural Conservation Laws for Neutral Currents, Phys. Rev. D 15 (1977) 1958 [INSPIRE]. [12] J. Liu and L. Wolfenstein, Spontaneous CP-violation in the SU(2)L U(1)Y Model with Two Higgs Doublets, Nucl. Phys. B 289 (1987) 1 [INSPIRE]. Multiple Higgs Doublets, Phys. Rev. D 35 (1987) 3484 [INSPIRE]. [13] T.P. Cheng and M. Sher, Mass Matrix Ansatz and Flavor Nonconservation in Models with [14] M.J. Savage, Constraining avor changing neutral currents with B ! , Phys. Lett. B 266 (1991) 135 [INSPIRE]. [15] A. Antaramian, L.J. Hall and A. Rasin, Flavor changing interactions mediated by scalars at the weak scale, Phys. Rev. Lett. 69 (1992) 1871 [hep-ph/9206205] [INSPIRE]. [16] L.J. Hall and S. Weinberg, Flavor changing scalar interactions, Phys. Rev. D 48 (1993) R979 [hep-ph/9303241] [INSPIRE]. [17] M.E. Luke and M.J. Savage, Flavor changing neutral currents in the Higgs sector and rare top decays, Phys. Lett. B 307 (1993) 387 [hep-ph/9303249] [INSPIRE]. [18] M. Aoki, S. Kanemura, K. Tsumura and K. Yagyu, Models of Yukawa interaction in the two Higgs doublet model and their collider phenomenology, Phys. Rev. D 80 (2009) 015017 [arXiv:0902.4665] [INSPIRE]. [19] N. Haba, H. Umeeda and T. Yamada, Semialigned two Higgs doublet model, Phys. Rev. D 97 (2018) 035004 [arXiv:1711.06499] [INSPIRE]. [20] S. Iguro, Y. Muramatsu, Y. Omura and Y. Shigekami, Flavor physics in the multi-Higgs doublet models induced by the left-right symmetry, arXiv:1804.07478 [INSPIRE]. [21] BaBar collaboration, J.P. Lees et al., Evidence for an excess of B ! D( ) Phys. Rev. Lett. 109 (2012) 101802 [arXiv:1205.5442] [INSPIRE]. [22] BaBar collaboration, J.P. Lees et al., Measurement of an Excess of B ! D( ) and Implications for Charged Higgs Bosons, Phys. Rev. D 88 (2013) 072012 decays, Decays [23] LHCb collaboration, Measurement of the ratio of branching fractions [arXiv:1303.0571] [INSPIRE]. B(B0 ! D + )=B(B0 ! D + [arXiv:1506.08614] [INSPIRE]. ), Phys. Rev. Lett. 115 (2015) 111803 in the decay B ! D B ! D( ) relative to B ! D( )` D 92 (2015) 072014 [arXiv:1507.03233] [INSPIRE]. ` decays with hadronic tagging at Belle, Phys. Rev. [25] Belle collaboration, Y. Sato et al., Measurement of the branching ratio of B0 ! D + relative to B0 ! D +` (2016) 072007 [arXiv:1607.07923] [INSPIRE]. ` decays with a semileptonic tagging method, Phys. Rev. D 94 [26] Belle collaboration, S. Hirose et al., Measurement of the lepton polarization and R(D ) , Phys. Rev. Lett. 118 (2017) 211801 [arXiv:1612.00529] overview, talk at The 15th meeting in the conference series of HJEP05(218)73 Flavor Physics & CP Violation (FPCP 2017), Prague, Czech Republic, 5{9 June 2017. [28] S. Jaiswal, S. Nandi and S.K. Patra, Extraction of jVcbj from B ! D( )` ` and the Standard Model predictions of R(D( )), JHEP 12 (2017) 060 [arXiv:1707.09977] [INSPIRE]. [29] A. Crivellin, C. Greub and A. Kokulu, Explaining B ! D , B ! D and B ! 2HDM of type-III, Phys. Rev. D 86 (2012) 054014 [arXiv:1206.2634] [INSPIRE]. B ! [30] A. Celis, M. Jung, X.-Q. Li and A. Pich, Sensitivity to charged scalars in B ! D( ) decays, JHEP 01 (2013) 054 [arXiv:1210.8443] [INSPIRE]. [31] M. Tanaka and R. Watanabe, New physics in the weak interaction of B ! D( ) , Phys. Rev. D 87 (2013) 034028 [arXiv:1212.1878] [INSPIRE]. in a and [32] A. Crivellin, A. Kokulu and C. Greub, Flavor-phenomenology of two-Higgs-doublet models with generic Yukawa structure, Phys. Rev. D 87 (2013) 094031 [arXiv:1303.5877] 075017 [arXiv:1512.02210] [INSPIRE]. [33] A. Crivellin, J. Heeck and P. Sto er, A perturbed lepton-speci c two-Higgs-doublet model facing experimental hints for physics beyond the Standard Model, Phys. Rev. Lett. 116 [34] J.M. Cline, Scalar doublet models confront and b anomalies, Phys. Rev. D 93 (2016) [35] P. Ko, Y. Omura, Y. Shigekami and C. Yu, LHCb anomaly and B physics in avored Z0 avored Higgs doublets, Phys. Rev. D 95 (2017) 115040 [arXiv:1702.08666] [36] P. Ko, Y. Omura and C. Yu, B ! D( ) and B ! in chiral U(1)0 models with avored multi Higgs doublets, JHEP 03 (2013) 151 [arXiv:1212.4607] [INSPIRE]. [37] S. Iguro and K. Tobe, R(D( )) in a general two Higgs doublet model, Nucl. Phys. B 925 (2017) 560 [arXiv:1708.06176] [INSPIRE]. [38] Q.-Y. Hu, X.-Q. Li and Y.-D. Yang, B0 ! K 0 + decay in the Aligned Two-Higgs-Doublet Model, Eur. Phys. J. C 77 (2017) 190 [arXiv:1612.08867] [INSPIRE]. [39] P. Arnan, D. Becirevic, F. Mescia and O. Sumensari, Two Higgs doublet models and b ! s exclusive decays, Eur. Phys. J. C 77 (2017) 796 [arXiv:1703.03426] [INSPIRE]. [40] A. Arhrib et al., RK( ) anomaly in type-III 2HDM, arXiv:1710.05898 [INSPIRE]. [41] L. Bian, S.-M. Choi, Y.-J. Kang and H.M. Lee, A minimal avored U(1)0 for B-meson anomalies, Phys. Rev. D 96 (2017) 075038 [arXiv:1707.04811] [INSPIRE]. B0 ! K 0 + [44] A.G. Akeroyd and C.-H. Chen, Constraint on the branching ratio of Bc ! and consequences for R(D( )) anomaly, Phys. Rev. D 96 (2017) 075011 from LEP1 [57] B. Altunkaynak, W.-S. Hou, C. Kao, M. Kohda and B. McCoy, Flavor Changing Heavy Higgs Interactions at the LHC, Phys. Lett. B 751 (2015) 135 [arXiv:1506.00651] [58] M. Misiak et al., Updated NNLO QCD predictions for the weak radiative B-meson decays, Phys. Rev. Lett. 114 (2015) 221801 [arXiv:1503.01789] [INSPIRE]. integrated luminosity, JHEP 02 (2016) 104 [arXiv:1512.04442] [INSPIRE]. [47] LHCb collaboration, Test of lepton universality with B0 ! K 0`+` decays, JHEP 08 (2017) 055 [arXiv:1705.05802] [INSPIRE]. [48] LHCb collaboration, Test of lepton universality using B+ ! K+`+` decays, Phys. Rev. Lett. 113 (2014) 151601 [arXiv:1406.6482] [INSPIRE]. [49] Y. Omura, E. Senaha and K. Tobe, Lepton- avor-violating Higgs decay h ! and muon anomalous magnetic moment in a general two Higgs doublet model, JHEP 05 (2015) 028 [arXiv:1502.07824] [INSPIRE]. [50] Y. Omura, E. Senaha and K. Tobe, - and -physics in a general two Higgs doublet model with avor violation, Phys. Rev. D 94 (2016) 055019 [arXiv:1511.08880] [INSPIRE]. [51] S. Davidson and H.E. Haber, Basis-independent methods for the two-Higgs-doublet model, Phys. Rev. D 72 (2005) 035004 [Erratum ibid. D 72 (2005) 099902] [hep-ph/0504050] [52] P. Ko, Y. Omura and C. Yu, Top Forward-Backward Asymmetry and the CDF W jj Excess in Leptophobic U(1)0 Flavor Models, Phys. Rev. D 85 (2012) 115010 [arXiv:1108.0350] [53] P. Ko, Y. Omura and C. Yu, Chiral U(1) avor models and avored Higgs doublets: The Top FB asymmetry and the Wjj, JHEP 01 (2012) 147 [arXiv:1108.4005] [INSPIRE]. [54] Y. Omura, K. Tobe and K. Tsumura, Survey of Higgs interpretations of the diboson excesses, Phys. Rev. D 92 (2015) 055015 [arXiv:1507.05028] [INSPIRE]. [55] C. Bobeth, A.J. Buras, A. Celis and M. Jung, Patterns of Flavour Violation in Models with Vector-Like Quarks, JHEP 04 (2017) 079 [arXiv:1609.04783] [INSPIRE]. [56] HFLAV collaboration, Y. Amhis et al., Averages of b-hadron, c-hadron and -lepton properties as of summer 2016, Eur. Phys. J. C 77 (2017) 895 [arXiv:1612.07233] [45] LHCb collaboration, Measurement of Form-Factor-Independent Observables in the Decay HJEP05(218)73 , Phys. Rev. Lett. 111 (2013) 191801 [arXiv:1308.1707] [INSPIRE]. in pp collisions at p [60] ATLAS collaboration, Search for avour-changing neutral current top quark decays t ! Hq s = 8 TeV with the ATLAS detector, JHEP 12 (2015) 061 [61] CMS collaboration, Search for top quark decays via Higgs-boson-mediated avor-changing neutral currents in pp collisions at p s = 8 TeV, JHEP 02 (2017) 079 [arXiv:1610.04857] [63] Particle Data Group collaboration, C. Patrignani et al., Review of Particle Physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE]. Lett. B 749 (2015) 337 [arXiv:1502.07400] [INSPIRE]. [64] CMS collaboration, Search for Lepton-Flavour-Violating Decays of the Higgs Boson, Phys. [65] ATLAS collaboration, Search for lepton- avour-violating decays of the Higgs and Z bosons with the ATLAS detector, Eur. Phys. J. C 77 (2017) 70 [arXiv:1604.07730] [INSPIRE]. e in proton-proton collisions at p s = 13 TeV, CMS-PAS-HIG-17-001. [66] CMS collaboration, Search for lepton avour violating decays of the Higgs boson to and [67] Belle collaboration, A. Abdesselam et al., Precise determination of the CKM matrix ` decays with hadronic tagging at Belle, element jVcbj with B0 ! D + ` arXiv:1702.01521 [INSPIRE]. [68] M. Tanaka and R. Watanabe, Tau longitudinal polarization in B ! D and its role in the search for charged Higgs boson, Phys. Rev. D 82 (2010) 034027 [arXiv:1005.4306] [69] S. Descotes-Genon, J. Matias and J. Virto, Understanding the B ! K Phys. Rev. D 88 (2013) 074002 [arXiv:1307.5683] [INSPIRE]. + Anomaly, [70] G. Hiller and M. Schmaltz, RK and future b ! s`` physics beyond the standard model opportunities, Phys. Rev. D 90 (2014) 054014 [arXiv:1408.1627] [INSPIRE]. [71] W. Altmannshofer and D.M. Straub, Implications of b ! s measurements, in proceedings of 50th Rencontres de Moriond Electroweak Interactions and Uni ed Theories, La Thuile, Italy, March 14{21, 2015, pp. 333{338 [arXiv:1503.06199] [INSPIRE]. [72] S. Descotes-Genon, L. Hofer, J. Matias and J. Virto, Global analysis of b ! s`` anomalies, JHEP 06 (2016) 092 [arXiv:1510.04239] [INSPIRE]. [73] T. Hurth, F. Mahmoudi and S. Neshatpour, On the anomalies in the latest LHCb data, Nucl. Phys. B 909 (2016) 737 [arXiv:1603.00865] [INSPIRE]. [74] W. Altmannshofer, P. Stangl and D.M. Straub, Interpreting Hints for Lepton Flavor Universality Violation, Phys. Rev. D 96 (2017) 055008 [arXiv:1704.05435] [INSPIRE]. [75] G. D'Amico et al., Flavour anomalies after the RK measurement, JHEP 09 (2017) 010 [arXiv:1704.05438] [INSPIRE]. [76] M. Ciuchini et al., On Flavourful Easter eggs for New Physics hunger and Lepton Flavour Universality violation, Eur. Phys. J. C 77 (2017) 688 [arXiv:1704.05447] [INSPIRE]. B 773 (2017) 505 [arXiv:1705.09305] [INSPIRE]. [78] LHCb collaboration, Measurement of the Bs0 ! + branching fraction and e ective decays, Phys. Rev. Lett. 118 (2017) 191801 2) and (MZ2 ) [80] M. Davier, Update of the Hadronic Vacuum Polarisation Contribution to the muon g 2, HJEP05(218)73 Nucl. Part. Phys. Proc. 287-288 (2017) 70 [arXiv:1612.02743] [INSPIRE]. [81] F. Jegerlehner, Muon g 2 theory: The hadronic part, EPJ Web Conf. 166 (2018) 00022 lifetime and search for B0 ! + 80 (2009) 095008 [arXiv:0906.3335] [INSPIRE]. [86] J. Kawamura, S. Okawa and Y. Omura, Interplay between the b! s`` anomalies and dark matter physics, Phys. Rev. D 96 (2017) 075041 [arXiv:1706.04344] [INSPIRE]. [87] P. Asadi, M.R. Buckley and D. Shih, It's all right(-handed neutrinos): a new W 0 model for the RD( ) anomaly, arXiv:1804.04135 [INSPIRE]. neutrinos, arXiv:1804.04642 [INSPIRE]. [88] A. Greljo, D.J. Robinson, B. Shakya and J. Zupan, R(D( )) from W 0 and right-handed [89] R.W. Brown, R.H. Hobbs, J. Smith and N. Stanko, Intermediate boson. iii. virtual-boson e ects in neutrino trident production, Phys. Rev. D 6 (1972) 3273 [INSPIRE]. [90] W. Altmannshofer, S. Gori, M. Pospelov and I. Yavin, Neutrino Trident Production: A Powerful Probe of New Physics with Neutrino Beams, Phys. Rev. Lett. 113 (2014) 091801 [arXiv:1406.2332] [INSPIRE]. [91] D. Atwood, S.K. Gupta and A. Soni, Same-sign Tops: A Powerful Diagnostic Test for Models of New Physics, JHEP 04 (2013) 035 [arXiv:1301.2250] [INSPIRE]. [92] R. Goldouzian, Search for top quark avor changing neutral currents in same-sign top quark production, Phys. Rev. D 91 (2015) 014022 [arXiv:1408.0493] [INSPIRE]. [93] N. Craig, F. D'Eramo, P. Draper, S. Thomas and H. Zhang, The Hunt for the Rest of the Higgs Bosons, JHEP 06 (2015) 137 [arXiv:1504.04630] [INSPIRE]. [94] C.-W. Chiang, H. Fukuda, M. Takeuchi and T.T. Yanagida, Flavor-Changing Neutral-Current Decays in Top-Speci c Variant Axion Model, JHEP 11 (2015) 057 [arXiv:1507.04354] [INSPIRE]. [95] C.S. Kim, Y.W. Yoon and X.-B. Yuan, Exploring top quark FCNC within 2HDM type-III in association with avor physics, JHEP 12 (2015) 038 [arXiv:1509.00491] [INSPIRE]. [arXiv:1602.02782] [INSPIRE]. [97] R. Patrick, P. Sharma and A.G. Williams, Exploring a heavy charged Higgs using jet substructure in a fully hadronic channel, Nucl. Phys. B 917 (2017) 19 [arXiv:1610.05917] interference in pp ! tH ! tW [arXiv:1712.05018] [INSPIRE]. Neutrino Masses and Absence of Flavor Changing Interactions in the 2HDM from Gauge Principles, JHEP 08 (2017) 092 [arXiv:1705.05388] [INSPIRE]. [100] S. Gori, C. Grojean, A. Juste and A. Paul, Heavy Higgs Searches: Flavour Matters, JHEP 01 (2018) 108 [arXiv:1710.03752] [INSPIRE]. [101] M. Kohda, T. Modak and W.-S. Hou, Searching for new scalar bosons via triple-top signature in cg ! tS0 ! ttt, Phys. Lett. B 776 (2018) 379 [arXiv:1710.07260] [INSPIRE]. [102] R. Patrick, P. Sharma and A.G. Williams, Triple top signal as a probe of charged Higgs in a 2HDM, Phys. Lett. B 780 (2018) 603 [arXiv:1710.08086] [INSPIRE]. [103] A. Arhrib, R. Benbrik, S. Moretti, R. Santos and P. Sharma, Signal to background bb at the LHC Run-II, Phys. Rev. D 97 (2018) 075037 [104] A. Belyaev, N.D. Christensen and A. Pukhov, CalcHEP 3.4 for collider physics within and beyond the Standard Model, Comput. Phys. Commun. 184 (2013) 1729 [arXiv:1207.6082] [105] ATLAS collaboration, Search for a new heavy gauge boson resonance decaying into a lepton and missing transverse momentum in 36 fb 1 of pp collisions at p s = 13 TeV with the ATLAS experiment, arXiv:1706.04786 [INSPIRE]. collisions at p collisions at p [arXiv:1801.06992] [INSPIRE]. s = 13 TeV with the ATLAS Detector, Phys. Rev. Lett. 120 (2018) 161802 [106] ATLAS collaboration, Search for High-Mass Resonances Decaying to in pp Collisions at [107] CMS collaboration, Search for W' decaying to tau lepton and neutrino in proton-proton s = 8 TeV, Phys. Lett. B 755 (2016) 196 [arXiv:1508.04308] [INSPIRE]. [108] CMS collaboration, Search for W' decaying to tau lepton and neutrino in proton-proton s = 13 TeV, CMS-PAS-EXO-16-006. [109] ATLAS collaboration, Search for invisible particles produced in association with single-top-quarks in proton-proton collisions at p Phys. J. C 75 (2015) 79 [arXiv:1410.5404] [INSPIRE]. s = 8 TeV with the ATLAS detector, Eur. [110] CMS collaboration, Search for Monotop Signatures in Proton-Proton Collisions at ps = 8 TeV, Phys. Rev. Lett. 114 (2015) 101801 [arXiv:1410.1149] [INSPIRE]. p leptons of same sign, missing transverse momentum and jets in proton-proton collisions at from lattice QCD for the Standard Model and beyond, Phys. Rev. D 93 (2016) 113016 J. Shigemitsu, B-Meson Decay Constants from Improved Lattice Nonrelativistic QCD with HJEP05(218)73 picture from full lattice QCD, Phys. Rev. D 91 (2015) 114509 [arXiv:1503.05762] B ! D ` form factor at zero recoil with three- avor lattice QCD, Phys. Rev. D 89 (2014) 114504 [arXiv:1403.0635] [INSPIRE]. =K and B ! QCD, Nucl. Phys. Proc. Suppl. 140 (2005) 461 [hep-lat/0409116] [INSPIRE]. [5] J.F. Donoghue and L.F. Li , Properties of Charged Higgs Bosons , Phys. Rev. D 19 ( 1979 ) [6] L.J. Hall and M.B. Wise , Flavor Changing Higgs-Boson Couplings , Nucl. Phys. B 187 [7] W.-S. Hou , Tree level t ! ch or h ! tc decays , Phys. Lett. B 296 ( 1992 ) 179 [INSPIRE]. [8] D. Chang , W.S. Hou and W.-Y. Keung, Two loop contributions of avor changing neutral [42] L. Bian , H.M. Lee and C.B. Park , B-meson anomalies and Higgs physics in avored U(1)0 model , Eur. Phys. J. C 78 ( 2018 ) 306 [arXiv: 1711 .08930] [INSPIRE]. [43] R. Alonso , B. Grinstein and J. Martin Camalich , Lifetime of Bc Constrains Explanations for Anomalies in B ! D( ) , Phys. Rev. Lett . 118 ( 2017 ) 081802 [arXiv: 1611 .06676] [46] LHCb collaboration, Angular analysis of the B0 ! K 0 + decay using 3 fb 1 of Prog . Part. Nucl. Phys . 92 ( 2017 ) 50 [arXiv: 1606 .00916] [INSPIRE]. [77] D. Bardhan , P. Byakti and D. Ghosh , Role of Tensor operators in RK and RK , Phys . Lett. [79] K. Hagiwara , R. Liao , A.D. Martin , D. Nomura and T. Teubner , (g re-evaluated using new precise data , J. Phys. G 38 ( 2011 ) 085003 [arXiv: 1105 .3149] [82] K. Hagiwara , A. Keshavarzi , A.D. Martin , D. Nomura and T. Teubner, g -2 of the muon: status report , Nucl. Part. Phys. Proc . 287 - 288 ( 2017 ) 33 [INSPIRE]. [83] A. Celis , J. Fuentes-Martin , A. Vicente and J. Virto , Gauge-invariant implications of the LHCb measurements on lepton- avor nonuniversality , Phys. Rev. D 96 ( 2017 ) 035026 [84] Planck collaboration, P.A.R. Ade et al., Planck 2013 results . XVI. Cosmological parameters , Astron. Astrophys . 571 ( 2014 ) A16 [arXiv: 1303 .5076] [INSPIRE]. [85] S.M. Davidson and H.E. Logan , Dirac neutrinos from a second Higgs doublet , Phys. Rev . D [96] S. Gori , I.-W. Kim , N.R. Shah and K.M. Zurek , Closing the Wedge: Search Strategies for Extended Higgs Sectors with Heavy Flavor Final States , Phys. Rev. D 93 ( 2016 ) 075038 [99] M.D. Campos , D. Cogollo , M. Lindner , T. Melo , F.S. Queiroz and W. Rodejohann, s = 13 TeV, Eur. Phys. J. C 77 ( 2017 ) 578 [arXiv: 1704 .07323] [INSPIRE]. [112] Fermilab Lattice, MILC collaborations, A . Bazavov et al., B ( 0s ) -mixing matrix elements [113] HPQCD collaboration , R.J. Dowdall , C.T.H. Davies , R.R. Horgan , C.J. Monahan and Physical u, d, s and c Quarks, Phys. Rev. Lett . 110 ( 2013 ) 222003 [arXiv: 1302 .2644] [116] M. Okamoto et al., Semileptonic D ! =D decays in 2 + 1 avor lattice


This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2FJHEP05%282018%29173.pdf

Syuhei Iguro, Yuji Omura. Status of the semileptonic B decays and muon g-2 in general 2HDMs with right-handed neutrinos, Journal of High Energy Physics, 2018, 173, DOI: 10.1007/JHEP05(2018)173